Three Essays on Hedge Fund Risk Taking, Hedge Fund Herding, and Audit Experts

Three Essays on Hedge Fund Risk Taking, Hedge Fund Herding, and Audit Experts Dissertation submitted for the degree of Doctor of Economics (Dr. rer. pol.) Presented by Achim Mattes at the Department of Economics Date of the oral examination: 2 July 2014 First supervisor: Prof. Dr. Jens Jackwerth Second supervisor: Prof. Dr. Axel Kind Committee chair: Prof. Dr. Dr. h.c. Günter Franke

Contents Summary 1 1 Hedge Fund Risk Taking 5 1.1 Introduction.................................... 6 1.2 Related Literature................................ 7 1.3 Data........................................ 11 1.3.1 General Properties of Hedge Fund Daily Returns........... 11 1.3.2 Time Series Properties of Hedge Fund Risk.............. 14 1.4 Methodology................................... 20 1.5 Empirical Results................................. 23 1.5.1 Managerial Risk-Taking: Quarter-Wise................ 23 1.5.2 Managerial Risk-Taking: Month-Wise Refinement.......... 27 1.5.3 Economic Significance of Managerial Risk Taking........... 28 1.6 Determinants of Changes in Hedge Fund Risk................ 29 1.6.1 Management Fees and Survival Probability.............. 29 1.6.2 High-Water Mark and Incentive Fees.................. 33 1.6.3 Hedge Fund Style............................. 35 1.7 Robustness Checks................................ 37 1.7.1 Managerial Competition......................... 40 1.7.2 Piecewise Continuous Linear Specification for Managerial Risk Taking 41 1.7.3 Excluding the Crisis Period....................... 42 1.7.4 Kernel Regression with Different Bandwidths............. 42 1.7.5 Alternative Specifications of the High-Water Mark.......... 42 1.7.6 Fund Outflows: An Alternative Explanation.............. 43 1.7.7 Alternative Risk Measures........................ 44 1.7.8 Hedge Fund Risk Relative to Market Risk............... 44 1.7.9 Controlling For Possible Multiple Share Classes............ 45 1.8 Conclusion.................................... 45 1.A Appendix..................................... 48 1.A.1 Cross-Sectional Analysis of Hedge Fund Risk............. 48 1.A.2 Linear Specification for the Fund Value Relative to the High-Water Mark................................... 58 Bibliography...................................... 62 i

Contents 2 Hedge Fund Herding 65 2.1 Introduction.................................... 66 2.2 Literature Review................................ 68 2.2.1 Theory on Herding............................ 68 2.2.2 Empirical Findings on Herding..................... 70 2.3 Data........................................ 72 2.4 Herding at the Security Level.......................... 75 2.4.1 LSV Measure............................... 76 2.4.2 General Results for Herding at the Security Level........... 79 2.4.3 Herding among Different Investment Styles.............. 83 2.4.4 Herding in Different Stocks....................... 84 2.4.5 Herding and Window Dressing..................... 90 2.4.6 Herding and Aggregate Fund Flows.................. 92 2.5 Herding at the Firm Level............................ 92 2.5.1 Firm Herding Measure.......................... 92 2.5.2 General Results for Herding at the Firm Level............ 94 2.5.3 Persistence of Firm Herding....................... 95 2.5.4 Dynamic Influences on Firm Herding.................. 97 2.5.5 Herding and Firm Characteristics.................... 101 2.6 Conclusion.................................... 103 2.A Appendix..................................... 105 2.A.1 Tracking CDA Institutional Investors................. 105 2.A.2 Name Match Algorithm......................... 105 2.A.3 Deleting Firms with Other Business.................. 106 2.A.4 Obtaining Trades from Filed Positions................. 107 Bibliography...................................... 109 3 Audit Experts 112 3.1 Introduction.................................... 113 3.2 Related Literature................................ 115 3.3 Hypotheses.................................... 117 3.4 Data........................................ 120 3.5 Method...................................... 123 3.5.1 Audit Fee Regression Model....................... 123 3.5.2 Discretionary Accruals.......................... 128 3.6 Main Results................................... 129 3.6.1 Audit Fees and Discretionary Accruals after an Audit Expert Appointment................................. 129 3.6.2 Dynamics of Audit Fees and Discretionary Accruals......... 133 3.6.3 Influence of the Audit Expert...................... 134 3.7 Robustness Checks................................ 136 3.7.1 Audit Firm Selection Bias........................ 136 3.7.2 Training Firm of the Audit Expert................... 136 ii

Contents 3.7.3 Alternative Model Specification..................... 138 3.7.4 Other Reasons for Changes in the Discretionary Accruals...... 140 3.8 Conclusion.................................... 140 3.A Appendix..................................... 142 3.A.1 FSA Register and Audit Firm Selection................ 142 3.A.2 Differences Among Firms With and Without an Audit Expert... 143 3.A.3 Univariate Analysis........................... 145 Bibliography...................................... 147 General Bibliography 153 Summary in German 164 Acknowledgments 168 Record of Achievements 169 iii

List of Figures 1.1 Time Series of Average Returns of Daily and Monthly Hedge Funds....................................... 14 1.2 Distribution of Styles of Daily and Monthly Hedge Funds.. 16 1.3 Individual Time Series of Hedge Fund Risk............... 17 1.4 Time Series of Aggregate Hedge Fund Risk and Market Risk... 18 1.5 Managerial Risk Taking: Quarter-Wise................. 25 1.6 Managerial Risk Taking: Piecewise Linear Specification....... 26 1.7 Managerial Risk Taking: Month-Wise.................. 27 1.8 Managerial Risk Taking: Piecewise Linear Specification Excluding Funds without Incentive Fee...................... 36 1.9 Managerial Risk Taking: Piecewise Continuous Linear Specification 41 1.10 Managerial Risk Taking: Piecewise Linear Specification Excluding the Crisis.................................. 43 2.1 Average Fraction of Buys over Time................... 79 2.2 Distribution of the Herding Measure................... 82 2.3 Distribution of the Firm Herding Measure............... 96 iv

List of Tables 1.1 Descriptive Statistics for the Hedge Fund Sample........... 13 1.2 Descriptive Statistics Across Hedge Fund Styles............ 15 1.3 Descriptive Statistics for Hedge Fund Risk............... 15 1.4 Autocorrelation in Hedge Fund Risk................... 19 1.5 Transition Probabilities for Hedge Fund Risk Categories...... 19 1.6 Panel Regressions of Hedge Fund Risk.................. 24 1.7 Piecewise Regressions of Residual Hedge Fund Risk......... 26 1.8 Determinants of Residual Hedge Fund Risk: Management Fee.. 31 1.9 Determinants of Residual Hedge Fund Risk: Notice Period, Performance, Age................................. 32 1.10 Determinants of Residual Hedge Fund Risk: HWM, Incentive Fees 34 1.11 Determinants of Residual Hedge Fund Risk: Market Correlation. 38 1.12 Determinants of Residual Hedge Fund Risk: Fund Style...... 39 1.13 Piecewise Regressions of Residual Hedge Fund Risk Excluding Potential Multiple Fund Share Classes.................. 45 1.14 Cross-Sectional Regressions of Hedge Fund Risk........... 52 1.15 Cross-Sectional Regressions of Hedge Fund Risk Excluding Controls 55 1.16 Cross-Sectional Regressions of Hedge Fund Risk Excluding the Crisis....................................... 57 1.17 Panel Regression of Hedge Fund Risk with a Linear Specification for Fund Value................................. 59 1.18 Panel Regressions of Hedge Fund Risk with a Linear Specification for Fund Value and Interaction Terms.................. 60 2.1 Sample of Hedge Fund Firms and Securities.............. 74 2.2 General Herding Results........................... 80 2.3 Herding Measures across Investment Styles.............. 83 2.4 Herding Measures Intertemporal Correlations............ 84 2.5 Herding Measures across Stock Sizes................... 85 2.6 Herding Measures across Stock Performance.............. 87 2.7 Abnormal Stock Returns across Different Levels of Herding... 90 2.8 Herding Measures for Different Quarters................ 91 2.9 Firm Herding Measure across Different Investment Styles..... 95 2.10 Firm Herding Measures Intertemporal Correlations......... 97 v

List of Tables 2.11 Panel Regression Results for Firm Herding............... 99 2.12 Cross-Sectional Regression Results for Firm Herding........ 102 3.1 Sample of Firms................................ 122 3.2 Description of Regression Variables.................... 126 3.3 Descriptive Statistics for Main Regression Variables......... 127 3.4 Panel Regression for Audit Fees...................... 130 3.5 Panel Regression of Discretionary Accruals............... 132 3.6 Panel Regression for Audit Fees with Alternative Sample Specifications..................................... 137 3.7 Panel Regression for Discretionary Accruals with Alternative Sample Specifications............................... 138 3.8 Panel Regression for Audit Fees with Alternative Audit Fee Model Specifications.................................. 139 3.9 Regression Variables Statistics - Splitted Sample........... 144 3.10 Univariate Analysis of Audit Fees and Discretionary Accruals... 145 3.11 Univariate Analysis of Audit Fee Dynamics............... 145 3.12 Detailed Univariate Analysis of Audit Fees and Discretionary Accruals....................................... 146 vi

Summary This dissertation is a collection of three research papers written during my studies in the Doctoral Programme in Quantitative Economics and Finance at the University of Konstanz. The first study analyzes the risk taking by hedge fund managers. The typical compensation contracts of hedge fund managers create incentives to alter the risk of their funds dynamically. The study recovers the resulting empirical risk taking over time and analyzes potential explanations for its revealed pattern. The second study analyzes whether hedge fund firms trade stocks independently of each other, or whether they herd into and out of stocks together. After finding a general tendency to herd by these firms, a detailed analysis addresses potential explanations and implications. The last study analyzes the effect on the audit effort and the financial reporting quality when firms appoint former audit firm employees to their boards. Since both variables of interest are not directly observable, the development of appropriate proxies, after the appointment of such audit experts, is considered instead. The dissertation is organized in three chapters, where each chapter contains one of the research papers. In the following, I summarize each of these studies. Chapter 1 (Hedge Fund Risk Taking) is joint work with Olga Kolokolova. We recover the managerial risk taking from a sample of 714 hedge funds that report daily returns to Bloomberg from 2001 to 2011. While most of the empirical hedge fund literature is based on monthly return data, we use this previously unattended dataset of daily hedge fund returns. The daily frequency of the observations allows us to construct a time series of monthly risk measures, i.e. the monthly standard deviation of daily returns, for each fund. From the resulting panel data of monthly fund risk observations, we statistically identify the dynamic managerial risk taking with a two step procedure. First, we regress the monthly risk levels on a set of explanatory variables, which are likely to influence the current fund risk level, but are not related to managerial risk taking. The managerial risk taking is then contained in the residuals from this dynamic panel regression. In the second step, we analyze the relation of the managerial risk taking (residuals) to the fund performance in different times of a year. The theoretical literature predicts a nonlinear relationship and we estimate it with nonparametric kernel regressions as well as parametric piecewise linear regressions. Our results indeed show a high nonlinearity and a strong seasonal pattern in managerial risk taking. During earlier months of a year, poorly performing funds reduce their risk. Towards the end of a year, on the contrary, poorly performing funds gamble for resurrection by increasing risk. Both risk changes are statistically and economically significant and we further explore the underling incentives 1

Summary by including experimental variables in the piecewise linear regression. We find that the risk reduction is stronger for funds with higher management fees, shorter notice periods prior to redemption, and recently deteriorating performance, which is consistent with a managerial aversion to early fund liquidation and to the loss of future management fees. The risk increase, however, is not related to these factors. The increase is not purely driven by high-water mark provisions and incentive fees, which points towards the existence of incentives that are not directly linked to the compensation scheme, like reporting good performance at year end. Moreover, we show that hedge fund risk is persistent and the managers take this into account for their dynamic risk adjustment. While not the main focus of our work, we provide an extensive cross-sectional analysis in the appendix and compare our findings to the results reported for monthly returns from established databases. We show that our funds are very similar, which means that future research can benefit from the high frequent return data. This research paper has been rather well perceived by the academic community and an earlier version received a best paper award at the FRAP Conference in Cambridge in 2013. In Chapter 2 (Hedge Fund Herding), I analyze the trading in large U.S. equity positions by a sample of 748 hedge fund firms over the period 1995 to 2009. The holdings data come from mandatory filings by large U.S. institutional investors, which are required to report such equity positions on a quarterly basis. To identify hedge fund firms which do not run any business other than hedge fund management, I use data from commercial hedge fund databases and a web search algorithm. I construct my novel dataset by further adding information on securities from several other sources. I start with analyzing the trading within quarters at the security level. Following the methodology proposed by Lakonishok, Shleifer, and Vishny (1992), I find that hedge fund firms show a tendency to herd into and out of the same stocks together. The level of herding in my sample is of comparable order of magnitude to the levels of herding found for mutual funds by earlier research, but varies significantly across firms following distinct investment strategies. A more detailed analysis shows, that the observed herding is consistent with either hedge fund firms trading on the same kind of signals independently of each other (correlated private information), or with hedge fund firms following the trades of their presumably better informed peers (informational cascades). A clear attribution of the observed herding to the two potential reasons is not possible when analyzing the herding at the stock level. However, I can clearly rule out aggregate flows of client money to the hedge fund industry as a potential explanation. Also, hedge fund firms buying recent winners and selling recent losers right before the portfolio holdings are reported to impress investors (window dressing) does not explain the herding. I cannot detect a common strategy where lagged returns act as a buying or selling signal (feedback trading) which results in herding, unlike the common momentum trading (positive-feedback trading) observed for mutual funds and other institutional investors by earlier research. The evidence suggests that hedge fund herds form on rather profitable opportunities and do not destabilize stock prices. In a next step, I develop a measure for herding at the firm level, which is based on an earlier proposed measure. Results from dynamic panel regressions show that the measured firm herding is 2

Summary also not related to individual flows of client money to the firms, but is significantly related to past performance. The firms in my sample seem to follow the equity trades by peers that outperformed just prior to the trading period. Hence, the observed herding can at least partially be attributed to hedge fund firms following each others trades. Cross-sectional regression results reveal a negative relation of firm herding to overall firm risk and to the size adjusted number of stocks in the firms equity portfolios, which is consistent with the two explanations proposed. Overall, my findings are consistent with some earlier reported evidence on joint stock-picking by hedge fund managers and do not confirm concerns of introduced excess volatility. At the same time, they raise a couple of questions for future research. Especially the high levels of herding observed for merger arbitrage firms provokes questions about the role of these (herds of) firms as shareholders in M&A transactions. This and further questions are addressed in ongoing research projects, which are not part of this dissertation, but build on my database constructed here. This research paper has been rather well perceived by the academic community and an earlier version received a best paper award at the ACDD Conference in Strasbourg in 2012. Chapter 3 (Audit Experts) is joint work with Benjamin Hess. We analyze how accounting expertise from former audit firm employees on company boards influences the audit effort and the reporting quality. More specifically, we analyze the development of the audit fees and the discretionary accruals after the appointment of such an audit expert to the board of a publicly listed company in the U.K. between 2002 and 2009. The audit fees proxy for the audit effort and the discretionary accruals serve as a proxy for the financial reporting quality. We measure the variation in both proxies within firms over time in panel regressions. Our estimation setup controls for general differences between individual firms and for common determinants of audit fees and discretionary accruals. This ensures a clean statistical identification of developments resulting from audit expert appointments. The setup, however, requires knowledge about the engagement start dates of audit experts. We use publicly available data on employment histories which allow us to track audit firm employees who switch to company boards with little or no time gap between their affiliations. We construct a novel panel dataset by connecting these data to information on board compositions, financial statement data, information on the audit firms, and capital market information from other sources. Our results show an increase in the audit fees in the first years after the appointment of an audit expert. We relate this fee increase to improvements in the financial reporting that must be audited, i.e. higher audit fees proxy for higher audit effort and come along with a higher reporting quality. Since a fee increase could also be the result of internal control problems or a demanded risk premium of the incumbent audit firm, we additionally analyze the discretionary accruals as a measure for the reporting quality. Our results show that the observed fee increase is indeed associated with a permanent decrease in the discretionary accruals. More detailed results reveal that both effects are driven by audit experts who become executive directors as well as by companies with weak governance structures and small boards. The findings correspond to a stronger accounting expertise effect when the influence of the expert in the board is strong, which confirms our suggested relation. Overall, our findings show that the 3

Summary firms stakeholders and other addressees of financial reports can expect more audit effort and an improved audit quality from the appointment of a former audit firm employee to the board. Our comprehensive empirical evidence is consistent with a rational ongoing appointment practice, but stands in contrast to some of the earlier findings for the effect of audit expert appointments on earnings management. Also, the results raise questions about the perception of audit expert appointments by financial markets, which were found to show no significant reaction to appointments of audit experts by earlier research. 4

Chapter 1 Hedge Fund Risk Taking Recovering Managerial Risk Taking from Daily Hedge Fund Returns: Incentives at Work? 5

Chapter 1 Hedge Fund Risk Taking 1.1 Introduction Hedge funds pose a challenging task from a risk management perspective. They are allowed to use exotic financial products of all kinds, they can rapidly change their strategy as well as the exposures to different risk factors, and often they are highly leveraged. Most managers have some personal wealth invested in their fund, and a typical compensation contract provides them with complex risk taking incentives. They earn a management fee, which is a constant share of the fund s assets paid out on a pro rata temporis basis. On top, they earn a performance fee calculate as a share of the fund s profits in excess of a high-water mark (previously achieved end-of-year maximum net asset value, henceforth HWM), which is often paid at the end of a calendar year. It creates a complex incentive scheme which theoretically induces highly nonlinear managerial risk taking with a potentially strong seasonal pattern (e.g., Hodder and Jackwerth (2007), and Lan, Wang, and Yang (2013)). In our paper, we analyze the dynamic risk taking by hedge fund managers empirically and, among other, address its intra-year variation. We use a previously unattended sample of daily hedge fund returns from Bloomberg. While the hedge funds in our sample behave very similar to the majority of funds reporting monthly returns with respect to their risk taking, the higher reporting frequency allows us to estimate fund risk on a monthly basis as the intra-month return standard deviation. We document a strong seasonal pattern in the risk taking, which is a nonlinear function of fund performance relative to the HWM. Conditional on fund underperformance relative to the HWM, hedge fund managers increase the fund risk, which is consistent with theoretical predictions in Hodder and Jackwerth (2007) and Buraschi, Kosowski, and Sritrakul (2012). It happens, however, only during later months of a year (particularly, during the fourth quarter), whereas the aforementioned models predict a uniform risk increase throughout the year. During earlier months of a year (second quarter), poorly performing funds, on the contrary, tend to reduce their risk. This risk down shift seems to be consistent with the predictions of the model in Lan, Wang, and Yang (2013). Comparing the assumptions underlying the different models suggests that at the beginning of a year, fund managers may perceive their evaluation horizon as very long, and seek to reduce the fund liquidation probability in order to keep earning management fees, whereas towards the end of a year poorly performing managers may perceive their investment horizon as rather short. Looking further into the incentives to reduce the risk in case of poor fund performance during earlier month of a year, we document that, indeed, those funds that charge higher management fees are more disposed to reduce risk. Similarly, funds with a shorter notice period prior to redemption, recently deteriorating performance, and younger age exhibit a stronger risk reduction, which is potentially driven by a higher liquidation probability of such funds. Remarkably, these factors do not have a significant impact on the documented risk increase at the end of a year, where all poorly performing managers gamble for resurrection. The end of year gamble for resurrection by poorly performing funds is not purely driven by the existence of high-water marks and incentive fees provisions. It is strongly 6

Chapter 1 Hedge Fund Risk Taking pronounced for funds, which are not charging incentive fees, too. This finding points towards the existence of other incentives (not explicitly linked to the managerial compensation scheme) that induce higher risk taking at the end of a calendar year. These might include reputational concerns, as the majority of hedge funds provide end-of-year reports to their clients. Remarkably, funds that exhibit higher return correlations with the market show a stronger risk increase at year end. These funds seem to follow more conventional strategies, which potentially allow for a more flexible risk adjustment. We also document that hedge fund risk is persistent. While finding general persistence in second moments of return distributions is not surprising, we show that managers take it into account when they adjust the fund risk. Risk adjustments happen in advance to assure the realization of desired risk levels at desired times. The second quarter risk decline of poorly performing funds is strongly pronounced in April and May, and not so in June; and the fourth quarter gambling starts as early as October, is pronounced in November, and no additional risk shifts can be detected in December. The rest of this chapter is organized as follows: Section 1.2 outlines the theoretical predictions of the existing models for hedge fund risk taking and reviews the existing empirical evidence. Section 1.3 introduces the data. Section 1.4 describes the methodology. Section 1.5 reports the main empirical results. Section 1.6 further investigates potential determinants of the observed risk changes. Section 1.7 discusses various robustness checks, and the last section concludes. 1.2 Related Literature In this section, we, first, review the theoretical predictions for managerial risk taking in hedge funds. While there is a vast literature on the optimal response to more general incentive schemes 1, we will focus on the most relevant models for hedge funds only. Then, we proceed by summarizing the existing empirical evidence. One of the first models, which covers most of the main characteristics of a typical incentive contract in a one-period as well as in a multi-period setting, is Hodder and Jackwerth (2007). The optimal risk taking is obtained for a risk-averse hedge fund manager, who has some personal wealth invested in the fund, receives a management fee as well as an inventive fee that is tied to a HWM, and possesses an option to liquidate the fund at her own discretion. The optimization is performed on a discretized grid of fund values and time. With a three year valuation horizon and incentive fee calculation and HWM resetting at the end of every year, the managerial risk taking increases if the fund value is substantially below the HWM. It reflects managerial gambling at a point, where the fund is close to liquidation. The simulation results by Hodder and Jackwerth (2007) suggest, that the liquidation boundary, endogenously chosen by managers, lies between fund values of 50% to 60% of the corresponding HWM. 1 See, e.g., Harris and Raviv (1979), Gibbons and Murphy (1992), Ross (2004), Basak, Pavlova, and Shapiro (2008) among others. 7

Chapter 1 Hedge Fund Risk Taking A limitation of the Hodder and Jackwerth (2007) model is that investor s behavior in response to hedge fund performance is not considered. Generally, investors respond to good fund performance by capital inflows to the fund, and tend do redeem shares after periods of poor performance (Ding, Getmansky, Liang, and Wermers (2009)). Although this response could be a minor issue for short valuation horizons, as redemptions are often restricted by lock-up and notice periods, it could have a substantial effect for longer horizons. A step forward in this direction is made by Buraschi, Kosowski, and Sritrakul (2012). Here, the authors search for an appropriate adjustment of hedge fund performance for managerial risk taking. Therefore, they develop a structural model of optimal risk taking. 2 The model considers a typical hedge fund incentive contract but does not explicitly include the manager s personal investment in a fund. Instead of an option for the manager to liquidate the fund, the authors model investors redemptions and potential brokerage funding restrictions through short put option positions. 3 The optimal investment problem is then solved using the martingale approach developed in Cox and Huang (1989). The theoretical solution of Buraschi, Kosowski, and Sritrakul (2012) suggests the highest risk taking at a fund value of approximately 60% of the HWM, with the risk taking still being bounded. If the short put options are ignored and only the performance fee is maximized (a long call option only), the model predicts unbounded risk taking. Compared to Hodder and Jackwerth (2007), where a poorly performing manager keeps increasing investment risk at lower fund values right until she optimally chooses to liquidate the fund and take-up outside opportunities, the investors and brokers options to redeem shares and suspend financing in Buraschi, Kosowski, and Sritrakul (2012) result in a gradual risk reduction after the fund value drops below a certain point and approaches the strike of the short put option. While Buraschi, Kosowski, and Sritrakul (2012) do not analyze differential times to expiration of the managerial incentive option explicitly, Panageas and Westerfield (2009) focus entirely on the effect of the managerial valuation horizon. They consider the optimal portfolio allocations for a risk-neutral manager disregarding personal managerial investments in the fund and management fees. The authors show, that even in such an extreme setting, an option like compensation contract results in infinitely high risk taking, only if the managerial valuation horizon is finite. With an infinite horizon, the optimal portfolio is constant with bounded risk. The above mentioned papers suggest the following testable hypotheses: 2 The model is based on Koijen (2013), who develops a structural model for optimal portfolios of mutual fund managers, taking into account managerial skill, incentives, and risk preferences. 3 Buraschi, Kosowski, and Sritrakul (2012) also analyze risk shifting empirically. But the authors focus on differences in the overall hedge fund return volatilities measured across a whole year, where they treat all observations alike in terms of time to expiration. The results are then used for performance adjustments and are not directly comparable to our empirical results. 8

Chapter 1 Hedge Fund Risk Taking Hypothesis A(i): Hypothesis A(ii): The average managerial risk taking is higher if the hedge fund value is below the HWM. Below the HWM, the relationship between fund value relative to the HWM and managerial risk taking is not linear but bellshaped. Lan, Wang, and Yang (2013) take a different avenue in modeling optimal hedge fund risk taking. The key difference to the models of Hodder and Jackwerth (2007) and Buraschi, Kosowski, and Sritrakul (2012) is the infinite valuation horizon of managers. Instead of maximising the utility at some terminal date, they maximize the present value of an infinite stream of management and incentive fees. The infinite investment horizon makes early liquidation of a fund extremely costly, and results in risk-averse behavior even for risk-neutral managers. This leads to lower risk taking at fund values below the HWM (where the fund liquidation probability is higher). Interestingly, management fees capture 75% of the total managerial surplus, with only 25% generated though incentive fees. In this continuous time structural model, the authors also incorporate other stylized facts of managerial investment strategies and compensation contracts, including the existence of alpha-generating strategies, drawdown and fund liquidation triggered by poor performance, leverage constraints, managerial ownership, new money inflow in response to good performance, as well as an endogenous managerial option to liquidate and re-start the fund at a cost. This model provides a competing hypothesis: Hypothesis B: The average managerial risk taking is lower for hedge funds below the HWM. Hypothesis A would be consistent with a relatively short valuation horizon of fund managers, whereas Hypothesis B would suggest the managers have a much longer valuation horizon. The scope of the existing empirical evidence on the managerial response to incentives in hedge funds is limited by the availability of hedge fund data. Generally, hedge fund return data are available only at a monthly frequency. Most of the existing studies choose to analyze changes in fund risk (measured as the return standard deviation) from the first half of a year to the second half of a year, with each of the standard deviation estimates being based on six monthly return observations only. With such a research design, Brown, Goetzmann, and Park (2001) find tournament behaviour among hedge funds but no relation of fund risk to absolute performance. In particular, the authors show that hedge funds delivering above average performance during the first half of a year, reduce the return volatility during the second half of the year, while those funds exhibiting below average performance, tend to increase return volatility. However, after conditioning on the estimated HWM, the significance of the volatility changes vanishes. Agarwal, Daniel, and Naik (2002) find similar results in their sample of hedge funds, i.e. no relation of risk to fund value relative to the HWM. More recently, however, Aragon and 9

Chapter 1 Hedge Fund Risk Taking Nanda (2012) and Buraschi, Kosowski, and Sritrakul (2012) do find evidence of endogenous and state dependent risk shifting. The paper by Aragon and Nanda (2012) is most closely related to our work. The authors investigate changes in hedge fund return standard deviations from the first to the second half of a year in a panel regression framework and confirm an average negative relation between fund performance and risk changes (which would be consistent with the predictions in Hodder and Jackwerth (2007) and Buraschi, Kosowski, and Sritrakul (2012)). They relate the risk changes to managerial incentives and find that the risk shifting is mitigated for hedge funds with a HWM provision and low risk of immediate liquidation, as well as for managers with a large personal capital stake invested in the fund. The paper focuses on tournament behavior by hedge fund managers, and the main performance measure is the relative rank of a fund with respect to its peers. The authors also repeat the analysis using the absolute fund performance, which is measured by an indicator variable of fund being below the HWM in the middle of a year. They find that funds which are below the HWM significantly increase risk taking from the first to the second half of a year. The existing empirical research does not consider the intra-year variation of risk taking in detail. We expect, however, that seasonality in risk taking might be rather pronounced in light of the existing evidence on seasonality in reported returns. Agarwal, Daniel, and Naik (2011) find that hedge funds (especially those with low incentives and high opportunities to manipulate returns) tend to underreport good returns, thus, smoothing performance throughout a year and then inflate their December returns by adding the underreported portion of returns. Such a strategy assures higher inflows as investors direct money into funds reporting a greater fraction of positive returns. The authors also find weak evidence of hedge funds inflating December returns through borrowing from January returns. Such a strategy increases the fees earned during the current year. Supporting this view, Ben-David, Franzoni, Landier, and Moussawi (2013) suggest possible stock price manipulations by large hedge funds that have to file end-of-quarter long equity holdings with the SEC through 13F reports. Stocks held by the hedge funds exhibit excessive price pressure during the last trading day of the quarter and earn abnormal returns, which are rapidly reverted during the first trading day following the quarter end. The majority of funds does not need to file quarterly reports with the SEC, but it still provides investors with end-of-year reports. Even such voluntarily reporting may induce changes in managerial investment behaviour. For example, Patton and Ramadorai (2013) show that hedge funds reporting voluntarily on monthly bases to commercial databases vary the factor exposures within months. The exposures decline from the beginning of a month towards the end, with the lowest point achieved just prior to the hedge fund reporting date. Reporting particularly good results at year end to the investors contributes to managerial reputation as well as increases immediately paid fees. Besides the aforementioned direct manipulations, higher returns in December can also be achieved by increasing the riskiness of the underlying portfolio beforehand. This leads us to a conjecture, that Hypothesis A(i) is more likely to hold at the end of a year, rather than at the beginning 10

Chapter 1 Hedge Fund Risk Taking of a year. 1.3 Data 1.3.1 General Properties of Hedge Fund Daily Returns Our sample consists of 714 single- and multi-strategy hedge funds retrieved from Bloomberg that report their returns on a daily basis in either USD or EUR from October 1, 2001 through April 29, 2011. 4 We retrieve time series of daily hedge fund returns and assets under management, together with some static information on fund characteristics, like the levels of the management and incentive fee, the use of a HWM, as well as the length of the lock-up and notice periods. The sample period starts once the number of fund-month observations for our main variable of interest (RISK) discussed later eventually remains above 50 in every month. The sample contains only individual hedge funds and no funds of funds. We clean two obvious outliers, where the daily returns exceed 100% and include only hedge funds, which report daily returns regularly over the entire lifetime. To ensure regular daily reporting, we delete all zero return information reported and impose restrictions on the number of trading days between two consecutive reporting dates. The average number of non-reporting days is not allowed to exceed 5/4 (at least 4 return observations per week on average), the maximum gap is 9 trading days (the fund never misses reporting for 2 weeks or more), and the standard deviation must lie below 0.5 (reporting gaps do not occur frequently). For the included funds, we later require at least 15 daily return observations per month (at least 4 per week for the shortest month, on average) to obtain a monthly risk estimate, and an AuM observation within the first and last 5 trading days of the month to obtain a monthly flow estimate. We also exclude one fund with less than one year of reported returns. Hedge funds reporting on a daily basis can be expected to be less opaque than those reporting on a monthly basis. Some of them are SICAVs 5, some work under the UCITS 6 jurisdiction, others may operate through managed accounts. We do not find any evidence for a backfilling bias at any horizon in our sample of hedge funds. Hence, we do not delete initial return observations for the following analysis. Table 1.1 summarizes the sample and reports the descriptive statistics of the hedge fund returns. The median returns for EUR hedge funds are lower than for USD hedge funds, which is partially due to inflation differences between the U.S. and the Euro-zone, and partially due to differences across the implemented strategies by the funds. Compared to hedge funds that report on a monthly basis to commercial databases commonly used in the hedge fund literature, the hedge funds in our sample seem to be slightly less profitable 4 The number of hedge funds reporting daily returns to Bloomberg in other currencies is generally small and develops unevenly over time, which is why we use EUR and USD funds only. 5 SICAV is a type of an open-ended collective investment vehicle operating in Western Europe. 6 UCITS directives allow investment funds to freely operate across the boarders in the European Union, being authorized in only a single member state. 11

Chapter 1 Hedge Fund Risk Taking and less risky. 7 This difference is consistent with the funds in our sample being more transparent and liquid, and, thus, able to report on a daily basis. Despite slightly lower levels of overall risk of funds in our sample, we expect the risk shifting patterns to be comparable to the funds reporting on monthly frequency, primarily because of similar managerial incentive schemes. 8 Further comparing the time-series dynamics of hedge funds returns in our sample and the ones reported on the monthly basis 9 we see that funds in both groups exhibit similar performance patterns. The correlation between average cross-sectional returns across these samples is 93%. The tail behaviour is also very similar with the correlation between returns of the bottom 5% of funds being 87%, and the correlation of the return of the top 5% of funds being 78%. Figure 1.1 depicts the time series of average monthly returns of hedge funds in our sample and funds reporting on a monthly basis. The two lines are closely related (reflecting the high correlation) and positive and negative spikes in the returns seem to coincide. This suggests that the sample of daily reporting hedge funds, apart from containing generally less risky and less profitable funds, is not systematically different from the conventionally used hedge funds. Hedge funds following different strategies exhibit different risk-return profiles. sample covers a wide range of hedge funds investment styles. Our Based on Bloomberg s classification, we assign each fund to one of nine categories (including Not defined ) as reported in Table 1.2. The highest mean return of 0.69% per month is earned by the Emerging Markets hedge funds, whereas the Managed Futures funds exhibit the highest return standard deviation of 5.77% per month. We compare the distribution of fund styles in the samples of daily reporting funds and funds reporting monthly to commercial databases and depict it in Figure 1.2. There is a difference in the percentage of Directional Equity and Equity Market Neutral funds across the two databases. These styles account for 24% and 17% respectively of daily reported funds and for 10% and 36% of monthly reporting styles. This discrepancy, however, might be driven by variations in style labeling across different database. Altogether, equity funds cover the largest and rather similar share across both samples 41% of daily reporting funds and 46% of monthly reporting funds. Another exception is Managed Futures funds that are relatively over-represented in the sample of daily reporting funds accounting for 18% of the sample, whereas they account for 5% of the sample of monthly reporting funds. Other styles have very similar distribution across the sample. Despite some differences, our sample of daily reporting hedge funds is not biased towards a single hedge fund style. It covers the whole spectrum of styles similar to other widely used samples of monthly 7 Hodder, Jackwerth, and Kolokolova (2013) report that for their combined sample of hedge funds the mean (median) return of USD funds is 0.55% (0.50%) with a corresponding standard deviation of 4.60%. 8 Throughout the paper, we compare our results to earlier results for more traditional hedge fund samples and show that they are in line. Moreover, in the Appendix we will present further evidence, e.g. on the cross-sectional determinants of risk levels, that suggests that our funds behave very much like monthly reporting funds. 9 Our comparison group includes more that 20000 hedge funds that report to five commercial databases BarclayHedge, Eurekahedge, Morningstar, HFR, and TASS, which is an updated database used in Hodder, Jackwerth, and Kolokolova (2013). The time period is matched to the one of our sample of daily reporting hedge funds. 12

Chapter 1 Hedge Fund Risk Taking Table 1.1: Descriptive Statistics for the Hedge Fund Sample EUR USD All Live Dead All Live Dead Panel A: Sample Funds 400 285 115 314 178 136 Monthly STD obs. 14 728 10 951 3 777 10 073 5 962 4 111 Mean life time 3.35 3.38 3.26 2.90 2.92 2.88 Median management fee (%) 1.5 1.5 1.5 1.5 1.5 1.3 Have incentive fee 284 209 75 222 131 91 Median incentive fee (%) 20 20 20 20 20 20 Have HWM 234 175 59 201 112 89 UCITS & SICAV 90 81 9 131 73 58 Report AuM 371 278 93 164 105 59 Monthly AuM obs. 8 544 7 063 1 481 3 370 2 184 1 186 Mean AuM (mil. USD) 369.52 431.73 150.56 103.70 135.11 43.80 Panel B: Daily returns Mean 0.01 0.02-0.01 0.01 0.03-0.01 Median 0.02 0.02 0.01 0.03 0.04 0.01 Min. -77.69-77.69-32.18-50.12-50.12-45.51 Max. 43.32 43.32 26.21 76.24 45.80 76.24 STD 0.56 0.58 0.50 0.89 0.76 1.06 Skewness -0.39-0.25-0.75-0.25-0.28-0.20 Kurtosis 23.01 19.37 32.02 26.01 18.24 36.17 Sharpe Ratio 0.02 0.04-0.03 0.02 0.04-0.01 Panel C: Monthly returns Mean 0.23 0.40-0.22 0.21 0.55-0.24 Median 0.24 0.34 0.11 0.39 0.54 0.23 Min. -77.85-77.85-40.34-66.28-50.53-66.28 Max. 57.80 40.90 57.80 94.83 94.83 55.54 STD 2.39 2.49 2.16 3.67 3.34 4.09 Skewness -0.43-0.36-0.62-0.31-0.23-0.41 Kurtosis 4.77 4.61 5.15 4.36 4.00 4.84 Sharpe Ratio 0.06 0.16-0.19 0.07 0.17-0.06 Panel A reports the general characteristics of the hedge funds in our sample, including the average fund size, life time in years, usage of a HWM and an incentive fee, working under UCITS regulation or being a SICAV, etc. Panel B reports the descriptive statistics of daily hedge fund returns. Panel C reports the descriptive statistics of the corresponding monthly returns. Returns are expresses in percent per day and month, respectively. reporting funds. The main focus of our paper is the risk of the hedge funds. We measure hedge fund risk as the standard deviation of daily returns within one month. For each hedge fund in our sample, a time-series of such monthly risk estimates is constructed. For the ease of presentation, we will henceforth refer to the natural logarithm of the intra-month standard deviation of daily hedge fund returns as RISK. In contrast, uncapitalized risk, will still be used to refer to the general notion of investment risk. Figure 1.3 shows an envelope plot 13

Chapter 1 Hedge Fund Risk Taking Figure 1.1: Time Series of Average Returns of Daily and Monthly Hedge Funds The figure presents time series plots of cross-sectinal average monthly returns from the funds in our sample (reporting daily to Bloomberg) as well as from funds reporting monthly to the commertial databases as defined in Section 1.3 between October 2001 and April 2011. The correlation between the two series is 93%. of the RISK time series for all individual hedge funds in our sample, revealing considerable cross-sectional variation in hedge fund risk taking. The corresponding cross-sectional average descriptive statistics of RISK are given in Table 1.3. The average return standard deviations reported are slightly lower than the ones from the previously reported descriptive statistics in Table 1.1 (0.47% vs. 0.56% for EUR funds and 0.74% vs. 0.89% for USD funds). The differences capture the variations in the average level of hedge funds returns over time. While for Table 1.1 only one estimate of return standard deviation is computed across the complete return history of each fund, the monthly estimates (Table 1.3) enable us to address the time variation in hedge fund risk. 1.3.2 Time Series Properties of Hedge Fund Risk Figure 1.4 plots the time series of the cross-sectional means of RISK for EUR and USD funds, as well as the corresponding time series for the MSCI-World index. The standard deviation of both EUR and USD hedge funds are smaller than that of the MSCI-World index. Despite living on different levels, all series seem to share the same dynamics. The correlation coefficients between all plotted series are very high, ranging from from 0.80 for MSCI-World and EUR funds to 0.84 for MSCI-World and USD funds. When analyzing the hedge funds risk taking and the associated managerial decisions on the desirable level 14

Chapter 1 Hedge Fund Risk Taking Table 1.2: Descriptive Statistics Across Hedge Fund Styles Funds Mean Median Min Max STD Panel A: Daily returns Eq Directional 168 0.03 0.03-16.94 26.84 1.03 Eq Mkt Neutral 120 0.01 0.01-50.12 76.24 1.16 Emerg Mkt 30 0.03 0.03-18.51 14.11 0.90 Event Driven 34 0.02 0.02-45.51 11.12 0.63 Fixed Income 68 0.01 0.01-42.22 45.80 0.46 Global Macro 76 0.01 0.01-14.38 17.60 0.86 Mgd Futures 125 0.02 0.02-77.69 43.32 1.52 Multi Strat 76 0.00 0.01-34.33 20.71 0.73 Not Defined 17-0.01 0.01-16.24 18.54 1.01 Panel B: Monthly returns Eq Directional 168 0.64 0.46-35.76 30.40 4.33 Eq Mkt Neutral 120 0.06 0.14-66.28 55.54 4.01 Emerg Mkt 30 0.69 0.42-34.79 28.78 4.21 Event Driven 34 0.39 0.50-44.77 14.71 3.09 Fixed Income 68 0.25 0.26-41.99 94.83 2.62 Global Macro 76 0.28 0.32-32.20 25.38 3.84 Mgd Futures 125 0.30 0.28-77.85 57.80 5.77 Multi Strat 76 0.09 0.24-37.95 26.84 3.27 Not Defined 17-0.10 0.17-45.48 14.69 5.24 The table reports the descriptive statistics of hedge fund returns separately for different hedge fund styles. Funds are classified in one of eight style groups according to the investment strategy reported to Bloomberg. The last group contains hedge funds for which no strategy classification is provided. Panel A is based on daily hedge fund returns, and Panel B is based on monthly returns. Returns are expresses in percent per day and month, respectively. Table 1.3: Descriptive Statistics for Hedge Fund Risk EUR USD All Live Dead All Live Dead Mean 0.47 0.50 0.42 0.74 0.67 0.83 Median 0.42 0.44 0.35 0.63 0.59 0.67 Min. 0.19 0.21 0.15 0.31 0.32 0.29 Max. 1.39 1.45 1.24 2.15 1.68 2.75 STD 0.25 0.26 0.25 0.42 0.30 0.58 The table reports descriptive statistics of hedge fund risk. Hedge fund risk is estimated on a monthly basis as the intra-month standard deviation of daily returns. The underlying daily returns are measured in percent per day. of risk, we will, therefore, condition on the overall market risk. Generally, return volatility is found to be rather persistent. In equity markets, for example, mixed evidence on the predictability of the first moments of stock returns coexists with strong evidence on the predictability of second moments (see Christoffersen and 15

Chapter 1 Hedge Fund Risk Taking Figure 1.2: Distribution of Styles of Daily and Monthly Hedge Funds The figure presents the reported styles distributions of funds in our sample (reporting daily to Bloomberg) as well as of funds reporting monthly to commertial databases as described in Section 1.3 between October 2001 and April 2011. The abbreviations stand for: EqDirec Directional Equity, EqMktNeu Equity Market Neutral, EmgMkt Emerging Markets, EvDriv Event Driven, FixedInc Fixed Income, GlobMac Global Marco, MgtFut Managed Futures, MultiStrat Multy Strategy, NotDefined - funds that do not clearly state their style or the style cannot be classified within any of the groups above, for example Tail Risk. Diebold (2006) and Christoffersen, Diebold, Mariano, Tay, and Tse (2007)). There exists some evidence on hedge fund return predictability (Avramov, Kosowski, Naik, and Teo (2011) and Wegener, von Nitzsch, and Cengiz (2010)), which suggests an even stronger predictability in the second moments of hedge fund returns. Also, hedge fund managers are known to specialize in particular investment strategies. Following one or several related strategies consistently could result in rather stable levels of fund risk, even if the underlying securities in the portfolio often change. There exists some empirical evidence supporting this view. Teo (2010), for instance, finds that the liquidity risk exposure of hedge fund portfolios is rather persistent. Ang, Gorovyy, and van Inwegen (2011) document high stability of hedge fund leverage. Additionally, the transaction costs that especially highrisk funds are facing can be substantial. Persistent leverage and the potentially costly closure of risky and illiquid positions point towards overall stability of hedge fund risk, too. At the same time, hedge funds are perceived as very dynamic investment vehicles, which frequently alter their exposures to different risk factors (Fung and Hsieh (2001), Billio, Getmansky, and Pelizzon (2012)). This could lead to considerable volatility of hedge fund risk, i.e. low risk persistence. To quantify the actual persistence in hedge fund risk, we estimate the serial correlation at the first 5 lags of RISK for each hedge fund separately and report the results in Table 1.4. 16

Chapter 1 Hedge Fund Risk Taking Figure 1.3: Individual Time Series of Hedge Fund Risk The figure presents an envelop plot from the individual time series of RISK (the natural logarithm of the intra-month standard deviations of daily hedge fund returns) of all individual hedge funds in our sample. The sample is described in Section 1.3 and contains 714 hedge funds that report their returns on a daily basis between October 2001 and April 2011. Hedge fund RISK appears to be rather persistent. The average first order serial correlation is 36%. For 91% of hedge funds, the first order serial correlation is positive, and it is significant for 51% of all hedge funds. We find negative estimates for the first order serial correlation for 9% of the hedge funds. These correlations are all small in absolute terms (with an average of -0.12) and we do not document a single case of a statistically significant negative autocorrelation coefficient of the first order and only few such correlations at the lags of higher order. The average correlation coefficients decrease substantially to levels below 0.10 after the third lag, namely to 0.07 at lag 4 and 0.02 at lag 5. Still, the coefficients at lag 5 are positive and significant for 11% of the hedge funds. 10 To understand the structure of the underlying data generating process and determine the optimal number of lags that should be used in the panel analysis, we compute the partial autocorrelations of RISK. Partial autocorrelations capture the relation between the values at lag zero and higher order lags in isolation of the lags in between. fractions of negative and significant partial serial correlations are, again, negligible and the fractions of significantly positive coefficients drop after the third lag to only 3% at lag 4. Hence, we will include three lags of RISK for the later analysis. So far, we focused on the short-term persistence in the riskiness of hedge funds. Investors, however, are often subject to notice periods prior to the redemption. Our database contains relatively liquid funds and the average notice period prior to the redemption is 10 This pattern is very stable across EUR and USD hedge funds. The EUR funds exhibit only slightly higher persistence in RISK, with 55% (45%) of the EUR (USD) funds having significantly positive first order coefficients. The 17

Chapter 1 Hedge Fund Risk Taking Figure 1.4: Time Series of Aggregate Hedge Fund Risk and Market Risk The figure plots the time series of the cross-sectional averages of RISK (the natural logarithm of the intra-month standard deviations of daily hedge fund returns). It shows the time series of averages from all hedge funds, as well as from hedge funds reporting in USD and EUR separately. The sample of hedge funds is described in Section 1.3 and contains 714 hedge funds that report their returns on a daily basis between October 2001 and April 2011. The time series of market risk over the sample period is measured as the natural logarithm of the intra-month standard deviations of daily returns on the MSCI World Index. only 20 days. But the maximum is 93 days, which means there can be a substantial lag between an investor s decision to exit the fund and the actual time of redemption. From an investor perspective it is, thus, important to understand the longer-term persistence in hedge fund risk, too. To address this issue, for every month, we sort the hedge funds into a high-risk and a low-risk group according to their RISK being above or below the median, and estimate the probabilities of transition across the groups for different horizons. Table 1.5 reports the transition probability matrix. The probability to stay in the same risk category over the following month is much higher than the probability to move to the other category, where the difference is highly statistically significant. The persistence is common for both high- and low-risk funds. We gradually increase the horizon with an increment of one month. The probability to stay in the current risk category is significantly higher than the probability to leave it at all horizons until 18 month, where we cannot reject the hypothesis of zero difference between the probabilities anymore for the first time. We repeat the analysis for high-risk and low-risk funds separately, for USD and EUR funds separately, as well as for changes in risk from December (one year) to January (the next year) only. The results remain virtually unchanged. Overall, we document that the level of risk taken by hedge funds is rather persistent. 18

Chapter 1 Hedge Fund Risk Taking Table 1.4: Autocorrelation in Hedge Fund Risk lag1 lag2 lag3 lag4 lag5 Mean 0.36 0.17 0.12 0.07 0.02 Median 0.38 0.18 0.14 0.06 0.01 STD 0.26 0.25 0.23 0.20 0.20 Min -0.34-0.55-0.53-0.40-0.45 Max 0.85 0.76 0.76 0.60 0.56 Fract. pos. 0.91 0.75 0.67 0.61 0.52 Fract. neg. 0.09 0.25 0.33 0.39 0.48 Mean pos. 0.41 0.28 0.25 0.20 0.18 Mean neg. -0.12-0.15-0.13-0.13-0.15 Fract. pos. sign. 0.51 0.30 0.22 0.15 0.11 Fract. neg. sign. 0.00 0.01 0.01 0.00 0.00 The table reports the descriptive statistics of autocorrelation coefficients estimated for different lags of the hedge fund s individual time series of RISK (the natural logarithm of the intra-month standard deviation of daily hedge fund returns). The last two rows of the table report the shares of significantly positive and significantly negative coefficient estimates among all hedge funds. Table 1.5: Transition Probabilities for Hedge Fund Risk Categories Low High Dead 1 Month Low 84.40*** 13.18 2.42 High 13.27 84.41*** 2.32 6 Month Low 49.78*** 36.67 13.56 High 36.91 49.82*** 13.27 12 Month Low 38.31*** 36.52 25.17 High 36.76 38.35*** 24.89 18 Month Low 32.55 32.24 35.21 High 32.45 32.58 34.96 The table reports the probabilities for hedge funds to move between high-risk and lowrisk groups for different horizons from 1 up to 18 months. The funds are sorted into the two risk categories according to RISK (the natural logarithm of the intra-month standard deviation of daily hedge fund returns) being above or below the median of all hedge funds in a given month. The probabilities are expressed in percent. ***, **, and * indicate that a probability to stay in the current risk category is significantly different from the corresponding probability to leave the category at the 1%, 5%, and 10% significance level, respectively. 19

Chapter 1 Hedge Fund Risk Taking To what extent trading cost and other frictions truly limit the ability of managers to alter fund risk rapidly, and to what extent risk persistence follows simply from general style constancy remains an open question, and we will revisit this issue when analyzing the impact of incentives on risk taking later. The overall stickiness of hedge fund risk levels suggests that while our focus is on time-varying drivers of hedge fund risk (e.g. fund value relative to the HWM), general cross-sectional differences, which potentially arise from differential managerial risk appetites and investment strategies, should not be ignored. Therefore, we will control for fund fixed effects in the panel analysis. Also, we supplement a cross-sectional analysis of an average hedge fund risk in Appendix 1.A.1. 1.4 Methodology We employ a semi-parametric panel regression approach to analyze the managerial risk taking in response to incentives. Here RISK (the natural logarithm of the monthly standard deviation of daily hedge fund returns) serves as the dependent variable. The timeseries properties of RISK analyzed in Section 1.3.2 suggest that RISK follows an AR(3) process and we specify a panel regression that includes 3 lags of the dependent variable as regressors. In such a dynamic panel regression, fund-specific effects are correlated with regressors, which renders random effect models inconsistent. Fixed effect models, however, do not allow for a joint analysis of time variant and time invariant regressors (such as fund characteristics). Hence, we include fund fixed effects in the panel regression, which capture variations in the average level of risk due to fund style, fees, redemption period, currency, and all other time-invariant characteristics, such as the manager s general appetite for risk. The interested reader finds a detailed cross-sectional analysis of the average fund risk in Appendix 1.A.1. As hedge fund risk is related to market risk (Figure 1.4), we include fixed effects in the time dimension, too, which control for variations in the market conditions and all other period specific effects jointly affecting all hedge funds. Following Aragon and Nanda (2012), we include the change in intra-month return first order serial correlations as an additional variable (DeltaCorr i,t ) to control for variations in the observed risk levels, which arise from changes in serial correlations rather than from managerial risk shifting. 11 As an additional control variable, we include the natural logarithm of the AuM of fund i at the beginning of month t (ln(aum i,t )) in the regression, where the minus sign as sub-index in t indicates the beginning of month t. The variable captures potential changes in the risk-taking pattern that result from fund size variations over time. We recognize that the second moments of hedge fund returns can be influenced by fund flows. Particularly, the effect of large outflows on fund risk could be pronounced 11 There are different potential reasons for a change in the serial correlation. A variation in the true underlying return generating process due to a deliberate change in the fund strategy by the managers can cause such a change. However, a change in the estimated correlation coefficient can be also artificially caused by not equally spaced observations of daily returns within consecutive months. The estimated correlation based on 15 returns per month can be different from that estimated on 22 returns, even though the underlying return process does not change. If the reporting frequency has any information on hedge fund risk, it will be also picked up by the change in the return serial correlation. 20

Chapter 1 Hedge Fund Risk Taking even without any deliberate managerial change to the investment strategy. Substantial redemptions force hedge funds to liquidate positions. To minimize the liquidation costs, managers are likely to close the most liquid positions first. The liquid positions are often among the less risky components of the fund s portfolio within each asset class. Thus, the remaining portfolio contains relatively fewer liquid assets and a larger share of riskier assets and it might take some time for the management to return to the desired level of risk. To address the fund-flow related risk changes, we calculate the fund flow over the previous month as F low i,t 1 = AuM i,t AuM i,t 1 CR i,t 1 AuM i,t 1, (1.1) where CR i,t is the cumulative return earned by fund i over month t. We then include a dummy variable, which indicates a flow below 5% and serves as a proxy for large outflows (OutflowLarge i,t ). 12 To identify risk shifting caused by the convex compensation contract, we include the value of the fund relative to its HWM at the beginning of a month, which is the variable of our main interest. For each fund the HWM is initially set to 1. It is then reset every 1st of January to the level of the cumulative return, if it exceeds the previous HWM, and it is kept unchanged if the cumulative return is below the previous HWM. 13 The fund value relative to the HWM is then the ratio of the total cumulative return of the hedge fund (that would correspond to the net asset value of 1 dollar or Euro invested in the fund at origination) over the corresponding HWM. Formally, V alue i,t = t 1 k=0 CR i,k HW M i,t. (1.2) The relationship between fund value relative to the HWM and managerial risk taking is expected to be nonlinear and to vary during a year (Hypotheses A and B). We capture it by introducing a nonparametric relation between fund risk and value. The relation is allowed to vary over K periods of a year, with I k indicating either the different quarters (K = 4) or months (K = 12) of a year. Our final semi-parametric model is given as 3 RISK i,t = α i + α t + β j RISK i,t j + γdeltacorr i,t + ζln(aum i,t ) j=1 + θoutflowlarge i,t 1 + K f k (V alue i,t )I k + ε i,t, (1.3) where α i and α t are the fund and time fixed effects, respectively. k=1 The regression in Equation 1.3 is estimated in two steps. First, RISK is regressed on all covariates excluding fund value. Then, the residuals from this regression (ê i,t ) are grouped according to calendar quarters or months. For each of the related four or twelve 12 Alternative potential relations of fund risk to fund flows are considered in Section 1.7.6. 13 In Section 1.7.5 we employ several other specifications for the HWM and find that the results remain virtually unchanged. 21

Chapter 1 Hedge Fund Risk Taking groups, a nonparametric kernel regression of the residuals on the corresponding fund value is estimated. Formally, ê i,t I k = f k (V alue i,t )I k + η i,t,k. (1.4) For the kernel regression, we use a Gaussian kernel with a fixed bandwidth of 0.07. 14 We restrict the support for our estimates to the closed interval, on which at least five observations are contained in each bandwidth window, to avoid inference over areas with few observations. We follow Yatchew (2003, p.161) to obtain bootstrapped confidence bounds around the estimated functions ˆf k. The procedure employs undersmoothing and a wild bootstrap with 10 000 iterations to correct for the asymptotic bias of the estimator and allow for heteroscedasticity of the residuals. Note that in the linear part of the Equation 1.3, the lagged values of RISK are correlated with the error term, which biases OLS estimates (Nickell (1981)). The most prominent solutions to this dynamic panel bias are GMM estimation techniques (e.g. Arellano and Bond (1991)) or an explicit bias correction (e.g. Kiviet (1995)). The former, however, is designed for small T panels and the latter is only feasible with balanced panels. Nickell (1981) derives an expression for the bias and shows that it approaches zero as T tends to infinity. In a simulation study, Judson and Owen (1999) show that for unbalanced panels, a fixed effects model outperforms the other alternatives already for T = 30. Therefore, we can well neglect the dynamic panel bias in our regression (with T = 115) and employ OLS. Bootstrapped panel robust standard errors take care of potentially remaining serial correlation and heteroscedasticity in the errors. 15 The analysis above allows us to capture potential nonlinearities in the relationship of fund risk and value and motivates the choice of breakpoints (if any) in this relationship. In order to give a more precise quantification of the strength of risk shifting, we repeat the analysis using a piecewise linear specification for the residuals instead of a kernel regression. We analyze the residuals from the linear part of Equation 1.3 for the different quarters of a year and allow the estimated coefficients on the value variable to vary within three intervals: (1) fund value lower than V (expressed in percent relative to the HWM); (2) fund value between V and the HWM; and (3) fund value above the HWM. The choice of a breakpoint value V will be motivated by the results from the kernel regressions (Equation 1.4). For each quarter of a year we estimate the following regression: 14 Cross-validations conducted separately for different quarters yield optimal bandwidths ranging from 0.01 to 0.10 and from 0.01 to 0.11 for month-wise regressions. To make sure that our results for different periods are not driven by differential smoothing, we keep the bandwidth fixed for all kernel regressions. From manually comparing regression results and trading-off smoothness and variance for all bandwidths within the range suggested by cross-validation, we chose 0.07 as our fixed bandwidth. As a robustness check, we re-estimate the regressions with different bandwidths in Section 1.7.4 and our findings remain qualitatively the same. 15 At the same time, we find that OLS standard errors are virtually identical to the bootstrapped ones, which indicates that our model does not produce serially correlated errors (Petersen (2009)). 22

Chapter 1 Hedge Fund Risk Taking α low + δ low V alue i,t + η i,t if V alue i,t < V ê i,t = α mid + δ mid V alue i,t + η i,t if V < V alue i,t < 1 α high + δ high V alue i,t + η i,t if V alue i,t > 1. (1.5) The standard errors are obtained via bootstrap. Here α-s indicate the average incremental risk taking in a given interval of fund values, whereas δ-s indicate the slope of the fund-risk to value relation within this interval. 16 1.5 Empirical Results 1.5.1 Managerial Risk-Taking: Quarter-Wise Column (I) in Table 1.6 reports the estimation results based on the linear part of Equation 1.3. Consistent with the time-series analysis of hedge fund risk in Section 1.3.2, past values of RISK are important predictors of the current risk level. As expected, the explanatory power is decreasing in the lag length, where the first lag obtains the highest loading of 0.50 with a corresponding t-statistic of above 50, and the coefficient estimates for the two- and three-month lags decrease to 0.09 and 0.07, respectively. We do not find any significant effect of variations in fund size on hedge fund risk in our sample, while our control variable DeltaCorr is positively related to hedge fund risk and significant at the 5% level. Outflows exceeding 5% of the AuM over the previous month lead to a significant increase in the fund risk. at the 1% level. The corresponding loading is positive (0.03) and significant Thus, after forced liquidation of presumably more liquid assets, the remaining hedge fund portfolio is riskier. We also include in the regression the fund flow directly as defined in Equation 1.1 at times (t 1) and (t 2), as well as an indicator function, which takes a value of one, if the corresponding flow is negative. In unreported results, none of these variables obtains a significant coefficient estimate. 17 Let us turn to analyzing the relation between fund value relative to the HWM and fund risk. Figure 1.5 plots the estimated kernel regression lines based on residuals from the linear part of Equation 1.3. Here fund and time fixed effect, risk persistence, effects of flows and size are already controlled for. The results are presented for four quarters of a year separately, together with 1%, 5%, and 10% confidence bounds around the regression lines. The figure suggests a clear seasonal pattern in risk taking. During the first quarter of a year, the fund value relative to the HWM does not seem to have any significant impact on the hedge fund risk as depicted in Figure 1.5 (a) at any conventional confidence level. During the second quarter managers tend to decrease the risk, if the fund value is some 25% below the HWM with the minimum achieved at a value of about 60% of the HWM. The decrease is significant at the 5% level. Thus, if a fund has been loosing 16 In the robustness Section 1.7.2 we further require the estimated relation to be piecewise continuous and find qualitatively similar results. 17 In Section 1.7.6 we will also see, that neither outflows preceded by poor performance, nor cumulative flows are driving the risk increase. 23

Chapter 1 Hedge Fund Risk Taking Table 1.6: Panel Regressions of Hedge Fund Risk (I) (II) RISK t 1 +0.50 *** (+53.07) +0.50 *** (+50.76) RISK t 2 +0.09 *** (+8.74) +0.10 *** (+9.01) RISK t 3 +0.07 *** (+7.19) +0.07 *** (+7.20) DeltaCorr t +0.03 ** (+2.13) +0.03 ** (+2.10) ln(aum t ) -0.01 (-1.36) -0.01 (-1.28) OutflowLarge t 1 +0.03 *** (+2.59) +0.03 *** (+2.59) ExcessP erf t 1-0.27 *** (-2.80) R-sqr. 0.90 0.90 Rbar-sqr. 0.89 0.89 Nobs 10 141 10 141 The table reports estimation results for panel regressions of RISK (the natural logarithm of the intra-month standard deviations of daily hedge fund returns) on a set of dynamic explanatory variables and controls. The regressions include fund and time fixed effects. The regressions and the included variables are described in Sections 1.4 and 1.7.1. The t-statistics from panel robust bootstrapped standard errors are given in parenthesis. ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively. money previously and by the beginning of the second quarter is substantially under water, managers reduce the fund risk. This finding supports our Hypothesis B and is consistent with Lan, Wang, and Yang (2013). Moving further towards the end of a year, the managerial risk taking reverts. It increases, if a hedge fund is substantially below the HWM. The increase is significant at the 5% level during the third quarter, and highly significant during the fourth quarter, consistent with Hypothesis A(i). Below the HWM the risk shifting does not increase monotonically, instead it is bell-shaped as suggested by Hypothesis A(ii). The substantial risk increase at low fund values displayed in Figure 1.5 (d) and its reversal for fund values below some 60% of the HWM is consistent with the predictions of Buraschi, Kosowski, and Sritrakul (2012): the managerial incentive option induces risk-taking, whereas investor redemptions and brokerage restrictions limit the risk shifting. We do not document significant managerial risk changes around the HWM itself (V alue = 1) in any quarter. The existence of the incentive option does not seem to induce an average manager to either increase the risk just below the HWM in order to push their incentive option into the money, or to decrease the risk right above the HWM to lock in the incentive pay as suggested, e.g., by the one-period model of Hodder and Jackwerth (2007). Significant alternations of fund risk seem to take place only when funds are substantially underperforming and their very existence is under question. This finding is consistent with the theoretical predictions in multi-period settings and reveals that managers are not myopic but seem to have longer, albeit finite, valuation horizons, instead. Hodder and Jackwerth (2007) explicitly consider the time dimension in their model, but predict a rather uniform risk increase at the liquidation boundary across all months 24

Chapter 1 Hedge Fund Risk Taking Figure 1.5: Managerial Risk Taking: Quarter-Wise (a) Quarter 1 (b) Quarter 2 (c) Quarter 3 (d) Quarter 4 The figure plots the result of the kernel regression specified in Section 1.4 for the different quarters of a year. On the horizontal axis is the fund value relative to the HWM. On the vertical axis is the managerial risk taking contained in the residuals from a panel regression of RISK (the natural logarithm of the intra-month standard deviations of daily hedge fund returns) on other factors explaining dynamic hedge fund risk. The shaded area around the regression line indicates the 1% confidence interval obtained from a bootstrap procedure. The 5% and 10% confidence bounds are given by the additional two lines. The regression uses a Gaussian kernel and a bandwidth of 0.07. The support is restricted to the closed interval on which each bandwidth window contains at least 5 observations. of a year. 18 Our empirical findings indicate, however, that the risk increase is pronounced only towards the end of a year. The risk does not increase during the first half year, to the contrary, it seems to decline for poorly performing funds. The results obtained using the piecewise linear specification confirm the documented pattern. We choose as a breakpoint V = 0.60. The estimated coefficients are reported in Table 1.7 and Figure 1.6 depicts the resulting regression lines, where we set insignificant regression coefficients to zero. The results replicate our main findings. No significant change in risk can be documented for the first quarter of a year for fund values below the HWM. During the second quarter, the incremental hedge fund risk decreases, if the fund value drops below the HWM, whereas in the same situation during the fourth quarter, fund risk increases. 18 See Figure 3 in Hodder and Jackwerth (2007). 25

Chapter 1 Hedge Fund Risk Taking Table 1.7: Piecewise Regressions of Residual Hedge Fund Risk Q1 Q2 Q3 Q4 ConstLow -0.02 (-0.58) +0.01 (+0.22) +0.04 (+1.05) -0.05 (-0.77) V alue t Low +0.13 (+1.27) +0.07 (+0.69) +0.00 (+0.02) +0.31 ** (+2.04) ConstMiddle +0.01 (+0.09) -0.45 *** (-3.68) +0.20 * (+1.72) +0.48 *** (+3.87) V alue t Middle -0.03 (-0.29) +0.49 *** (+3.71) -0.21 * (-1.67) -0.50 *** (-3.74) ConstHigh -0.52 (-1.46) +0.32 (+1.29) +0.32 (+1.23) -0.00 (-0.03) V alue t High +0.53 (+1.52) -0.31 (-1.31) -0.31 (-1.26) -0.01 (-0.08) The table reports estimation results for piecesise linear regressions of residual fund RISK as discussed in Section 1.4. The t-statistics from panel robust bootstrapped standard errors are given in parenthesis. ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively. Figure 1.6: Managerial Risk Taking: Piecewise Linear Specification The figure plots the regression results for managerial risk taking on the fund value relative to the HWM as specified in the piecewise panel regression in Equation 1.5 for four quarters of a year. The linear relation between fund value relative to the HWM and RISK (the natural logarithm of the intra-month standard deviations of daily hedge fund returns) is allowed to vary for fund values below 0.6, between 0.6 and 1, and above 1 without any continuity restriction. On the horizontal axis is the fund value relative to the HWM. On the vertical axis is the managerial incremental risk taking as a function of the fund value. Insignificant regression coefficients are set to zero. Overall, the documented seasonality in risk taking considered together with the existing theoretical models suggests that the perceived managerial valuation horizon can vary over a year. While at the beginning of a year managers might see themselves as operating long-term funds, by the end of the year, poorly performing funds might be treated more 26

Chapter 1 Hedge Fund Risk Taking like short term projects for the managers. We will address other possible determinants for the seasonality in Section 1.6 in more detail. 1.5.2 Managerial Risk-Taking: Month-Wise Refinement We show that managers significantly decrease fund risk during the second quarter and increase the risk during the fourth quarter when a fund is substantially below the HWM. Now, we take a closer look at the two quarters and re-estimate the corresponding kernel regressions for each month separately. Figure 1.7 reports the estimated regression lines together with 1%, 5%, and 10% confidence bounds. As we keep the requirement of a minimum of five observations per window, the support of the month-wise estimates shrinks compared to the quarter-wise results. Figure 1.7: Managerial Risk Taking: Month-Wise (a) April (b) May (c) June (d) October (e) November (f) December The figure plots the results of kernel regressions specified in Section 1.4 for each month in the second and the fourth quarter of a year. On the horizontal axis is the fund value relative to the HWM. On the vertical axis is the managerial risk taking contained in the residuals from a panel regression of RISK (the natural logarithm of the intramonth standard deviations of daily hedge fund returns) on other factors explaining dynamic hedge fund risk. The shaded area around the regression line indicates the 1% confidence interval obtained from a bootstrap procedure. The 5% and 10% confidence bounds are given by the additional two lines. The regression uses a Gaussian kernel and a bandwidth of 0.07. The support is restricted to the closed interval on which each bandwidth window contains at least 5 observations. Despite lower numbers of observations at the edges, the pattern of low risk taking in the second quarter and high risk taking in the forth quarter, conditional on the fund value being substantially below the HWM, remains pronounced. At the same time, the results suggest that the decision to alter the portfolio risk is taken at the beginning of a respective quarter. For the second quarter, we observe a managerial risk reduction in April which is significant at the 1% level. In May, the decrease is still pronounced being significant at 27

Chapter 1 Hedge Fund Risk Taking the 5% level. In June, we do not find managerial risk taking which is distinguishable from zero-mean noise around the expected level of risk. A similar pattern emerges in the fourth quarter. The increase in risk taking is highly significant in October and November, and it vanishes in December. These results suggest that fund managers act rather early in moving the fund risk up and down towards the desired levels. If they want to increase fund risk towards the end of a year in response to a low fund value, it does not seem to be sufficient to switch to a riskier investment strategy (or increase the leverage) only in December. The time may be too short for the realized returns to cover past losses. Instead, managers seem to take persistent risk levels into account. Given that risk is sticky, assigning more weight to riskier assets in October and November assures that the portfolio risk remains high in December as well. At the same time, early adjustments make sure that the alternations in fund risk do not strongly transmit to subsequent quarters, where the desired risk levels can be different. Technically speaking, a desired level of expected future fund risk is achieved by adding a desired shock to the autoregressive process in foresight. This finding stands in stark contrast to the assumption of the theoretical models that hedge fund managers alter fund risk swiftly. 1.5.3 Economic Significance of Managerial Risk Taking Having discussed the qualitative impact and statistical significance of managerial risk taking, we now briefly illustrate the economic significance of the documented risk shifts by a simplified example. Consider a hedge fund that reports its performance in USD. The average intra-month standard deviation of daily returns of such a fund is 0.74% and the standard deviation thereof is 0.42%. Other things being equal, a one standard deviation increase in the risk at time t will result in a 25% increase in the risk during the following month (e 0.50 ln((0.74+0.42)/0.74) = 1.25). The results reported in Table 1.7 suggest, that the maximum risk decline for an average fund happens in the second quarter at a fund value of 0.60 of the HWM. The corresponding coefficients α of -0.45 and γ of +0.49 suggest that the impact on risk is a 14% decline relative to its expected level (e 0.45+0.49 0.60 = 0.86). Similarly, the maximum risk increase achieved in the fourth quarter is 20% of the expected level of risk (e +0.48 0.50 0.50 = 1.20). Hence, although the changes in the riskiness of hedge funds induced by the managerial response to poor fund performance can be rather substantial (from 14% decrease to 20% increase), they are slightly smaller than a shift induced by one cross-sectional standard deviation in the past level of risk (25%). Still, investors should be aware of managerial risk taking as it is strongly pronounced even on average. This can imply extremely high risk taking for certain funds that can relatively easy alter their risk levels or have relatively strong incentives to do so. Also, as pointed out by Aragon and Nanda (2012), if a substantial fraction of hedge funds slides into a portion of the state space that induces high risk taking, this might be of systemic concern. 28

Chapter 1 Hedge Fund Risk Taking 1.6 Determinants of Changes in Hedge Fund Risk 1.6.1 Management Fees and Survival Probability The documented risk reduction by poorly performing hedge funds at the beginning of a year is, to the best of our knowledge, a novel empirical result. In this section, we take a closer look at the determinants of such reductions. As Lan, Wang, and Yang (2013) point out, poorly performing hedge fund managers with very long (infinite) investment horizons optimally reduce the fund risk in order to avoid liquidation. Fund liquidation is extremely costly for mangers as they loose an infinite stream of future management and incentive fees. Management fees, in particular, account for 75% of the total managerial surplus according to the model. The higher the management fee, the more a manager looses in case of fund liquidation. This suggests: Hypothesis C: Below the HWM, hedge funds with higher management fees are more disposed to reduce risk during the second quarter. Similarly, those funds that face a higher liquidation probability at the beginning of a year should have stronger incentives to reduce risk. By reducing the risk taking during earlier months of a year, poorly performing managers can improve the chances of survival of their funds as there exists a well documented positive relation between fund liquidation probability and fund risk (see, e.g. Liang and Park (2010) among others). We compare the attrition rates of hedge funds in our sample between the first and the last six months and find that indeed in an average year, only 38.1% of all defunct funds die during the first half of a year, while 61.9% die during the second half. The difference is statistically significant (p-value 4.31%). At the same time, we do not observe any significant intra-year variation for hedge fund inceptions and fund flows. Directly relating the managerial decision to alter fund risk to estimated liquidation probabilities in a regression framework might be inaccurate due to endogeneity. Actual fund survival depends on fund risk, which is, in turn, an optimal managerial response to the fund liquidation probability. We suggest to use three instruments that are related to the liquidation probability, but are not directly affected by the risk taking decisions of a manager: notice period prior to redemption, recent fund performance, and fund age. 19 The length of the notice period prior to redemption, recent fund performance, and age are negatively related to liquidation probability (see Liang and Park (2010) and Aragon and Nanda (2012) among others). Funds having longer notice periods, exhibiting positive returns over the previous quarter, and being of older age have lower liquidation probabilities and, thus, they should have weaker incentives to reduce risk taking. 19 Another potential instrument linked to liquidation probability is managerial personal investment (Aragon and Nanda (2012)). This information, however, is not available for our sample of hedge funds. 29

Chapter 1 Hedge Fund Risk Taking Hypothesis D: Below the HWM, hedge funds with a longer notice period prior to redemption, positive returns over the previous quarter, and older age are less disposed to reduce risk during the second quarter. In order to test Hypotheses C and D, we use the piecewise linear specification as in Equation 1.5. For each fund value range we introduce four indicator variables in turn (denoted by γ-s) and estimate Equation 1.6 given below. The indicator variables represent funds with (1) higher than median management fees (M gtf eelarge) to test Hypothesis C, (2) higher than median notice periods prior to redemption (N oticelarge), (3) positive cumulative returns over the preceding quarter (equivalent to increasing fund values relative to the HWM, V alue t > 0), and (4) larger than median age (AgeLarge) to test Hypothesis D. α low + γ low + δ low V alue i,t + η i,t if V alue i,t < 0.6 ê i,t = α mid + γ mid + δ mid V alue i,t + η i,t if 0.6 < V alue i,t < 1 α high + γ high + δ high V alue i,t + η i,t if V alue i,t > 1. (1.6) If, for instance, MgtF eelarge is used, a negative and significant γ mid in the second quarter would imply that hedge funds with higher management fees reduce risk more strongly during the second quarter if their value is below the HWM but above 60% of the HWM. The estimation results are reported in Tables 1.8 and 1.9. Consistent with Hypothesis C, hedge funds charging higher than median management fees show a stronger decline in the risk taking during the second quarter conditional on being below the HWM. The corresponding coefficient of 0.05 is significant at the 10% level. Hedge funds that are likely to face a lower liquidation probability because of a longer notice period prior to redemption, positive cumulative returns over the preceding quarter, and older age show a less pronounced risk decline during the second quarter of a year confirming Hypothesis D. The coefficients of +0.13, +0.06, and +0.07 in Table 1.9, respectively, are all highly significant. Remarkably, we do not detect any significant impact of these factors on risk shifting behavior at the end of a year. These findings contribute to a further discussion of Aragon and Nanda (2012), who document that changes in fund risk (between the first six months and the second six months of a year) are positively related to fund liquidation probabilities. Our results suggest that this relation may be driven not only by the excessive risk taking during the second half-year, but also by risk reduction during earlier months. And it is the earlier risk reduction that is more pronounced for funds with higher liquidation probability, and not the later risk increase. The empirical results also shed some light on the managerial risk-taking behavior when the fund value is above its HWM. The theoretical models by Hodder and Jackwerth (2007) and Buraschi, Kosowski, and Sritrakul (2012) suggest that at fund values above the HWM, managers choose lower risk levels than an investor with a CRRA utility function would desire. Hodder and Jackwerth (2007) argue that by doing so managers lock in the incentive 30

Chapter 1 Hedge Fund Risk Taking Table 1.8: Determinants of Residual Hedge Fund Risk: Management Fee Q1 Q2 Q3 Q4 ConstLow -0.03 (-0.37) +0.05 (+0.66) -0.05 (-0.71) -0.03 (-0.26) MgtF eelarge IV aluet Low +0.00 (+0.04) -0.04 (-0.64) +0.10 (+1.64) -0.02 (-0.26) V Low aluet +0.14 (+1.12) +0.04 (+0.35) +0.09 (+0.74) +0.28 (+1.58) ConstM iddle +0.02 (+0.15) -0.40 *** (-3.19) +0.21 * (+1.80) +0.47 *** (+3.72) MgtF eelarge IV aluet Middle -0.01 (-0.46) -0.05 * (-1.88) -0.02 (-0.72) +0.03 (+1.16) V aluet Middle -0.04 (-0.32) +0.46 *** (+3.40) -0.21 * (-1.72) -0.50 *** (-3.69) ConstHigh -0.48 (-1.36) +0.29 (+1.17) +0.36 (+1.38) +0.01 (+0.09) MgtF eelarge IV aluet High +0.03 (+1.55) -0.02 (-0.81) +0.03 (+0.97) +0.02 (+0.75) V aluet High +0.49 (+1.40) -0.28 (-1.15) -0.36 (-1.44) -0.03 (-0.23) The table reports estimation results for piecesise linear regressions of residual fund RISK as discussed in Section 1.6. M gtf eelarge indicates funds with higher than median management fee. The t-statistics from panel robust bootstrapped standard errors are given in parenthesis. ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively. 31

Chapter 1 Hedge Fund Risk Taking Table 1.9: Determinants of Residual Hedge Fund Risk: Notice Period, Performance, Age Q1 Q2 Q3 Q4 Panel A: Redemption Period Effect ConstLow +0.04 (+0.53) +0.05 (+0.64) +0.08 (+0.97) -0.13 (-1.36) RedemLarge IV aluet Low -0.04 (-0.69) -0.04 (-0.51) -0.02 (-0.32) +0.08 (+1.01) V aluet Low -0.05 (-0.36) -0.08 (-0.47) -0.12 (-0.73) +0.45 ** (+2.22) ConstMiddle -0.11 (-1.28) -0.49 *** (-4.57) +0.17 * (+1.66) +0.44 *** (+3.83) RedemLarge IV aluet Middle -0.01 (-0.54) +0.13 *** (+3.87) -0.03 (-1.02) -0.00 (-0.08) V aluet Middle +0.11 (+1.21) +0.53 *** (+4.57) -0.19 (-1.63) -0.47 *** (-3.76) ConstHigh -0.35 (-0.69) +0.13 (+0.43) +0.40 (+1.33) +0.12 (+0.68) RedemLarge IV aluet High -0.04 (-0.89) -0.03 (-0.61) -0.04 (-0.78) -0.03 (-0.92) V aluet High +0.38 (+0.75) -0.14 (-0.48) -0.38 (-1.33) -0.13 (-0.74) Panel B: Recent Performance Effect ConstLow +0.04 (+0.78) +0.05 (+1.07) +0.04 (+0.97) -0.01 (-0.12) V aluet > 0 IV aluet Low -0.08 * (-1.68) -0.09 * (-1.73) +0.04 (+0.82) -0.13 ** (-2.36) V aluet Low -0.02 (-0.18) +0.03 (+0.23) -0.10 (-0.93) +0.33 ** (+2.37) ConstMiddle -0.11 (-1.23) -0.45 *** (-4.17) +0.18 * (+1.67) +0.44 *** (+3.88) V aluet > 0 IV aluet Middle -0.02 (-0.93) +0.06 *** (+2.84) -0.03 (-1.53) -0.02 (-0.67) V aluet Middle +0.11 (+1.20) +0.47 *** (+4.06) -0.18 (-1.57) -0.46 *** (-3.70) ConstHigh -0.22 (-0.42) +0.13 (+0.43) +0.40 (+1.33) +0.12 (+0.66) V aluet > 0 IV aluet High +0.04 (+1.26) -0.02 (-0.33) -0.12 *** (-3.55) -0.05 (-1.59) V aluet High +0.23 (+0.45) -0.12 (-0.43) -0.29 (-1.00) -0.08 (-0.47) Panel C: Age Effect ConstLow -0.01 (-0.16) +0.04 (+0.40) +0.01 (+0.15) -0.09 (-0.87) AgeLarge IV aluet Low -0.01 (-0.17) -0.03 (-0.35) +0.03 (+0.36) +0.04 (+0.52) V aluet Low +0.13 (+1.13) +0.06 (+0.56) +0.02 (+0.16) +0.33 ** (+2.10) ConstMiddle +0.05 (+0.46) -0.49 *** (-3.99) +0.19 (+1.58) +0.44 *** (+3.40) AgeLarge IV aluet Middle -0.05 ** (-2.57) +0.07 *** (+2.88) +0.01 (+0.25) +0.04 (+1.41) V aluet Middle -0.05 (-0.41) +0.49 *** (+3.74) -0.20 (-1.58) -0.48 *** (-3.50) ConstHigh -0.56 (-1.54) +0.31 (+1.27) +0.33 (+1.28) -0.00 (-0.03) AgeLarge IV aluet High -0.03 (-1.58) -0.02 (-0.97) -0.04 (-1.39) +0.00 (+0.11) V aluet High +0.59 (+1.65) -0.29 (-1.23) -0.30 (-1.23) -0.01 (-0.09) The table reports estimation results for piecesise linear regressions of residual fund RISK as discussed in Section 1.6. In Panel A RedemLarge indicates funds with higher than median notice period prior to redemption. In Panel B V > 0 captures funds with positive cumulative return aluet over the preceeding quarter. In Panel C AgeLarge indicates funds older than the median fund at the beginnig of a quarter. The t-statistics from panel robust bootstrapped standard errors are given in parenthesis. ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively. 32

Chapter 1 Hedge Fund Risk Taking fees earned so far. 20 In all our previously discussed results, however, we did not detect any significant risk variations for fund values above the HWM. Panel B of Table 1.9 presents a notable exception. Those hedge funds, that end up above the HWM at the middle of a year and came from below the cumulative return over the preceding quarter was positive pushing the managerial inventive option in-the-money significantly reduce their risk during the third quarter. The highly significant coefficient of 0.12 supports the proposition of locking in fund performance. 1.6.2 High-Water Mark and Incentive Fees We now turn our attention to the impact of the HWM on the risk taking. As Panageas and Westerfield (2009) suggest, managers of funds with a HMW provision possess not a single incentive option, but a sequence of multiple future incentive options. They avoid excess risks taking throughout the year, to minimize the likelihood of losing their future compensation options. This result is consistent with the empirical findings of Aragon and Nanda (2012), that the existence of a HWM mitigates the documented relative risk increase from the first to the second half of a year by poorly performing funds. We test this proposition in our time-varying setting. Hypothesis E: Below the HWM, hedge funds with a high-water mark provision are less disposed to increase risk at the end of a year. We test this hypothesis using Equation 1.6, with γ-s taking a value of one for funds having a HWM provision (HaveHW M). The results are reported in Panel A of Table 1.10. The estimated coefficients remain virtually unchanged as compared to the main results in Table 1.7. This suggests that, overall, hedge funds that do have and funds that do not have a HWM provision adjust their risk taking in a similar way, depending on their performance and the time of a year. A HWM provision indeed somewhat offsets the risk increase during the second half of a year consistent with Hypothesis D and the prior findings. However, the effect is detected only during the third quarter with the corresponding loading of -0.04 being significant at the 10% level. The risk mitigating incentives provided by the HWM provisions are not sufficient to prevent managers from risk shifting towards the very end of a year. If managers enter the fourth quarter with a fund under water, they significantly increase fund risk regardless of the existence of a HWM provision in the fund. In Panel B of Table 1.10 we perform a similar analysis but using a dummy variable indicating the existence of a positive incentive fee (HaveIveF ee). In our main sample, about 30% of the hedge funds do not report a positive incentive fee. Some of these funds report a zero incentive fee, while others do not provide any information, i.e. may or may not charge an incentive fee. The estimation results are somewhat more noisy during the first quarter, but we still do not find any significant relation between charging incentive fees and increasing risk at the end of a year. 20 Personal discussions with hedge fund managers confirmed that this practice of going flat after a certain level of fund value is achieved is indeed used by some of their peers. 33

Chapter 1 Hedge Fund Risk Taking Table 1.10: Determinants of Residual Hedge Fund Risk: HWM, Incentive Fees Q1 Q2 Q3 Q4 Panel A: HWM Effect ConstLow -0.02 (-0.55) +0.01 (+0.25) +0.04 (+1.02) -0.04 (-0.76) HaveHW M IV aluet Low -0.03 (-0.63) +0.02 (+0.33) -0.05 (-0.81) -0.04 (-0.47) V aluet Low +0.18 (+1.42) +0.04 (+0.25) +0.06 (+0.48) +0.35 ** (+2.00) ConstM iddle +0.01 (+0.09) -0.44 *** (-3.57) +0.22 * (+1.92) +0.48 *** (+3.85) HaveHW M IV aluet Middle -0.00 (-0.01) -0.01 (-0.62) -0.04 * (-1.91) +0.01 (+0.52) V Middle aluet -0.03 (-0.29) +0.49 *** (+3.70) -0.21 * (-1.67) -0.51 *** (-3.76) ConstHigh -0.51 (-1.43) +0.30 (+1.19) +0.32 (+1.24) -0.03 (-0.20) HaveHW M IV aluet High -0.01 (-0.30) +0.02 (+0.65) -0.00 (-0.08) +0.03 (+1.41) V aluet High +0.53 (+1.51) -0.30 (-1.24) -0.31 (-1.27) -0.00 (-0.01) Panel B: Incentive Fee Effect ConstLow -0.03 (-0.61) +0.02 (+0.48) +0.04 (+1.05) -0.05 (-0.78) HaveIveF ee IV aluet Low -0.10 (-1.49) +0.19 ** (+2.55) -0.07 (-1.23) +0.05 (+0.59) V Low aluet +0.30 * (+1.95) -0.22 (-1.43) +0.10 (+0.75) +0.22 (+1.04) ConstM iddle -0.00 (-0.04) -0.43 *** (-3.41) +0.22 * (+1.86) +0.46 *** (+3.66) HaveIveF ee IV aluet Middle +0.02 (+0.70) -0.02 (-0.80) -0.02 (-0.73) +0.02 (+0.85) V Middle aluet -0.03 (-0.26) +0.48 *** (+3.65) -0.21 * (-1.72) -0.51 *** (-3.73) ConstHigh -0.55 (-1.55) +0.32 (+1.29) +0.31 (+1.19) -0.01 (-0.04) HaveIveF ee IV aluet High +0.06 *** (+3.11) -0.04 * (-1.68) -0.05 * (-1.74) +0.02 (+0.74) V aluet High +0.52 (+1.49) -0.28 (-1.19) -0.27 (-1.09) -0.02 (-0.14) The table reports estimation results for piecesise linear regressions of residual fund RISK as discussed in Section 1.6. In Panel A HaveHW M indicates funds that report having a high-water mark provision. In Panel B HaveIveF ee indicates funds that report non-zero incentive fees. The t-statistics from panel robust bootstrapped standard errors are given in parenthesis. ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively. 34

Chapter 1 Hedge Fund Risk Taking The findings above suggest that the increased risk taking at the end of a year may not be solely driven by the incentives provide by managerial option-like compensation contracts. To further investigate this issue, we exclude all funds that do not report a positive incentive fee from the sample and repeat the complete analysis starting from the estimation of the parameters of the linear part of the panel regression. The regression lines depicted in Figure 1.8 indicate that the exclusion of funds without a reported incentive fee does not affect our main findings. The general risk taking pattern remains, and only the positive relationship for very low fund values in the last quarter is no longer significant, resulting in a flat rather than upward sloping line in that area. In the underlying (untabulated) regression results the corresponding coefficient estimates have the same signs and orders of magnitude as in the main run. Only their significance vanishes, which can result from having fewer observations. Generally, all the coefficients are marginally larger, pointing towards stronger risk taking, but the differences are far from being statistically and economically significant. We then further reduce the sample to include only funds that do explicitly report a nonzero incentive fee as well as the use of a HWM. In the unreported results, we see only marginal changes to the risk taking, which, in this case, points to slightly milder risk shifts. The findings confirm a minor role of the incentive option tied to a HWM or not for seasonal changes in the managerial risk taking. There seem to be other incentives present that induce risk shifts towards the end of a year. As pointed out by Chevalier and Ellison (1997), the convexity in the managerial compensation can be induced by a flow-performance relationship even without an explicit incentive fee. At the same time, managers may face pure reporting incentives. The majority of hedge funds provides end-of-year reports to their clients. Reporting better figures may lead to an improvement of the managerial reputation, which in turn could, for example, make the launching of consecutive funds easier. The existence of reporting-induced behaviour was documented by Agarwal, Daniel, and Naik (2011), who show that hedge fund managers tend to inflate their reported December returns by borrowing from the previous months returns. 21 Ben-David, Franzoni, Landier, and Moussawi (2013) argue that hedge funds that manipulate prices of stocks that they hold just prior to the 13F reporting date. Our evidence is consistent with the end-of-year reporting inducing excessive risk taking several month before the report date. 1.6.3 Hedge Fund Style The overall portfolio risk can be changed by adjusting the leverage while keeping the core investment strategy unchanged, by changing the core investment strategy, e.g., by moving towards riskier assets, or by a combination of the two. For many funds, the first option may seem preferable as it does not require additional research on new core assets. 21 We find that in our sample of hedge funds the reported average returns in December are also significantly higher than during all other months. This again indicates that the funds in our sample exhibit general patterns common to the funds reporting on a monthly basis. Inflated returns reported in December do not influence our risk-related results. The return STD is computed every month and takes into consideration mean differences. The monthwise results in Figure 1.7 also indicate that there is no significant risk alteration in December. 35

Chapter 1 Hedge Fund Risk Taking Figure 1.8: Managerial Risk Taking: Piecewise Linear Specification Excluding Funds without Incentive Fee The figure plots the regression results for managerial risk taking on the fund value relative to the HWM as specified in the piecewise panel regression in Equation 1.5 for four quarters of a year. Here, funds that do not explicitly report a positive incentive fee are excluded from the sample. The relation between fund value relative to the HWM and RISK (the natural logarithm of the intra-month standard deviations of daily hedge fund returns) is allowed to vary for fund values below 0.6, between 0.6 and 1, and above 1 without any continuity restriction. On the horizontal axis is the fund value relative to the HWM. On the vertical axis is the managerial incremental risk taking as a function of the fund value. Insignificant regression coefficients are set to zero. However, not all funds are equally able to scale their core strategy through leverage. For example, it is likely to be more straightforward for funds with long only equity positions as compared to event driven funds that bet on special corporate events. We expect that risk increase towards year-end should be more pronounced for funds that can easily scale their strategy through leverage. As we do not observe the exact portfolio composition of hedge funds, we compute correlations between their reported returns and the market (proxied by the MSCI-World index). Funds exhibiting higher correlation with the market are likely to follow more conventional strategies which can be easier to scale. Hypothesis F: Below the HWM, hedge funds with a higher return correlation with the market are more disposed to increase risk at the end of a year. Again, we estimate Equation 1.6 using an indicator variable CorrHigh taking a value 36

Chapter 1 Hedge Fund Risk Taking of one if the fund s returns have higher than median correlation with the market returns. The results reported in Table 1.11 suggest that indeed such hedge funds exhibit a stronger risk increase during the last quarter of a year. The corresponding coefficient of +0.05 is significant at the 5% level. Interestingly, the risk shifting during third quarter is reduced by the same magnitude. The result may suggest that those funds that can easily level up their risk do not need to adjust it early. Instead, they can scale the risk up right when they need it at the end of a year. We now consider variations in the changes in risk with respect to fund style. In the Equation 1.6 we use dummy variables (γ-s) for each of the reported styles, respectively. As the data requirements are substantial (we need to make sure that in each quarter for each fund value band we have enough observations in each style) we are not able to single out all the reported styles. However, we are able to estimate the regression for the three largest styles: Directional Equity (EqDirec), Equity Market Neutral (EqM ktn eu), and Managed Futures (M anf ut). Whenever one of those styles is singled out, the average risk shifting pattern among all other funds constitutes the reference case. Directional Equity funds (Panel A of Table 1.12) behave differently than other funds in the area above the HWM. Profitable funds have higher risk taking during the first quarter (+0.10), but then reduce it in the second and the third quarters of a year (-0.09 and -0.11 respectively). All these changes are significant at the 1% level. There is no significant risk changes of well performing funds during the last quarter of a year. In terms of risk variation in case of poor performance, we do not detect any significant difference with respect to other funds. For Directional Equity funds below the HWM, the risk declines earlier in a year and then increases toward the end of a year at the same magnitude as for an average fund following other styles. Poorly performing Equity Market Neutral funds (Panel B of Table 1.12) are somewhat less disposed to increase risk during the fourth quarter of a year (with the loading of -0.07 significant at the 5% level). Despite being slightly milder, the overall risk increase in this region is still pronounced. Managed Futures funds (Panel C of Table 1.12) do not exhibit any significant difference relative to other funds in terms of risk shifting at the end of a year. However, they seem to have stronger risk reduction in the second quarter in case of poor performance. The corresponding loading of -0.08 is significant at the 1% level. Overall, the results from Table 1.12 indicate some statistically significant differences in the magnitude of risk-shifting across different hedge fund styles, but these differences cannot drive away the main seasonal pattern of risk taking. 1.7 Robustness Checks In this section, we perform multiple robustness checks with respect to methodology and sample filtering. The results are predominantly inline with the main conclusions, and we tabulate only relevant results. 37

Chapter 1 Hedge Fund Risk Taking Table 1.11: Determinants of Residual Hedge Fund Risk: Market Correlation Q1 Q2 Q3 Q4 ConstLow -0.01 (-0.08) +0.02 (+0.30) +0.08 (+1.50) +0.00 (+0.02) CorrHigh IV aluet Low -0.03 (-0.34) -0.01 (-0.22) -0.07 (-1.06) -0.08 (-0.97) V Low aluet +0.16 (+1.26) +0.09 (+0.71) +0.06 (+0.49) +0.35 ** (+2.24) ConstM iddle +0.05 (+0.44) -0.41 *** (-3.13) +0.27 ** (+2.29) +0.37 *** (+2.79) CorrHigh IV aluet Middle -0.02 (-1.12) -0.02 (-0.92) -0.05 *** (-2.62) +0.05 ** (+2.12) V aluet Middle -0.06 (-0.55) +0.46 *** (+3.32) -0.26 ** (-2.05) -0.42 *** (-2.95) ConstHigh -0.52 (-1.44) +0.32 (+1.31) +0.30 (+1.16) -0.00 (-0.01) CorrHigh IV aluet High +0.01 (+0.84) +0.02 (+0.99) -0.03 (-0.95) +0.02 (+0.82) V aluet High +0.53 (+1.48) -0.33 (-1.36) -0.29 (-1.15) -0.02 (-0.14) The table reports estimation results for piecesise linear regressions of residual fund RISK as discussed in Section 1.6. CorrHigh indicates funds which exhibit higher than median return correlation with the market (MSCI-World index). The t-statistics from panel robust bootstrapped standard errors are given in parenthesis. ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively. 38

Chapter 1 Hedge Fund Risk Taking Table 1.12: Determinants of Residual Hedge Fund Risk: Fund Style Q1 Q2 Q3 Q4 Panel A: Directional Equity ConstLow -0.03 (-0.68) +0.01 (+0.22) +0.05 (+1.11) -0.05 (-0.79) EqDirec IV aluet Low +0.07 (+1.16) +0.07 (+1.06) -0.05 (-0.81) +0.02 (+0.25) V aluet Low +0.10 (+0.96) +0.03 (+0.22) +0.03 (+0.28) +0.29 * (+1.90) ConstMiddle +0.01 (+0.09) -0.45 *** (-3.68) +0.16 (+1.41) +0.46 *** (+3.69) EqDirec IV aluet Middle -0.00 (-0.03) -0.01 (-0.42) +0.04 (+1.45) +0.03 (+0.88) V aluet Middle -0.03 (-0.29) +0.49 *** (+3.73) -0.18 (-1.41) -0.49 *** (-3.61) ConstHigh -0.56 (-1.59) +0.27 (+1.07) +0.27 (+1.03) -0.01 (-0.05) EqDirec IV aluet High +0.10 *** (+4.37) -0.09 *** (-2.76) -0.11 *** (-2.94) -0.01 (-0.35) V aluet High +0.56 (+1.60) -0.25 (-1.03) -0.25 (-1.01) -0.01 (-0.04) Panel B: Equity Market Neutral ConstLow -0.03 (-0.57) +0.01 (+0.19) +0.04 (+0.97) -0.04 (-0.75) EqMktNeu IV aluet Low -0.01 (-0.14) -0.23 * (-1.86) -0.17 (-1.43) +0.02 (+0.16) V aluet Low +0.14 (+1.23) +0.11 (+1.04) +0.04 (+0.38) +0.30 * (+1.87) ConstMiddle +0.00 (+0.02) -0.45 *** (-3.66) +0.20 * (+1.72) +0.48 *** (+3.90) EqMktNeu IV aluet Middle +0.02 (+0.80) -0.01 (-0.31) +0.02 (+0.95) -0.07 ** (-2.51) V aluet Middle -0.03 (-0.26) +0.49 *** (+3.71) -0.21 * (-1.73) -0.48 *** (-3.58) ConstHigh -0.52 (-1.45) +0.32 (+1.30) +0.31 (+1.21) +0.02 (+0.10) EqMktNeu IV aluet High +0.01 (+0.44) +0.01 (+0.42) +0.11 *** (+2.83) -0.07 ** (-2.12) V aluet High +0.53 (+1.51) -0.32 (-1.32) -0.32 (-1.31) -0.02 (-0.16) Panel C: Managed Futures ConstLow +0.06 (+0.79) +0.01 (+0.11) -0.03 (-0.35) -0.05 (-0.56) ManF ut IV aluet Low -0.08 (-1.36) +0.00 (+0.01) +0.07 (+1.15) +0.01 (+0.12) V aluet Low +0.02 (+0.13) +0.08 (+0.56) +0.08 (+0.60) +0.32 * (+1.71) ConstMiddle +0.01 (+0.09) -0.38 *** (-3.03) +0.19 (+1.61) +0.45 *** (+3.57) ManF ut IV aluet Middle +0.00 (+0.01) -0.08 *** (-2.80) +0.01 (+0.48) +0.04 (+1.27) V aluet Middle -0.03 (-0.29) +0.43 *** (+3.24) -0.20 (-1.58) -0.49 *** (-3.53) ConstHigh -0.49 (-1.34) +0.31 (+1.23) +0.32 (+1.23) +0.01 (+0.07) ManF ut IV aluet High +0.01 (+0.48) -0.00 (-0.14) +0.00 (+0.01) +0.03 (+0.95) V aluet High +0.50 (+1.40) -0.31 (-1.24) -0.31 (-1.26) -0.03 (-0.20) The table reports estimation results for piecesise linear regressions of residual fund RISK as discussed in Section 1.6. In Panel A EqDirec indicates Directional Equity funds, in Panel B EqMktNeu indicates Equity Market Neutral funds, in Panel C ManF ut indicates Managed Futures funds. The t-statistics from panel robust bootstrapped standard errors are given in parenthesis. ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively. 39

Chapter 1 Hedge Fund Risk Taking 1.7.1 Managerial Competition Our findings show that hedge fund risk clearly depends on the fund value relative to the HWM, which is determined by the past hedge fund performance. However, not only the absolute fund performance over a potentially extended period, but the performance relative to the industry peers might play an important role, too. As hedge funds compete for investors and investor flows chase past performance (Agarwal, Daniel, and Naik (2004)), fund managers may try to enhance the realized performance by taking excessive risks, if they underperform relative to their peers. Investigating changes in hedge fund risk from the first to the second half of a year, Aragon and Nanda (2012) indeed find that funds, which are poorly ranked relative to their peers, tend to engage in tournament behavior and increase the risk. Brown, Goetzmann, and Park (2001) also show that fund survival depends on the fund performance relative to other funds within the industry. The question arises, whether short term hedge fund underperformance relative to the competitors leads to an average increase in risk taking in our sample. And if it does, how such risk shifting relates to the risk shifting induced by the fund being below or above the HWM as analyzed earlier. To address these questions, we measure short-term fund performance relative to the peers as the cumulative return earned by fund i over month t (CR i,t ) in excess of the average cumulative industry return over the same month. We define, ExcessP erf i,t = CR i,t 1 N t N t i=1 CR i,t, (1.7) where N t is the total number of hedge funds in our sample in the corresponding month. We add the lagged value of this variable to Equation 1.3 and re-run the regression. The estimation results in Column (II) of Table 1.6 reveal that short-term underperformance relative to the competitors indeed leads to increased fund risk. The estimated loading of 0.27 is highly significant. 22 The long-term absolute fund performance will be still captured by the fund value relative to the HWM (V alue i,t ). We re-run the kernel regressions using the residuals from the panel regression given in Column (II) of Table 1.6. The resulting regression lines remain qualitatively unchanged as compared to our main results. Hence, while we observe some short-term tournament behavior, the nonlinear and time varying managerial response to absolute performance remains pronounced as we control for the short-term tournament. This finding complements Aragon and Nanda (2012). The authors document tournament behavior of hedge fund managers on the halfyear horizon. We show now that this phenomenon has both a short-term driver (recent underperformance relative to the industry), as well as a longer-term driver (absolute fund success captured by fund value relative to the HWM). 22 In unreported results, we find that other performance proxies (e.g. dummy variables for underperformance, or relative performance based on Sharpe and Sortino Ratios) are also significant with their explanatory power concentrated at the first lag. The latter observation points to a truly short-term effect. 40

Chapter 1 Hedge Fund Risk Taking 1.7.2 Piecewise Continuous Linear Specification for Managerial Risk Taking We re-estimate a piecewise linear specification of the model given in Equation 1.5, but this time we require that the resulting regression line is piecewise continuous. We impose continuity restrictions at the breakpoints, and obtain the following regression for each quarter of a year: ê i,t = α + δ low V alue i,t + δ mid (V alue i,t 0.6) + + δ high (V alue i,t 1) + + η i,t. (1.8) Figure 1.9 depicts the resulting regression lines, where we set insignificant regression coefficients to zero. The results support the main findings in Section 1.5 from the kernel regression and the unrestricted version of the piecewise linear specification. We see a risk decline for poorly performing funds during the second quarter and a risk increase during the fourth quarter of a year. Figure 1.9: Managerial Risk Taking: Piecewise Continuous Linear Specification The figure plots the regression results for managerial risk taking on the fund value relative to the HWM as specified in the piecewise-continious panel regression in Equation 1.8 for four quarters of a year. The relation between fund value relative to the HWM and RISK (the natural logarithm of the intra-month standard deviations of daily hedge fund returns) is allowed to vary for fund values below 0.6, between 0.6 and 1, and above 1. Continuity is required at the breakpoints. On the horizontal axis is the fund value relative to the HWM. On the vertical axis is the managerial incremental risk taking as a function of the fund value. Insignificant regression coefficients are set to zero. 41

Chapter 1 Hedge Fund Risk Taking 1.7.3 Excluding the Crisis Period The first signs of financial turmoil appeared in July 2007, a year before the collapse of Lehman Brothers. The TED spread (the spread between three-month LIBOR and threemonth T-bill rates) spiked up and one month later both the U.S. Federal Reserve and the European Central Bank injected some 90bn USD into financial markets. We exclude observations from July 2007 onwards from the sample and repeat the analysis. The results are generally consistent with the ones reported in Table 1.6, with the minor difference, that the third lag of the dependent variable is, albeit still positive, no longer significant. When we exclude the observations from the crisis period, a much lower fraction of fund-month observations lie in the low fund value region. During the complete sample period, about 7% of all sample observations are in the area of fund values between 0.4 and 0.8, whereas when the crisis period is excluded, this share drops to below 2%. The total number of remaining observations in this area is then clearly too low to obtain meaningful kernel regression results. Therefore, we use the piecewise linear specification for the value variable in the form of Equation 1.5, and find a significant risk decline for low fund values relative to the HWM at the beginning of a year, and a significant risk increase towards the end of a year in Figure 1.10. It shows that the risk decline is shifted forward and is now pronounced during the first quarter of a year and not during the second quarter, whereas risk increase is still strongly pronounced during the fourth quarter. 1.7.4 Kernel Regression with Different Bandwidths To make sure that our results are not influenced by a particular bandwidth choice, we re-estimate the kernel regressions for managerial risk taking using alternative bandwidths. First, we use a smaller bandwidth of 0.05 (compared to 0.07 used in the main specification), and then we use a larger bandwidth of 0.09. Naturally, the regression line is less (more) smooth with a smaller (larger) bandwidth, but the results do not qualitatively change from the ones reported in the body of the paper. 1.7.5 Alternative Specifications of the High-Water Mark In the main specification used in the paper, the HWM is set to 1 at hedge fund origination. It then increases to the highest net asset value achieved by the end of December each year. This type of HWM would correspond to investors that initially joined the fund. However, if investors purchase fund shares later on, they can have different HWMs. Therefore, we employ several other procedures to estimate the current value of the HWM, which attempt to capture the average HWM for money invested in the fund at different times. Similar to the main specification, we re-set the HWM every January to the highest value of the cumulative return achieved during the previous years. However, instead of considering the compete return history of a fund since inception, we use only the two or three preceding years. To make sure the intra-year variations found for managerial risk taking are not influenced by the end-of-year resetting of the HWM, we also consider resetting the HWM every month to the highest cumulative return earned since inception, as well as over the 42

Chapter 1 Hedge Fund Risk Taking Figure 1.10: Managerial Risk Taking: Piecewise Linear Specification Excluding the Crisis The figure plots the regression results for managerial risk taking on the fund value relative to the HWM as specified in the piecewise panel regression in Equation 1.5 for four quarters of a year. Here, The financial crisis is excluded from the sample period, which now spans October 1st, 2001 only to June 30th, 2007. The relation between fund value relative to the HWM and RISK (the natural logarithm of the intra-month standard deviations of daily hedge fund returns) is allowed to vary for fund values below 0.6, between 0.6 and 1, and above 1 without any continuity restriction. On the horizontal axis is the fund value relative to the HWM. On the vertical axis is the managerial incremental risk taking as a function of the fund value. Insignificant regression coefficients are set to zero. last two and three years. The results remain virtually unchanged compared to our main specification for fund values below the HWM. 23 1.7.6 Fund Outflows: An Alternative Explanation In Section 1.5, we show that large fund outflows over the previous month exceeding 5% of the assets (OutflowLarge i,t 1 ) lead to increased hedge fund risk. We attributed the finding to the forced liquidation of more liquid and less risky assets upon massive fund outflows, which leaves a riskier portfolio behind. Now, we test an alternative explanation of the observed relation, which suggests a more active role of the fund management. If an outflow is triggered by bad past performance, a hedge fund manager could deliberately increase the fund risk in an attempt to boost performance. We add as an additional term to Equation 1.3 the product of OutflowLarge i,t 1 23 When resetting the HWM at monthly frequency we lack observations with fund values above the HWM and we can consider only the results below the HWM. 43

Chapter 1 Hedge Fund Risk Taking and a dummy variable, which takes a value of one, whenever the cumulative return over the preceding month was below the industry mean (ExcessP erf i,t 2 < 0). A positive and significant loading on this interaction term would indicate that the increase in fund risk is (partly) explained by the managerial response to large outflows following poor performance. We do not find any significant loading on the interaction term in unreported estimates of various model specifications. For mutual funds, flows tend to be sticky, which gives some prediction power to fund managers (e.g. Warther (1995)). We also include the cumulative flows over several preceding months into the regression and do not find any significant results. In line with our explanation in the main section, the outflows driving the risk changes seem to come unexpected and they should be large in magnitude. 1.7.7 Alternative Risk Measures We consider two different measures for hedge funds risk. Instead of RISK (the natural logarithm of the intra-month standard deviation of daily hedge fund returns), first, we use the the natural logarithm of the intra-month left semi-standard deviation of daily returns, which takes only negative deviations from the mean into account. Second, we use the 10% Value-at-Risk (V ar 10% ) computed for each month. The results for the semi-standard deviation remain virtually unchanged as compared to the overall return standard deviation. The results for the linear part of the panel regression for V ar 10% also remain similar to our main results. V ar 10% is persistent, with all three lags of the variable being positively and highly significantly related to its current value. The kernel regression results (as well as the piecewise linear results) become much noisier. The reason is that we use a rather imprecise sample VaR estimate. The number of observations per month ranges from 15 to 22, and thus, V ar 10% corresponds to the second lowest return earned during a given month. Nevertheless, we still observe a significant risk increase in the last quarter of a year a the significant risk decline during the second quarter. 1.7.8 Hedge Fund Risk Relative to Market Risk Throughout the paper, we analyze the absolute level of hedge fund risk. We also show, that the cross-sectional average hedge fund risk is highly correlated with market risk. Time fixed effects in our panel regressions are supposed to control for all period specific effects including market risk. Now, we repeat the analysis using a relative specification of hedge fund risk with respect to market risk. Every month, we calculate the ratio of the intra-month standard deviation of fund returns over the intra-month standard deviation of the returns on the MSCI-world index, and then take the natural logarithm thereof ( RISKi,t M = ln ST D i,t ST D(Market) t ). (1.9) The unreported results remain virtually unchanged as compared to the main results in Table 1.6, which indicates that the time dummies fully capture the impact of changing 44

Chapter 1 Hedge Fund Risk Taking market risk over time. We also try to adjust for market movements and other risk factors by using an asset pricing model. We fit the Carhart (1997) 4-factor model to daily returns of each hedge fund, and then repeat our analysis using the residuals from this model instead of the returns themselves. 24 The results for risk taking remain largely unchanged, which is partly due to the poor explanatory power of the Carhart (1997) model (the median adjusted R-squared is about 5%). 1.7.9 Controlling For Possible Multiple Share Classes Hedge fund investment companies often control more than one hedge fund (Kolokolova (2011)). Such multiple funds can be either self-contained individual products or different share classes of the same fund. The sample used in the paper contains 195 unique investment companies. 85 of them control a single fund, 42 control two funds, and 68 control more than two funds. In order to identify potential multiple share classes of the same fund, for each pair of funds belonging to the same investment company we compute return correlations. The mean return correlation of such funds is 0.83, and it ranges from as low as -1 to as high as +1. We consider funds exhibiting pairwise return correlations higher than 98% and exclude one fund from each such pair with the shorter return history. In total, we exclude 207 hedge funds, and repeat the complete analysis based on the remaining sample. Results in Table 1.13 indicate no qualitative change to the main compulsion of the paper when the reduced sample is used. Table 1.13: Piecewise Regressions of Residual Hedge Fund Risk Excluding Potential Multiple Fund Share Classes Q1 Q2 Q3 Q4 ConstLow -0.02 (-0.51) +0.01 (+0.18) +0.04 (+1.08) -0.04 (-0.73) V alue t Low +0.10 (+0.95) +0.07 (+0.61) +0.02 (+0.23) +0.34 ** (+2.18) ConstMiddle -0.01 (-0.09) -0.34 ** (-2.35) +0.02 (+0.11) +0.55 *** (+3.32) V alue t Middle -0.01 (-0.04) +0.38 ** (+2.44) -0.00 (-0.02) -0.58 *** (-3.23) ConstHigh -0.71 (-1.62) +0.31 (+1.08) +0.14 (+0.53) -0.02 (-0.13) V alue t High +0.72 * (+1.68) -0.31 (-1.12) -0.15 (-0.59) +0.01 (+0.03) The table reports estimation results for piecesise linear regressions of residual fund RISK when 207 hedge funds exhibiting return correlations above 98% with other funds within the same investment company are excluded from the sample. The t-statistics from panel robust bootstrapped standard errors are given in parenthesis. ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively. 1.8 Conclusion We use a previously unattended dataset of daily hedge fund returns from Bloomberg, which allows us to construct time-series of monthly risk estimates for individual hedge funds and 24 Using more advanced option-based hedge fund factors (three portfolios of lookback straddle options) developed by Fung and Hsieh (2004) is feasible only for monthly data, as also pointed out by Patton and Ramadorai (2013). 45

Chapter 1 Hedge Fund Risk Taking recover the complete surface of managerial risk taking across fund values and time of a year. The recovered risk taking surface reveals that hedge fund managers dynamically adjust the fund risk. The risk taking is highly nonlinear and exhibits a strong seasonal pattern. At the beginning of a year, poorly performing hedge fund managers tend to reduce the risk taking. The risk reduction is particularly pronounced at fund values between 50% and 75% of the high-water mark. This result may suggest that earlier in the year managers perceive their valuation horizon as very long and behave in a more risk averse way as in the model by Lan, Wang, and Yang (2013). Early liquidation is more costly for managers charging high management fees, and consistent with this, we find that such managers exhibit an even stronger risk reduction. Managers that are threatened less by the risk of immediate liquidation because of longer notice periods prior to redemption, positive recent performance, and older age, on the contrary, exhibit a milder risk reduction. Towards the end of a year, managers considerably increase fund risk at low fund values relative to the high-water mark. This gamble for resurrection is in line with the existing models of risk taking by risk-averse hedge fund managers with finite valuation horizons. We find a bell-shaped relation between risk taking and fund value below the high-water mark, which is consistent with the existence of exogenous brokerage restrictions and investors redemptions as suggested by Buraschi, Kosowski, and Sritrakul (2012). Importantly, the gamble for resurrection is not purely driven by the existence of incentive fees and high-water mark provisions. In fact, it is also strongly pronounced for funds not charging incentive fees at all. It suggests that there are other incentives to report better performance at the end of a year. They may be linked to managerial reputation concerns as the majority of funds issues detailed end-of-year reports to their clients and perspective investors. Such risk shifting is pronounced for hedge funds in all investment styles, but it is even stronger for funds that follow strategies more closely linked to the equity market. The findings contribute to our understanding of the economics behind the previously documented negative association between changes in risk from the first to the second half of a year and fund performance (Aragon and Nanda (2012)). It seems to be driven not only by the excessive risk taking during later months of a year, but also by risk reductions earlier in a year. Our results also show that hedge fund risk is persistent and managers do take its persistence into account when adjusting their risk taking. For example, higher levels of fund risk at the end of a year are induced by upward risk adjustments in October and November, and not in December. The estimated maximum average risk shifts are economically significant and span from a 14% decrease to a 20% increase relative to the expected risk levels. They are, however, slightly smaller than a risk shift induced by one cross-sectional standard deviation in the past level of risk (25%). In the presence of significant managerial risk taking, standard hedge fund performance measures can be misleading and should be adjusted, as Buraschi, Kosowski, and Sritrakul (2012) point out. Investors and creditors should be aware of the dynamic managerial risk taking and assess the implications of this operational risk 46

Chapter 1 Hedge Fund Risk Taking factor for their portfolios, standard compensation practices, and credit risk assessments. Regulators might be interested in monitoring situations, in which a large fraction of hedge funds slides into the areas of the state space that induce high risk taking, as this can result in systemic concern. Our findings also contribute to an on-going discussion on obligatory reporting and disclosure by hedge funds. It seems that scheduled reporting dates (although seeking to achieve transparency) might induce (unwanted) changes in the investment behaviour of hedge fund managers. Our results throughout the paper are robust to various changes in the methodology and sample filtering. Whenever we obtain results in a form directly comparable to the earlier empirical findings for hedge fund risk based on widely used monthly hedge fund return data, they are are predominantly in line. Hence, although being technically restricted to our sample of more transparent and less volatile hedge funds reporting on a daily basis, we are confident, that our findings (at least qualitatively) transfer to the larger part of the hedge fund universe with monthly reporting. 47

Chapter 1 Hedge Fund Risk Taking 1.A Appendix 1.A.1 Cross-Sectional Analysis of Hedge Fund Risk This paper finds that hedge fund risk is rather persistent. Here, we investigate its crosssectional determinants. We also compare our results to earlier cross-sectional studies of hedge fund risk, and show, that hedge funds in our sample generally behave much like hedge funds that report returns on a monthly basis. We run cross-sectional regressions, in which the dependent variable measures the average level of risk for each hedge fund. It is calculated as the natural logarithm of the average intra-month standard deviation of daily hedge fund returns (ln ( ) ST D i ). The set of explanatory variables includes hedge fund characteristics potentially influencing the overall fund risk (X i ) and several control variables (Z i ). The regression equation is given as ln(st D i ) = α + X iβ + Z iγ + ɛ i. (1.10) The cross-sectional analysis is structured as follows: We first discuss potential determinants of hedge fund risk and introduce some control variables. Then, we present the estimation results and continue with some robustness checks similar to the ones conducted for the panel analysis earlier. 1.A.1.1 Managerial Incentives and Flexibility Managerial incentives and flexibility can affect the average level of risk-taking by hedge funds. The general consensus in the literature is that the existence of a HWM provision, the levels of incentive and management fees, as well as the length of lock-up and notice periods have a substantial impact on the managerial risk taking. The empirical as well as the theoretical evidence on the directions of the relationships between these factors and the level of risk is, however, mixed. Hedge fund managers (especially those with a short investment horizon) increase the risk of their investments, if their compensation contract is convex, that is, if there exists a HWM and managers receive an incentive fee, once the fund value is above the HWM by the end of a year (Hodder and Jackwerth (2007)). At the same time, as the investment horizon increases, the existence of a HWM can limit the risk taking, as in this case the manager possesses sequential options (Panageas and Westerfield (2009)). This observation is in line with the theoretical finding by Ross (2004), that a convex compensation contract does not necessarily lead to increased risk taking. Aragon and Nanda (2012) report supporting empirical evidence that managers of hedge funds with a HWM provision are less disposed to shift risk, when their fund is below water. To the contrary, Kouwenberg and Ziemba (2007) argue, that loss averse managers with higher incentive fees tend to increase the risk of their investments. They find supporting empirical evidence using the Zurich hedge fund universe for both hedge funds and funds of funds. The managerial option is more valuable, if hedge fund performance fees are high. The performance fees, however, are set by managers at their own discretion. Possibly, only well performing and highly skilled managers with a well established reputation are able to 48

Chapter 1 Hedge Fund Risk Taking set high performance fees. Cassar and Gerakos (2010) also show that manages of hedge funds with better internal controls charge higher fees. The riskiness of the investment strategies of reputable and well controlled managers might be different from that of an average manager. To analyze the impact of a convex compensation contract on the average level of fund risk, we consider two regression specifications using the information on the HWM and the incentive fee. First, we include as a proxy for managerial incentives the level of the incentive fee (IncF ee i ). Second, we use a dummy variable for an incentive fee being above the median (IncF eelarge i ) instead. In both specifications, we use a dummy variable indicating funds with a HWM. It allows us to disentangle the pure effect of the existence of a HWM from a high incentive fee. While the managerial compensation resulting from the existence of a performance fee is convex in fund profitability, the compensation generated by the management fee is linear in hedge fund size, as it pays a fixed percentage of the assets under management (AuM). Other things being equal, hedge fund managers would prefer to increase the size of their funds to boost their fee income. There is much evidence in the literature on the convexity of the relationship between fund performance and consecutive fund flows for mutual funds (see Chevalier and Ellison (1997)). Clients tend to invest after superior fund performance more actively, as compared to divestiture as a response to poor fund performance. The findings for hedge funds are mixed. Agarwal, Daniel, and Naik (2004) find a convex relationship, whereas Goetzmann, Ingersoll, and Ross (2003) document a concave flow-performance relationship. Ding, Getmansky, Liang, and Wermers (2009) reconcile this issue, and show that the flow-performance relationship is more complex, changing from convex to concave, if a hedge fund imposes share restrictions including longer lock-up and notice periods and has illiquid securities in the portfolio. The higher the management fee, the larger is the share of managerial compensation, which is generated by the part of the compensation contract, that is linear in fund size, and, thus, works just like the mutual fund type of contract. If hedge fund managers themselves perceive the flow-performance relationship as convex, increasing fund risk would be a beneficial strategy. The expected gains in case of investment success are larger than the expected losses in case of investment failure. The hedge funds in our sample are rather liquid, with relatively loose share restrictions. Most of the funds in our sample, for example, do not impose any lock-up period. In fact, only seven funds report a non-zero period. According to Ding, Getmansky, Liang, and Wermers (2009), one could indeed expect a convex flow-performance relationship for such funds. Thus, we expect hedge funds with high management fees to be characterized by a higher level of average fund risk. In order to empirically capture this relationship, we, first, include the level of the management fee as reported to the database (MmtF ee i ) in the regression. Second, we use a dummy variable taking a value of one, if the management fee is above the median level (MmtF eelarge i ). Third, we recognize that the management fee effect can be more pronounced for large funds. In addition to the management fee dummy, we include the product of the dummy variable indicating a management fee above the median and a 49

Chapter 1 Hedge Fund Risk Taking dummy indicating an average fund size above the industry median. 25 Lock-up and redemption periods imposed by hedge funds on their investors assure that hedge fund managers are more flexible in their investment strategies, as the investors cannot demand immediate redemption of their shares. Using monthly data, Agarwal, Daniel, and Naik (2009) find that funds with higher managerial flexibility tend to outperform their peers. More managerial flexibility also makes excessive risk taking easier. Thus, we expect funds with greater managerial flexibility to exhibit higher risk levels. We measure managerial flexibility by the length of the redemption period expressed in months as reported to the database. 26 Again, we include the level (Redem i ) and a dummy variable indicating a value above the industry median (RedemLarge i ) into the regression. 1.A.1.2 Other Determinants of Hedge Fund Risk and Control Variables The hedge funds in our sample report their returns in different currencies with 56% (44%) of all funds reporting in EUR (USD). The average fund return standard deviations are different between EUR and USD funds (see Table 1.1) and this difference is highly statistically significant. We pool the estimated return standard deviations of EUR and USD funds together, but include a dummy variable for funds reporting in EUR as a control (EUR i ). Eighteen hedge funds (2.52% of our sample) report their returns in EUR but are domiciled in the U.S. We include the product of the dummy variable for funds reporting in EUR, and another dummy variable indicating U.S. domicile, as an additional control (EUR US i ). As long as hedge fund managers do not switch between completely orthogonal strategies frequently and major alternations in the management teams are rare, the fund risk should be largely determined by the implemented strategy together with the unobserved managerial risk preferences. Hedge funds following different styles, therefore, are likely to exhibit different levels of risk. For example, the average return standard deviation for Emerging Market funds is likely to be higher than for Equity Market Neutral funds, as found by Chan, Getmansky, Haas, and Lo (2007, Table 6.4, p.255). To capture style variations in the average hedge fund risk, we include eight style dummies in the regression, one for each hedge fund style excluding the largest style (Directional Equity), which serves as the reference category. The hedge fund styles are self reported and style drifts might affect their information content. 27 We introduce two additional controls to better capture the nature of the hedge fund strategies. The first is the correlation coefficient between the hedge fund returns and the returns on the MSCI World Index over the entire life time of the hedge fund (MarketCorr i ). It proxies for the average exposure of a hedge fund to global equity markets. Given the distribution of funds over the different styles in our sample, the vast majority of all funds can be expected to exhibit a positive correlation with the global equity market, and we expect to find a positive coefficient for this control variable. Second, we 25 There are 61 hedge funds that do not report a management fee and we set the fee to zero here. The results do not change, if we exclude the funds from the analysis. 26 We do not consider lock-up periods because only 7 of our 714 funds report a non-zero period. 27 Gibson and Gyger (2007) provide a detailed discussion on hedge fund style classification. 50

Chapter 1 Hedge Fund Risk Taking include the standard deviation of the monthly estimates of RISK over a fund s life time (ST D(RISK i )). It captures the likelihood of style drifts and considerable risk shifting by the hedge fund managers. The cross-sectional correlation coefficient between the standard deviation of RISK and average RISK is -0.13 and significant at the 5% level. Funds that take higher risks on average, alter their risk levels less and stick more firmly to their risky strategies. Thus, we expect to find a negative coefficient on the standard deviation of risk. The life times of the hedge funds in our sample span different time periods. The riskiness of funds operating predominantly during the economic boom in 2005-2006 can substantially differ from the riskiness of funds operating during the sub-prime mortgage crisis of 2007 and the following financial crisis. To control for these differences, the natural logarithm of the average intra-month standard deviation of the daily returns on the MSCI World Index over the life time of a hedge fund (ln(st D(Market) i )) is included in the regression. Return serial correlation proxies for investment illiquidity and deliberate return smoothing by fund managers (Getmansky, Lo, and Makarov (2004)). Although return smoothing is less likely to be a problem for more transparent hedge funds reporting on a daily basis, if it does take place, the estimated return standard deviation will be biased downwards relative to its true value. At the same time, technically, if daily returns follow an AR(1) process, their total variance increases in the level of the autocorrelation keeping the variance of innovations constant. Hence, we include the first order return serial correlation for each fund (ReturnCorr i ) as an additional control. In order to control for possible differences in risk levels between live and defunct funds, we include a dummy variable (Dead i ), which takes a value of one for hedge funds that stop reporting their performance prior to the final date of the sample. Hedge fund managers often start their career operating small funds and being rather aggressive in terms of their investment strategy and associated risk taking. However, as funds grow older and larger, they tend to become more conservative. Their outstanding performance tends to deteriorate (e.g. Aggarwal and Jorion (2010)) and the riskiness of their investments can decline. This is largely due to two factors. First, there are diseconomies of scale (Goetzmann, Ingersoll, and Ross (2003)). The scope for truly alternative strategies and arbitrage opportunities is limited. As hedge funds grow larger, the profitable opportunities targeted by the management are getting exploited and exhausted. The new capital has to be allocated to more conventional and liquid investments, which are typically less risky. Second, managers of the established larger and older funds have more to lose in terms of reputation and fee income in the case of fund failure. Thus, the risk taking of larger and older funds is expected to be lower relative to younger and smaller funds. There is, however, contrasting evidence for funds of hedge funds by Li and Mehran (2009), who show that younger funds of funds exhibit less total and less systemic risk taking. Similar to the previously discussed factors, we, first, include the average AuM across the life of a hedge fund converted to millions USD (ln(aum i )) as a measure of size, and the age of a fund expressed in years at the last available return date (LifeT ime i ) in 51

Chapter 1 Hedge Fund Risk Taking the regression. Second, we use two indicator variables: a dummy for fund being larger than the median (ln(aum)large i ) and a dummy for fund being older that the median (LifeT imelarge i ). 1.A.1.3 Main Cross-Sectional Regression Results Table 1.14 reports the estimation results with bootstrapped standard errors for different specifications of Equation 1.10. Table 1.14: Cross-Sectional Regressions of Hedge Fund Risk (I) (II) Const -1.22 * (-1.72) -1.81 ** (-2.45) EUR -0.47 *** (-6.78) -0.46 *** (-6.68) EU R U S +0.17 (+0.80) +0.19 (+0.85) EqM ktn eutral -0.10 (-0.98) -0.12 (-1.16) EmergMkt -0.34 ** (-1.98) -0.35 ** (-2.03) EventDriven -0.38 *** (-2.68) -0.35 ** (-2.31) F ixedincome -0.88 *** (-6.93) -0.89 *** (-7.72) GlobalM acro -0.12 (-0.93) -0.06 (-0.49) MgdF utures +0.46 *** (+4.46) +0.45 *** (+4.31) MultiStrat -0.34 *** (-3.00) -0.31 *** (-2.79) NotDefined -0.67 *** (-2.78) -0.62 ** (-2.57) MarketCorr +0.60 *** (+5.73) +0.64 *** (+6.17) ST D(RISK) -0.45 *** (-3.41) -0.35 *** (-2.62) ln(st D(M arket)) +0.80 *** (+5.73) +0.72 *** (+4.81) ReturnCorr +0.01 (+0.04) -0.07 (-0.32) Dead -0.15 * (-1.90) -0.07 (-0.96) HW M -0.05 (-0.58) -0.01 (-0.15) IveF ee -0.00 (-0.76) IveF eelarge -0.48 *** (-3.86) MmtF ee +0.26 *** (+6.34) M mtf eelarge +0.30 *** (+4.49) Redem +0.08 ** (+1.99) RedemLarge +0.12 * (+1.73) ln(aum) -0.07 *** (-3.56) ln(aum)large -0.10 (-1.50) Lif et ime +0.01 (+1.05) Lif et imelarge +0.14 ** (+1.97) R-sqr. 0.45 0.44 Rbar-sqr. 0.43 0.41 Nobs 535 535 The table reports estimation results for cross-sectional regressions of the natural logarithm of the average intra-month standard deviation of daily hedge fund returns on a set of hedge fund characteristics and a set of controls. The regressions and the included variables are described in Section 1.A.1. The t-statistics from bootstrapped standard errors are given in parenthesis. ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively. 52

Chapter 1 Hedge Fund Risk Taking We find considerable variation in fund risk taking with respect to fund style. The Managed Futures funds are the riskiest in our sample with the corresponding loading of +0.46 being highly significant and the Fixed Income funds exhibit the lowest overall risk with a highly significant coefficient of -0.88. The summary statistics in Section 1.3 already revealed that EUR funds are less risky, which results in a negative and significant loading on the corresponding dummy, but a U.S. domicile for EUR funds does not have a significant impact. The two further factors included to control for hedge fund style are both highly statistically significant and show the expected signs. Funds having a higher return correlation with the market tent to be riskier, whereas funds with volatile risk levels take lower risk on average. A positive and significant coefficient on the mean market risk over the fund life corresponds to hedge fund risk moving in line with market risk, as documented in Figure 1.4. Our control variable for illiquidity and return smoothing concerns is not significantly different from zero, and the control for dead funds is significant at the 10% level only in one regression specification. With regard to the relationship between the existence of the HWM provision and the average risk taking, we cannot find any significant results. The indicator variable for the existence of the HWM is not significant in any of our specifications. There are several reasons that can explain the lack of significance. First, there is still no consensus in the theoretical literature on whether the existence of a HWM should induce higher or lower risk taking. Theoretically, it depends on the type of the utility function of the manager and, thus, there might not be any significant effect on average. Second, the relationship between the existence of a HWM and the level of risk is not static and it depends on other time-varying fund characteristics, such as the current position of the fund value relative to the HWM. In this case, on the aggregate level there can be no clear result. Also, the information content of the HMW provision can be covered by the level of the performance fee, also included in the regression. The level of the incentive fee does not seem to be a valuable determinant of the average level of risk due to its low cross-sectional variation. At the same time, the coefficient on the dummy variable indicating a fee above the median level is negative and highly significant. Hence, the result suggests that there is a negative relationship between the level of the incentive fee and hedge fund risk taking, however, it is driven only by funds charging a fee above the median of 20%. The empirical results strongly support a positive relationship between the level of the management fee and average fund risk taking. The loadings on both corresponding variables are positive and highly significant. Hedge funds charging higher management fee tend to take higher risks, which is consistent with managerial incentives to exploit the convex flow-performance relationship and increase the fund size. Managerial discretion as measured by the length of the notice period is positively related to fund risk. On the aggregate level, funds imposing longer notice periods do take higher risks. The corresponding loadings are +0.08 for the length of the notice period 53

Chapter 1 Hedge Fund Risk Taking prior to redemption and +0.12 for the long-redemption-period dummy, significant at the 5% and 10% levels, respectively. Fund size is negatively related to the risk taking. The loading on the natural logarithm of the average AuM converted to USD is -0.07 and significant at the 1% level and the loading on the corresponding large-fund dummy is -0.10 and it is no longer significant indicating that the relation is not only driven by some large funds. Including an interaction term between the high management fee dummy and the large fund size dummy does not reveal any significnt difference between the partial and the average effects and is dropped from the regression and the reported results. There is some evidence on a positive relation between fund life time and fund risk. The dummy variable for life times above the median is positive and significant at the 5% level. Overall, the cross-sectional analysis suggests that hedge fund risk taking does vary considerably across hedge fund strategies. Larger funds as well as funds charging above median incentive fees tend to be less risky, whereas funds with longer notice periods prior to the redemption can implement riskier investment strategies. The strongest effect by any means is documented for management fees. Higher management fees induce higher risk taking by hedge funds managers. The impact of a HWM is not strongly pronounced in cross-sectional regressions. 1.A.1.4 Cross-Sectional Regression Without Control Variables In Section 1.A.1, we included two control variables into the regression equation. The correlation between the returns of hedge fund i and the market returns (MarketCorr i ) served as a data driven proxy for investment style, and the standard deviation of RISK over the fund life time (ST D(RISK i )) controled for unstable risk taking potentially resulting from style drifts. Together with the included dummy variables for self reported styles, these two controls capture the part of the overall fund risk, related to fund investment strategy. In order to assess the stability of our results, we systematically drop these control variables from our regression. The corresponding estimation results in Table 1.15 show, that the key cross-sectional differences in the average levels of hedge fund risk remain highly significant. Hedge fund risk increases in the level of the management fee as well as the length of the notice period, and it decreases with fund size. We conclude that our main findings are robust to variations in the control variables capturing investment style. Considering the actual controls, we see that the return correlation with the market indeed partially captures style effects. The exclusion of this variable changes the estimated loadings on the style dummies. The most pronounced effect is documented for the Equity Market Neutral funds. In Table 1.14, the loadings on the style dummy are not significant. As Equity Market Neutral funds exhibit little correlation with the market, they were unaffected by the large positive loading on MarketCorr in Table 1.14, in contrast to other styles. Thus, other things being equal, Equity Market Neutral funds exhibit lower levels of fund risk than their peers having higher return correlation with the market. This 54

Chapter 1 Hedge Fund Risk Taking Table 1.15: Cross-Sectional Regressions of Hedge Fund Risk Excluding Controls (I) (II) (III) (IV) (V) (VI) Const -0.68 (-0.95) -1.01 (-1.36) -1.89 *** (-2.82) -2.17 *** (-2.89) -1.56 ** (-2.30) -1.45 * (-1.96) EUR -0.51 *** (-7.05) -0.52 *** (-7.08) -0.50 *** (-6.86) -0.49 *** (-6.83) -0.56 *** (-7.47) -0.56 *** (-7.26) EUR US +0.16 (+0.73) +0.20 (+0.95) +0.13 (+0.63) +0.15 (+0.69) +0.11 (+0.48) +0.14 (+0.68) EqMktNeutral -0.24 ** (-2.38) -0.26 ** (-2.58) -0.06 (-0.62) -0.08 (-0.81) -0.21 ** (-2.10) -0.22 ** (-2.09) EmergMkt -0.45 ** (-2.54) -0.47 *** (-2.62) -0.36 ** (-2.04) -0.37 ** (-2.14) -0.50 *** (-2.68) -0.51 *** (-2.70) EventDriven -0.28 * (-1.89) -0.26 * (-1.80) -0.42 *** (-2.98) -0.38 ** (-2.45) -0.33 ** (-2.24) -0.30 * (-1.92) F ixedincome -1.00 *** (-8.06) -1.01 *** (-8.81) -0.88 *** (-7.06) -0.89 *** (-7.43) -1.02 *** (-8.04) -1.02 *** (-8.04) GlobalMacro -0.15 (-1.22) -0.10 (-0.76) -0.11 (-0.85) -0.05 (-0.43) -0.15 (-1.12) -0.09 (-0.72) MgdF utures +0.33 *** (+3.07) +0.34 *** (+3.33) +0.51 *** (+4.72) +0.50 *** (+4.74) +0.38 *** (+3.63) +0.40 *** (+3.58) MultiStrat -0.47 *** (-4.28) -0.44 *** (-4.09) -0.34 *** (-2.97) -0.30 *** (-2.80) -0.49 *** (-4.40) -0.45 *** (-3.95) NotDefined -0.79 *** (-3.18) -0.70 *** (-2.73) -0.55 ** (-2.25) -0.52 ** (-2.14) -0.65 *** (-2.72) -0.57 ** (-2.30) MarketCorr +0.68 *** (+6.37) +0.69 *** (+6.50) ST D(RISK) -0.62 *** (-4.61) -0.51 *** (-3.86) ln(st D(Market)) +0.84 *** (+5.88) +0.81 *** (+5.36) +0.70 *** (+5.15) +0.67 *** (+4.42) +0.71 *** (+5.09) +0.76 *** (+5.05) ReturnCorr +0.16 (+0.66) +0.05 (+0.22) -0.03 (-0.12) -0.11 (-0.45) +0.13 (+0.54) +0.02 (+0.10) Dead -0.16 ** (-2.04) -0.08 (-1.02) -0.23 *** (-3.14) -0.14 ** (-1.98) -0.28 *** (-3.92) -0.19 ** (-2.58) HW M -0.03 (-0.37) +0.00 (+0.02) -0.01 (-0.08) +0.01 (+0.21) +0.03 (+0.38) +0.04 (+0.55) IveF ee -0.00 (-0.79) -0.00 (-0.90) -0.00 (-1.04) IveF eelarge -0.47 *** (-3.69) -0.50 *** (-4.03) -0.50 *** (-3.80) MmtF ee +0.26 *** (+5.97) +0.25 *** (+5.78) +0.25 *** (+5.71) MmtF eelarge +0.30 *** (+4.31) +0.29 *** (+4.22) +0.29 *** (+4.20) Redem +0.08 ** (+2.22) +0.07 * (+1.82) +0.07 * (+1.90) RedemLarge +0.15 ** (+2.15) +0.13 * (+1.83) +0.17 ** (+2.37) ln(aum) -0.07 *** (-3.37) -0.07 *** (-3.31) -0.07 *** (-3.12) ln(aum)large -0.05 (-0.73) -0.10 (-1.43) -0.04 (-0.59) LifeT ime +0.00 (+0.16) +0.01 (+0.86) -0.00 (-0.25) LifeT imelarge +0.05 (+0.74) +0.11 (+1.52) -0.00 (-0.05) R-sqr. 0.42 0.40 0.44 0.43 0.39 0.39 Rbar-sqr. 0.39 0.38 0.42 0.41 0.37 0.36 Nobs 535 535 535 535 535 535 The table reports estimation results for cross-sectional regressions of the natural logarithm of the average intra-month standard deviation of daily hedge fund returns on a set of hedge fund characteristics and a set of controls. The regressions and the included variables are described in Section 1.A.1.4. Compared to the base line cross-sectional regression, two control variables that capture hedge fund style and style drift are systematically dropped from the regression. The t-statistics from bootstrapped standard errors are given in parenthesis. ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively. 55

Chapter 1 Hedge Fund Risk Taking effect translates into a negative and significant loading on the Equity Market Neutral style dummy in Table 1.15, when M arketcorr is excluded. The loading is significant at the 5% level and its estimated value varies from -0.21 to -0.26 depending on the regression specification. Comparing the loadings with and without ST D(RISK) (Table 1.14 vs. Columns (III) and (IV) in Table 1.15), we do not find evidence of any significant changes. Although the coefficient on the ST D(RISK) is highly significant in Table 1.14, the R 2 drops only slightly when this variable is dropped from the regression. 1.A.1.5 Cross-Sectional Regression With a Relative Measure of Risk In this subsection, we define hedge fund risk not in absolute terms, but relative to market risk. We now measure risk as the natural logarithm of the average ratio of the funds intra-month return standard deviation over the intra-month standard deviation of returns on the MSCI-world index over the same month ( ) ST D i,t RISKM i = ln. (1.11) ST D(Market) t The key difference with respect ) to the results reported in Table 1.14 is that the market risk variable ln (ST D (Market) i is no longer significant in this regression. It is not surprising, as market risk is taken out from the dependent variable straight away. The remaining results remain stable. 1.A.1.6 Cross-Sectional Regression Excluding Funds without Incentive Fee We repeated the cross-sectional analysis excluding 30% of hedge funds that do not report incentive fee. The results remain very similar to the ones for the compete sample reported in Table 1.14. The largest change is in the loading on the dummy variable IveF eelarge, which increases in absolute value from -0.48 to -0.55, and remains highly significant. 1.A.1.7 Cross-Sectional Regression Excluding the Crisis Period In this subsection, the cross-sectional analysis is repeated on a pre-crisis subsample, excluding data after July 2007. The results reported in Table 1.16 are consistent with the ones from Table 1.14 and seem to be even more pronounced. Most of the significant coefficients increase in absolute values. The main difference is that the interaction dummy variable for funds reporting their performance in EUR while being domiciled in the U.S. gains statistical significance and is positively related to hedge fund risk. Fund size is now significant only at the 10% level. To summarize the results, besides the hedge fund style, also the management and incentive fees, the fund size, and the length of the notice period prior to redemption are important drivers of the cross-sectional variation in the average levels of hedge fund risk. Funds with higher than the median incentive fee take lower risk, whereas smaller funds, funds having longer notice periods, and funds with higher management fees tend to be riskier. The level of the management fee has by far the strongest effect on fund risk. It is linked to the incentives of hedge fund managers to increase the fund size by exploiting 56

Chapter 1 Hedge Fund Risk Taking Table 1.16: Cross-Sectional Regressions of Hedge Fund Risk Excluding the Crisis (I) (II) Const -6.94 *** (-2.81) -4.22 ** (-2.16) EUR -0.81 *** (-6.24) -0.68 *** (-5.39) EUR US +0.81 ** (+2.25) +0.65 * (+1.89) EqM ktn eutral -0.12 (-0.50) -0.28 (-1.15) EmergM kt -0.45 (-1.45) -0.49 (-1.62) EventDriven -0.94 *** (-2.61) -0.81 ** (-2.27) F ixedincome -0.62 *** (-2.70) -0.63 *** (-2.96) GlobalM acro +0.03 (+0.12) +0.09 (+0.34) MgdF utures +0.55 *** (+2.66) +0.60 *** (+2.97) M ultistrat -0.27 (-1.08) -0.27 (-1.02) N otdef ined -0.28 (-0.81) -0.38 (-1.18) M arketcorr +0.33 (+1.37) +0.31 (+1.25) ST D(RISK) -0.82 *** (-3.03) -0.67 *** (-2.68) ln(st D(M arket)) -0.33 (-0.72) +0.21 (+0.57) ReturnCorr +0.50 (+1.11) +0.34 (+0.81) Dead -0.17 (-1.14) -0.25 * (-1.91) HW M +0.22 (+1.42) +0.07 (+0.54) IveF ee -0.01 * (-1.82) IveF eelarge -0.59 ** (-2.57) MmtF ee +0.33 *** (+4.42) M mtf eelarge +0.58 *** (+5.22) Redem +0.07 (+1.41) RedemLarge +0.23 * (+1.93) ln(aum) -0.06 * (-1.91) ln(aum)large -0.18 (-1.33) Lif et ime +0.04 (+1.64) Lif et imelarge +0.11 (+0.74) R-sqr. 0.52 0.54 Rbar-sqr. 0.47 0.49 Nobs 201 201 The table reports estimation results for cross-sectional regressions of the natural logarithm of the average intra-month standard deviation of daily hedge fund returns on a set of hedge fund characteristics and a set of controls. The regressions and the included variables are described in Section 1.A.1.7. Compared to the base line crosssectional regression, the financial crisis (starting from June 30th, 2007 onwards) is excluded from the sample period.the t-statistics from bootstrapped standard errors are given in parenthesis. ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively. the convex flow-performance relationship. Investors should therefore be aware that a high management fee does not only, ceteris paribus, decrease their post-fee return, and must be offset by the performance of the manager, but can also induce increased risk taking. 57

Chapter 1 Hedge Fund Risk Taking 1.A.2 Linear Specification for the Fund Value Relative to the High- Water Mark Our main analysis differs from earlier empirical research with respect to data and methodology. The sample of hedge funds used in the paper consists of rather liquid funds that report their returns on a daily basis and have generally slightly lower and less volatile returns than funds that report on a monthly basis (see Section 1.3). In terms of methodology, we employ a semi-parametric approach that enables us to reveal a nonlinear and time-varying relation of fund value relative to the HWM to fund risk. In this section, we use a linear specification of this relation instead. It allows us to directly compare our findings to earlier papers and analyze the drivers of differential results. We modify Equation 1.3 to include a linear specification for the relationship between fund value and the managerial risk taking to the following form 3 RISK i,t = α i + α t + β j RISK i,t j + γdeltacorr i,t + ζln(aum i,t ) j=1 + θoutflowlarge i,t 1 + κv alue i,t + ε i,t. (1.12) The estimation results reported in Column (I) of Table 1.17 show that on average, across all fund values and time, we find a negative relationship between fund profitability and risk taking. This finding is consistent with recent research that uses a linear statistical identification (e.g., Aragon and Nanda (2012)). The loading on V alue i,t of -0.19 is significant at the 1% level. The other estimated parameters remain largely unchanged as compared to our main results in Table 1.6. In Section 1.7.3 of the main paper, we exclude the crisis period from the sample, and saw that the number of observations associated with low fund values drops more than proportionally. When we run the linear regression 1.12 for the non-crisis period only, the coefficient estimate for the value variable, albeit still negative, becomes insignificant, while the truly nonlinear managerial risk taking is still present (Figure 1.10). Besides hiding the truly nonlinear nature of the managerial risk taking, a linear specification can, hence, fail to identify managerial risk taking altogether, which could explain the insignificant results in some earlier papers (e.g. Brown, Goetzmann, and Park (2001) or Agarwal, Daniel, and Naik (2002)). This problem seems to be more pronounced for samples that lack a significant fraction of poorly performing funds, i.e. sample periods that are characterized by bullish markets. We then include the relative fund performance with respect to the peers as measured in Equation 1.7 into the regression. Similar to our findings in Section 1.7.1, both, the fund relative to the HWM as well as the short term performance relative to the industry are negatively related to fund risk. The coefficients of -0.17 and -0.19 are significant at the 1% and 10% levels respectively (Column (II), Table 1.17). 58

Chapter 1 Hedge Fund Risk Taking Table 1.17: Panel Regression of Hedge Fund Risk with a Linear Specification for Fund Value (I) (II) RISK t 1 +0.50 *** (+50.54) +0.50 *** (+51.85) RISK t 2 +0.09 *** (+8.88) +0.09 *** (+9.14) RISK t 3 +0.07 *** (+6.99) +0.07 *** (+7.27) DeltaCorr t +0.03 ** (+2.11) +0.03 ** (+2.24) ln(aum t ) 0.00 (-0.97) 0.00 (-1.01) OutflowLarge t 1 +0.02 ** (+2.18) +0.02 ** (+2.13) V alue t -0.19 *** (-3.96) -0.17 *** (-3.36) ExcessP erf t 1-0.19 * (-1.92) R-sqr. 0.90 0.90 Rbar-sqr. 0.89 0.89 Nobs 10 141 10 141 The table reports estimation results for panel regressions of RISK (the natural logarithm of the intra-month standard deviations of daily hedge fund returns) on a set of dynamic explanatory variables and controls. The regression includes fund and time fixed effects. The regressions and the included variables are described in Section 1.A.2. Compared to the main panel regression in Equation 1.12, the fund value variable is added to the regression as a linear specification of managerial risk taking. The t- statistics from panel robust bootstrapped standard errors are given in parenthesis. ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively. 1.A.2.1 Hedge Fund Fixed Characteristics and Their Impact on Risk Shifting The cross-sectional results suggest that the average level of risk depends on a fund s fixed characteristics, such as fees, size, and redemption period. We now test, if the risk shifting pattern at low fund values is influenced by these characteristics. To capture the effects of the factors, we re-estimate the panel regression specified in Equation 1.12 and include interaction terms between the fund value variable and (1) a dummy for the use of a HWM; (2) a dummy for the incentive fee being above the median; (3) a dummy for the management fee being above the median; and (4) a dummy for the redemption period being above the median. The results are reported in Table 1.18. Consistent with Aragon and Nanda (2012), the existence of the HWM does mitigate the risk shifting incentives of hedge fund managers (Column (I) of Table 1.18). The corresponding loading on the interaction term is positive (+0.15) and significant at the 10% level. Similarly, high management fees mitigate the impact of fund value with the associated loading of +0.17 being significant at the 5% level. High incentives fees and long redemption periods, to the contrary, amplify the effect of the fund value, with estimated coefficients of -0.48 and -0.20, which are significant at the 10% and 5% levels, respectively. Overall, the results are consistent with earlier empirical research. It shows that the funds in our sample behave very similar with respect to risk taking to funds that report on a monthly basis to more widely used databases. At the same time, using the linear specification does not allow to capture trully nonlinear risk taking and seassonality in the 59

Chapter 1 Hedge Fund Risk Taking Table 1.18: Panel Regressions of Hedge Fund Risk with a Linear Specification for Fund Value and Interaction Terms (I) (II) (III) (IV) RISKt 1 +0.50 *** (+50.62) +0.50 *** (+49.01) +0.50 *** (+47.81) +0.50 *** (+49.86) RISKt 2 +0.09 *** (+8.87) +0.09 *** (+8.67) +0.09 *** (+8.90) +0.09 *** (+9.22) RISKt 3 +0.07 *** (+7.07) +0.07 *** (+7.08) +0.07 *** (+7.30) +0.07 *** (+7.12) DeltaCorrt +0.03 ** (+2.02) +0.03 ** (+2.16) +0.03 ** (+2.15) +0.03 ** (+2.11) ln(aumt ) 0.00 (-0.94) 0.00 (-0.98) 0.00 (-0.91) 0.00 (-1.10) OutflowLarget 1 +0.02 ** (+2.27) +0.02 ** (+2.13) +0.02 ** (+2.10) +0.02 ** (+2.28) V aluet -0.28 *** (-4.08) -0.18 *** (-3.86) -0.27 *** (-4.21) -0.12 ** (-2.16) V aluet HW M +0.15 * (+1.73) V aluet IveF eelarge -0.48 ** (-1.99) V aluet MmtF eelarge +0.17 ** (+2.00) V aluet RedemLarge -0.20 ** (-2.23) R-sqr. 0.90 0.90 0.90 0.90 Rbar-sqr. 0.89 0.89 0.89 0.89 Nobs 10 141 10 141 10 141 10 141 The table reports estimation results for panel regressions of RISK (the natural logarithm of the intra-month standard deviations of daily hedge fund returns) on a set of dynamic explanatory variables and controls. The regressions include fund and time fixed effects. The regressions and the included variables are described in Section 1.A.2.1. Compared to the panel regression in Equation 1.12, additional interaction terms between the fund value variable and several fund characteristics are included. The t-statistics from panel robust bootstrapped standard errors are given in parenthesis. ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively. 60

Chapter 1 Hedge Fund Risk Taking impact of various fixed hedge fund characteristics. It seems that the interpretaion of the economic mechanism of risk shifting might be missleading if the true seasonlity is not taken into account. 61

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Chapter 2 Hedge Fund Herding On Correlated Trading in the Large Equity Positions of U.S. Hedge Fund Firms 65

Chapter 2 Hedge Fund Herding 2.1 Introduction Understanding the formation of security prices is one of the central challenges in financial economics. The security prices are the result of the trading of the market participants. That is why an extensive literature exists on the trading of institutional investors, who are the most important players on financial markets in terms of trading volume. Over the last decades a new class of institutional investors has tremendously grown and is generally estimated to account for about one quarter of all trading at NYSE nowadays: hedge funds. 1 But because of the low regulatory requirements and the generally high discretion in this industry, little is known about the trading activity of hedge fund firms. The majority of hedge fund firms is domiciled in the U.S. where the regulatory authority (SEC) only requires large hedge fund firms to report their long positions in stocks and some other securities under certain conditions on a quarterly basis (13F filings). The quarterly filings are the only public data on the compositions of the hedge fund firms portfolios available. Many hedge funds voluntarily report to well known commercial databases on a monthly horizon. Here, they publish their monthly returns and assets under management mainly for advertising reasons, and they do not report any information on their portfolio positions. As opposed to the voluntarily reported return data, the mandatory filings of the portfolio holdings have gained rather little attention by the literature. All existing papers, which use the filings data, focus on the portfolio choices of individual hedge fund firms. Griffin and Xu (2009) and Agarwal et al. (2009), for example, use the security positions to analyze the ability of hedge fund managers to invest profitably. It is an open question, whether the trades of one hedge fund firm are independent of the trades of the other hedge fund firms, or whether their trading is somehow correlated. If the trading of distinct hedge fund firms is not independent, this raises several questions with potentially wide ranging implications, given the significant size of their trades. For example, if trade correlations results from the joint use of feedback trading strategies 2, like a momentum trading rule 3, the question arises, whether the feedback trading is stabilizing or destabilizing security prices. If irrational joint buying and selling of the same securities pushes prices above or below their fundamental values, their joint trading introduces excess volatility, which calls for considering stronger regulation. In Chapter 1 we discussed several earlier findings on return manipulation by hedge funds to inflate reported returns. The associated trading activity is clearly not related to fundamentals and could result in such joint irrational trading. On the other hand, if hedge fund firms herd into undervalued and out of overvalued securities, they speed up the incorporation of information 1 For example, Black (2004) states that Hedge funds have emerged from the shadows of Wall Street to become one of today s fastest-growing investment classes, accounting for 25 percent of trading volume on the NYSE. In his survey article on the hedge fund industry, Stulz (2007) notes that Several hedge funds are known to account individually for several percent of the trading volume of the New York Stock Exchange. 2 Feedback trading refers to trading rules where the decision to buy or sell securities is a function of the securities past returns. The joint use of a common feedback trading rule results in correlated trading, i.e. herding. 3 Wermers (1999) provides a detailed discussion of feedback trading rules in general and momentum trading rules (positive-feedback trading) in particular. 66

Chapter 2 Hedge Fund Herding into security prices and contribute to market efficiency. 4 Also, correlated trading would raise questions for investors, such as potential implications for portfolio diversification. Furthermore, a detailed analysis such trade correlations adds to our understanding of the trading by hedge fund firms. In this chapter, we address the question whether the within-quarter trading of hedge fund firms is random and independent across individual securities. If the firms tend to buy and sell the same securities jointly, this means that their trading is not independent - they herd. Using this definition of herding among money managers and the corresponding identification methodology introduced by Lakonishok, Shleifer, and Vishny (1992) (LSV measure), we analyze the quarterly holdings from 13F filings of a sample of 748 hedge fund firms over the period 1995-2009. Our aim is to identify whether herding is present, identify potential reasons why the trading is correlated, and assess potential implications for the formation of security prices. As discussed in detail later, several theoretical explanations for correlated trading among money managers were proposed in the literature. 5 The empirical studies on herding among institutional investors started with a seminal paper by Lakonishok, Shleifer, and Vishny (1992) who found that pension fund managers show a tendency to herd. Thereafter, an empirical literature on herding behavior emerged that covers mutual funds, all institutional investors (including banks etc.), and individual investors. The interdependencies of the trades of hedge fund managers have not been analyzed, yet. On the one hand, intuition suggests several reasons why significant herding effects are unlikely to be present in our sample. First, hedge fund firms face virtually no restrictions concerning the types of securities they can trade and they can take short positions, too. That is why the trades from their long positions in 13F securities, which we observe, are only a fraction of all their trades. Second, hedge funds trade on a rather high frequency, while our observations are only on a quarterly horizon. Third, hedge fund managers argue that higher disclosure standards would enable others to steal their valuable investment ideas. Also, hedge funds justify demanding fees from their investors that are substantially above the fees of their mutual fund peers by asserting to have superior investment skill, which enables them to find and exploit market inefficiencies. This could suggest that individual hedge fund firms have unique investment ideas, which they do not share with their peers. Finally, hedge funds are known to follow distinct investment strategies (hedge fund styles ). On the other hand, hedge fund firms which follow similar strategies could be expected to identify and trade on the same opportunities. Gray (2009) shows that hedge fund managers who do have stock picking skill share some of their profitable ideas with their peers. Overall, the theoretical explanations brought forward in the literature for herding among institutional investors should apply to hedge fund firms, to some extent, alike. Our results show that the firms in our sample herd into and out of stocks together. The level of herding over the full sample period is of comparable order of magnitude to the levels 4 Discussions on how herding relates to equilibrium prices are provided in, e.g., Lakonishok, Shleifer, and Vishny (1992) and in Nofsinger and Sias (1999). 5 Both strands of the literature, theoretical and empirical, will be discussed in Section 2.2. 67

Chapter 2 Hedge Fund Herding of herding found for mutual funds by earlier research (e.g. Grinblatt, Titman, and Wermers (1995), Wermers (1999)), but varies significantly across firms following distinct investment strategies. To gain more insights in the potentially underlying forces, which drive hedge fund firms to trade together, we condition the herding measurement on different kinds of stocks and on hedge fund firms following different investment styles. The results are most consistent with hedge fund firms either trading on the same investment signals without observing the trades of their peers (Froot, Scharfstein, and Stein (1992)), or observing and following the trades of each other (Bikhchandani, Hirshleifer, and Welch (1992)), or both. While the quarterly frequency of the data still allows to identify herding behavior among the firms which is statistically and economically significant, it does not allow for a clear attribution to the two potential reasons, when analyzing the herding at the stock level. On the other hand, we can rule out window dressing 6 and aggregate flows of client money into and out of the hedge fund industry as potential explanations. In contrast to the earlier findings for for mutual funds and all institutional investors together, joint feedback trading strategies do not serve as a major explanation for the observed herding either (e.g. Wermers (1999), Sias (2004)). Our results suggests that herds form on rather profitable opportunities and do not destabilize stock prices. After analyzing the herding in the hedge fund industry at the stock level, we introduce a new measure that captures the tendency of a firm to trade with the herd, which is our second contribution to the literature. Panel regressions on time varying factors that might explain the herding reveal that the firms in our sample seem to follow the equity trades by peers that outperformed just prior to the trading period. Again, the observed herding can at least partially be attributed to hedge fund firms following each others trades. The finding is consistent with the evidence of shared investment ideas reported by Gray (2009). In contrast, herding is not related to individual money flows. Finally, we consider the relation between the general tendency of firms to herd and firm characteristics. We find that overall firm risk and the number of stocks in the equity portfolio are negatively related to herding, which is consistent with herding from followed trades and correlated private information. The structure of the remainder of this chapter is as follows. In Section 2.2 we discuss the theoretical background and the empirical findings on herding. Section 2.3 explains the data and the construction of the sample. Section 2.4 presents the LSV measure and various results on the herding at the stock level. In Section 2.5 we introduce the firm herding measure and analyze the herding at the firm level. Section 2.6 concludes. 2.2 Literature Review 2.2.1 Theory on Herding A considerable literature exits on the theoretical foundations for institutional herding. Typically, several such explanations are not mutually exclusive, which is why we restrict 6 Window dressing refers to money managers selling (buying) past losers (winners) right before portfolio holdings are reported to... impress the sponsors with the looks of their portfolios. (Lakonishok, Shleifer, Thaler, and Vishny (1991)). 68

Chapter 2 Hedge Fund Herding our discussion here to the most commonly named theoretical foundations for institutional herding. 7 Note that the statistical identification of one such explanation over the other from observed trades is often not possible. We will follow the earlier literature (e.g. Lakonishok, Shleifer, and Vishny (1992), Wermers (1999)) and aim at identifying one or several of the proposed theories later via sensitivity analysis for different subsets of securities and traders. In their seminal paper Scharfstein and Stein (1990) found that money managers might herd in response to facing a reputational risk. If managers do not follow the herd, this involves some reputational cost, which can induce money managers to trade with the herd, rather than trade on their private information. Bikhchandani, Hirshleifer, and Welch (1992) argue that managers infer information from the trades of their presumably better informed peers. Obviously this requires the possibility to observe the trading of the others in the industry. Herding behavior is then a consequence of individual investment decisions depending on the decisions of the others in the industry. This is commonly referred to as herding from informational cascades. Money managers frequently trade on investment signals, which they obtain from some kind of research that is independent of the trading decisions of their peers. Here, the signals represent private information to the managers. Froot, Scharfstein, and Stein (1992) point out that one potential reason for private information being correlated is that managers might trade on the same kinds of signals. Herding is then observed because the private information is cross-sectionally correlated. It results in a situation, where the individual security selection is independent of the selection decisions of others. But since this selection is based on a common valuation methodology, it induces managers to trade the same securities in the same direction. The use of feedback trading rules are one example for herding due to correlated private information. It is important to stress that in some earlier papers (e.g. Lakonishok, Shleifer, and Vishny (1992)), correlated private information was not included in the definition of herding. Therefore, feedback trading was seen as distinct from herding. Bikhchandani and Sharma (2001) also label herding from correlated private information spurious herding. But the more recent literature defines herding as correlated trading, which is the definition that we follow and which focuses on an observable fact and is, therefore, more consistent with the measurement. For example, Nofsinger and Sias (1999) clarified that Feedback trading, a special case of herding, results when lag returns, or variables correlated with lag returns (e.g., earnings momentum, decisions of previous traders, changes in firm characteristics, etc.), act as the common signal. A further explanation presents what is often called habit investing. Falkenstein (1996) argues that herding in and out of certain securities can be due to several money managers sharing the same attraction or aversion to certain security characteristics. If, for example, a fraction of managers dislikes small stocks, they might all together sell stocks that have substantially dropped in value. Then, they form a herd on the sell side of the trading in these stocks. 7 A comprehensive survey on the theoretical foundations of herding in financial markets is Devenow and Welch (1996). 69

Chapter 2 Hedge Fund Herding Many other potential explanations have been brought forward by the theoretical literature on herding behavior among money managers. For example, Shiller, Fischer, and Friedman (1984) argue that agents act as herds under the presence of fads. These mechanisms apply to different kinds of institutional investors in a different way. Wermers (1999), for example, argues that growth funds, which are funds that hold smaller stocks on average than other mutual funds, have stronger incentives to herd. Because information on the future earnings of small (growth) stocks is less precise, herding should be more pronounced under all theoretical explanations. Hedge fund firms hold smaller and more opaque securities than mutual funds (e.g. Griffin and Xu (2009)), which could imply that hedge fund firms should herd more. On the other hand, distinct hedge fund firms are known to follow different investment strategies, which would weaken the expected herding among all firms under most explanations. We will link our results to potential theoretical foundations and the special environment and characteristics of hedge fund firms throughout the analysis. 2.2.2 Empirical Findings on Herding A large literature deals with the empirical herding behavior of individual investors and institutional investors. While most studies on the trading behavior of individuals link herding to some joint irrational attraction to fads and sentiment, the potential reasons found for institutions to herd are more diverse. Our focus is on the herding by institutional investors at the security level in the domestic stock market. 8 In their seminal paper Lakonishok, Shleifer, and Vishny (1992) analyze herding behavior among a sample of tax-exempt (predominantly pension) funds over the period 1985-1989. They identify positive levels of herding among those funds, which seems to be more pronounced in small stocks. Also, they report evidence of positive feedback trading in small stocks. The correlation between herding in a given stock during a quarter and the returns over the same quarter is very small in their sample. Lakonishok, Shleifer, and Vishny (1992) conclude that the trading of institutional investors does not destabilize stock prices. The herding measure (LSV) they define has become the standard measure for identifying within observation period herding and is also the main measure used in our analysis. Grinblatt, Titman, and Wermers (1995) use a sample of quarterly holdings data (CDA) over the period 1974 to 1984 to analyze the degree of momentum investing and herding among mutual funds and how it relates to fund performance. 77% of the mutual funds in their sample consistently buy past winners but most do not persistently sell past losers. The funds that follow momentum strategies significantly outperform the funds following contrarian strategies. The funds degree of momentum investing is highly correlated with fund performance. They also report evidence that mutual funds herd. The tendency of funds to trade with the herd is also highly correlated to performance, but the relationship largely disappears when controlling for the propensity to buy past winners. Grinblatt, Titman, and Wermers (1995) conclude that the remarkable performance of some mutual 8 Other strands of the empirical herding literature comprise, amongst others, herding in (emerging) markets and herding in response to analyst recommendations. A good survey on the herding literature is Bikhchandani and Sharma (2001). 70

Chapter 2 Hedge Fund Herding funds in their sample was created by following a simple momentum trading rule rather than superior information. Wermers (1999) analyzes the herding behavior among mutual funds and its impact on security prices. His quarterly holdings data span over the period 1974-1994. The funds show a slightly greater tendency to herd than the pension funds considered by Lakonishok, Shleifer, and Vishny (1992). However, the levels are significantly higher for certain subgroups of funds and subsets of considered stocks. Especially for small stocks the herding is significantly larger, which is mainly driven by sell side herding. But on average, herds form as often on the buy side as they do on the sell side. He finds that growth funds are more likely to herd and attributes this finding to incentives for herding in growth stocks, for which information on the future performance is less precise, being larger under all theoretical explanations of herding. Positive feedback strategies explain some of the herding by growth funds. The size-adjusted returns difference between stocks that herds most strongly buy and those that herds most strongly sell is almost 9% during the formation quarter. It is not possible to distinguish between price impacts or positive feedback strategies during the quarter being the reason for this large difference. Regarding the future returns of stocks traded by herds, Wermers (1999) finds that stocks bought by herds still outperform those sold by herds, but the return difference is smaller than during the formation quarter. This result is most consistent with herds speeding up the price adjustment process rather than introducing excess volatility. A large part of the difference in future abnormal returns results from the one year momentum effect. Given the large bid-ask spreads for small stocks, where herding is strongest, Wermers (1999) doubts that herding is still profitable after costs. Nofsinger and Sias (1999) analyze the herding and feedback trading of individual and institutional investors. Their data contain information on the fraction of shares held by institutional investors on an annual basis for all NYSE firms over the period 1977 to 1996. In contrast to most other empirical studies, they do not use the LSV measure. On an annual basis they find a strong relationship between ownership by institutions and returns over the same year. Both, stronger positive feedback trading by institutional investors and a larger price impact of institutional herding as compared to individual investors play a role in explaining this correlation. Stocks that the institutions buy outperform those they sell over the following year. They also attribute institutional herding to momentum since it is positively correlated to lagged returns. Up to this point, the herding literature focused on herding within the observation period, which is mostly one quarter of a year. The herding behavior of institutional investors over subsequent observation periods is analyzed in Sias (2004). He uses the quarterly 13F filings of institutional investors, which are used in our analysis, too. He finds that institutions herd and that momentum trading does not serve as a major explanation. The demand of institutional investors for a given security is more related to their lagged demand in the same security than to lagged returns. The relation to lagged demand is partly explained by herding, but also by institutions following their own past trades. Their security demand is correlated with the returns over the same quarter and also weakly positively correlated 71

Chapter 2 Hedge Fund Herding with future returns. Similarly to previous studies, he finds that herding is strongest in small stocks. Using the classification scheme provided by the database, he also distinguishes different types of institutional investors and shows substantially different herding for different types of institutional investors. Also, institutions are more likely to follow the trades of other institutions of the same class. The classification scheme does not allow to identify hedge fund firms, which are the main focus of our work. 9 Since our focus is on hedge fund firms, which trade at a much higher frequency than other institutional investors (e.g. Griffin and Xu (2009)), the second major difference to our study is that we focus on within-quarter herding rather than herding over subsequent quarters. For hedge fund firms, an identification approach as in Sias (2004) could fail to identify herding at a high frequency. 2.3 Data Our data come from several sources which we describe in the following. The security holdings come from the Thomson Financial 13F Ownership Data for institutional investors, which is also known as CDA/Spectrum S34 (CDA henceforth). Market price and return data come from Thomson One and Thomson Reuters Datastream. Hedge fund data come from a merge of 6 major commercial hedge fund databases. The SEC s Securities Exchange Act of 1934 was amended in 1975 including the Section 13F. It requires every institutional investor that exercises investment discretion over more than $100 mio. to file all holdings in 13F positions exceeding either 10 000 shares or $200 000 in fair market value at the end of each calendar quarter within 45 days with the SEC. A list of all 13F securities is published by the SEC and includes stocks, some options, debt securities, warrants, and more. 10 Short positions, however, are not subject to the filings requirement. Also, any institutional investor can apply for secrecy for all or some of the positions which must be filed. If the SEC approves the request, the filing will be made public only after a certain secrecy period. 11 It is important to stress that 13F positions are filed on the institutions level. That is the reported holdings are for the whole hedge fund firm rather than for the individual funds of the firm. Our whole analysis is therefore based on the trading of the hedge fund firms. The SEC provides all filings on a server called EDGAR to the public but the format of the filings is not standardized and it is virtually impossible to machine read the filings and compile a holdings dataset directly from the filings. That is why empirical studies using the 13F filings either rely on the commercial database by Thomson or restrict themselves to small hand collected samples. For an analysis of herding behavior it is important to capture the universe of traders under consideration as completely as possible, which is why we use the CDA database in this paper. The CDA database compiled by Thomson holds the information from the 13F filings 9 A detailed discussion of this problem is provided by Agarwal, Fos, and Jiang (2013). 10 Under http://www.sec.gov/divisions/investment/13flists.htm the SEC provides a list of all 13F securities. 11 For more details see http://www.sec.gov/about/forms/form13f.pdf. 72

Chapter 2 Hedge Fund Herding of all institutional investors. It has been used by previous studies on hedge funds portfolio holdings, too, but suffers from several well known shortcomings. Agarwal, Jiang, Tang, and Yang (2009) find that confidential filings are generally not included. They use a hand collected sample of 13F filings directly from EDGAR. In their sample 4.5% of all filing institutions have used confidential treatment over the observation period 1999-2007 at least once. Also, the holdings in options, and several other securities other than stocks, appear incomplete in CDA. 12 However, our focus is on the herding behavior in the trading of the hedge fund firms, rather than in the performance of the overall firms 13F portfolios, like in many of the papers that resort to hand collected samples. Still, our analysis is limited to herding behavior in the 13F positions of the considered hedge fund firms, which are captured by the CDA database. The database is for the time period January 1980 to December 2010 and contains 47 102 170 13F holdings for 6 662 unique institutional investors. 13 Our hedge fund data, which is used to identify hedge fund firms, come from the hedge fund database of Hodder, Jackwerth, and Kolokolova (2013). They construct a merged database, which consist of the following 6 commercial hedge fund databases: Altvest, Barclay, CISDM, TASS, HFR, and Eureka. In total it includes 8 072 hedge fund firms with 17 914 individual hedge funds and represents one of the largest hedge fund databases reported in the literature, which allows us to capture the hedge fund firm universe as completely as possible. It contains information on the fund level on the management firm, the reported investment objective, and time series of monthly returns and assets under management. The data is for the period January 1970 to June 2009. The merged database allows to distinguish between hedge fund firms that run only funds following an investment style that belongs to the equity long/short category 14, which we label equity firms. As a second group, we identify all firms that manage only funds with investment styles which are based on merger arbitrage strategies. We label those firms merger arbitrage firms. Finally, we identify a group of firms that have only funds with investment objectives that neither belong to our equity group, nor to our merger arbitrage group, which serves as a control group that we label other firms. 15 To identify the institutional investors that are hedge fund firms, we match all institutional investors firm names from CDA to all names of the hedge fund firms from the merged hedge fund database. The name match algorithm is described in Appendix 2.A.2. This way we identify hedge fund firms which file 13F reports over our sample period. But since the 13F positions are filed on the institution level, rather than on the individual fund level, the firms filings might include positions from side business in areas other than hedge fund management. We use an automated web search to identify firms with other 12 Agarwal, Fos, and Jiang (2013) provide a detailed discussion on the shortcomings of the CDA database, too. 13 How we deal with name changes and different spellings of the names of the institutional investors is explained in Appendix 2.A.1. 14 We rely on the self reported styles of the funds here. Most declared equity styles do not have the term short in their style description, which means the funds we are aggregating here have an significant focus on long equity positions. 15 Note that the remaining firms have some funds belonging to the equity funds category and funds following a merger arbitrage strategy. These firms are not included in the category other. 73

Chapter 2 Hedge Fund Herding side business. Excluding those firms makes sure that, for example, Goldman Sachs is not a hedge fund firm in our sample. Precise numbers and details on the web search algorithm are given in Appendix 2.A.3. Finally, since hedge fund data before the mid 1990 s is known to be problematic, we select our sample period for the time thereafter where the two databases overlap: Jan 1995 to June 2009. The numbers of firms included in the final sample are given in Table 2.1. The security holding information in CDA specifies securities by CUSIP identifiers. Since Datastream does not recognize this identifier we use Thomson One to obtain Datastream codes for the securities first. We obtain Datastream codes for 29 458 (84%) of all 35 019 unique CUSIPs filed by all hedge fund firms in our sample. 16 For those, we retrieve the information on prices, numbers of shares outstanding etc. from Datastream. Table 2.1 presents the final sample. Table 2.1: Sample of Hedge Fund Firms and Securities Panel A: Number of Hedge Fund Firms 1995-2009 1995-1999 2000-2004 2005-2009 Total 748 275 448 619 Equity Style 253 78 141 219 Merger Arbitrage 49 19 26 46 Other 178 63 90 128 Panel B: Number of Distinct Securities Total 27 673 15 885 15 739 14 288 Datastream 24 567 14 620 14 155 13 018 Datastream U.S. Stocks 18 904 12 281 11 172 9 324 Panel C: Mean Number of Positions Total 209 141 197 246 Datastream 207 137 195 244 Datastream U.S. Stocks 192 129 182 224 The table contains the numbers of observations in our final sample over different periods. In Panel A, the numbers of hedge fund firms belonging to different style classifications are given. Panel B shows the numbers of distinct securities held by all hedge fund firms. Panel C shows the mean number of positions held by the firms. In Panels B and C, the top rows refer to all securities (unique CUSIPs) included in CDA, the middle rows refer to all securities which are also included in Datastream, and the bottom rows refer to all securities which are included in Datastream and are U.S. stocks. The trades of the hedge fund firms in our sample are given as the changes in the numbers of shares held in the 13F positions from CDA. To make sure the herding measures are not biased by new issues, stock splits, missing reports, or positions crossing the minimum filings threshold, we apply a series of filters to the changes to be included. Due to the 16 The lower number of distinct securities in Datastream is partly explained by CUSIP identifiers containing information on the issue date. That is, one and the same stock can have different CUSIP identifiers if our firms hold shares issued at different dates. Our link to Datastream codes ensures we treat one and the same stock as one security. 74

Chapter 2 Hedge Fund Herding minimum filings threshold we do not know the precise size of the trades and use a proxy instead. All details are given in Appendix 2.A.4. Our final sample contains 4 266 014 buys, 1 138 695 holds, and 4 109 334 sales. The number of holds indicates that the firms in our sample hold at least some positions over several quarters. Griffin and Xu (2009) propose the following proxy for firm i s portfolio turnover in quarter t, turnover i,t = min(value buys i,t, value sales i,t ) holdings i,t 1 (2.1) where taking the minimum of the total value of buys or sells cancels the trading volume resulting from capital flows in or out of the firms. Still, the quarterly turnover from the measure can be larger than 100% if there is an extreme change in the total value of all holdings. An annualized turnover measure of 400% means that the firm changes all its positions over one quarter. Since trades within the quarter are not observed, the measure is only an estimate, which is likely to understate the true turnover. The estimated annualized mean turnover in the U.S. stock positions included in Datastream for the firms in our sample is 90%. Griffin and Xu (2009) find that the value is lower for mutual funds (63%). Given the rather high turnover, we take a within-quarter herding perspective later in the analysis rather than considering trades over subsequent quarters like in Sias (2004). The average value of the firms 13F U.S. stock portfolio is 2 169 million USD. The total value of all hedge fund firms together corresponds on average to about 10% of the S&P500 total market value, which is commonly estimated to account for about 50% of the publicly traded wealth. Hence, hedge fund firms hold a significant fraction of the traded equity and their trading behavior is clearly of major interest to all market participants. Even though the hedge fund firms in our sample represent a significant subset of all traders, there are enough counterparties to their trades like other institutional investors or individual investors, which can trade on the other side of the market than the buying or selling hedge fund herds. The securities other than stocks which are in Datastream and for which Datastream provides information on the security type, consist among others of ADRs, Closed End Funds, Convertible Bonds, ETFs, and Investment Trusts. We restrict our sample to U.S. stocks identified in Datastream which account for 92% of all filed positions. For the small fraction of securities other than U.S. stocks, it is not clear whether they were included in the SEC s list of 13F securities, which changes over time, during the entire sample period. Changes in the filings requirement, however, would significantly bias the herding measures. Also, focusing on the stock positions allows for a comparison to empirical findings for stock herding by other institutional investors (e.g. mutual funds). 2.4 Herding at the Security Level We now turn to the analysis of herding among hedge fund firms at the security level. First, we introduce the measure that statistically identifies if a given stock exhibits correlated trading from several firms. We then use the measure to obtain results for all trades in our sample of hedge fund firms. Then, we continue with several sensitivity analyses, where we 75

Chapter 2 Hedge Fund Herding consider herding for different subsets of trading firms or for different subsets of securities to differentiate among alternative underlying reasons for herding and to gain further insights into the trading by our firms. 2.4.1 LSV Measure Various measures for herding behavior among money managers were proposed in the literature. The diversity is mainly explained by the different datasets used, which reach from daily stock return data (e.g. Christie and Huang (1995)) to annual ownership data (e.g. Nofsinger and Sias (1999)). On the other hand, different herding measures aim at capturing different kinds of herding. For example, Oehler (1998) puts a special focus on herding into a common benchmark and develops an according measure. Even though all measures have been subject to critique, for quarterly holdings data and the herding within one quarter, the LSV measure has become standard in the herding literature and serves as our main measure. Potential drawbacks and some prominent alternatives will be discussed after introducing the LSV measure. The 13F filings that we use are filed on a quarterly basis. We follow the common terminology and refer to one particular stock i over one quarter from t 1 to t, as stock quarter i,t. For the trading in a given stock quarter i,t we denote, B i,t = no. of firms buying stock-quarter i,t N i,t = no. of firms trading stock-quarter i,t. The LSV measure is then defined as, with, H i,t = p i,t E[p i,t ] E p i,t E[p i,t ] } {{ } AF i,t (2.2) p i,t = B i,t N i,t, (2.3) E[p i,t ] = 1 I t I t i=1 p i,t, (2.4) where I t is the number of all stocks traded by at least one of the firms over the quarter t, and p i,t is the proportion of firms buying stock i over quarter t, among all firms trading stock i. The true expectation of this fraction E(p i,t ) is unknown. As a proxy, the average of p i,t over all i at t is used. Hence, the expected proportion of buyers is the same for all stocks at one quarter, and changes only over time. However, it is not the same for different sets of considered firms, as well as for different subsets of included stocks. Note, that this expectation must not be zero because the firms can be net buyers or net sellers over a given quarter. The first term in Equation 2.4.1 captures the absolute deviation of the actual fraction of buyers in stock i from the expected fraction of buyers. It is positive, even if the regarded trades exhibit cross-sectional temporal independence. Therefore, the second term serves as 76

Chapter 2 Hedge Fund Herding an adjustment factor, which is deducted to keep the expectation of H i,t at zero under the null hypothesis of independent trading. The adjustment factor is positive and approaches zero as the number of traders N i,t grows large. Under the null hypothesis, the number of firms that are buyers in B i,t follows a binomial distribution with intensity E[p i,t ]. Given the total number of funds trading N i,t, and the expected fraction of buyers E[p i,t ], the probability of observing exactly b i,t funds being buyers, and the adjustment factor are given as Pr(B i,t = b i,t ) = ( ni,t b i,t ) E[p i,t ] b i,t (1 E[p i,t ]) n i,t b i,t, (2.5) AF i,t = N i,t b i,t =0 Pr(B i,t = b i,t ) b i,t E[p i,t ] N i,t. (2.6) The null hypothesis of independent trading is rejected if H is significantly different from zero because the AF translates random fluctuations to fluctuations around zero. To measure the herding for a given set of firms trading a given set of stocks over a given period, the measures H i,t are averaged across all included stock-quarters to obtain the overall herding measure H. Differences in means (H) can be tested with t-tests and, as in the earlier papers using the LSV measure (e.g. Lakonishok, Shleifer, and Vishny (1992), Wermers (1999)), t-tests will be used to assess if the null holds. The measure can be interpreted as the tendency of the considered firms to buy or sell securities together more often than expected under random and independent trading. For example, a H of 2% means that for a stock-quarter that is traded by 100 firms, on average two more firms either buy or sell the stock-quarter than expected under random and independent trading. Note that if the majority of the included stock-quarters exhibit little or no herding (H i,t close to zero), an average value of 2% could imply much higher levels of herding for some of the included stock-quarters. Because the LSV measure captures herding on the buy and on the sell side alike, Grinblatt, Titman, and Wermers (1995) introduced two modified measures to distinguish buy side from sell side herding. The buy side herding measure B and the sell side herding measure S are defined as B i,t = H i,t p i,t > E[p i,t ], S i,t = H i,t p i,t < E[p i,t ]. (2.7) The two measures represent conditional versions of H. This conditioning implies that the adjustment factors must be calculated separately for both measures to assure that under the null hypothesis the measures are zero in expectation. If herding behavior is identified by the unconditional measure, the relative sizes of the two conditional measures to each other give an indication, whether this herding comes from funds jointly trading into or out of securities. The conditional measures are averaged over security-quarters and over time in the same way as the unconditional measure H. 77

Chapter 2 Hedge Fund Herding A critique that applies to most herding measures is that they do not take the size of trades into account. But the definition of herding as correlated trading depends only on the direction of the trades. The trade sizes are, however, of particular importance when potential impacts of herding (e.g. on share prices or overall fund firm performance) rather than the potential underlying reasons for such behavior are analyzed. That is why the strand of the literature that focuses on impacts took various approaches to capture the size of the trades. Lakonishok, Shleifer, and Vishny (1992)) for example augment the analysis by additional size measures. An adequate measurement of the size and especially of the significance of one trade for an overall stock portfolio prove difficult, when neither the precise time (price) of the trade within the quarter, nor the benchmark, nor the rebalancing frequency are known. That is why measures that aim at showing the sizes of trades and associated money flows are problematic, and why no convincing herding measure that takes the relative importance of trades into account is available. Bikhchandani and Sharma (2001) provide a detailed discussion of this issue. They also discuss a measure that was proposed by Wermers (1995) in an unpublished earlier version of Wermers (1999), but not included in the final paper. Eventually, even though trade sizes would be captured adequately, the herding literature that focuses on potential price impacts still suffers from a lack of precise knowledge about the price elasticities for the stocks. Hence, we will stick to the LSV measure for our analysis of herding at the security level. However, we need to make sure that herding does not only result from small portfolio adjustments. Otherwise joint reweighting to a common benchmark could explain the correlation in trades, and we address this issue in Section 2.4.2. Bikhchandani and Sharma (2001) point out that the LSV measure does not reveal intertemporal persistence in the herding at the security and at the firm level. That is, it does not show whether the securities that herds trade in one quarter are more likely to be traded by herds in the following quarter. We consider the issue by augmenting our analysis and measuring the persistence as proposed by Barber, Odean, and Zhu (2003). Also, we use a firm herding measure and check for intertemporal persistence at the firm level in Section 2.5. A critique that applies to the LSV measure in particular was brought forward by Oehler (1998). His point can be illustrated by the following example. Assume all considered firms hold the benchmark portfolio. They trade the benchmark in response to flows of client money over the quarters and do not engage in any other trading. The LSV measure is zero in this case because LSV controls for aggregate money flows by E[p i,t ] being equal to the observed fraction of buyers p i, t in all stock-quarters. If all firms enjoy money inflows, all firms would buy the stocks in the benchmark portfolio, rather than picking stocks individually and independently, or investing in securities other than stocks. Oehler (1998) argues that this scenario represents bench mark herding by the firms, which has a potentially large impact on share prices, and that the LSV measure captures only excess herding and is rather too conservative. Therefore, it is important to stress that the correlation in trades measured by LSV is the correlation that is not explained by aggregate money flows and benchmark herding. We will address these issues later 78

Chapter 2 Hedge Fund Herding and consider if E[p i,t ] takes extreme values, which would be an indication of benchmark herding, in Section 2.4.2. Also, we will analyze if aggregate money flows to the industry explain some of the observed herding in Section 2.4.6. Eventually, we will also address individual money flows at the firm level later in Section 2.5.4. A further critique was expressed by Frey, Herbst, and Walter (2006), who show that the LSV measure can be biased downwards. The bias depends on the characteristics of the data and generally decreases when the number of traders increases. They introduce a slightly modified measure. However, Bellando (2010) shows that their measure is unbiased only under special conditions and otherwise can be biased upwards. Since we provide the first evidence that hedge fund firms herd, we prefer to use the more conservative LSV measure, rather than using a measure that is potentially biased upwards. 2.4.2 General Results for Herding at the Security Level We start the empirical analysis with calculating herding measures including the trades of all hedge fund firms in all stocks in our sample. The average proxy for E[p i,t ] over all securities and all quarters is 0.51. It shows that the firms are on average net buyers, which corresponds to growth of the hedge fund industry over this period. The time series of the quarterly E[p i,t ] is given in Figure 2.1. Coming back to the critique by Oehler (1998), we see that E[p i,t ] does not take extreme values during the sample period. Strong benchmark herding by our firms should, however, result in rather large deviations, and does not seem to play a major role in our sample. Figure 2.1: Average Fraction of Buys over Time The figure shows the time series of the average fraction of buys across all traded securities at every quarter by all firms on our sample. The average fraction is used as a proxy for the expected fraction of buyers E[p i,t ]. Table 2.2 shows the results for the herding measures. We see positive levels of herding 79

Chapter 2 Hedge Fund Herding Table 2.2: General Herding Results min. 1 trader min. 2 traders min. 5 traders min. 10 traders min. 20 traders min. 50 traders min. 100 traders 1995-2009 H 2.16 (0.00) [270 870] 2.66 (0.00) [222 292] 2.71 (0.00) [165 239] 2.60 (0.00) [119 182] 2.43 (0.00) [66 948] 2.27 (0.00) [12 673] 1.96 (0.00) [1 219] B 1.95 (0.00) [135 779] 2.37 (0.00) [111 836] 2.55 (0.00) [85 391] 2.40 (0.00) [61 491] 2.12 (0.00) [33 801] 1.77 (0.00) [5 685] 1.83 (0.00) [467] S 2.11 (0.00) [135 091] 2.58 (0.00) [110 456] 2.80 (0.00) [79 848] 2.77 (0.00) [57 691] 2.73 (0.00) [33 147] 2.66 (0.00) [6 988] 2.03 (0.00) [752] 1995-1999 H 1.83 (0.00) [92 809] 2.39 (0.00) [71 763] 2.68 (0.00) [44 144] 2.69 (0.00) [24 050] 2.91 (0.00) [8 430] 4.51 (0.00) [677] 7.15 (2.69) [13] B 1.61 (0.00) [45 770] 2.08 (0.00) [35 407] 2.44 (0.00) [22 649] 2.31 (0.00) [12 218] 2.42 (0.00) [4 118] 4.84 (0.00) [272] 18.02 (23.51) [3] S 1.73 (0.00) [47 039] 2.23 (0.00) [36 356] 2.84 (0.00) [21 495] 3.03 (0.00) [11 832] 3.35 (0.00) [4 312] 4.27 (0.00) [405] 3.84 (0.22) [10] 2000-2004 H 2.57 (0.00) [91 967] 3.11 (0.00) [75 860] 2.96 (0.00) [58 275] 2.76 (0.00) [43 230] 2.42 (0.00) [24 060] 2.40 (0.00) [4 113] 2.28 (0.00) [312] B 2.27 (0.00) [45 430] 2.74 (0.00) [37 729] 2.89 (0.00) [30 142] 2.70 (0.00) [22 321] 2.10 (0.00) [11 972] 1.66 (0.00) [1 717] 3.20 (0.06) [106] S 2.52 (0.00) [46 537] 3.07 (0.00) [38 131] 2.94 (0.00) [28 133] 2.76 (0.00) [20 909] 2.73 (0.00) [12 088] 2.93 (0.00) [2 396] 1.81 (0.00) [206] 2005-2009 H 2.09 (0.00) [86 094] 2.45 (0.00) [74 669] 2.50 (0.00) [62 820] 2.43 (0.00) [51 902] 2.32 (0.00) [34 458] 2.01 (0.00) [7 883] 1.77 (0.00) [894] B 1.97 (0.00) [44 579] 2.27 (0.00) [38 700] 2.30 (0.00) [32 600] 2.18 (0.00) [26 952] 2.06 (0.00) [17 711] 1.60 (0.00) [3 696] 1.29 (0.00) [358] S 2.08 (0.00) [41 515] 2.40 (0.00) [35 969] 2.64 (0.00) [30 220] 2.65 (0.00) [24 950] 2.57 (0.00) [16 747] 2.35 (0.00) [4 187] 2.08 (0.00) [536] The table contains the herding measures for all security-quarters traded over different time periods. For a security-quarter to be included, we require different minimum numbers of hedge fund firms which must trade the security-quarter. The measures are explained in Section 2.4.1. For each measure, the table presents the corresponding p-value in percent in parenthesis, and the number of included security-quarters in squared brackets. 80

Chapter 2 Hedge Fund Herding in all periods. Over the full observation period the mean herding measure for all stocks traded by at least 5 hedge fund firms is 2.71 percent. Corresponding to the large numbers of stock-quarters included for the calculation of the measures, nearly all values are highly significantly different from zero. The values for the direction herding measures indicate that the identified herding seems to result from funds buying stocks together as well as from selling together. The levels of herding do not vary much over different subperiods. We require a certain minimum number of firms trading a security-quarter to be included in the calculation, because, arguably, the herding might depend on the number of firms trading. The columns of Table 2.2 correspond to different minimum numbers of required traders. The results reveal that this requirement does not influence the values in a systematic way. We follow the common convention in the literature, and restrict our further analysis to stock-quarters traded by at least 5 of the hedge fund firms under consideration. Most of the existing research on herding among professional money managers is based on quarterly holding data and the LSV measure what makes our results directly comparable in terms of methodology. However, mutual funds file positions on the individual fund s level rather than at the firm level, which is why most of the paper by Wermers (1999) is for mutual funds rather than mutual fund firms. But he also provides the herding measures on the mutual fund firm level. He finds an average LSV measure for mutual fund firms over the period 1975-1994 of 2.22%. To compare his sample to earlier research, Sias (2004) also uses the LSV measure for within-quarter herding. For his sample, which comprises all institutional investors, he finds a level of herding of 1.78 percent over the period 1983-1997. Having in mind that the time periods do not overlap, the 2.71 percent in our sample suggest that the herding of hedge fund firms is of comparable order of magnitude or even slightly higher than the herding found for mutual fund firms and other institutional investors by earlier research. Our result is highly statistically different from these values. Also, we usually argue for non-randomness of our herding measure outcomes by them being statistically significantly different from zero, which corresponds to the null hypothesis of no herding. Given the large sample size it is, however, not surprising that most presented measures are statistically different from zero, and from each other. Before we turn to potential explanations for herding, we conduct a robustness check to assure that the identified herding is not a statistical fluke resulting from random correlations among the trades, which are arguably likely to appear in a large sample. Following Wermers (1999), we obtain the distribution of all H i,t under the null from a Monte Carlo simulation, and compare it to the actual distribution. We obtain 10 simulated measures Hi,t for each security-quarter that was traded by at least 5 hedge fund firms over the sample period. Given the actual number of firms that trade a given stock-quarter N i,t and the proxy for E[p i,t ] in the quarter, the number of buyers is simulated by drawing N i,t times from a Bernoulli distribution with intensity E[p i,t ]. The sum of the draws gives one simulated number of buyers B under random trading, and the according simulated fraction of buyers is p i,t = B N i,t. The simulated measure H i,t is then calculated using the actual E[p i,t], and the simulated p i,t. 81

Chapter 2 Hedge Fund Herding Figure 2.2 shows the actual and the simulated distributions of the herding measure. Figure 2.2: Distribution of the Herding Measure The figure shows on the left the distribution of the herding measure H i,t for all stockquarters in our sample. On the right is the distribution of the corresponding simulated measure Hi,t which come from a Monte Carlo simulation as described in Section 2.4.2. Comparing the two distributions, the actual distribution has more probability mass in the right tail, which corresponds to the overall herding measure values resulting from a relatively small number of stock-quarters exhibiting large herding. The mean and median of the simulated measure show that the measure is zero and unbiased under independent trading in our sample. The herding which we identify does, hence, clearly not result from random matching of the firms trades. As a further robustness check, we ensure the herding does not result from small trades only. Wermers (1995) notes that small portfolio adjustments, e.g. a common reweighting to a joint benchmark, would result in positive values for the LSV measure. Recall that due to the minimum filings threshold we do not know the precise size of the trades and use a proxy as described in Appendix 2.A.4 instead. At every quarter we include only the largest 25% of all trades, where the trade size is measured as relative size of our proxy for trade size to the overall 13F stock portfolio, to ensure that small and large firms are equally contained. The H is slightly larger than the average 2.71 percent in all trades. Hence, the identified herding is not resulting from unimportant trades only. 82

Chapter 2 Hedge Fund Herding 2.4.3 Herding among Different Investment Styles Herding is defined as non-independent and non-random trading, i.e. correlated trading. The trading of the fund firms results from their investment strategies. Hedge funds are known to follow very different kinds of investment strategies, which are commonly referred to as hedge fund styles. Under all theoretical explanations for herding the more homogeneous the investment strategies of a sample of traders are, the stronger are the incentives to herd. Wermers (1999) as well as Sias (2004) find that the herding behavior varies across mutual fund styles and different types of institutional investors, respectively. Hence, the levels and the potential reasons of herding should vary across hedge fund firm styles, too. Therefore, in our first detailed analysis, we measure herding separately for different hedge fund firm styles. 17 Table 2.3: Herding Measures across Investment Styles All Equity Style Merger Arbitrage Other H 2.71 [165 239] 1.52 [85 283] 7.63 [1 936] 0.76 [25 151] B 2.55 [85 391] 1.43 [43 647] 5.99 [1 029] 0.51 [12 568] S 2.80 [79 848] 1.57 [41 636] 8.96 [907] 0.96 [12 583] The table contains the herding measures for all stock-quarters traded by at least 5 hedge fund firms belonging to different style classes. The measures are explained in Section 2.4.1 and the number of security-quarters considered are given in squared brackets. All p-values are zero. In Table 2.3 we see herding among all considered style groups, though, it substantially differs for different styles. 18 The equity style group is a very broad category in terms of the trading objective. For example, firms that focus on stock picking in very special industries and technical traders that trade in all stocks are equally contained in this style group. The potentially higher heterogeneity serves as an explanation why firms in the style group other exhibit even lower levels of herding. The merger arbitrage firms show a very high propensity to trade the same securities together and in the same direction. If merger events, which provide the profitable opportunities to these firms, are rather limited relative to the number of firms, this would result in herding in and out of these securities partly together. This corresponds to explanations of herding due to either correlated private information or informational cascades. On top of following a more coherent investment strategy than alternative style groups, the more limited nature of trading opportunities serves as an explanation for fiercer herding by these firms. 17 The style classification is as defined in Section 2.3. 18 The differences are all highly statistically significant. 83

Chapter 2 Hedge Fund Herding 2.4.4 Herding in Different Stocks 2.4.4.1 Herding Persistence in Stocks We start our more detailed analysis of herding across various stock characteristics with an assessment of the persistence in the herding at the stock level. The persistence could give some indication what kind of characteristics attract herds. Low persistence would indicate that herds do not tend to form on the same stocks subsequently, and we should direct our further focus more on dynamic characteristics, such as lagged returns. To the contrary, high persistence would imply that herds are attracted by stock characteristics which do not change rapidly over time. The LSV measure indicates the level of herding in the average stock-quarter. A critique mentioned earlier already is that LSV does not reveal whether the stocks which are traded by herds in one quarter are more likely to be traded by herds in the following quarter. Therefore, similar to Barber, Odean, and Zhu (2003), we analyze the intertemporal persistence of herding at the security level by calculating the mean correlations between the herding in a given stock-quarter and the herding in the same stock during the following quarters. That is, for each stock-quarter that is traded by at least 5 firms at time t, we obtain corr(h i,t, H i,t+τ ), for τ = 0,..., 5 given that the stock-quarter was still traded by at least 5 firms at t + τ. We average all correlations over each τ to obtain the mean correlation for the particular time gap. The results are given in Table 2.4. Table 2.4: Herding Measures Intertemporal Correlations quarter mean corr. fraction traded t 100.00 (0.00) 100.00 t + 1 2.44 (0.00) 90.94 t + 2 1.19 (0.05) 87.53 t + 3 0.61 (10.37) 84.90 t + 4 0.65 (6.51) 82.50 t + 5 0.76 (6.96) 80.26 The table contains the mean of the correlations between the herding measures for all stock-quarters traded by at least 5 hedge fund firms at time t and the 5 subsequent quarters. The mean correlation coefficients are given in percent and associated p- values are given in percent in parenthesis. The right column shows the fraction of the stock-quarters for which the corresponding stock is still traded by at least 5 hedge fund firms at subsequent quarters in percent. For the two quarters directly following the trading quarter, the correlations are positive and statistically significantly different from zero, but extremely small. If hedge fund herds are attracted by stock characteristics that do not change over time (e.g. industry classification), the low persistence implies that they herd in different stocks with the same characteristic in subsequent quarters. More likely, however, low persistence means that they form on dynamically changing signals like past or current returns. We will, therefore, direct our further analysis to non-static stock characteristics. 84

Chapter 2 Hedge Fund Herding To make sure that the averaging is not diluting a potentially high persistence in stockquarters that exhibit high levels of herding, we repeat the analysis and only include stockquarters for which H i,t > 10%. The results do not change significantly, which means that the persistence is low also in stock-quarters that exhibit high levels of herding. Note also, that low persistence rules out that herding simply results from firms reducing or increasing positions in particular stocks over several quarters. 2.4.4.2 Herding in Stock Sizes The first (potentially) dynamic stock characteristic, which we consider is the size of the stocks. Similar to earlier research we aim at using the differentiation across stock sizes to distinguish alternative potential explanations for the observed herding. We sort the securities according to their market capitalization, and, for every quarter, we use all stocks held by any of our firms to calculate size quintiles. We calculate the time series of size quintile breakpoints to sort all considered stock-quarters into their respective quintiles. Then, we average the herding measures across all stock-quarters belonging to a given size quintile. Table 2.5: Herding Measures across Stock Sizes S-Q1 (small) S-Q2 S-Q3 S-Q4 S-Q5 (large) H 5.31 [3 501] 2.72 [18 924] 2.65 [39 009] 2.59 [49 840] 2.70 [53 952] B 2.46 [1 420] 2.42 [9 382] 2.89 [20 827] 2.53 [26 628] 2.35 [27 130] S 7.13 [2 081] 2.89 [9 542] 2.25 [18 182] 2.54 [23 212] 3.03 [26 822] The table contains the herding measures for all security-quarters traded by at least 5 hedge fund firms over the full sample period. The measures are calculated for securities belonging to different quarterly size quintiles separately. The measures are explained in Section 2.4.1 and the number of security-quarters considered are given in squared brackets. All p-values are zero. Table 2.5 shows that most of the stock-quarters traded by more than 5 firms belong to the largest size quintile, but herds form more often among small stocks, where most of the herding results from selling small stocks jointly. Across all other size quintiles, the overall herding measures are close to the sample average and buy and sell side herding seems roughly equally present. Note that this rules out that money flows, which could affecting the largest stocks most, explain the slightly larger levels of herding in the largest stocks. Wermers (1999) argues that herding from money flows should on average result in stronger buy herding over periods with net money inflows to the considered traders, like in our sample. 19 If hedge fund firms trade at a rather high frequency they would prefer stocks for which there is a deep and liquid market such that they can place large trades without a large price impact. Also, research is usually less expensive for larger stocks. So if 19 Due to the large numbers of included observations, the mentioned differences are all highly statistically significant. Even differences which we argue are not economically meaningful are mostly statistically significant. 85

Chapter 2 Hedge Fund Herding the market capitalization of a stock decreases, it becomes less attractive. The high sell side herding in small stocks was found in the previous studies for pension funds and mutual funds, too. Mutual funds trade at a lower frequency, but share the problem of potential price impacts by large trades, and costly research. These papers argue that this is most consistent with habit investing. Wermers (1999), who obtained the same effect for his mutual funds sample, argues that herding due to characteristics should be more present in large securities, whereas herding resulting from informational cascades should be more present in small securities. Herding from informational cascades is more likely to be observed in small stocks, because there the signals are noisier, which increases the incentives to try to infer information from peer trading. 2.4.4.3 Herding in Stock Returns We now sort the securities according to their lagged, present, and future returns. Separating stocks according to their prior quarter absolute returns, for example, should reveal to what extent hedge fund firms engage in feedback trading strategies. Since, for example, equity style firms could be more likely to use such strategies, we analyze the herding in different returns separately for different strategies. 20 Again, for every quarter, we use all securities held by any of the firms to calculate return quintiles. Returns from the beginning to the end of each quarter are calculated using a total return index from Datastream which assumes dividends are reinvested. The time series of return quintile breakpoints is calculated and all traded security-quarters are sorted according to their return over the quarter preceding the trading quarter. The herding measures are then averaged across all considered quintiles. Again, due to the large numbers of included observations, differences that appear economically meaningful by simply comparing the relative sizes of the reported herding measure estimates are always statistically significantly different, too. For the ease of reading we do not report the associated p-values when making comparing statements on the reported results. The top row of Panel A in Table 2.6 shows the herding in prior return qunitiles by all firms. Herding is strongest for the securities with high past returns, where herds tend to form on the buy side about as often as on the sell side. The securities belonging to the smallest past return quintile exhibit high herding, too. The joint selling of past losers seems to explain most of the herding there. Selling past losers is consistent with several explanations for herding. Window dressing could explain the high sell herding here, since Agarwal, Daniel, and Naik (2011) found that hedge funds tend to inflate their prices in the last month of the year. Window dressing is therefore analyzed in detail later in Section 2.4.5. When we consider only equity style firms, again, the herding is strongest in high prior return stocks, where the buy side herding is slightly more pronounced than the sell side herding. For the lowest prior returns the herding is mainly driven by sell side herding as we found for all firms, too. Buying past winners and selling past losers is consistent with 20 Earlier we found low levels of herding by firms managing only funds following styles not related to equity or merger arbitrage. Therefore, we do not analyze the herding in returns for those firms. 86

Chapter 2 Hedge Fund Herding Table 2.6: Herding Measures across Stock Performance R-Q1 (small) R-Q2 R-Q3 R-Q4 R-Q5 (large) Panel A: Prior quarter return quintiles All H 2.61 (0.00) [26 728] 2.12 (0.00) [33 476] 2.31 (0.00) [34 680] 2.62 (0.00) [36 316] 3.86 (0.00) [33 949] B 1.31 (0.00) [11 192] 1.89 (0.00) [16 195] 2.27 (0.00) [18 161] 2.78 (0.00) [20 056] 3.79 (0.00) [19 745] S 3.55 (0.00) [15 536] 2.27 (0.00) [17 281] 2.30 (0.00) [16 519] 2.31 (0.00) [16 260] 3.75 (0.00) [14 204] Equity Style H 1.41 (0.00) [12 927] 1.30 (0.00) [17 277] 1.49 (0.00) [18 353] 1.38 (0.00) [19 217] 2.02 (0.00) [17 480] B 0.59 (0.01) [6 056] 1.09 (0.00) [8 616] 1.41 (0.00) [9 276] 1.46 (0.00) [10 169] 2.24 (0.00) [9 514] S 2.04 (0.00) [6 871] 1.41 (0.00) [8 661] 1.51 (0.00) [9 077] 1.29 (0.00) [9 048] 1.73 (0.00) [7 966] Merger Arbitrage H 6.12 (0.00) [312] 6.94 (0.00) [343] 7.12 (0.00) [455] 7.50 (0.00) [385] 9.89 (0.00) [440] B 7.04 (0.00) [171] 6.84 (0.00) [197] 3.97 (0.00) [242] 5.69 (0.00) [201] 6.91 (0.00) [217] S 3.66 (0.22) [141] 6.77 (0.00) [146] 10.33 (0.00) [213] 9.10 (0.00) [184] 12.32 (0.00) [223] Panel B: Current quarter cumulative abnormal return quintiles All H 2.39 (0.00) [30 912] 1.97 (0.00) [35 510] 3.25 (0.00) [34 792] 2.34 (0.00) [35 771] 3.79 (0.00) [28 245] B 1.52 (0.00) [13 780] 1.76 (0.00) [17 864] 1.96 (0.00) [17 121] 2.60 (0.00) [19 322] 4.68 (0.00) [17 302] S 3.05 (0.00) [17 132] 2.13 (0.00) [17 646] 4.42 (0.00) [17 671] 1.95 (0.00) [16 449] 2.14 (0.00) [10 943] Equity Style H 1.26 (0.00) [14 662] 1.07 (0.00) [18 370] 1.63 (0.00) [18 464] 1.35 (0.00) [19 038] 2.44 (0.00) [14 748] B 0.53 (0.01) [6 920] 0.87 (0.00) [9 003] 0.71 (0.00) [8 949] 1.63 (0.00) [10 033] 3.20 (0.00) [8 741] S 1.88 (0.00) [7 742] 1.26 (0.00) [9 367] 2.42 (0.00) [9 515] 0.99 (0.00) [9 005] 1.17 (0.00) [6 007] Merger Arbitrage H 4.24 (0.00) [269] 5.40 (0.00) [354] 10.16 (0.00) [516] 5.98 (0.00) [414] 10.45 (0.00) [383] B 4.27 (0.03) [150] 4.94 (0.00) [171] 4.59 (0.00) [229] 3.22 (0.06) [213] 11.05 (0.00) [266] S 4.05 (0.32) [119] 5.05 (0.00) [183] 14.36 (0.00) [287] 8.32 (0.00) [201] 7.91 (0.00) [117] Panel C: Following quarter cumulative abnormal return quintiles All H 2.44 (0.00) [31 430] 2.00 (0.00) [35 631] 3.81 (0.00) [34 892] 1.99 (0.00) [35 755] 2.66 (0.00) [26 897] B 2.64 (0.00) [16 164] 2.40 (0.00) [18 536] 2.25 (0.00) [17 390] 2.46 (0.00) [19 048] 3.10 (0.00) [14 247] S 2.11 (0.00) [15 266] 1.47 (0.00) [17 095] 5.31 (0.00) [17 502] 1.39 (0.00) [16 707] 2.05 (0.00) [12 650] Equity Style H 1.53 (0.00) [14 807] 1.14 (0.00) [18 504] 2.04 (0.00) [18 549] 1.19 (0.00) [19 190] 1.40 (0.00) [14 053] B 1.73 (0.00) [7 664] 1.26 (0.00) [9 535] 1.14 (0.00) [9 120] 1.36 (0.00) [9 900] 1.76 (0.00) [7 427] S 1.28 (0.00) [7 143] 0.97 (0.00) [8 969] 2.86 (0.00) [9 429] 0.98 (0.00) [9 290] 0.85 (0.00) [6 626] Merger Arbitrage H 4.80 (0.00) [226] 3.95 (0.00) [385] 11.84 (0.00) [642] 4.79 (0.00) [392] 5.67 (0.00) [246] B 5.35 (0.01) [114] 4.26 (0.00) [226] 6.90 (0.00) [316] 6.83 (0.00) [245] 5.76 (0.00) [128] S 3.70 (0.60) [112] 2.90 (0.70) [159] 16.14 (0.00) [326] 0.88 (40.84) [147] 4.86 (0.04) [118] The table contains the herding measures for all stock-quarters traded by at least 5 hedge fund firms of a given style over the full sample period. The measures are calculated for stocks belonging to different previous quarter return quintiles in Panel A. For Panels B and C the measures are calculated for stocks belonging to different current and future cumulative abnormal return quintiles. The measures are explained in Section 2.4.1. For each measure, the table presents the corresponding p-value in percent in parenthesis, and the number of security-quarters in squared brackets. 87

Chapter 2 Hedge Fund Herding positive feedback trading (momentum) but there is also considerable sell herding for high prior return stocks and the herding in the middle prior return quintile is relatively large to the herding in extreme prior returns. 21 Hence, positive feedback trading strategies do not serve as a major explanation for the observed herding like earlier research found for mutual funds (Wermers (1999)) and institutional investors in general (Sias (2004)). Small firms in general tend to be more risky and have higher returns. Therefore the high levels of herding in small stocks may correspond to the high levels of herding in the high return stocks. However, for the small firms the herds tend to form on the sell side, whereas for the large returns the herds tend to form on both sides. For the merger arbitrage firms the high prior return stocks are traded by herds most strongly but the herding on the sell side is much more pronounced. The overall herding is roughly equally distributed over the other prior returns and only for the lowest past returns herds from more strongly on the buy side. The joint selling of prior high return stocks is consistent with merger arbitrage firms selling the stocks that rose due to some merger event over the last quarter. If the firms show some heterogeneity in their bets on which companies are likely to profit from a future merger event, they will not buy strictly the same stocks, at least not over the same quarter. However, if a merger took place, there is no reason for being invested in the affected stocks any longer, and we should observe highly correlated selling, i.e. herding from correlated private information on the sell side. This could explain the larger herding on the sell side among merger arbitrage firms. To assess the performance of the traded securities and potential return reversions, we repeat the exercise for cumulative abnormal returns over the current and subsequent quarters. We estimate cumulative abnormal returns (CAR) from the Carhart (1997) four factor model in each quarter separately using daily stock return data. The CAR are sorted into quintiles and we calculate the herding measures separately for all stock-quarters in each quintile. The results for the CAR in Panel B of Table 2.6 reveal that all hedge fund firms together tend to buy current winners and sell current losers, but the sell herding is actually strongest in the middle CAR quintile. For equity firms only, the pattern is the same. Since the holdings are reported at the beginning and the end of each considered quarter, we do not know when, within the quarter, the funds buy or sell the considered stocks. Therefore, we cannot distinguish whether the herds buy high return stocks before the abnormal returns are realized or thereafter. The latter would indicate a positive feedback trading strategy within the quarter that they jointly use. If the subsequent abnormal returns are nonnegative, the previous would correspond to valuable stock picking, potentially based on the same kind of analysis (correlated private information). Alternatively, firms buying and selling subsequently and following each other in the trades (informational cascades) is consistent with the results, too. If, on the other hand, the subsequent CAR are negative, the current CAR could simply result from a price impact by the large hedge fund firm trades. For the merger arbitrage firms, the herding is relatively low for current losers and 21 For example, the herding in the middle prior return quintile is highly statistically significantly larger that the herding in the lowest return quintile, while the difference is not economically meaningful. 88

Chapter 2 Hedge Fund Herding results form buy and sell side herding alike. The strongest sell herding is in the middle quintitle and the strongest buy herding is in current winners. Again, this is consistent with the firms jointly buying into profitable opportunities and jointly selling after the merger events when the stocks exhibit no significant abnormal returns. The profitability also means that the merger arbitrage firms do not suffer by large from failed merger battles and are either good at betting on the right merger events, or can influence the procedure to their benefit. Our results for the herding of these firms raise several question concerning their role as share holders in M&A transactions, which are beyond the scope of this work. Sorting for subsequent quarter abnormal returns in Panel C of Table 2.6 reveals that the herding is now clearly centered in the middle quintile, where we observe strong sell herding relative to the overall levels of herding for all firms as well as for our subsets of firms following different styles. Strong herding in the CAR center quintile for the following quarter is consistent with herding resulting from the joint trading on profitable trading possibilities in the stock market. In our framework, however, we cannot distinguish, whether the firms infer their information from the same but independent trading signals (correlated private information), or whether the firms infer it from each others trades (informational cascades). The findings are also consistent with Gray (2009), who finds evidence that hedge fund managers do have stock picking skill and actually share their profitable investment ideas with their peers (informational cascades). Overall, we find no evidence that the firms engage in destabilizing (feedback) trading strategies. 2.4.4.4 Profitability of Herding To more specifically assess the profitability of herding we look at the buy side herding and the sell side herding separately. We calculate quintile breakpoints over all stock-quarters where the fraction of buyers exceeds the expected fraction of buyers (B > 0) as well as where it is below the expected fraction of buyers (S > 0). Since for some periods, the herding on one side of the market is very strong and, thus, there is no meaningful herding on the other side, we calculate the break points over all stock-quarters rather than for each quarter. The average quarterly CAR for all stock-quarters belonging to the highest and lowest B and S quintiles respectively, are given in Table 2.7. The results reveal that the stocks most strongly bought (sold) by herds, exhibit large positive (negative) CAR. For the strong buy herding the following quarter CAR is also positive, which means there is no mean reversion over the following period. For the strong sell herding there is a small positive CAR over the following quarter but it is far from offsetting the large negative CAR from the trading period. Since most of the sell herding is in small securities it is likely that the hedge fund firms large trades have a price impact, which would explain a mild reversion over the subsequent period. To what extend the firms act as price takers and to what extend they actively drive prices cannot be clearly said. But, again, the trades we are considering in our sample are rather large, and hedge fund firms usually perceived as well informed investors by the market. It is reasonable to assume that they do not only act as price takers. Overall, our findings suggest that 89

Chapter 2 Hedge Fund Herding Table 2.7: Abnormal Stock Returns across Different Levels of Herding t-1 t t+1 Panel A: Buy herding B Q1 (small) 1.91 (0.00) [17 082] 1.79 (0.00) [17 082] 0.78 (0.02) [17 082] B Q5 (large) 8.44 (0.00) [17 077] 10.57 (0.00) [17 077] 1.75 (0.00) [17 077] Panel B: Sell herding S Q1 (small) 0.49 (2.67) [15 977] -0.28 (18.92) [15 977] 0.59 (0.77) [15 977] S Q5 (large) -1.38 (0.00) [15 970] -4.58 (0.00) [15 970] 0.84 (0.12) [15 970] Panel C: Zero cost portfolio B Q5 - S Q5 0.17 (55.61) [58] 0.58 (3.79) [58] -0.36 (4.78) [58] The table contains the average quarterly cumulative abnormal returns for all stockquarters traded by at least 5 hedge fund firms over the entire sample period belonging to the highest and lowest buy herding and sell herding quintiles in Panels A and B. Panel C contains the cumulative abnormal returns of a zero cost portfolio that is revised at every quarter. The portfolio consists of equally weighted long positions in all stocks that belong to the highest buy herding quintile (B Q5) and equally weighted short positions in all stocks belonging to the highest sell herding quintile (S Q5). The previous, current, and future quintile cumulative abnormal returns are given in different columns. The measures are explained in Section 2.4.1. For each measure, the table presents the corresponding p-value in percent in parenthesis, and the number of considered observations in squared brackets. herding by hedge fund firms drives prices towards their fundamental values rather than adding to excess volatility. In Panel C, the average CAR of a zero cost portfolio are given. In the absence of trading costs, the CAR are calculated for every quarter as the difference between the CAR of an portfolio of equally weighted long positions in each stock belonging to the highest buy herding quinitle and the CAR of an portfolio of equally weighted short positions in each stock belonging to the highest sell herding quintile. It implies that in a period with strong herding on one side of the market, the relatively many stocks that exhibit this side of herding obtain the same weight as the few stocks on the other side. Therefore, the CAR of the zero cost portfolio are much smaller than the difference between the CAR for the largest buy and sell herding stock-quarters as given in Panels A and B. 22 The results suggest investing in the zero cost portfolio would be profitable over the trading quarter but not over the subsequent quarter. Besides the problem that 13F reports must be filed only within 45 days after the end of the quarter, investors could not profit from following such a strategy. 2.4.5 Herding and Window Dressing As we found earlier, window dressing could serve as a potential explanation for herding. Given the typical compensation scheme for hedge fund managers, the incentives to push up the performance are very high in hedge fund firms. Typically, the incentive fee is 22 The percentile break points are the same as used before and calculated over all stock-quarters ex post. The break points for the largest quintiles are 10.26 and 9.74 percent for buy and sell herding respectively, but the results are robust to varying breakpoints for strong directional herding in a reasonable interval. 90

Chapter 2 Hedge Fund Herding calculated based on the fund value at year-end. In Chapter 1 we show that hedge funds risk taking displays a strong seasonality and provide a detailed discussion on the incentives to report good year-end results. Agarwal, Daniel, and Naik (2007) for example find that hedge funds inflate their returns in the month of December. 23 In their seminal paper on window dressing, Lakonishok, Shleifer, Thaler, and Vishny (1991) argue that (t)o impress sponsors, fund managers may alter these portfolios at the end of the quarter, and especially at the end of the year, that is, window dress.. Consistently, they find some evidence of stronger window dressing at year-end in their sample of pension funds. If window dressing serves as an explanation for the observed herding, we should observe higher levels of herding in the trading during the last quarter of the year, given the strong incentives to engage in such performance increasing activities particularly towards the end of the year in hedge fund firms. Table 2.8: Herding Measures for Different Quarters Quarter 4 Quarters 1-3 H 2.60 [40 398] 2.75 [124 841] B 2.48 [20 685] 2.57 [20 685] S 2.64 [19 713] 2.85 [60 135] The table contains the herding measures for all security-quarters traded by at least 5 hedge fund firms, where the measure is calculated separately for the forth quarter and for the first 3 quarters of each year. The measures are explained in Section 2.4.1 and the number of security-quarters considered are given in squared brackets. All p-values are zero. Table 2.8, however, reveals that the herding measure is not higher when calculated only for the last quarters of each year and the observed herding results from buy and from sell side herding alike for both. In contrast, the measure is slightly higher for the first 3 quarters. 24 So window dressing in the last quarter does not serve as an explanation for herding among hedge fund firms. Ben-David, Franzoni, Landier, and Moussawi (2013) find evidence that hedge fund firms buy up the stocks held in their portfolios on the last trading day just before trading ends in order to inflate their quarterly performance in all quarters. We cannot directly check whether this kind of quarter-end window dressing explains some of the herding found for our hedge fund firms. However, we find that herds form on the buy side as well as on the sell side. Hence, this does not serve as a major explanation for the overall levels herding that we identify. 23 Cici, Kempf, and Puetz (2010) find evidence that hedge fund firms systematically manipulate released information. They compare the reported prices of 13F positions to the prices from CRISP and find that systematic missmarking is present. Note that we use the price information from Datastream, rather than the reported prices so we do not introduce a bias here. 24 Again, due to the large numbers of included observations the difference in the means of H is significant on the 5% level (p-value 2.97%), while it is not economically meaningful. 91

Chapter 2 Hedge Fund Herding 2.4.6 Herding and Aggregate Fund Flows An intuitive suspicion is that joint buying and selling of securities happens in response to large client money in- and outflows to the firms funds. The LSV measure takes aggregate flows to the hedge fund industry into account by controlling for the total fraction of trades which are buys. Still, the herding among the firms could be more pronounced in periods with large money flows in the industry. For example, the managers might show a tendency to simply buy low risk blue chips or a diversified portfolio of small stocks with a relatively high expected return in response to large inflows. To explore the relation we calculate the correlation between aggregate flows to our hedge fund firms and the herding measure over this period. For each hedge fund firm we obtain the percentage change in the return adjusted assets under management over all quarters, where the data is available. Then, we average over all firms for each quarter to proxy for the aggregate change at every quarter. Alternatively, we recalculate the time series with a proxy that uses absolute flows rather than percentage changes in the assets under management of the firms, and we also take the absolute (i.e. unsigned) values of both proxies. For all alternatives, corr(h t, flow t ) and corr(h t, flow t 1 ) are not significantly different from zero. Warther (1995), who analyzes the relationship between mutual fund flows and security prices, argues, that flows should be disentangled into expected and unexpected in- and outflows, because the flows follow and autoregressive process, which is presumably known by the fund managers. Given that our data on assets under management are rather incomplete and the above presented correlation does not indicate a strong impact of fund flows, we do not follow his methodology and rather restrict ourselves to the statement that aggregate fund flows (expected and unexpected) do not explain the herding behavior. 2.5 Herding at the Firm Level 2.5.1 Firm Herding Measure While various measures for the herding at the security level were proposed, the use of measures for the herding on investor level is rather limited. We introduce a new firm herding measure (FHM) for the propensity of a given firm to trade with the herd, which is based on a measure introduced by Grinblatt, Titman, and Wermers (1995). They first define a measure for the direction of the herding or signed stock herding measure that indicates whether a given firm is trading with or against the herd in a particular stock quarter i,t. The direction of herding measure (DHM) is also the basis of our measure and defined as DHM i,t = I i,t H i,t E[I i,t H i,t ] } {{ } AF i,t, (2.8) 92

Chapter 2 Hedge Fund Herding with, 0 if H i,t 0 1 if H i,t > 0 and p i,t > E[p i,t ] and firm buys i 1 if H i,t > 0 and I i,t = or p i,t < E[p i,t ] and firm sells i. p i,t > E[p i,t ] and firm sells i or p i,t < E[p i,t ] and firm buys i. (2.9) The H i,t is our standard herding measure from Section 2.4.1, which captures the herding in stock quarter i,t, i.e. the herding at the security level. It is multiplied by the indicator I i,t, which takes a value of (minus) one, if the firm is trading with (against) the herd. If there is no herding in stock quarter i,t, I i,t is zero. A minimum of at least 5 firms trading stock quarter i,t is required to make sure that there is a reasonable way to trade with or against the herd. The adjustment factor makes sure that the measure is zero for a firm that is trading independently of herds. Grinblatt, Titman, and Wermers (1995) show that the adjustment factor AF i,t must take the joint probability of b funds being buyers and the firm being a buyer in stock quarter i,t into account. For the ease of notation, we skip the indexes and denote by AF the adjustment factor for firm j trading stock quarter i,t, which is given as AF = (2p 1)H(p) Pr(B = b) p: H(p)>0 p>e[p] p: H(p)>0 p<e[p] (2p 1)H(p) Pr(B = b). (2.10) Given the number of traders N and the proxy for the expected number of buyers E[p], Pr(B = b) is given by Equation 2.4.1. H(p) is the herding measure at the stock level and is calculated for different possible fractions of buyers p and is, hence, expressed as a function of this fraction. 25 Our firm herding measure for the trading of a given firm over the period t = 1 to T is then defined as F HM = 1 T t=1 I t T I t DHM i,t. (2.11) t=1 i=1 where I t is the number of stock quarters traded by the firm at time t and which are traded by at least 5 firms. It measures the average DHM from all trades of the firm in the considered period, where each trade obtains the same weight. The FHM can take all values in the interval [+H, H], where H is the herding measure on stock level, averaged 25 Note that we do not use the conditional measures B and S as introduced in 2.4.1. Both are based on conditional adjustment factors, which make sure that each measure is zero in expectation under the null. That is why H B + S. In contrast, for the F HM it is required that the sum of both is zero under the null. 93

Chapter 2 Hedge Fund Herding over all stock-quarters traded by the firm in the period. H gives the average herding in the stocks that the firm trades. Therefore, a large (small) value for H implies that the firm trades stocks that exhibit strong (little) herding. For the FHM, a value of +H, for example, would imply that the firm is always trading with the herd, if there is herding in a security-quarter. The interpretation for less extreme cases is that a large (positive) value of FHM implies that the firm is trading with the herd more often than expected if the firm s trading was independent of the herding by the other firms. A small (negative) value would imply that the firm shows a propensity to trade against herds, and a value of zero means, that the firm s trading decisions are independent of the herding by other firms. Note, that a value of zero does not mean that there is no herding. It means that, given the herding by the other firms, the trades of the firm under consideration are not related to the herding. Compared to the original FHM of Grinblatt, Titman, and Wermers (1995), our measure represents an equally weighted and scaled version of their measure. The first difference is that they additionally weigh every DHM i,t with the absolute change in the portfolio weight of stock i in the firm s portfolio over the quarter, which takes the relative importance of each trade into account for the FHM. Since the portfolio weight of one asset can change due to changes in other positions, this implies that herding in stocks which the firm does not trade contribute to the herding measure. 26 Besides the general difficulty of measuring the size or importance of trades 27, weighing the DHM, which does not take trade sizes into account, with the trade size makes the measure difficult to interpret. Assume for example, a firm trades 10 stock-quarters and all stock-quarters exhibit the same buy herding. A firm that is a buyer in 9 of the stock-quarters and a seller in only 1 of the stock-quarters can still be an anti-herder, if the size of the sell was very large, even though it traded with the herd in 9 out of 10 trades. We stick with the original view that solely considers the direction of trades and do not introduce such a weighting scheme for our measure. The second difference is that they do not scale the FHM by the number of trades by the firm. The measure is then not bounded and its value, given some tendency to trade with or against herds, highly depends on the number of trades. 2.5.2 General Results for Herding at the Firm Level We calculate the firm herding measure for each firm F HM j, which is given as the mean over all F HM j,t for firm j. Under the null of no herding by a given firm, this mean (F HM j ) is not significantly different from zero. Differences in means can be tested with t-test, similar to the t-test used for security level herding measure (LSV). However, to distinguish between firm herding from trading with the herd and from trading against the herd, we can directly employ one-sided t-tests here, rather than specifying separate measures as for LSV (buy and sell side herding measures). One-sided t-test show that 82.45% of all firms show a significantly positive propensity to trade with the herd but no firm shows a significant tendency to trade against the herd, which means there is no 26 Merli and Roger (2011), for example, propose to weigh each trade by its dollar value (average price over the quarter times number of shares traded) instead. 27 We discussed this issue in Section 2.4.1. 94

Chapter 2 Hedge Fund Herding anti-herder. Table 2.9 shows the mean F HM j over all firms following different styles. All style groups show a significant propensity to trade with the herd. Merger arbitrage firms herd most, which is in line with our findings from Section 2.4.3. Table 2.9: Firm Herding Measure across Different Investment Styles All Equity Style Merger Arbitrage Other F HM 2.62 (0.00) 2.03 (0.00) 5.66 (0.00) 2.58 (0.00) The table contains the firm herding measures for all firms belonging to different style classes in percent. The measure is explained in Section 2.5.1. P-values are given in percent in parenthesis. To show that our fund herding measure is zero for a firm that is making its trading decisions independent of the herding by the other firms, we conduct a Monte Carlo simulation in a similar way as in Section 2.4.2. For each firm j at every quarter t where active, we use the actual number of trades N j,t, and the actual number of buys B j,t, and the particular stock-quarters (stock quarter i,t to stock quarter I,t ) which the firm trades. We then randomize the security selection by the firm. From the actual set of N j,t stockquarters traded by the firm at time t, we randomly select B j,t particular stock-quarters to be bought, and the remaining N j,t B j,t stock-quarters to be sold. Note that the fraction of buys p j,t remains the same and therefore the proxy for E[p i,t ] is not affected. The simulated security selection is repeated for every quarter where firm j was active and the simulated F HMj,t is calculated using the simulated security selections and the actual levels of herding in the traded securities. The F HMj,t is simulated for every firm and the distribution is given on the right of Figure 2.3 and the distribution of the actual F HM j,t is given on the left. Note, that not all firms can be trading independently, as we assume for the simulation exercise. Otherwise, there would not be any herding at the security level either, i.e. H = 0. Figure 2.3 rather captures random deviations of FHM around zero for each individual firm, if it is trading truly independently and where herding only results from the trading of other firms. Figure 2.3 shows that random deviations of the measure do not explain the positive values of FHM found for the firms. But we see that the averaging leads to the measure taking only very small values. If, for example, a firm follows the herd only in some trades but a significant fraction of the trading is independent of the herds, the averaging will lead to FHM increasing only slightly over this quarter. 2.5.3 Persistence of Firm Herding Similar to the LSV measure used earlier, our firm herding measure does not show whether the firm herding results from the same firms herding together permanently or from herding by various firms. The persistence in the firm herding gives an indication whether a further exploration of dynamic or static firm characteristics is likely to reveal valuable insights. To analyze the extent to which the propensity of a given firm to trade with the herd 95

Chapter 2 Hedge Fund Herding Figure 2.3: Distribution of the Firm Herding Measure The figure shows on the left the distribution of the firm herding measure F HM j,t for all firms in our sample. On the right, it shows the distribution of the corresponding simulated measure F HMj,t which come from a Monte Carlo simulation as described in Section 2.5.2. persists over time, we use the same methodology as we used in Section 2.4.4.1 to analyze the persistence in the stock herding. First, we calculate the FHM separately for each quarter and each firm where the firm is active. Then, we calculate the mean correlations between the FHM in one quarter and the following quarters. That is for each firm at each quarter t where the firm is active, we obtain corr(f HM i,t, F HM i,t+τ ), for τ = 0,..., 5 given that the firm was still active at t + τ. We average all correlations that refer to the same time gap τ to obtain the mean correlation for the particular gap. The results are given in Table 2.10. The mean correlations in Table 2.10 show a much higher persistence in the herding for firms than what we saw for the stocks. Besides influences that change dynamically, also static factors (firm characteristics) could play a role in determining, whether a firm is a herder, anti-herder, or no herder over a given quarter. Therefore, we explore potential dynamic and static factors that could influence the herding in the following. Still, the persistence is too low to indicate that the observed herding results from only a subgroup of firms herding together permanently. 96

Chapter 2 Hedge Fund Herding Table 2.10: Firm Herding Measures Intertemporal Correlations quarter mean corr. fraction active t 100.00 (0.00) 100.00 t + 1 40.73 (0.00) 96.19 t + 2 39.33 (0.00) 92.81 t + 3 38.79 (0.00) 91.22 t + 4 38.27 (0.00) 89.89 t + 5 38.30 (0.00) 88.68 The table contains the mean of the correlations between the firm herding measure at some time t and the 5 subsequent quarters. The mean correlation coefficients are given in percent and associated p-values are given in percent in parenthesis. The right column shows the fraction of the firms which are still active at subsequent quarters in percent. 2.5.4 Dynamic Influences on Firm Herding We run a panel regression of the quarterly F HM i,t on a set of time variant regressors which might influence the firms herding propensity dynamically. To specify the regression model, we include fixed effects in the time dimension to control for potential period specific effects which affect all firms. Then, we run a regression with fixed effects in the firm dimension and a model with random effects in the firm dimension. A Hausman test yields a test statistic of 78.3235 with an associated p-value of 4.70%. Hence, the null hypothesis of random effects in the firm dimension is rejected at the 5% significance level, and we specify a model with fixed effects in both dimensions. The basic regression model is given as ( ) ( ) ( ) ( ) F HM j,t = αj F + αt T β 1 F HM j,t 1 γ 1 F LOW j,t + + β 2 F HM j,t 2 γ 2 F LOW j,t 1 P ERF j,t,m3 P ERF 1.. j,t,m2 (2.12) + P ERF j,t,m1 δ P ERF + ζst D(R j,t 2,m1, R j,t 1,m3 ) + ɛ j,t j,t 1,m3 δ 6 P ERF j,t 1,m2 P ERF j,t 1,m1 where α F and α T are the N firm and T 1 time fixed effects. Such a model yields consistent coefficient estimates of the time varying regressors also for unbalanced panels. 28 To account for the observed persistence in the firm herding measure, we include two lags of F HM as regressors. 29 Firms with large inflows or outflows might show a greater propensity to herd under several explanations for herding. Therefore, F LOW measures the return adjusted percentage change in the assets under management (AUM) over a 28 We rerun all panel regressions with bootstrapped panel robust standard errors which account for potentially remaining autocorrelation and heteroscedasticity in the errors. In unreported results, the standard errors remain virtually unchanged, which confirms that the errors produced by the model do not exhibit significant autocorrelation and heteroscedasticity (Petersen (2009)). 29 This introduces a dynamic panel bias, and Chapter 1 provides a discussion why this is not an issue for unbalanced panels with large T. 97

Chapter 2 Hedge Fund Herding quarter of all funds of the given firm that are in the hedge fund database and report AUM. Hence, at least one fund of the firm must report its AUM at the beginning and at the end of a considered quarter to obtain the observation. If informational cascades explain the herding, we should see that firms that performed well are followed in their trades by other firms. This means that the well performing firms show a greater tendency to herd since the within-quarter herding is measured across all traders. In Chapter 1 we found that hedge funds react to their short-term performance relative to their peers, which is in line with earlier research. In line with these studies, we measure the short-term relative performance by the simple excess firm return over the benchmark, rather than by some more advanced performance measure, which takes the risk and serial-correlation in returns into account. Therefore, P ERF is a performance measure that relates the overall hedge fund firm s monthly return to a benchmark (BM) return and we include the standard deviation of the 6 monthly returns preceding the trading quarter (ST D) as a control variable only. The firms monthly returns are calculated as the AUM weighted return of all the firm s funds in the hedge fund database. 30 We use the mean monthly returns of all firms as one benchmark (Industry BM) and the mean monthly returns of all firms of the same style as an alternative BM (Style BM). Column I of Table 2.11 shows the results of the basic panel regression given by Equation 2.5.4, where including lagged variables and variables that need information on returns and AUM from the hedge fund data base reduces our number of observations significantly. The results for the lagged dependent variable show that the propensity to herd is positively related to the herding in the previous quarter, but the estimated coefficient is small. This result is not surprising because even if firms trade together (for whatever reason) only for a short period of time, there is a positive probability that the mandatory reporting date for the 13F filing is within this period of joint trading. The results for F LOW show that herding is not related to in- and outflows to the firms. 31 The coefficient estimates for the performance reveal that the propensity to trade with the herd is positively related to the performance in the last month of the previous quarter. The corresponding estimated coefficients for both benchmark specifications in Columns I and II are statistically significant but small. The observed results are consistent with hedge fund firms following the trades of peer firms that have performed well over the recent past (informational cascades). If the number of firms that are followers is relative large to the number of firms that are leaders, the coefficient estimate would be small. Because we cannot distinguish between the two groups, the increased dependent variable of both groups is regressed on only a few observations with outperformance and a rather large number of observations with overall average performance. It would result in a small estimated coefficient even in the presence of a strong underlying effect. Due to the lack of identification, we cannot statistically rule out that the leader-follower structure is vice 30 If AUM are not reported for a fund at a given month, we use the closest AUM observation for the fund to proxy for its size. If the fund never reports AUM, it is assumed to be of average size among all the firm s funds and if none of the funds report AUM, the return is simply the mean return among all the firm s funds. 31 In unreported results, we included the flows on a monthly level, rather than the flows over the entire quarter. The estimates for monthly flows are not significantly different from zero at any lag either. 98

Chapter 2 Hedge Fund Herding Table 2.11: Panel Regression Results for Firm Herding Dep. var.: F HMt N = 5709 I II III IV V Industry BM Style BM 1IndustryBM 1StyleBM 13F Stock Portfolio F HMt 1 +0.000240 *** (0.48) +0.000240 *** (0.47) +0.000239 *** (0.50) +0.000238 *** (0.51) +0.000226 *** (0.95) F HMt 2 +0.000151 * (8.09) +0.000151 * (8.11) +0.000158 * (6.85) +0.000158 * (6.86) +0.000147 * (8.96) F LOWt +0.000019 (68.62) +0.000019 (68.15) +0.000017 (71.35) +0.000017 (71.76) F LOWt 1 +0.000002 (96.08) +0.000002 (96.10) +0.000001 (97.91) +0.000002 (97.20) P ERFt,m3 +0.008685 (31.00) +0.009920 (25.15) +0.000047 (94.98) +0.000369 (61.82) P ERFt,m2-0.000631 (94.17) -0.002112 (80.88) +0.000800 (24.89) +0.000326 (64.08) P ERFt,m1 +0.012045 (13.07) +0.010620 (18.99) +0.001665 ** (2.07) +0.001767 ** (1.46) P ERFt 1,m3 +0.017858 ** (3.99) +0.019350 ** (2.77) +0.002280 *** (0.22) +0.001488 ** (4.55) P ERFt 1,m2-0.010580 (18.17) -0.009209 (25.06) -0.000075 (91.73) -0.000289 (68.92) P ERFt 1,m1-0.000978 (91.05) +0.000721 (93.46) +0.000437 (52.92) +0.000628 (36.68) ST D(Rt 2,m1, Rt 1,m3) -0.000226 (15.77) -0.000226 (15.82) -0.000243 (12.60) -0.000234 (14.14) 13F F LOWt -0.000000 (85.68) 13F F LOWt 1-0.000001 (68.32) 13F P ERFt 1 +0.000000 (55.31) 13F P ERFt 2 +0.000000 (49.12) R 2 0.4789 0.4789 0.4796 0.4791 0.4779 The table contains the coefficient estimates of a panel regression with fixed effects in both dimensions of F HMj,t on a set of time variant regressors. Columns I-IV refer to regressions as specified by Equation 2.5.4 with alternative definitions of perf ormance and Column V refers to a regression on variables on the 13F stock portfolio level, rather than the overall firm level. All variables are explained in Section 2.5.4. The first/second/third month of a given quarter t are denoted by m1/m2/m3. P-values are given in percent in parenthesis and ***/**/* refer to significance on the 10/5/1 percent level. 99

Chapter 2 Hedge Fund Herding versa. Firms that outperformed recently could tend to follow the crowd, for example, to contain the relative outperformance until year end. However, reputational concerns of this type are more likely to result in benchmark herding, which is not what we capture here. 32 Therefore, we conclude that our findings are most consistent with herding from informational cascades. In Columns III and IV we replace the performance measures by dummy variables, which take a value of one, if the difference between the firms monthly return and the BM return for a given firm is larger than one standard deviation of all return differentials for all other firms (of the same style) during the month. For both alternative BM the statistical significance is higher but the coefficient estimates are still small. 33 It shows that relation is truly driven by outperformance rather than underperformance. For the dummy performance measures the coefficients for the first month of the trading quarter are also significant. The month lies already within the trading period where we observe the herding. However, the correlated trading could occur only over the latter two month of the quarter. The information revealed over the first month could thus still be impacting the later trading. correlation, which could also explain the observation. On the other hand, hedge fund returns exhibit serial We do not aim at disentangling the two explanations since our finding, namely that herding is related to outperformance around the beginning of the trading period, remains unchanged. A more precise attribution of the effect requires an identification of followers and leaders from an over-the-quarter perspective, which is beyond the scope of this paper, and given the high frequent formation of herds suggested by our findings, is unlikely to allow for such an identification. Also, our number of observations is too small to run the panel regression separately for firms following different styles, which would potentially deliver further insights. In Column V of Table 2.11 we change the variables to capture flows and performance at the 13F stock portfolio level rather than at the firm level. 13F FLOW proxies for the percentage change in the value of the 13F stock portfolio that is not explained by stock returns. 13F PERF is given as the CAR of an equally weighted trade portfolio in the absence of trading costs. Even though the herding is measured as the correlated equity trading, the results suggest that the performance measured on the 13F stock portfolio level is not related to the firms propensities to trade with the herd, as the overall firm performance is. A potential explanation is the lower frequency at which we observe the portfolio holdings, as compared to the monthly frequency of the overall firm performance. Since we saw that only the overall firm performance over the last month of the previous quarter is significantly related to herding, the overall returns over this month might serve 32 If there is no common benchmark that can be invested in and there is no herding among nonoutperforming peers, the outperforming firms would need to pick some other firms to follow in the case of such a vice versa dependence. Most likely they would pick their closest competitors, which, again, results in following the trades of well performing peers (by firms which are outperformers themselves). 33 The mean monthly STD of P ERF using the style BM is 418.61bp. For example, the estimated coefficient for P ERF t 1,m3 when using the Style BM in Column II is +0.015471. Increasing the monthly return by 418.61bbp leads to an approximate increase in the FHM of only 0.0648 percentage points. For the according dummy, the coefficient estimate in Column IV of +0.001480 corresponds to an increase of the herding measure of only 0.1480 percentage points in response to an outperformance of one STD or more. 100

Chapter 2 Hedge Fund Herding as a better proxy for recent stock picking abilities than the 13F trade portfolio, which assumes the full quarter as the holding period and ignores the trade sizes. 2.5.5 Herding and Firm Characteristics In the next step, we explore which static firm characteristics influence the propensity to herd. The high persistence in the firm herding measure found earlier suggests that static firm characteristics could also be related to firm herding. In the presence of fixed effects, all models that allow for including time invariant regressors in a panel regression lead to inconsistent coefficient estimates. 34 In our fixed effects model the time invariant component of the firms herding are captured by the estimates of the firm fixed effects ˆα F j. But fixed effects estimates are only consistent if T j, which is clearly violated in our unbalanced panel. Having this shortcoming in mind, we run a linear regression of ˆα j F on a set of time invariant firm characteristics, which might be related to herding. We also use the mean firm herding measure F HM j as alternative to the fixed effect estimates. Since both dependent variables are estimates, we estimate the linear regression model using OLS with bootstrapped standard errors. Since several regressors are potentially highly correlated to the size the firm (and to each other), we run several regressions include them one after another. 35 The regression results are given in Table 2.12, where EQUITY, MERGER, and OTHER are style dummies. The coefficient estimates for the dummies confirm our earlier results. Merger arbitrage firms herd more, equity firms slightly less, and the other category does not herd significantly different from the base group. AUM is the log of the mean of the firm s AUM as specified before over the life time, which proxies for the overall size of the firms. It is not significant in any specification, so the herding is not related to overall firm size. The mean of the monthly number of funds of one firm active in the hedge fund data base is given by FUNDS, which does not have any explanatory power either. It reveals that we do not have a strong dilution effect from the aggregation of the holdings from the fund to the firm level in the 13F data. If a firm holds several funds, which trade independently of each other, the trades observed at the firm level might dilute the true direction of trading by one of the funds. For example, if one fund follows the herd and buys a particular stock but one or several other funds of the firm sell the same stock during the quarter, the firm can be a net seller and the herding remains unobserved. If the firm runs only one fund, there is no such potential dilution. Note, however, that offsetting trades imply that funds of the same firm trade the same stocks in the opposite direction. On the other hand, if the funds rather trade the same stocks in the same direction, for example due to trading on the same information from 34 E.g. pooled OLS. Petersen (2009) explicitly shows that model misspecification is rather common in the asset pricing and corporate finance literature. 35 The fixed effects coefficient estimates come from panel regression as specified by Equation 2.5.4. However, to improve the estimates by maximizing the number of included observations per firm, we include only the regressors that are significantly different from zero in Column I of Table 2.11. From 10 784 firm-quarter observations that include 57 periods we obtain estimates for 634 firms and the estimated standard errors identify 73.14% as significantly different from zero and the regression results do not change significantly from the results in Table 2.11. 101

Chapter 2 Hedge Fund Herding Table 2.12: Cross-Sectional Regression Results for Firm Herding N = 607 I II III IV V Panel A: Dep. var.: ˆα F j constant +0.016495 * (8.50) +0.021988 *** (0.00) +0.041641 *** (0.00) +0.024612 *** (0.00) +0.029180 ** (1.56) EQUITY -0.003882 * (5.32) -0.004165 ** (4.51) -0.005014 ** (1.17) -0.005372 *** (0.62) -0.005419 ** (1.09) MERGER +0.033740 *** (0.00) +0.033458 *** (0.00) +0.032643 *** (0.00) +0.031987 *** (0.00) +0.032015 *** (0.00) OTHER -0.002496 (37.50) -0.002865 (32.41) -0.004228 (12.57) -0.003796 (16.58) -0.004113 (15.93) AUM +0.000296 (55.65) +0.000348 (50.88) FUNDS +0.000010 (97.13) -0.000073 (78.91) 13F VALUE -0.000927 *** (0.74) -0.000533 (13.81) 13F STOCKS -0.000010 *** (0.05) -0.000008 ** (1.11) EXCESS STD -0.000799 ** (1.35) -0.000819 ** (1.29) -0.000756 ** (1.59) -0.000935 *** (0.31) -0.000855 *** (0.84) ALPHA +0.105647 (37.12) +0.107964 (35.16) +0.136507 (26.53) +0.105691 (38.29) +0.119192 (30.44) R 2 0.1188 0.1183 0.1295 0.1357 0.1349 Panel B: Dep. var.: F HM j constant +0.021319 *** (0.74) +0.027783 *** (0.00) +0.027968 *** (0.00) +0.028473 *** (0.00) +0.017698 * (9.59) EQUITY -0.005926 *** (0.10) -0.006455 *** (0.03) -0.006285 *** (0.03) -0.006740 *** (0.01) -0.006604 *** (0.04) MERGER +0.030037 *** (0.00) +0.029510 *** (0.00) +0.029679 *** (0.00) +0.029117 *** (0.00) +0.029228 *** (0.00) OTHER -0.002129 (37.62) -0.002788 (24.68) -0.002603 (29.52) -0.002931 (22.09) -0.002596 (32.35) AUM +0.000328 (43.41) +0.000391 (38.05) FUNDS -0.000083 (72.54) -0.000154 (53.86) 13F VALUE -0.000025 (92.95) +0.000205 (52.98) 13F STOCKS -0.000004 (10.36) -0.000005 * (8.87) EXCESS STD -0.000651 ** (1.76) -0.000679 ** (1.46) -0.000672 ** (1.15) -0.000720 *** (0.87) -0.000726 *** (0.89) ALPHA -0.010114 (92.20) -0.008595 (93.21) -0.006891 (94.41) -0.008545 (93.56) -0.019665 (85.05) R 2 0.1471 0.1464 0.1463 0.1500 0.1518 The table contains the coefficient estimates of a linear regression of estimated firm fixed effects ˆα j F and the mean firm herding measures F HM j on firm characteristics. The regression model is estimated using OLS with bootstrapped standard errors. All variables are explained in Section 2.5.5. P-values are given in percent in parenthesis and ***/**/* refer to significance on the 10/5/1 percent level. 102

Chapter 2 Hedge Fund Herding the firm s research division, there would be unobserved within-firm herding, rather than a dilution of herding with outside firms. 13F VALUE is the log of the mean of the total value of the firm s 13F stock portfolio, and 13F STOCKS contains the average number of stock positions filed in the firm s 13F reports. In Panel A of Table 2.12 the value of the 13F portfolio is significant only when the number of stocks is not included. In Panel B it is never significant but the number of stocks is still significant in Column V. When controlling for size, the number of distinct stocks could be viewed as a proxy for the focus on trading in long equity positions. Firms placing a given amount over relatively more distinct stocks might be less focused on stock-picking. Under all theoretical explanations for herding, the incentives to herd are positively related to the importance of the trades to the firms. Note that the numbers of stocks in the 13F portfolios are very large and diversification benefits from a relatively larger number of stocks should be negligible. The difference between the standard deviation of the firms monthly returns and the mean standard deviation of all firms following the same style over the same period (BM) is measured by EXCESS STD. The regression results suggest that less risky firms seem to herd more. Earlier we saw that the herding is strongest in small and high return stocks and argued that this is most consistent with herding from informational cascades in stocks with noisy signals. A generally more conservative firm has stronger incentives to follow its presumably better informed peers in such stocks than a high risk firm because the latter should be generally less reluctant to gamble on its own beliefs and minimize reputational risks. Note, that merger arbitrage style firms, which herd most, have lower risk levels, which could also explain the finding. To analyze whether the ability of herds to form on profitable opportunities translates into herders outperforming the no-herders, we include ALP HA as a measure for overall firm performance in the regression. It is the alpha from the Fung and Hsieh (2004) factor model, which we estimate separately for each firm. The coefficient estimates are insignificant in all regression specifications, so the herding does not seem to translate into overall firm performance. 2.6 Conclusion Analyzing the trades in the 13F stock positions of hedge fund firms, we find that the firms show a tendency to herd into and out of securities together. Our findings suggest that hedge fund herds form on profitable trading opportunities and do not introduce excess volatility. When we analyze herding at the security level, our results are most consistent with firms trading on the same kind of signals (correlated private information) or with following each others trades (informational cascades). We cannot clearly attribute the observed herding to one or the other of the two explanations, but when analyzing herding at the firm level, we find that the firms show a tendency to follow peer firms that outperformed just prior to the observed trading period. Hence, at least some of the herding can be attributed to firms following each other in their trades, which is consistent with the evidence of shared stock-picking ideas among hedge fund managers reported in 103

Chapter 2 Hedge Fund Herding Gray (2009). Moreover, we can rule out feedback trading, window dressing, and individual as well as aggregate flows of client money as explanations. A concern commonly expressed by hedge fund managers, is that further disclosure requirements would harm their industry because it would enable others to steal their valuable investment ideas. On the one hand, herding stands in contrast to secret strategies that are not known by others. On the other hand, our evidence is consistent with hedge fund firms trying to follow the trading of successful peers. Another concern, which frequently leads to proposals for stronger regulation, is about potentially destabilizing joint trading activities by hedge funds. We do not find evidence that hedge fund herding is destabilizing equity prices. In a survey article on the hedge fund literature, Stulz (2007) argues that given the growth of the hedge fund industry over time, and a limited number of profitable investment opportunities, hedge funds could be expected to become more similar to each other and more similar to mutual funds over time. Our findings seem to confirm his argument. The herding we find is strongest for merger arbitrage style firms, where the number of opportunities is arguably limited. Also, the levels of herding we find are comparable to the levels found for mutual funds by earlier research. Investors should have the findings in mind when assessing potential benefits from investing in hedge funds, such as diversification, and when paying high fees. Our results open several directions for future research. An over-the-quarter perspective could be used to analyze whether some follower firms persistently follow the trades of a group of leaders and how this translates into overall firm performance. It could allow quantifying how much of the observed herding results from informational cascades. However, given the high frequent nature of hedge fund trading and hedge fund herding on the one hand, and quarterly holdings data on the other hand, extending the observation window could prove to be misleading as such a long observation window might hide the within-quarter herding which we find. A further question that is raised by our results is the role of (herds of) hedge fund firms as share holders in M&A transactions. We show that merger arbitrage style firms herd most and trade into and out of profitable opportunities together. Their joint stakes in the firms might give them the power to influence management decisions to their benefit if they act together. At the same time, this joint power might not be revealed by mandatory filings of significant ownership since the corresponding ownership threshold applies to individual investors, i.e. single hedge fund firms. Finally, across all investment styles with a focus on long equity positions, the ability to detect profitable equity trading opportunities could be linked to overall firm performance, for example, to analyze whether this ability might serve as measure of investment skill which is more persistent than traditional hedge fund performance measures. 104

Chapter 2 Hedge Fund Herding 2.A Appendix 2.A.1 Tracking CDA Institutional Investors A well known issue with the CDA database is that there is no unique identifier that allows to track what is one and the same firm throughout its full life time. Instead the numeric firm identifier given (mgrno) is reused again. Also, the firm names are differently abbreviated 36 for different filings. Eventually, a company might have an official name change, too. In the original SEC s database EDGAR, however, the SEC uses an unique firm identifier 37 which does not change if a firm changes its name. Also, official name changes are properly recorded, i.e. former company names are visible. A manual check of several relevant cases reveals that the CDA identifiers are only reused after an extended period of time, which is clearly longer than one quarter. Moreover, some filings state the date of the previous report date, that is the quarter for which this firm filed the last 13F report. 38 We use this information to apply the following steps to identify firms in the CDA over time and give them an unique identifier. First, we standardize all firm names and make sure that one firm name is written in exactly the same way in all cases. Then, companies with different names but the same mgrno are considered to be the same company, which had a name change, if the filings continue from one quarter to the subsequent quarter. Also, if the stated date of the previous filing with the new company name is available, it is required to be equal to the last filing date under the previous company name. In contrast, if the first filing date under one name is not perfectly subsequent to the last filing date under the other name, they are treated as different companies. We start with 12 428 unique non standardized CDA names for the full time period of the data base 1980-2010 and obtain 10 011 unique standardized firm names and 6 662 unique firms. 2.A.2 Name Match Algorithm In the following we describe the name matching procedure that compares the firm names of all institutional investors from the CDA database to all firm names in the merged hedge fund database in order to identify institutional investors that are hedge fund management firms. For the name matching we use the firms from the entire periods from both databases. The numbers of firms that live in the period of our final sample (Q1 1995 - Q2 2009) are given in Table 2.1. As described in Appendix 2.A.1 we already took care of firm name changes in the CDA database. The hedge fund database, however, is a compiled database from several commercial hedge fund databases. There, name changes of the parent holding companies are not perfectly tracked. Taking this into account, the algorithm that we apply works as follows. 36 E.g. AIM MGMT GROUP INC vs. AIM MANAGEMENT GROUP, INC. 37 The SEC s firm identifier is called CIK. 38 This is called prdate. 105

Chapter 2 Hedge Fund Herding We compare all 10 011 unique standardized names from the CDA to all 8 072 unique standardized names from the merged database. First, we get 351 names from the merged database that perfectly match to some CDA name. Then, we compare every name from CDA to the 7 721 remaining names from the merged database. From all firm names we delete the separate words that belong to a manually defined set of less relevant words, like the abbreviation for the legal form of the firm (e.g. Inc.) because sometimes firm names appear with and sometimes without this abbreviation. From all remaining words, we consider a pair of names a match, if the first words match perfectly and all other words are the same but the order is irrelevant. A manual check shows that this algorithm works very well. In contrast, algorithms that require only some weaker similarity between the remaining relevant words are sometimes matching distinct firms, while not adding a significant number of new relevant matches because our algorithm seems to detect virtually all relevant matches already. We obtain 1 004 CDA firms out of all 6 662 unique CDA firms that have at least one matching firm from the merged hedge fund database. 1 202 out of all 8 072 firm names from the hedge fund database are matched this way. The mean (median) number of hedge fund firms matched per unique CDA firm is 1.14 (1), and the mean (median) number of individual hedge funds matched per unique CDA firm is 5.41 (3). We have 302 unique CDA firms with only one individual hedge fund in the merged database. 2.A.3 Deleting Firms with Other Business For every institutional investor which was matched to a hedge fund firm we use the most current firm name and perform an automated search with the Google API for each firm name after replacing abbreviations. the Google search. 39 The algorithm retrieves the first 4 hits (links) for The 4 pages for each firm are downloaded as html files. We obtain the number of all words for every file and search for keywords that we expect to appear differently for firms with an without side business. We then manually check the pages of a random sample of 10 firms and see that 1 does not contain any info related to that firm, 2 seem to have mutual fund or other side business. It shows that the webpages that are not containing any relevant information can be filtered out by not considering files that do not contain the name of the firm. This is true for 166 out of 1004 (16.53%) of firms and does not affect firms that live earlier in our sample differently then firms that live later in our sample. For the others, we find that, for example, the terms mutual fund or banking appear much more often for the firms having some side business. Filtering the remaining firms for all files where the detected keywords do not account for more than 1% of all words, we label 775 firms pure hedge fund firms. A second manual check of a random sample of 20 firms shows that the procedure identifies 3 firms as having side business but out only 2 of them have. Hence, the estimated mistake it makes is rather small and rather biased towards being too conservative in the 39 Sources appearing most oftern are the firm webpage (if existing), investing.businessweek.com, bloomberg.com/news, and several hedge fund information providers like hedgetracker.com and blogs like marketfolly.com. 106

Chapter 2 Hedge Fund Herding selection of pure hedge fund firms. Out of all 838 firms for which we have relevant pages, 7.5% are identified as firms that run some side business. Cici, Gibson, and Moussawi (2010) analyze differences between hedge fund firms that also run one or several mutual funds and those that do not have any business other than hedge fund management. The main source from which they obtain the names of hedge fund management firms is CISDM, which is also included in the compiled hedge fund database that we use. In order to detect those firms that also run side-by-side mutual funds, they run a name match to the firm names of all mutual fund firms included in the CDA/Spectrum S12. This database is the U.S mutual fund counterpart to the CDA database we are using for U.S. institutional investors. The standard CDA/Spectrum S12 database contains only fund names and not the names of the parent firms. But Cici, Gibson, and Moussawi (2010) have access to a proprietary file which links fund names to firm names. For 1 979 hedge fund firms they find that only 72 (3.6%) also manage mutual funds. Our ratio is slightly higher which corresponds to our algorithm being more conservative than only considering mutual fund side business in the CDA/Spectrum S12 database. 2.A.4 Obtaining Trades from Filed Positions Our identified 748 hedge fund firms reported 8 879 750 holdings in 13F securities over the full sample period. First, we have to delete 4.09% of the holdings because there is a gap in the two dates stated for the quarter that the filing refers to. 40 The remaining holdings (8 516 064) contain only unique security-firm-quarter observations, i.e. no firm has several holdings reported at the same time in the same security. We consider only filings in securities which we can identify in Thomsone One and for which we have information in Datastream. The trades of the firms are then given as the changes in the filed positions. But for a change in the filing to be included in our sample as a trade, we impose several requirements to circumvent potential biases for our herding measure. First, we consider only changes over strictly subsequent quarters. That is, the firm must have filed at least one 13F position at the end of the previous quarter. Second, we require every considered security at every quarter where it is traded by any of our firms to have price information in Datastream also at least 2 quarters before the given quarter, and also at least 2 quarters after the given quarter. This restriction makes sure the herding measures are not biased by (de)listing securities. 41 Then, we neglect all trades in securities where the number of shares outstanding changes by more than 20 percent over the quarter. This is to make sure that, for example, stock splits do not affect the herding measurement. Finally, we require the considered portfolio position to be above the minimum size requirements for the filing obligation at the beginning and at the end 40 The date in rdate is not equal to the date in fdate. It is not perfectly clear how the two relate to the actual filings period in a different way and there is some indication that their use changed over time. Since this problem exists only for a small number of filings, we delete those filings. 41 (De)listing therefore refers to securities being (excluded) included in the joint Thomson One and Datastream universe. 107

Chapter 2 Hedge Fund Herding of the period when assuming the number of shares held did not change. Alternatively, we could only consider changes where the position is filed at both subsequent reporting dates. On the one hand, we would then know the trade size of all considered trades. But on the other hand, it would imply losing potentially large (important) trades (e.g. sale of whole position). Since our main focus is on herding measures that do not take the size of the trades into account, we do include the trades in our sample for which we do not know the precise trade size. For those trades we use the average of the minimum potential trade size (e.g. a sale must be at least large enough to reduce the position to a value/number of shares which is below the filings requirement) and the maximum potential trade size (e.g. sale of whole position) as a size proxy. 108

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Chapter 2 Hedge Fund Herding Cici, G., A. Kempf, and A. Puetz (2010). Caught in the act: How hedge funds manipulate their equity positions. Working Paper, University of Cologne. Devenow, A. and I. Welch (1996). Rational herding in financial economics. European Economic Review 40 (3-5), 603 615. Falkenstein, E. G. (1996). Preferences for stock characteristics as revealed by mutual fund portfolio holdings. The Journal of Finance 51 (1), 111 135. Frey, S., P. Herbst, and A. Walter (2006). Measuring mutual fund herding - a structural approach. Froot, K. A., D. S. Scharfstein, and J. C. Stein (1992). Herd on the street: Informational innefficiencies in a market with short-term speculation. The Journal of Finance 47 (4), 1461 1484. Fung, W. and D. A. Hsieh (2004). Hedge fund benchmarks: A risk-based approach. Financial Analysts Journal 60 (5), 65 80. Gray, W. R. (2009). Do hedge fund managers identify and share profitable ideas? Working Paper, University of Chicago. Griffin, J. M. and J. Xu (2009). How smart are the smart guys?: A unique view from hedge fund stock holdings. Review of Financial Studies 22 (7), 2531 2570. Grinblatt, M., S. Titman, and R. Wermers (1995). Momentum investment strategies, portfolio performance, and herding: A study of mutual fund behavior. The American Economic Review 85 (5), 1088 1105. Hodder, J. E. and J. C. Jackwerth (2007). Incentive contracts and hedge fund management. Journal of Financial and Quantitative Analysis 42 (4), 811 826. Hodder, J. E., J. C. Jackwerth, and O. Kolokolova (2013). Recovering delisting returns of hedge funds. Journal of Financial and Quantitative Analysis, forthcoming. Lakonishok, J., A. Shleifer, R. Thaler, and R. W. Vishny (1991). Window dressing by pension fund managers. American Economic Review 81 (2), 227 231. Lakonishok, J., A. Shleifer, and R. W. Vishny (1992). The impact of institutional trading on stock prices. Journal of financial economics 32 (1), 23 43. Merli, M. and T. Roger (2011). What drives the herding behavior of individual investors? Working Paper, University of Grenoble. Nofsinger, J. R. and R. W. Sias (1999). Herding and feedback trading by institutional and individual investors. The Journal of Finance 54 (6), 2263 2295. Oehler, A. (1998). Do mutual funds specializing in german stocks herd? Markets and Portfolio Management 12 (4), 452 465. Financial Petersen, M. A. (2009). Estimating standard errors in finance panel data sets: Comparing approaches. Review of Financial Studies 22 (1), 435 480. Scharfstein, D. S. and J. C. Stein (1990). Herd behavior and investment. The American Economic Review 80 (3), 65 479. 110

Chapter 2 Hedge Fund Herding Shiller, R. J., S. Fischer, and B. M. Friedman (1984). Stock prices and social dynamics. Brookings Papers on Economic Activity (2), 457 510. Sias, R. W. (2004). Institutional herding. Review of Financial Studies 17 (1), 165 206. Stulz, R. M. (2007). Hedge funds: Perspectives 21 (2), 175 194. Past, present, and future. Journal of Economic Warther, V. A. (1995). Aggregate mutual fund flows and security returns. Journal of Financial Economics 39 (2-3), 209 235. Wermers, R. (1995). Herding, trade reversals, and cascading by institutional investors. Unpublished Working Paper, University of Colorado at Boulder. Wermers, R. (1999). Mutual fund herding and the impact on stock prices. The Journal of Finance 54 (2), 581 622. 111

Chapter 3 Audit Experts The Development of Audit Fees and Discretionary Accruals after the Appointment of Former Audit Firm Employees to Boards 112

Chapter 3 Audit Experts 3.1 Introduction The appointment of former audit firm employees, i.e. audit experts 1, to the board of directors is a common, long established practice, which has also been subject to a critical discussion for decades. 2 The debate centered around the special case when an audit firm employee switches to board of a client firm, where he was actively involved in the audit process - so called revolving door hires. Regulators feared that the potential conflicts of interest could impair the independence of the auditor and reduce the audit quality. After the high ranking accounting scandals around the beginning of the century (e.g. FlowTex 2000 (Germany), Enron-Andersen 2001 (U.S.), Worldcom 2002 (U.S.), Parmalat 2003 (Italy)), among other regulations, most countries also imposed restrictions on such appointments. 3 The previous literature has mainly focused on this special revolving door cases and the potential impairment of the audit quality. At the same time, such appointments made up for only a fraction of all appointments of audit experts even before the restrictions became effective. 4 Instead, our focus is on appointments of audit experts from any audit firm and with no relation to recent audits of the particular firm 5, which has gained little research attention so far. Also, we consider the era after several stronger regulations for the audit profession became effective. The intuitive reason for an appointment of an audit expert as director is the accounting expertise and the audit industry background (e.g. Basioudis (2007), Naiker and Sharma (2009)). But the general effects on the financial reporting from adding such expertise to the board are still not well understood (Basioudis (2007), Krishnan and Visvanathan (2008), Dhaliwal, Naiker and Navissi (2010)) and the limited empirical findings are mixed (e.g. Geiger, North, and O Connell (2005) vs. Geiger and North (2006)). In addition, the 1 Note that former audit firm employees are often denoted as financial experts which is consistent with the definition of a financial expert given in Section 407 (b) of the Sarbanes-Oxley Act from 2002. A financial expert is a person with (1) an understanding of generally accepted accounting principles and financial statements; (2) experience in (A) the preparation or auditing of financial statements of generally comparable issuers; and (B) the application of such principles in connection with the accounting for estimates, accruals, and reserves; (3) experience with internal accounting controls, and (4) an understanding of audit committee functions. The Act associates this knowledge to persons with education and experience as a public accountant or auditor or a principal financial officer, controller, or principal accounting officer of an issuer, or from a position involving the performance of similar functions. 2 Matthews, Anderson, and Edwards (1997) provide the first detailed analysis for the U.K, and Imhoff (1978) refers to critical reports from the U.S. congress starting in 1976. 3 With the tighter regulations for the audit profession regulators also introduced hiring restrictions for former audit firm employees. In the U.S., Section 407 of the Sarbanes-Oxley Act (SOX) directed the issue to the SEC, which introduced a cooling-off period on revolving door appointments of three years, which became effective in 2004. Furthermore, Section 101 (e2) specifies that only two members of the board might be Certified Public Accountants (CPA). Also the European Union introduced a cooling-off period of two years for key audit partners joining their former clients with Art. 42(3) of the Statutory Audit Directive in 2006 (European Parliament and European Council (2006)). In the U.K. a cooling-off period of two years is laid down in the Ethical Standard 2 of the Auditing Practices Board (APB) (see Auditing Practices Board (APB) (2010)) and in place since 2002 (Basioudis (2007)). 4 For the U.S. in the period prior to the introduction of hiring restrictions, Geiger, Lennox, and North (2008) report a fraction of 17% revolving door hires within all hires of accounting officers with an audit industry background. 5 Our sample does not contain revolving door hires with a recent involvement in the audit (see Section 3.4). However, it still contains some experts with their last employment at the incumbent audit firm and we address the issue in Section 3.7. 113

Chapter 3 Audit Experts stock market shows no significant reaction to appointments of independent audit experts (Geiger, Lennox, and North (2008)). However, appointing former audit firm employees to boards is still ongoing practice. Therefore, what to expect from such appointments is of interest to all addressees of financial statements, while, empirically, it is not clear, if and how the quality of the firm s financial reporting benefits from appointing such audit experts. In this chapter, we analyze how accounting expertise from former audit firm employees on company boards impacts audit effort and reporting quality. More specifically, we analyze the development of the audit fees and the discretionary accruals after the appointment of an audit expert to the board of a publicly listed company in the U.K. between 2002 and 2009. The audit fees serve as a proxy for the audit effort (Davis, Richicute, and Trompeter (1993), O Keefe, Simunic, and Stein (1994), Bell, Landsman, and Shackelford (2001), Bedard and Johnstone (2010)) and we use the discretionary accruals as a measure for the financial reporting quality (Dechow, Ge, and Schrand (2010)). In contrast to prior literature, we consider both developments to gain a better understanding of the observed changes resulting from the appointments of an audit expert. We measure the variation in the audit fees and discretionary accruals within firms over time in a panel regression framework that controls for general differences between individual firms and for common determinants. This setup ensures a clean statistical identification of audit fee and discretionary accrual developments resulting from the audit experts appointments. In contrast to cross-sectional studies, our setup requires knowledge about the engagement start dates of audit experts. We use publicly available data on the employment histories to construct a novel panel data set which allows us to track audit firm employees who switch to company boards with little or no time gap between their affiliations. Earlier research on audit expertise and its influence on the reporting quality often identifies former audit firm employees by considering the training firms where they received their accounting qualification. More recent employments are often ignored in this literature since... historical employment data is typically not available... (Naiker and Sharma (2009), p.584). This can imply extended time gaps between the affiliations, while the common view is that the shorter the gap, the stronger is the link to the audit profession (e.g. Dowdell and Krishnan (2002), Basioudis (2007), Lennox and Park (2007), Naiker and Sharma (2009)). We contribute to the existing literature in several ways. Our study is the first empirical analysis of the relation between former audit firm employees on the board, audit fees, and earnings management after several restrictions for the audit profession became effective. We provide the first detailed analysis of the general appointment effect of an audit expert on the financial reporting quality and its development over several periods. We show that after the appointment of an audit expert the audit fees increase, while at the same time the discretionary accruals decrease. The findings are consistent with the view that the appointment of an audit expert is associated with an increase in the audit effort and the financial reporting quality. While the audit fee increase concentrates on the initial years of 114

Chapter 3 Audit Experts the engagement, we observe a permanently lower level of the discretionary accruals after the appointment. Both effects are driven by audit experts who become executive directors and by companies with weak corporate governance structures and small boards. The remainder of this chapter is organized as follows. Section 3.2 reviews the literature on accounting expertise in boards. In Section 3.3 we develop our hypotheses and Section 3.4 presents the data. We introduce the empirical methodology to test our hypotheses in Section 3.5. Section 3.6 presents our main results and Section 3.7 provides several robustness checks. Section 3.8 concludes. 3.2 Related Literature So far, there are only few studies that investigate audit expert appointments to the board or the existing level of audit expertise on the board and their effect on the quality of the audit process and the financial reporting. For example, Geiger, North, and O Connell (2005) analyze the development of discretionary accruals around the appointment of new financial reporting executives by U.S. firms. They find that the accruals are stable and do not significantly change after the appointment of former audit firm employees. Their main focus is on the revolving door case, and they consider only former audit firm employees that were at manager or partner level in the audit firm. However, they also consider various control samples and find the same result. Namely, for executives from audit firms other than the company s incumbent audit firm, executives from non-audit firms, and firms that did not hire new financial reporting executives at all. In contrast, Geiger and North (2006) do not primarily focus on former audit firm employees and find that there is, similar to the more established finding for CEOs, a significant increase in the discretionary accruals before the appointment of a new CFO, followed by a significant reduction thereafter. But in line with Geiger, North, and O Connell (2005) they also report no significant difference between the discretionary accruals around the appointment of new CFO directly from the current audit firm (revolving door), as compared to appointments from other audit firms, or from non-audit firms. To the best of our knowledge, the only paper that analyzes the specific relation between audit experts on the board and audit fees is Basioudis (2007). In a cross-sectional analysis he compares the audit fees paid by companies in the U.K. in 1996/1997. His sample comprises only companies with at least one director who is a qualified chartered accountant. He distinguishes between boards with former audit firm employees who received their qualification at the incumbent audit firm, and former audit employees who received their qualification elsewhere. However, he does not consider other employments of the experts. Basioudis (2007) reports that companies with executive directors trained at the incumbent audit firm pay significantly lower audit fees than companies with former audit firm employees who were either trained at some other audit firm, or who serve only as non-executive directors. He relates the findings to a reduced engagement risk for the audit firm in these cases. In contrast, Carcello et al. (2002) use a different definition of 115

Chapter 3 Audit Experts board expertise 6 and find that higher board expertise is positively related to the audit fees. They interpret their findings as evidence for a higher-quality audit service demand from boards with more expertise. Another strand of the literature on the influence of expertise on the financial reporting is based on the expertise in the audit committee. Abbott, Parker, and Peters (2004) use U.S. data from 1991 to 1999 and analyze the association of financial expertise in the audit committee and the occurrence of a restatement or a fraud. Without distinguishing between accounting and non-accounting expertise 7, they report that firms with an audit committee that contains at least one financial expert have a lower probability of a restatement or a fraud. But more recent studies differentiate between the expert types and find that mainly accounting financial expertise drives the effects. More specifically, for U.S. data from 2000 to 2002 Krishnan and Visvanathan (2008) find that only accounting expertise has a significant positive effect on conservatism. In line with their results, for post SOX U.S. data, Dhaliwal, Naiker and Navissi (2010) also report that only accounting expertise significantly increases the accrual quality. However, they also show that a combination of accounting and non-accounting experts is most beneficial for the firms reporting quality. Naiker and Sharma (2009) go one step further and investigate the relation of former audit firm partners in the audit committee and internal controls. They analyze U.S. companies in 2004 that reported internal control deficiencies (ICDs), which are internal control weaknesses that must be disclosed under SOX 404. They find that the presence of audit experts in the audit committees is inversely related to ICDs. This holds for experts who were partners at the company s incumbent audit firm, at one of the company s former audit firms, as well as at some other audit firm. The authors conclude that the knowledge of the experts helps the firms by establishing better internal controls. In addition, they report that former audit firm employees from the current or previous audit firm are negatively related to performance-adjusted discretionary accruals. While this effect is significantly weaker when the appointment happens after a time gap of three years or more after leaving the audit firm, former audit firm employees from other audit firms with no relation to the company show no significant effect. The result of Naiker and Sharma (2009) is in line with the more general finding of Krishnan (2005) who does not differentiate between accounting and non-accounting experts and shows that expertise in the audit committee is negatively associated with internal control problems. There are only few studies that analyze the effect of audit committee expertise on the audit fees. Abbott et al. (2003a) use data from the U.S. in the pre SOX era. They do not differentiate between accounting and non-accounting experts and find that firms with expertise in the audit committee pay higher audit fees. They interpret their results as evidence for an increased demand for audit coverage. And in line with this result, Hoitash 6 They define board expertise as... the average number of outside directorships held in other corporations by non-management directors... (Carcello et al. (2002, p.372)). 7 In contrast to most of the research on expertise on the board, studies that investigate the expertise in the audit committee do not only consider accounting financial expertise (e.g. former audit firm employees), but also take into account non-accounting financial expertise (e.g. supervisory financial experts) (see Cohen et al. (2014)). The SOX definition of financial expertise follows the recommendation of the Blue Ribbon Committee s report, Improving the Effectiveness of Corporate Audit Committees, from 1999 which is also included in Section 407 (b) of the Sarbanes-Oxley Act from 2002. 116

Chapter 3 Audit Experts and Hoitash (2009) find a positive effect of accounting and non-accounting experts on the audit fees in the U.S., also for the post SOX era. 3.3 Hypotheses We focus in our analysis on the development of the audit fees and on the development of the discretionary accruals over a short time period around the appointment of an audit expert. The audit fees serve as a proxy for the audit firm s effort 8 and in line with prior literature we regard a higher level of audit fees as an indicator for a higher level of assurance (see Abbott et al. (2003b), Francis (2004), Knechel and Willekens (2006), Hoitash and Hoitash (2009)). The discretionary accruals indicate the quality of the financial statement. They reflect the part of the accruals that cannot be explained by the fundamental performance and can be interpreted as earnings management (see Dechow et al. (2010)). Also, the discretionary accruals are the most prominent proxy for audit quality, where lower levels of discretionary accruals indicate a higher audit quality. 9 Someone who has been working for an audit firm until recently adds accounting expertise to the board. Most of the existing empirical studies find that companies with more expertise on the board or in the audit committee pay higher audit fees in the cross-section (e.g. Carcello et al. (2002), Abbott et al. (2003a), Goodwin-Stewart and Kent (2006)). The common explanation is that greater expertise creates a higher demand for audit quality. But a former audit firm employee who aims at improving the accounting system can not only demand more external audit effort, but also increase the internal effort to establish better reporting mechanisms and internal controls. In line with this interpretation, Naiker and Sharma (2009) and Krishnan (2005) show that the knowledge of former audit firm employees can help firms by establishing better internal controls. The empirical evidence on whether the two efforts are generally complementary with respect to audit fees, i.e. both increase the fees, or substitutive, is mixed. Felix, Gramling, and Maletta (2001) find that internal audit effort, such as investing in the availability of internal audit, internal audit quality, and the coordination between internal and external auditors can reduce the audit fees. In line with these result, Davidson and Willie (1996) find that investments in the audit planning reduces the audit fees. In contrast, more recent studies find that internal and external audit effort are complementary (e.g. Goodwin- Stewart and Kent (2006), Hay, Knechel, and Ling (2008)). Griffin and Lont (2007) do not rely on cross-sectional differences but analyze the temporal development of audit fees around SOX. They attribute a significant part of an observed increase in audit fees to enforced internal control improvements. Griffin and Lont (2007, p.187) conclude that it... simply required auditors to apply more time and resources to examine and evaluate a costlier accounting and disclosure system. However, parts of the observed fee increase might also be a result of additional changes in the regulatory environment contained in 8 Studies that contain both, auditor hours worked and audit fees, show that audit fees can generally be used as a proxy for the audit firm s effort (e.g. Davis, Richicute, and Trompeter (1993), O Keefe, Simunic, and Stein (1994), Bell, Landsman, and Shackelford (2001), Bedard and Johnstone (2010)). 9 See Geiger and North (2006) for a detailed discussion. 117

Chapter 3 Audit Experts SOX (see Gosh and Pawlewicz (2009) for a more detailed discussion). When the appointment of an audit expert is in line with changes in the internal reporting mechanisms, the external auditor must adapt to the changes and assure the accuracy. Together with the recent empirical evidence, we conclude that the internal and external audit efforts are complementary, at least in the short run. Hence, under the view that more total effort is exerted to improve the accounting accuracy after the appointment of an audit expert, the audit fees will be higher. Also, a simply higher demand for audit services would result in higher audit fees, too. Therefore, our first hypothesis is: H1a: When a firm appoints an audit expert to the board, the audit fees will increase. From the company s perspective, the appointment of an audit expert to obtain accounting expertise in an attempt to improve the financial reporting system is rational if the expected positive relation between an expert appointment, audit effort, and accounting accuracy holds. A board that agreed on the appointment of an audit expert in the first place, should also back a resulting higher audit effort thereafter. Under this scenario, the appointment can result from an attractive job offer to an audit expert by the company, which seeks to improve its reporting quality. 10 positive relation between audit effort and audit quality. Caramanis and Lennox (2008) confirm a To the extent that audit fees proxy for audit effort, the fees should also be positively related to the audit quality. However, the empirical evidence on the general relation between audit fees and audit quality is ambiguous (see the discussion in Larcker and Richardson (2004)), because an increase in audit fees can not only result from an increase in the audit effort induced by improvements in the accounting system that must be approved by the auditor. For example, the audit expert could expose more serious internal control problems, potentially undetected in previous audits. The audit firm should respond to the higher levels of information risk by exerting more effort or by demanding a risk premium and in both cases the audit fees would increase according to the audit risk model and as suggested by the empirical evidence (e.g. Hogan and Wilkins (2008)). Also the audit expert might just be willing to accept higher audit fees. This might be the case when a former audit firm employee wants to benefit a former employer due to the social and emotional ties, without demanding anything in return for the audit client Herda and Lavelle (2011) label such behavior post-employment citizenship and explain it with theories of social exchange. Moreover, the audit expert could also offer a more lucrative deal to the statutory audit firm to make it more economically dependent on the client and, thus, reluctant to punish aggressive accounting (economic dependence). Frankel, Johnson, and Nelson (2002, p.72) point out that... although recent concerns about auditor independence have focused on the provision of nonaudit services to audit clients, it is possible that audit fees create 10 In contrast, other theories explaining the presence and consequences of audit experts on boards have to resort to more complex hiring procedures and relationships. For example, the engagement risk theory by Basioudis (2007) assumes that audit firms actively outplace employees to client firms. Herda and Lavelle (2011) rely on a strong commitment to the ex-employer after the audit firm employee quit, which continues after he works as a director for another company. 118

Chapter 3 Audit Experts similar bonding or reputational incentives. Hoitash, Markelevich, and Barragato (2007) provide some empirical evidence in support of this concern. When the proposed increase in the audit fees is also associated with an increase in the reporting quality, we should observe lower levels of discretionary accruals after the appointment of an audit expert. The alternative explanations for a fee increase give either no reason for a change in the discretionary accruals (e.g. higher control risk or social ties) or should be related to an increase in the discretionary accruals (e.g. economic dependence). Therefore, our hypothesis for the discretionary accruals corresponding to our stated audit fee hypothesis is: H1b: When a firm appoints an audit expert to the board, the discretionary accruals will decrease. If there is a higher demand for audit services from the newly appointed audit expert, the audit fees in the observed periods with the expert on the board will be higher. If, however, the audit expert manages to establish better internal controls, the quality and availability of internal audit will increase. Most likely, this will dampen the related increase of the audit fees over time (Felix, Gramling, and Maletta (2001)). Resources for internal audit could be freed up or invested in audit planning and coordination with the external auditor with a similar effect on the audit fees (Davidson and Willie (1996), Felix, Gramling, and Maletta (2001)). The company s audit firm will have approved the changes in internal structures and will have adapted its regular controlling procedures. Also, the audit firm will adapt to the newly composed board s demand for external audit services. Over time, the external audit firm also learns about the former audit firm employee s expertise and motivation. Earlier research found that auditors have greater confidence in the information received from clients when the client signals accounting competence (e.g. Beaulieu (2001)). Therefore, under our view of an increased audit effort due to changes in the financial reporting, we expect higher audit fees especially in the first engagement periods of the audit expert. H2a: The audit fee increase after the appointment of an audit expert to the board is pronounced at the beginning of the engagement and becomes weaker over time. A higher audit effort that is induced by improvements in the accounting system should permanently reduce the level of earnings management. In contrast to relatively higher audit fees at the beginning of the audit expert s engagement, the corresponding decreasing effect on the discretionary accruals should be lasting: H2b: The level of discretionary accruals is lower in all periods after the appointment of an audit expert to the board. Prior literature shows that an individual board member in an executive position has a larger impact on the company s actions than in a non-executive position (e.g. Basioudis 119

Chapter 3 Audit Experts (2007), Law (2010)). In addition, Goodwin-Stewart and Kent (2006) find that the positive link between audit fees and audit expertise on the board is stronger when the board independence is low. Also several other empirical studies document a relation between corporate governance and the audit procedure. Hereby, strong corporate governance is associated with a higher internal control effort (e.g. Larcker and Richardson (2004)), higher audit fees (e.g. Carcello et al. (2002), Abbott et al. (2003a)), a lower probability of internal control problems (e.g. Krishnan (2005)), lower earnings management (e.g. Dechow, Sloan, and Sweeney (1996), Carcello et al. (2006)), and a lower probability of a financial statement fraud (e.g. Beasley (1996)). Hence, the effect of the appointment of an audit expert on the audit fees and the reporting quality should depend on the influence of the audit expert on the board. Our hypotheses are: H3a: H3b: The audit fees will increase, when the appointed audit expert has a strong influence in the board. The discretionary accruals will decrease, when the appointed audit expert has a strong influence in the board. 3.4 Data We construct our dataset in several steps by combining information from the Reuters Fundamentals database (RF), Datastream, and the Financial Service Authority (FSA) Register. 11 The initial sample consists of all publicly listed firms with their headquarters in the U.K. available in RF (in July 2010) between 2002 and 2009 (1 942 firms). exclude all firms without a Thomson identification code (32 firms) and all financials (SIC classification equals 6; 580 firms) as common in the audit literature (e.g. We Whisenant, Sankaraguruswamy, and Raghunandan (2003)). For the remaining 1 330 firms we collected financial statement data and information about the audit firm from RF, and retrieve additional capital market information from Datastream. RF also provides information on the board members, and we obtain a list of 18 848 board members including name, position description, tenure, and age. 12 The information on audit firm employment comes from mandatory filings of the audit firms with the FSA. 13 The FSA requires firms that engage in certain regulated activities to report information on their employees. This information is available in the Financial Services Register. 14 It contains names of current and former audit firm employees together with the start and end dates of their engagements. We retrieve the information of the current and former employees from the 11 largest audit firms in the U.K. (measured by client share), which audit 81% of the companies in our dataset in 2009. For each audit 11 Further details on the construction of our dataset are given in Appendix 3.A.1. 12 RF does not provide a download function for this information and blocks usual parsing via html. We employ an algorithm with graphical parsing to retrieve the data. 13 The FSA data has also been used in Gerritzen, Jackwerth, and Plazzi (2014). 14 http://www.fsa.gov.uk/register/home.do (17 March 2014) 120

Chapter 3 Audit Experts firm employee we extract the full history of filed jobs at any FSA regulated firm and sort the jobs chronologically. We focus on audit experts with the last engagement at one of the considered audit firms only to have a minimum of elapsed time between the employment end at the audit firm and the job start on the board. Our earliest auditor job filing starts in December 2001, which is also the general start date of the register, and our observation period ends in April 2010. There are 3 875 individual audit firm employees registered over this period. 2 582 thereof end their last audit firm affiliation before the end of our final sample period (end of 2009). We run a name match algorithm, which compares the names of all 18 848 board members from RF to the names of the 2 582 former auditors and identifies 1 547 potential matches. We manually check the potential matches by comparing all available information from RF such as title, start and end dates of positions, age, education 15, and biographic information to ensure that the board member is indeed the audit expert from the FSA data. 16 We detect 110 (8.3%) firms in our sample with an identified audit expert on the board and 1 220 (91.7%) firms without an expert in our observed period. For the multivariate analyses we drop all observations with missing information on the audit firm (audit firm name, audit fees, non-audit fees) and other relevant information. Column (I) of Table 3.1 shows the resulting sample. From the increase in the number of firm-year observations for firms that appoint an audit expert (109 firms), a rather even distribution of appointments over time is visible. We make the same observation for the termination dates of the last audit firm affiliations in the FSA data, which indicates that the switching is not concentrated around special events (e.g. financial crisis, regulatory actions), but rather seems to be common business. Column (II) of Table 3.1 shows our final sample for the audit fee regressions, again separated in firms with and without an audit expert on the board. The overall sample consists of 3 742 firm-year observations from 1 042 firms. For the remaining 104 firms that appoint an audit expert we observe 474 firm-years, where 126 firm-years are before the appointment and 388 are thereafter. Column (III) of Table 3.1 shows the number of observations for the discretionary accrual regressions after dropping further 1 678 firmyear observations due to missing data. Note that the final sample period is 2003 to 2009 only because information from the previous year is required for the construction of some control variables (e.g. audit firm change). Our unique panel dataset offers two important perspectives. First, while most of the empirical work on former audit firm employees considers audit firm affiliations starting from the initial accounting training firm onwards, where a gap of several decades between an audit firm affiliation and considered non-audit firm position can be present, our sample only tracks near term switches. In fact, the median time gap between the audit firm exit 15 The audit firm engagement is required to represent a considerable career step for the individual, typically by explicitly being mentioned in the RF biography. The information on education of the board members labels only 85 of our 110 finally identified former auditors as qualified accountants and does not provide any useful information on the others. 16 The information on committee membership is incomplete. But our focus is on the board expertise anyway because the board can affect the audit committee s effectiveness (see Bedard and Gendron (2010)). In addition, Carcello et al (2002) show that the reported significant effects of the audit committee characteristics vanish when the board characteristics are taken into account. 121

Chapter 3 Audit Experts Table 3.1: Sample of Firms Column (I) Column (II) Column (III) after dropping missing auditor data after dropping further missing data for audit fee regressions after dropping further missing data for discretionary accrual regressions year with expert w/o expert all with expert w/o expert all with expert w/o expert all firm- 2002 39 202 241 - - - - years 2003 46 225 271 39 184 223 36 147 183 2004 52 262 314 45 199 244 40 149 189 2005 57 249 306 48 194 242 38 146 184 2006 71 353 424 60 279 339 42 189 231 2007 90 733 823 81 629 710 60 414 474 2008 104 1 023 1 127 100 883 983 77 592 669 2009 106 1 063 1 169 101 900 1 001 76 598 674 sum 565 4 110 4 675 474 3 268 3 742 369 2 235 2 064 before expert appointment 175 126 109 after expert appointment 390 348 260 firms 109 1 124 1 233 104 938 1 042 79 617 696 The table reports the numbers of firms and firm-years included in our sample in each year. The construction of the sample is described in Section 3.4. Column (I) shows the remaining sample after dropping only observations with missing information on the auditor and audit fees. Column (II) shows the remaining sample after dropping observations with further missing information needed for the multivariate analysis of the audit fees and Column (III) shows the remaining sample after dropping observations with missing information needed for the discretionary accruals models. The columns with expert (w/o expert) refer to observations from firms where we do (do not) observe an appointment of a former audit firm employee on the board in our sample period. 122

Chapter 3 Audit Experts and the appointment to the board is only one year. 17 18 Second, the time-series dimension of the dataset allows us to analyze the development of audit fees and discretionary accruals over time, i.e. distinguish the periods before and after the audit expert is on the board, rather than considering only cross-sectional differences. A relevant limitation of our dataset is the low number of firms with an appointment of an audit expert to the board, which restricts the statistical ability for a comparative analysis of certain subsets of firms with an audit expert or certain characteristics of audit experts. Further, while the sample relies on mandatory filings, it is not complete in the sense that it tracks each appointment of a former audit firm employee. Boards can still obtain audit experts that we do not capture, e.g. due to missing or incomplete biographic information in RF, or former audit firm employees from smaller audit firms as well as audit firms outside the U.K., which are not subject to FSA filing requirements. Also, we do not know the former position of the audit expert in the audit firms. Our analysis will be restricted by these limitations and we will address them throughout the paper. However, in most of the cases they should dilute a truly existent audit fee increases and discretionary accrual decrease and act against their statistical identification. 3.5 Method 3.5.1 Audit Fee Regression Model To identify the audit expert s effect on audit fees, we use a multivariate approach and estimate an established structural audit fee model. Similar to previous studies that analyze the role of former audit firm employees, it relies on the classical production theory motivated linear regression model for audit fees proposed by Simunic (1980) and Simunic (1984). As our literature survey shows, earlier research is predominantly based on cross-sectional regressions, which identify differences between firms (e.g. Basioudis (2007)). Instead, we take the time dimension into account and use a panel regression model, which measures the variation in the audit fees within firms over time. A Hausman test yields a large test statistic (196.211) and clearly rejects the null of a non-systematic difference in coefficients (p-value 0.000). Hence, we use a fixed effects model, where firm fixed effects capture all time invariant firm characteristics that potentially influence audit fees, like industry, and location within the U.K. (e.g. Basiudis (2007)). However, this limits our statistical ability to analyze how such characteristics affect the role of the audit experts on audit fees, and we have to resort to interaction terms. To our advantage, omitted static variables are not an issue for consistency and the fixed effects rule out a selection bias with respect to special (time-invariant) firm characteristics that influence the appointment of an audit expert. In a fixed effects panel model, 17 Note that as we work with annual data, we treat all precise start/end days during one year alike. E.g. an audit firm exit in December and board entry in the following January receives a gap value of 1 year. 18 Given that a cooling-off period of at least two years for revolving door auditors is present in our sample period, it is, thus, unlikely that our sample contains former audit firm employees that switch to ex-client s where they were recently involved in the auditing process. Still, the dataset contains both, audit experts with no connection to the incumbent audit firm (76.9%) and experts with their last employment at the incumbent audit firm (23.1%) and we control for possible differences in a robustness check in Section 3.7. 123

Chapter 3 Audit Experts a selection bias is only a problem when the selection is related to the idiosyncratic error u it, which is unlikely in short panels. We selected the audit fee determinants according to the meta-analysis of Hay, Knechel, and Wong (2006), who summarize the audit fee literature until 2003, and from relevant subsequent audit fee studies (Larcker and Richardson (2004), Basiudis (2007), Choi et al. (2008), Ghosh and Pawlewicz (2009)). For the firm size we use the natural logarithm of the total assets (lnta) and the total current assets (lntca). In line with prior literature we expect both variables to be positively related to the audit fees (e.g. Simunic (1980), Craswell, Francis, and Taylor (1995), Ghosh and Lustgarten (2006)). 19 We approximate the clients risk by an indicator variable for a loss in the fiscal year (loss), the leverage ratio (levratio), the current ratio (curratio), the return-on-assets (roa) and the Tobin s Q (tobin). While we expect a negative influence of the current ratio and the return-on-assets on the audit fees due to the lower audit risk, we expect positive signs for the loss indicator and the leverage ratio as they are positively related to audit risk (e.g. Simunic (1980), Seetharaman, Gul, and Lynn (2002), Ashbaugh, LaFond, and Mayhew (2003)). The relation of the Tobin s Q to audit fees is, however, unclear. On the one hand, an increasing value indicates better growth expectations (e.g. Daske et al. (2008)) and should, ceteris paribus, decrease the auditor s risk and lead to lower fees. On the other hand, the Tobin s Q is related to the firm performance and the diversification, which increases the complexity and, thus, the audit fees (e.g. Lang and Stulz (1994) and Ashbaugh, LaFond, and Mayhew (2003)). The Tobin s Q is similar to the commonly used market-to-book ratio (e.g. Daske et al. (2008)), but the descriptive statistics show that there is a weak significant difference in the Tobin s Q between firms with and without an appointment of an audit expert. Therefore, we use the Tobin s Q in our regressions to control for this difference, but we exchange the two variables in a robustness check in Section 3.7. For the client s complexity we use an indicator variable for IFRS (ifrs) as the client s accounting standards where the baseline standard is the national U.K. GAAP. Although the U.K. GAAP is similar to IFRS with respect to its legal origin, we follow Kim, Liu, and Zheng (2012) who show that firms with IFRS as accounting standard generally pay higher fees than firms with a local GAAP. Further, we include the absolute value of the accruals (acc) as calculated in Barth, Landsman, and Lang (2008). We expect that higher accruals induce higher audit fees because more effort is needed to validate the information (e.g. Antle et al. (2006)). To control for audit firm engagement attributes, we insert the natural logarithm of the non-audit fees (lnnaf ). The direction of the influence of non-audit fees on audit fees, however, is unclear. For example, Simunic (1984) argues that the influence depends on the price elasticity of the demand for audit services, and Wu (2006) states that the influence of the non-audit fees on the audit fees depends on the competition in the audit market. 19 It is more common in audit fee literature to use the accounts receivables together with the total inventory, rather than the total current assets, but we would lose a large number of firm-year observations for the total inventory (758). Since the total assets und the total current assets are highly correlated, we use only the accounts receivables in a robustness check in Section 3.7 to rule out misleading results due to multicollinearity. 124

Chapter 3 Audit Experts Therefore, a positive or a negative influence is possible. Also the empirical evidence shows mixed results (see the literature reviews of Beattie and Fearnley (2002), Hay, Knechel, and Wong (2006), and Schneider, Church, and Ely (2006)). Hence, there is no clear prediction for the sign of the coefficient. We also include an indicator for the first year of the audit firm engagement (initial) and follow the low-balling hypothesis by DeAngelo (1981), which is confirmed by the frequently reported lower audit fees in the initial years (e.g. Baber, Brooks, and Ricks (1987), Ettredge and Greenberg (1990), Craswell and Francis (1999), Whisenant, Sankaraguruswamy, and Raghunandan (2003)). Therefore, we expect a negative sign for the first year indicator. We include further indicators for an audit firm from the Big4 group (big4 ) and the fiscal year-end in the busy season (busy). In line with prior studies, we expect both to obtain positive coefficients because of the reported premium for potentially higher audit quality by Big4 audit firms and the general higher workload during the busy season (e.g. DeFond, Francis, and Wong (2000), Choi et al. (2008)). Furthermore, we include the reporting lag in days (lag), i.e. the time between the fiscal year end and the publication of the annual report. A higher reporting lag might be associated with a disagreement between the audit firm and the board or more effort needed due to complex structures or weak corporate governance mechanisms (see Hashim and Rahman (2011)). We follow the general agreement to expect increasing fees with an increasing reporting lag (e.g. Whisenant, Sankaraguruswamy, and Raghunandan (2003)). To control for any period specific influences that can affect the audit fees of all firms, like changes in the regulatory or market environment, we include time fixed effects, too. The resulting fixed effects model takes the form K ln (auditfees) it = α i + α t + β k expvars kit + γ 1 lnta it + γ 2 lntac it k=1 + γ 3 loss it + γ 4 levratio it + γ 5 curratio it + γ 6 roa it (3.1) + γ 7 ifrs it + γ 8 tobin it + γ 9 acc it + γ 10 lnnnaf it + γ 11 initial it + γ 12 big4 it + γ 13 busy it + γ 14 lag it + u it. where α i and α t are the firm and time fixed effects. The K experimental variables (expvars) test our hypotheses and we explain them together with their results. The model can be estimated using OLS, and we employ panel robust standard errors that deal with potentially remaining autocorrelation and heteroscedasticity in the error term u it throughout. A definition of all variables is given in Table 3.2 and descriptive statistics for the whole sample are presented in Table 3.3. Appendix 3.A.2 provides separate descriptive statistics for firms with and without an audit expert in our sample period together with statistical tests for differences in the determinants. The tests show that there are only minor differences, which rules out that our results are driven by client related risks that are not captured by the audit fee model. Also, we found no difference with respect to the number of audit firm changes, although prior research documented a relation between former audit firm employees and auditor changes (Lennox (2005), Lennox and Park (2007). 20 In 20 We observe 21 audit firm changes in the 348 firm-years with former audit firm employees on the board 125

Chapter 3 Audit Experts Table 3.2: Description of Regression Variables Dependent Variables ln(audit fees) = natural logarithm of audit fees. dacc = discretionary accruals. Main Experimental Variable audexp = dummy variable, equal to 1 if an audit expert is on the board. Other Experimental Variables audexp τ = dummy variables, equal to 1 if an audit expert is on the board and is in the τ s year of engagement, with τ = 1, 2, 3, 4, 5+, i.e. fifth and later years of engagement are collected in audexp5+. execu dummy variable, equal to 1 if an audit expert is on the board who is = (nonexecu) a (non-) executive director. largefirm dummy variable, equal to 1 if an audit expert is on the board and = (smallfirm) the firm size is above (below) the median. largeboard dummy variable, equal to 1 if an audit expert is on the board and = (smallboard) the board size is above (below) the median. highindep dummy variable, equal to 1 if an audit expert is on the board and = (lowindep) fraction of indep. directors on the board is above (below) median. highinsideown (lowinsideown) = dummy variable, equal to 1 if an audit expert is on the board and the inside ownership in the firm measured as the percentage of closely held shares is above (below) the median. Determinants lnta = natural logarithm of total assets at year-end. lntca = natural logarithm of total current assets at year-end. loss = dummy variable equal to 1if net income is negative. levratio = total liabilities divided by total assets, both at year-end. curratio = total current assets divided by total current liabilities, both at year-end. roa = net income divided by year-end total assets. ifrs = dummy variable equal to 1 if accounting standard is IFRS. tobin = total assets minus book value of equity plus market value of equity divided by total assets, all at year-end. acc = absolute value of net income before extraordinary items minus cash flow from operating activities divided by year-and total assets. lnnaf = natural logarithm of non-audit fees. initial = dummy variable equal to 1 if auditor is in first year of engagement. big4 = dummy variable equal to 1 if statutory audit firm is a Big4 audit firm. busy = dummy variable equal to 1 if the fiscal year-end is between November and March. lag = days between fiscal year-end and announcement date of annual report. yeart = dummy variable equal to 1 if year is equal to t. cta = percentage change in total assets over the year. cfo = cash flow from operations divided by total assets at year-end. lloss = dummy variable equal to 1 if company reported negative net income in previous year. The table gives descriptions of all variables used in the regression analysis. All variables are firm-year observations. The time index (t) and the firm index (i) are skipped for simplicity. 126

Chapter 3 Audit Experts Table 3.3: Descriptive Statistics for Main Regression Variables variable mean std dev median 1% 99% ln(audit fees) 4.726 1.483 4.605 1.792 8.7 audexp 0.093 0.29 0 0 1 lnta 11.289 2.301 11.292 6.269 17.031 lntca 10.34 2.258 10.396 5.052 15.809 loss 0.351 0.477 0 0 1 levratio 0.496 0.274 0.496 0.015 1.315 curratio 3.423 16.931 1.416 0.23 36.31 roa -0.036 0.272 0.033-1.144 0.348 ifrs 0.77 0.421 1 0 1 tobin 1.895 1.99 1.399 0.42 9.051 acc 0.105 0.161 0.06 0.001 0.787 lnnaf 4.038 2.19 4.227 0 8.7 initial 0.063 0.242 0 0 1 big4 0.597 0.491 1 0 1 busy 0.71 0.454 1 0 1 lag 87.632 38.066 77 29 183 dacc -0.011 0.129-0.006-0.576 0.362 cfo 0.055 0.182 0.078-0.742 0.352 cta 0.251 2.234 0.065-0.487 3.069 lloss 0.253 0.435 0 0 1 The table reports descriptive statistics for the variables used in the regression analysis introduced in Section 3.5. The underlying sample contains 3 742 (2 604) firm-year observations for variables used in the audit fee (discretionary accruals) regressions from 1 042 (696) firms (with and without an audit expert appointment) as explained in Section 3.4. Brief descriptions of the variables are given in Table 3.2. addition to the earlier described advantage of a fixed effect models, the small differences further indicates that a selection biases with respect to the firms observed characteristics is unlikely. For the selection of the control variables, we have to take into account that there is a large variety in the cited audit fee studies with respect to the underlying sample periods and the regression model specifications, i.e. single year cross-sections (e.g. Lee (1996) with OLS, or Whisenant, Sankaraguruswamy, and Raghunandan (2003) with two-stage estimation) or pooled cross-sections from multiple years (e.g. Asthana, Balsam, and Kim (2009) with OLS, or Hay, Knechel, and Li (2006) with two-stage estimation). Therefore, some of the reported coefficient estimates might be different (see Hay, Knechel, and Wong (2006)). (6.03%) and 201 audit firm changes in the 3 268 firm-years without (6.15%). Hence, audit firm changes are not differently distributed (Chi-squared p-value 0.524) among companies with and without former audit firm employees. Our sample is too small to analyze if the selection of a particular audit firm in case of a change is related to previous employments of the former audit firm employee on the board. 127

Chapter 3 Audit Experts In addition, Hay, Knechel, and Wong (2006) describe that endogeneity is one of the major problems in audit fee studies. Especially in cross-sectional models, the non-audit fees (e.g. Whisenant, Sankaraguruswamy, and Raghunandan (2003), Antle et al. (2006)) or the accruals (e.g. Antle et al. (2006)) might be endogenous. Also endogeneity can result from omitted variables (e.g. Nikolaev and van Lent (2005)). The fixed effects in our model capture the unobserved heterogeneity among firms and the exogeneity of the regressors in the time dimension matters only. Since our multivariate analysis rests on the assumption of a correctly specified audit fee model, we will address potential model misspecifications in several robustness checks in Section 3.7. To rule out any endogeneity of the nonaudit fees and the accruals we employ a test for fixed effect panel regressions described in Davidson and MacKinnon (1993, p.237ff.). The null is that the tested determinates are not endogenous. For the non-audit fees (p-value 0.694) and the accruals (p-value 0.113) the hypotheses cannot be rejected, which shows that our single-equation model is appropriate. Also, we supplement our findings with univariate tests. 21 3.5.2 Discretionary Accruals To test our hypotheses that a change in the audit fees is in line with an improvement in financial reporting or internal controls, we investigate the influence of the newly appointed audit experts on the discretionary accruals. The discretionary accruals are the most prominent measure for earnings management. They reflect the part of the accruals that cannot be explained by the fundamental performance and therefore can be interpreted as opportunistic earnings manipulation (see Dechow, Ge, and Schrand (2010)). In line with this interpretation, higher levels of discretionary accruals are generally seen as an indicator for lower reporting quality (see Dechow, Ge, and Schrand (2010)). However, in analytical models earnings management can reflect parts of the manager s communication with the market and therefore higher discretionary accruals could also be positively related to the reporting quality (e.g. Ewert and Wagenhofer (2012)). We follow the interpretation of the empirical studies and assume that lower levels of discretionary accruals indicate a higher reporting quality. We calculate the discretionary accruals (dacc) according to the modified Jones Model. The discretionary accruals are the residuals from a regression of the normal accruals on a function of sales growth, growth in credit sales, and property, plant, and equipment for each year and industry with at least 10 observations. This is in line with Geiger and North (2006) and Geiger, Lennox, and North (2008), who also focus on within-firm differences in the earnings management surrounding the appointment of new personnel. 22 21 To univariately test for differences in the audit fees before and after the hiring of an audit expert, we use a paired t-test from the class of parametric tests and the nonparametric (Wilcoxon) signed rank test. We apply the tests for differences in the audit fees and discretionary accruals to a sample that includes all possible firms with an audit expert that contain at least one observation before and one after the expert appointment to the board. We additionally require that there is no audit firm change in the included observed period, because prior research found that audit fees might decrease after an audit firm change (e.g. Simon and Francis (1988), Ettredge and Greenberg (1990), Turpen (1990), Craswell and Francis (1999)) and audit quality might be lower (see Ewelt-Knauer, Gold and Pott (2012) for an overview of various empirical studies). 22 See Geiger and North (2006) for a discussion of the methodology. For the model specification, we follow 128

Chapter 3 Audit Experts To test our hypotheses related to discretionary accruals, we use the same fixed effect panel regression framework as specified in Section 3.5.1. 23 It measures the within-firm variation in the discretionary accruals, which now serve as the left-hand side variable. As common determinants, the regression model contains the firm characteristics and audit firm attributes proposed by Dechow, Ge, and Schrand (2010). More specifically, we include firm size (lnta), performance (cfo, lloss, roa), debt (levratio), growth (cta) and the accounting standard (ifrs) as firm characteristics. To account for audit firm attributes we include the size of the audit firm (big4 ) and an indicator for the first engagement year (initial) of the audit firm. To control for any period specific influences, we also include time fixed effects. Definitions of all variables are given in Table 3.2 and descriptive statistics for the whole sample are presented in Table 3.3. Again, we supplement our findings with univariate tests. The formal regression equation for our analysis is dacc it = α i + α t + K beta k expvars kit + γ 1 lnta it + γ 2 cfo it + γ 3 loss it k=1 + γ 4 roa it + γ 5 levratio it + γ 6 cta it + γ 7 ifrs it + γ 8 big4 it + γ 9 initial it + u it. (3.2) 3.6 Main Results 3.6.1 Audit Fees and Discretionary Accruals after an Audit Expert Appointment Our main experimental variable to test our hypotheses (H1a, H1b), is an indicator which takes a value of one if a former audit firm employee, i.e. an audit expert, is on the board (audexp). 3.6.1.1 Audit Fees The results of the corresponding audit fee regression are given in Table 3.4 in Column (I). The coefficient of our variable of main interest (audexp) is positive (0.096) and significant at the 5% level. Hence, the result indicates that the audit fees increase after the appointment of an audit expert. This finding confirms our main hypothesis (H1a) that after the appointment of an audit expert the audit fees increase. There is no earlier research with a comparable setup, so our finding provides novel empirical evidence on the role of audit experts on company boards in the period under stricter regulations for the audit profession. The univariate tests also show significantly higher fees after a new audit expert is part of the board (p-values paired two-sided t-test: 0.011; signed rank test: 0.000; see Table 3.10 in Appendix 3.A.3). Geiger, Lennox, and North (2008) who additionally include property, plant and equipment in comparison to Geiger and North (2006). Only the industry classification is used as in Barth, Beaver, and Landsman (1998) due to the available data for each industry class to avoid a large loss of observations. 23 The model specification tests (Hausman and exogeneity of coefficients) confirm the accuracy of the model. 129

Chapter 3 Audit Experts Table 3.4: Panel Regression for Audit Fees Hypothesis I Hypothesis II Hypothesis III Column (I) Column (II) Column (III) Column (IV) Column (V) variable coeff sign t-stat coeff sign t-stat coeff sign t-stat coeff sign t-stat coeff sign t-stat audexp 0.096 ** (2.00) audexp1 0.163 ** (1.99) audexp2 0.209 *** (2.77) audexp3 0.101 (1.38) audexp4 0.069 (0.93) audexp5+ -0.058 (-0.72) execu 0.135 ** (2.14) nonexecu 0.047 (0.66) highindep 0.045 (0.73) lowindep 0.171 ** (2.40) largeboard 0.021 (0.32) smallboard 0.180 *** (2.70) lnta 0.501 *** (17.15) 0.501 *** (17.12) 0.502 *** (17.16) 0.500 *** (16.96) 0.503 *** (17.08) lntca -0.054 ** (-2.20) -0.054 ** (-2.21) -0.053 ** (-2.20) -0.055 ** (-2.27) -0.057 ** (-2.35) loss 0.062 *** (2.77) 0.063 *** (2.79) 0.062 *** (2.75) 0.066 *** (2.89) 0.067 *** (2.93) levratio 0.030 (0.53) 0.031 (0.56) 0.028 (0.50) 0.026 (0.46) 0.022 (0.39) curratio -0.001 ** (-2.44) -0.001 ** (-2.42) -0.001 ** (-2.44) -0.001 ** (-2.36) -0.001 ** (-2.36) roa -0.111 *** (-2.57) -0.110 ** (-2.55) -0.111 *** (-2.57) -0.103 ** (-2.36) -0.102 ** (-2.35) ifrs 0.050 (1.49) 0.054 (1.60) 0.049 (1.48) 0.064 * (1.90) 0.062 * (1.84) tobin 0.007 (1.28) 0.007 (1.23) 0.007 (1.25) 0.009 * (1.71) 0.009 * (1.70) acc 0.175 *** (3.24) 0.176 *** (3.26) 0.174 *** (3.23) 0.179 *** (3.31) 0.178 *** (3.28) lnnaf -0.038 *** (-5.89) -0.038 *** (-5.92) -0.038 *** (-5.89) -0.039 *** (-5.97) -0.039 *** (-5.97) initial -0.070 ** (-2.43) -0.070 ** (-2.44) -0.070 ** (-2.41) -0.074 ** (-2.51) -0.075 ** (-2.55) big4 0.251 *** (4.80) 0.248 *** (4.73) 0.249 *** (4.76) 0.248 *** (4.64) 0.246 *** (4.61) busy 0.155 ** (2.56) 0.150 ** (2.47) 0.155 ** (2.56) 0.159 *** (2.61) 0.151 ** (2.48) lag -0.001 (-1.63) -0.001 (-1.52) -0.001 (-1.64) -0.001 (-1.60) -0.001 (-1.62) firm-years 3 742 3 742 3 742 3 628 3 628 firms 1 042 1 042 1 042 1 010 1 010 R-sqr. 0.765 0.765 0.765 0.766 0.765 The table reports estimation results from panel regressions of the log audit fees on a set of audit fee determinants and experimental variables. The regressions include (not tabulated) firm fixed effects and time fixed effects with the base year 2003. The regressions and the included variables are described in Section 3.5, and brief descriptions of the variables are given in Table 3.2. The t-statistics from panel robust standard errors are given in parenthesis. ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively. 130

Chapter 3 Audit Experts The coefficient estimates of the control variables in the audit fee model predominantly show the expected signs. In line with prior research, the coefficient estimates for the total assets, the loss indicator, the Big4 audit firm indicator, and the indicator for the fiscal year-end in the busy season are positive and significant. Higher accruals also significantly increase the audit fees. As expected, a higher current ratio and a higher return-on-assets significantly decrease the audit fees as well as the first year of an audit firm engagement. In contrast, the negative significant coefficient of the total current assets deviates from our prediction. The coefficients of the leverage ratio, the IFRS indicator and the reporting lag are not significant. For the non-audit fees we could not derive a clear theoretical prediction, and obtain a negative and highly significant coefficient. Hay, Knechel, and Wong (2006) report positive estimates for most of the earlier audit fees studies based on single year cross-sectional or pooled cross-sectional models. Also subsequent studies for such models mainly confirm the finding (e.g. Antle et al. (2006), Hay, Knechel, and Li (2006), Asthana, Balsam, and Kim (2009). However, Krishnan and Yu (2011) also use a panel regression model and find a negative and significant coefficient, which is in line with our result. The unreported coefficients of the time fixed effects do not indicate any time trend which could have influenced the results. 3.6.1.2 Discretionary Accruals Column (I) of Table 3.5 presents our results from the discretionary accruals regression. The coefficient estimate for our audexp variable is negative (-0.018) and significant at the 10% level. The observed decrease in discretionary accruals confirms our hypothesis (H1b) that the appointment of an audit expert is associated with an increase in the reporting quality. In line with the findings, the univariate tests also show a significant decrease in the discretionary accruals (p-values paired two-sided t-test: 0.050; signed rank test: 0.025; see Table 3.10 in Appendix 3.A.3). Earlier research that analyzes earnings management in the presence of former audit firm employees mainly focuses on the revolving door case and finds mixed results. The setup most similar to ours is Geiger, North, and O Connell (2005). They do not find changes in the discretionary accruals after former audit firm managers and partners become a member of the board irrespective from which audit firm the former employees come. Hence, they do not find a... possible public accounting general knowledge effect... (Geiger, North, and O Connell (2005, p.9)). However, they analyze the relation before hiring restrictions became effective, and consider only high ranking audit firm employees. As a more general result, Geiger, North, and O Connell (2005) also find that newly appointed board members without a recent audit industry background have no significant influence on the discretionary accruals. Hence, there is no evidence that changes in discretionary accruals are driven by a general hiring effect rather than by the accounting expertise of the former audit firm employees. For the control variables we find a significant negative influence on the discretionary accruals for the cash flow from operations (cfo) and the leverage ratio (levratio) and a significant positive influence for the lagged loss (lloss), the return-on-assets (roa), the 131

Chapter 3 Audit Experts Table 3.5: Panel Regression of Discretionary Accruals Hypothesis I Hypothesis II Hypothesis III Column (I) Column (II) Column (III) Column (IV) Column (V) variable coeff sign t-stat coeff sign t-stat coeff sign t-stat coeff sign t-stat coeff sign t-stat audexp -0.018 * (-1.73) audexp1-0.027 ** (-2.08) audexp2 0.004 (0.28) audexp3-0.029 * (-1.92) audexp4-0.027 (-1.55) audexp5+ -0.026 (-1.42) execu -0.027 ** (-1.96) nonexecu -0.007 (-0.49) highindep -0.012 (-0.76) lowindep -0.024 * (-1.77) largeboard -0.008 (-0.6) smallboard -0.033 ** (-2.11) lnta -0.001 (-0.09) -0.001 (-0.10) -0.001 (-0.15) -0.001 (-0.10) -0.001 (-0.08) cfo -0.684 *** (-39.84) -0.682 *** (-39.67) -0.684 *** (-39.85) -0.675 *** (-38.49) -0.675 *** (-38.52) lloss 0.013 ** (2.29) 0.012 ** (2.17) 0.013 ** (2.28) 0.012 ** (2.04) 0.011 ** (2.03) roa 0.644 *** (53.44) 0.642 *** (53.24) 0.644 *** (53.45) 0.640 *** (52.49) 0.640 *** (52.51) levratio -0.035 ** (-2.39) -0.035 ** (-2.41) -0.035 ** (-2.36) -0.032 ** (-2.17) -0.031 ** (-2.07) cta 0.002 ** (2.22) 0.002 ** (2.23) 0.002 ** (2.22) 0.002 ** (2.24) 0.002 ** (2.24) ifrs -0.001 (-0.13) -0.002 (-0.24) -0.001 (-0.15) -0.001 (-0.16) -0.001 (-0.16) big4-0.003 (-0.23) -0.003 (-0.24) -0.003 (-0.21) -0.002 (-0.17) -0.001 (-0.1) initial 0.017 ** (2.25) 0.017 ** (2.24) 0.017 ** (2.23) 0.017 ** (2.18) 0.017 ** (2.19) firm-years 2 604 2 604 2 604 2 526 2 526 firms 696 696 696 676 676 R-sqr. 0.609 0.609 0.608 0.609 0.608 The table reports estimation results from panel regressions of the discretionary accruals on a set of determinants and experimental variables. The regressions include (not tabulated) firm fixed effects and time fixed effects with the base year 2003. The regressions and the included variables are described in Section 3.5, and brief descriptions of the variables are given in Table 3.2. The t-statistics from panel robust standard errors are given in parenthesis. ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively. 132

Chapter 3 Audit Experts change in total assets (cta) and the first year of the audit firm engagement (initial). All significant coefficients show the expected signs. Again, the unreported coefficients of the time fixed effects do not indicate any time trend. 3.6.2 Dynamics of Audit Fees and Discretionary Accruals To investigate the development of the audit fees and the discretionary accruals after the appointment of an audit expert to the board, we refine our analysis and consider the exact year of the engagement. For the statistical identification, we include five indicator variables into the regression that are equal to one if the audit expert is in the τ s year of engagement, with τ = 1, 2, 3, 4, 5 +. We collect the fifth and later years of engagement in one variable (audexp 5+ ) due to the decreasing number of observations for later years. 24 3.6.2.1 Audit Fees The results for the audit fee regression are given in Column (II) of Table 3.4. The coefficient of audexp 1 shows the effect for a zero time gap, i.e. in the start year of the engagement. The coefficient is positive (0.163) and significant at the 5% level, which indicates that former audit firm employees have a positive effect on the audit fees already in the initial engagement year. The coefficient for the second engagement year (audexp 2 ) obtains the largest estimate (0.209) and is highly significant. 25 Note, that we treat all starting dates in one year alike, therefore audexp 2 denotes the first full year with the audit expert on the board 26 which explains a maximum impact here. As the tenure increases, the positive effect on audit fees becomes weaker. The coefficients, albeit still positive for all but five or more years of tenure, are thus steadily decreasing and none is significantly different from zero anymore. The univariate tests even show higher fees in the first three (four) engagement periods compared to one year (two years) before the audit expert is part of the board (Table 3.11 in Appendix 3.A.3). The coefficients of the control variables are in line with our main regression. Overall, the results confirm our hypothesis that the increase in audit fees is centered around the first years of the audit experts engagements (H2a). Furthermore, the result highlight that the time dimension should not be ignored when analyzing the influence of former audit firm employees on the accounting procedures. 3.6.2.2 Discretionary Accruals Column (II) of Table 3.5 presents the results for the analysis of the development of the discretionary accruals over time. negative sign. Most of the audexp n coefficients show the expected Moreover, based on standard two-sided tests audexp 1 and audexp 3 are significant. The unreported one sided-tests show that also all other negative coefficients of the audexp indicators are significant. With respect to the size of the coefficients, there is no visible and statistical difference in the negative coefficients. Only the coefficient of 24 While for a three year gap (audexp 4) we still have 43 nonzero firm-year observations, the number drops to only 29 for a four year gap and even lower numbers for longer gaps. 25 Tests for differences in the coefficient, however, show that they are not significantly different from each other. 26 Unless the start day is January 1st. 133

Chapter 3 Audit Experts audexp 2 is positive but not significant with any test. The results are in line with our hypothesis (H2b) that an audit expert has a lasting effect on the reporting quality. The coefficients of the control variables are in line with our main regression. 27 3.6.3 Influence of the Audit Expert We use three proxies to test our hypothesis (H3a, H3b) that it depends on the influence of the audit expert in the board whether the audit fees and the discretionary accruals will change. For the analysis, we run one regression for each proxy. Our first proxy for the influence is the position of the audit expert on the board and we differentiate between executive and non-executive positions. Out of the 104 observed firms with an audit expert on the board, 55 (45) of these experts have a (non-)executive function. For the analysis, we include two dummy variables which indicate the executive (execu) or non-executive (nonexecu) function. In addition, we use the share of independent board members as a measure for the corporate governance to proxy for the influence of the audit expert. 28 The share of independent board members is the most widely accepted measure for corporate governance (e.g. Larcker and Richardson (2004)). We include the two dummy variables highindep and lowindep, which indicate if there is an audit expert on the board and the company has an above/below median 29 value of the governance proxy. 30 A low share of independent members indicates a lower level of corporate governance and more possible influence or potential for improvements for the audit expert. Finally, we use the board size measured by the number of board members. It captures different aspects of the firm. The size of the board is related to the size of the firm, where larger firms have larger boards. 31 Apart from the naturally higher workload, the existing level of external audit effort should be relatively higher in larger firms due to higher reputational risks for the audit firm (e.g. Hoitash, Markelevich, and Barragato (2007)). Moreover, Geiger, Lennox, and North (2008, p.63) argue, that for a small company... the internal control system (... ) may be less sophisticated than that of a large company. An already high audit effort and good internal controls might constrain potential improvements from the audit expert. Also, the size of the board is related to the complexity of the firm and we expect that the extent and the pace, at which a newly appointed audit expert can change accounting procedures to be more limited in a complex environment. 27 Unreported univariate tests partly confirm the results, but suffer from very low numbers of included observations and are not reliable. 28 For the governance proxies we use the number of board members at the end of our observation period. 29 We use the median of all firms in our sample. For each separation dummy, we test whether it is distributed differently across firm with and without an audit expert. We find no significant group differences for all our separation dummies. 30 Note that this is statistically identical to keeping the audexp variable and adding an interaction term, e.g. audexp times a strong governance indicator. The coefficient of audexp then shows the effect for weak governance firms and the interaction term captures the difference in the effect. To obtain this standard interpretation for interaction terms, both main effects must be included. Here, one main effect (strong governance firm indicator) is static and, hence, integrated in the firm fixed effect. While its estimated coefficient is not observable, the interpretation of the other two components of the interaction expression does not change. 31 The Spearman rank correlations between the mean total assets the board size is 0.67. 134

Chapter 3 Audit Experts In addition, the influence of a single board member in a large board should per se be more limited than in a small board. Overall, we expect more potential influence in smaller boards. In the regression we include the two indicators largeboard and smallboard for the identification, which indicate if there is an audit expert on the board and the company has an above/below median board size. 3.6.3.1 Audit Fees Columns (III), (IV) and (V) of Table 3.4 show the audit fee regression results for the position in the board (III), the share of independent board members (IV), and the board size (VI), respectively. In Column (III) the coefficient of the executive indicator (execu) is positive (0.135) and significant at the 5% level. The coefficient of the non-executive indicator (nonexecu) is also positive (0.047), but not significant (p-value 0.507). Hence, we obtain a significant fee increase for executive audit experts but not for non-executives experts. The regression result in Column (IV) of Table 3.4 shows that when the percentage of independence board members is low (lowindep), the audit experts have a positive (0.171) and significant (5% level) effect on the audit fees. In firms with a high fraction of independent members (highindep), the estimated coefficient is still positive (0.045) but not significant (p-value 0.468). Column (V) of Table 3.4 shows the coefficients for our last proxy, the size of the board. We observe a highly significant positive (0.180) effect for the audit expert in firms with a small board size (smallboard), but for large boards (largeboard), the coefficient is also positive (0.021) but not significant. The univariate tests confirm the regression results (Table 3.12 in the Appendix 3.A.3) and the coefficients of the control variables are in line with our main regression. Overall, the findings confirm our hypothesis (H3a) that the effect of a former audit firm employee on the audit fees is higher when the audit expert has more influence. 3.6.3.2 Discretionary Accruals Columns (III), (IV) and (V) of Table 3.5 present the corresponding results for the discretionary accruals regressions. Again, we observe significant effects for the executive position, a low percentage of independent board members, and in small boards but not in their counter groups. In particular, the coefficient of the executive indicator (execu) is negative (-0.027) and significant at the 5% level. The audit experts also have a significant (10% level) negative (-0.024) effect on the discretionary accruals when the board independence is low (lowindep), and a significant (10% level) negative (-0.024) effect in boards with a small number of members (smallboard). Hence, the results are in line with our hypothesis (H3b) and show that also the effect of the audit expert on the discretionary accruals depends on the influence of the expert. 32 The results for the control variables are in line with our main regression. Also the univariate comparisons show the same results. However, due to the splitting of the sample into two groups, the number of observations 32 Unreported results show that our findings also hold when we use the percentage of closely held shares as governance measure, where a high insider ownership indicates a lower governance (high share coefficient -0.035; p-value 0.020, low share coefficient -0.003; p-value 0.820). 135

Chapter 3 Audit Experts in the tests is rather low and the differences are not significant on a conventional level (Table 3.12 in Appendix 3.A.3). 3.7 Robustness Checks 3.7.1 Audit Firm Selection Bias As described above we observe audit experts only from the largest 11 audit firms, and we need to make sure that our key results are not driven by a selection bias with respect to the audit firms. From the 938 (617) firms without an audit expert in our audit fee (discretionary accruals) sample, we exclude 148 (72) firms with an audit firm for which we do not have employee information from the FSA database. With our new sample that consists of only audit firms for which we also have data from the FSA, we can rule out misleading results due to the audit firm selection. Column (I) of Table 3.6 for the audit fees and Column (I) of Table 3.7 for the discretionary accruals show the corresponding results. They do not significantly deviate from our main regression results. The coefficient of our experimental variable audexp in the audit fee regression is positive (0.096) and significant (p-value 0.048), similar to our main results. Also for the discretionary accruals regression, the audexp coefficient is in line with our main regression (-0.017; p-value: 0.089). The control variables are also similar. Therefore, the audit firms without information from the FSA do not influence our results. 3.7.2 Training Firm of the Audit Expert Among all 104 audit expert appointments, there are 24 cases (23.1%) where the former employer of the audit expert is the incumbent audit firm at the date of the appointment. This ratio is in line with Geiger, Lennox, and North (2008, p.65). 33 If there is a strong link between the audit expert and the incumbent audit firm, the reporting mechanisms and related control procedures, which the audit expert could suggest to a company, are more similar to the routines of the former employer than to those of other audit firms (e.g. Geiger, Lennox, and North (2008)). Moreover, the detailed knowledge about the external audit firm s requirements and testing procedures (e.g. Geiger, North, and O Connell (2005)) would allow to improve the audit planning and to reduce the audit costs (e.g. Davidson and Willie (1996)). Hence, the observed effect on the audit fees could be weaker in comparison to audit experts from other audit firms. This would be in line with the finding in Basioudis (2007). He reports that companies who employ executive directors who obtained their accounting qualification at the incumbent audit firm pay relatively less audit fees in the cross-section than companies employing other chartered accountant directors. Basioudis (2007) relates this to a reduction of the external audit firm s risk of losing on the engagement (engagement risk) in the presence of a former employee on the board. However, it is also possible that a former audit firm employee wants to benefit the former employer due to the social and emotional ties (Herda and Lavelle (2011)). In 33 Out of 1 141 hires of accounting and finance officers who previously worked for an audit firm, they observe 193 (16.9%) who were formerly employed by the incumbent audit firm. 136

Chapter 3 Audit Experts Table 3.6: Panel Regression for Audit Fees with Alternative Sample Specifications Column (I) Column (II) variable coeff sign t-stat coeff sign t-stat audexp 0.096 ** (1.98) 0.109 ** (2.06) lnta 0.522 *** (16.31) 0.487 *** (16.33) lntca -0.057 ** (-2.08) -0.055 ** (-2.23) loss 0.062 ** (2.54) 0.067 *** (2.92) levratio -0.004 (-0.06) 0.012 (0.21) curratio -0.001 *** (-2.66) -0.001 ** (-2.36) roa -0.087 * (-1.81) -0.093 ** (-2.15) ifrs 0.044 (1.22) 0.045 (1.35) tobin 0.008 (1.34) 0.009 (1.61) acc 0.202 *** (3.45) 0.151 *** (2.79) lnnaf -0.042 *** (-6.17) -0.038 *** (-5.9) initial -0.086 *** (-2.6) -0.060 ** (-2.05) big4 0.279 *** (4.68) 0.210 *** (3.79) busy 0.149 ** (2.36) 0.169 *** (2.75) lag -0.001 (-0.70) 0.000 (-1.33) firm-years 3 292 3 648 firms 894 1 023 R-sqr. 0.731 0.760 The table reports estimation results from panel regressions of the log audit fees on a set of audit fee determinants and an experimental variable. The regressions include (not tabulated) firm fixed effects and time fixed effects with the base year 2003. The regressions and the included variables are described in Section 3.7 and brief descriptions of the variables are given in Table 3.2. Compared to the sample summarized in Column (II) of Table 3.1, for the regression in Column (I) we dropped additional 128 firms without an audit expert because they have an audit firm for which we do not obtain employee information from the FSA. Compared to the sample summarized in Column (II) of Table 3.1, for the regression in Column (II) we dropped additional 19 firms because at these firms the training firm of the audit expert is the incumbent audit firm. ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively. this case, the fees could increase even more compared to other audit experts. Also, a fee increase from economic bonding is more likely in this case, as the evidence in Ye, Carson, and Simnett (2011) shows. To rule out an influence of the 24 cases where the former employer of the audit expert is the incumbent audit firm on our results, we exclude these cases in a robustness check for the audit fee and the discretionary accrual regression. Column (II) of Table 3.6 for the audit fees and Column (II) of Table 3.7 for the discretionary accruals show the results when the variable audexp does not contain the case when the training firm of the audit expert is the incumbent audit firm. 137

Chapter 3 Audit Experts Table 3.7: Panel Regression for Discretionary Accruals with Alternative Sample Specifications Column (I) Column (II) variable coeff sign t-stat coeff sign t-stat audexp -0.017 * (-1.7) -0.02 * (-1.93) lnta 0.001 (0.22) 0.001 (0.21) cfo -0.703 *** (-38.72) -0.672 *** (-38.69) lloss 0.017 *** (3.05) 0.012 ** (2.19) roa 0.636 *** (50.82) 0.635 *** (52.05) levratio -0.043 *** (-2.83) -0.031 ** (-2.06) cta 0.002 ** (2.13) 0.002 ** (2.34) ifrs -0.004 (-0.48) -0.001 (-0.14) big4 0.002 (0.13) -0.003 (-0.17) initial 0.027 *** (3.31) 0.018 ** (2.35) firm-years 2 389 2 529 firms 624 681 R-sqr. 0.598 0.605 The table reports estimation results from panel regressions of the discretionary accruals on a set of determinants and an experimental variable. The regressions include (not tabulated) firm fixed effects and time fixed effects with the base year 2003. The regressions and the included variables are described in Section 3.7 and brief descriptions of the variables are given in Table 3.2. Compared to the sample summarized in Column (III) of Table 3.1, for the regression in Column (I) we dropped additional 72 firms without an audit expert because they have an audit firm for which we do not obtain employee information from the FSA. Compared to the sample summarized in Column (III) of Table 3.1, for the regression in Column (II) we dropped additional 15 firms because at these firms the training firm of the audit expert is the incumbent audit firm. ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively. The coefficient of our experimental variable audexp has the same sign and significance level and is slightly larger (smaller) in the regression on audit fees (discretionary accruals). Also the control variables are in line with our main regressions. Therefore, our results are not biased due to audit expert from the incumbent audit firm. We refrain from a detailed analysis of these experts because of the low number of observations for this case. 3.7.3 Alternative Model Specification In the audit fee literature there is a large variety in the control variables for the audit fee regression model. To ensure that our results do not depend on the particular specification of our audit fee model, we repeat our main regression with alternative audit fee determinants suggested by prior literature and explained in detail in Section 3.5.1. First, we use the accounts receivables (lnacrec) instead of the total current assets (tca) to rule out related multicollinearity problems (Column (I)). In a second variation, we exclude the 138

Chapter 3 Audit Experts accruals from our model because they were rarely used in prior literature (Column (II)). In a third robustness check, we replace the Tobin s Q (tobin) in favor of the market-to-book ratio (mbr), which is also commonly used in audit fee studies (Column (III)). Table 3.8: Panel Regression for Audit Fees with Alternative Audit Fee Model Specifications Column (I) Column (II) Column (III) variable coeff sign t-stat coeff sign t-stat coeff sign t-stat audexp 0.093 * (1.90) 0.100 ** (2.10) 0.094 ** (1.97) lnta 0.455 *** (18.88) 0.484 *** (16.81) 0.494 *** (17.27) lntca -0.046 * (-1.91) -0.051 ** (-2.10) lnacrec 0.028 *** (3.00) loss 0.070 *** (3.02) 0.068 *** (3.00) 0.062 *** (2.74) levratio -0.004 (-0.07) 0.031 (0.56) 0.036 (0.64) curratio -0.001 ** (-2.29) -0.001 ** (-2.42) -0.001 ** (-2.45) roa -0.075 (-1.64) -0.144 *** (-3.42) -0.113 *** (-2.62) ifrs 0.056 (1.63) 0.053 (1.58) 0.048 (1.45) tobin 0.006 (1.01) 0.007 (1.23) mbr 0.001 (1.47) acc 0.203 *** (3.54) 0.174 *** (3.23) lnnaf -0.043 *** (-6.43) -0.037 *** (-5.71) -0.038 *** (-5.88) initial -0.054 * (-1.80) -0.071 ** (-2.45) -0.069 ** (-2.40) big4 0.258 *** (4.82) 0.255 *** (4.86) 0.250 *** (4.77) busy 0.162 *** (2.60) 0.142 ** (2.35) 0.158 *** (2.61) lag 0.000 (-0.75) -0.001 (-1.48) -0.001 * (-1.72) firm-years 3 564 3 742 3 742 firms 1 000 1 042 1 042 R-sqr. 0.777 0.765 0.765 The table reports estimation results from panel regressions of the log audit fees on a set of audit fee determinants and experimental variables. The regressions include (not tabulated) firm fixed effects and time fixed effects with the base year 2003. The regressions and the included variables are described in Section 3.7. Brief descriptions of the main variables are given in Table 3.2. For the tabulated regressions, we use some other additional variables: In Column (I) we use the accounts receivables (lnacrec) instead of the total current assets (lntca). In Column (II) we exclude the accruals (acc). In Column (III) we use the market-to-book ratio (mbr) instead of Tobins Q (tobin). Compared to the sample summarized in Column (II) of Table 3.1, we dropped additional 42 firms without an audit expert due to incomplete information on the accounts receivables (Column (I)). The t-statistics from panel robust standard errors are given in parenthesis. ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively. The results in Table 3.8 are in line with our main result. The coefficient estimates and associated t-statistics for our main experimental variable audexp are stable and vary only slightly from one model specification to another. Also, the audit fee determinants show no 139

Chapter 3 Audit Experts differences with respect to the signs of the estimated coefficients and only minor changes in their significance levels. 3.7.4 Other Reasons for Changes in the Discretionary Accruals Geiger and North (2006) find that there is a significant increase in the discretionary accruals before the appointment of a new CFO, followed by a significant reduction thereafter. Moreover, with accrual accounting it is possible to shift earnings into other periods, but without a sustainable effect. Higher earnings through a high level of accruals in the past might possibly yield to lower levels of accruals in future periods. Hence, the observed decrease in discretionary accruals could simply result from the reverting of the accruals, rather than from any deliberate reporting activities after the appointment of an audit expert. To address these concerns, we include an additional variable that indicates the year before the appointment of the audit expert. In unreported results, the estimated coefficient on the indicator variable is clearly not significant (p-value 0.306), and the coefficient of the variable audexp remains negative (-0.025) and is significant at the 5% level. Thus, the observed decrease of the discretionary accrual is indeed a result of the audit expert. 3.8 Conclusion This is the first empirical work that analyses the development of the audit fees and the discretionary accruals resulting from the appointment of a former audit firm employee to the board of directors in one study. Our focus is on the effect of accounting expertise, and we use data from the U.K. after several restrictions for the audit profession became effective. The results indicate that an appointment of an audit expert improves the quality of the financial reporting. More specifically, we find that after an audit expert becomes a member of the board, the audit fees increase while at the same time the discretionary accruals decrease. Our results show higher audit fees in the first years of the expert s engagement. We relate this fee increase to improvements in the financial reporting that must be audited, i.e. higher audit fees proxy for higher audit effort and come along with a higher reporting quality. Since a fee increase could also be the result of internal control problems or a demanded risk premium, we additionally analyze the discretionary accruals as a measure for the reporting quality. Our results show that the observed fee increase is indeed associated with a permanent decrease in the discretionary accruals. Both effects are driven by cases where the influence of the expert in the board is strong. Our results are robust with respect to the choice of the control variables and various sample selections. We show that the firms stakeholders and other addressees of financial reports can expect more audit effort and an improved audit quality after the appointment of a former audit firm employee to the board. Our comprehensive empirical evidence is consistent with a rational ongoing appointment practice but stands in contrast to some earlier findings on the effect of audit expert appointments on earnings management (e.g. Geiger, North, and 140

Chapter 3 Audit Experts O Connell (2005)). Also, our results raise questions about the perception of audit expert appointments by financial markets. Geiger, Lennox, and North (2008) find that the market values a direct appointment of an audit expert from the incumbent audit firm positively, but shows no significant reaction to appointments of other audit experts. 34 If this positive reaction is not solely attributable to positive signaling about the firms future prospects, but at least partly based on the expectation of an improved financial reporting, the market should reconsider its evaluation of audit experts. In addition, our findings add to the understanding of the relation between board oversight and the audit process. Also, the results highlight the need to consider the time dimension when analyzing the influence of audit experts on the financial reporting. There are several remaining questions calling for future research. When larger data sets become available, the effects from audit experts over longer horizons could be considered. Also, the analysis of factors that drive the decision to appoint a former audit firm employee could provide further insights into the practice. Moreover, longer employment histories would allow to investigate the relation of different previous career steps on the experts influence. Considering the audit experts exits from the company boards and following their subsequent career paths could lend new evidence on their motivation and expectations when taking up such a position. 34 Geiger, Lennox, and North (2008) analyze cumulative abnormal stock returns surrounding the announcement dates of appointing former audit firm employees directly from Big5 audit firms as senior accounting and finance officers in U.S. firms. The market values direct hires from the incumbent audit firm positively, but shows no significant reaction to hires of former employees from other Big5 firms and to hires of individuals with no audit industry background. 141

Chapter 3 Audit Experts 3.A Appendix 3.A.1 FSA Register and Audit Firm Selection The published guidelines by the FSA on filing requirements are very general and do not contain any details on the specifications for audit firms. Unfortunately, the FSA does not respond to research questions. The requirement to file employees seems to be triggered by a firm carrying out certain regulated activities, and most of these are in the area of finance. But the total number of audit firm employees in the register is rather large (3 875) and suggests that it is not only a few number of employees attached to side business other than auditing (e.g. consulting), which are listed. To ensure the accuracy of the FSA information, we checked the biographic and all further given information (e.g. education) in RF for all matches. 35 To identify the audit firms in the FSA Register, we started with the names of the 15 largest audit firms by client share in 2009, which we calculate using the audit firm information in RF. Using the register s search function, we find that Arthur Andersen, who was largely incorporated into Deloitte & Touch in summer 2002, never filed. Also, those auditors that are organized in networks rather than as standalone firms (e.g. Nexia) do not file as separate entities. Hence, we are left with the 11 largest audit firms that appear in the register. Since what appears to be one audit firm can have several FSA registered firms, we set the name search function to partial and carefully search for all major name parts of our identified audit firms. We include all of the found filers that appear to belong to the same audit firm (e.g. PKF (UK) LLP and PKF ACCOUNTANTS exist as separately filing firms) and we treat all filed jobs as jobs within one firm, to make sure we do not lose matches from separate filing. The incorporation of Arthur Andersen into Deloitte & Touch (2002) and the acquisition of RSM Robson Rhodes by Grant Thornton (2007) are dealt with the common firm continuance assumption. The job records also contain information on the position within the filing firm ( CF Code ). While previous research found that the rank in the audit firm plays an important role (e.g. Basioudis (2007), Law (2010)), the provided information is inconclusive and we cannot rely on it. 36 Generally, the FSA Register contains a few jobs with start dates starting from 1972/02/12, but the total number of job filings at all regulated firms explodes in December 2001 (start dates), which, therefore, appears to be the date when a widespread filing requirement became effective. Accordingly, our earliest audit job start and end dates are both in December 2001 and we use this as the start date for our FSA data. 35 For the name match algorithm, we start with stripping out all titles and nick names from the names in RF, which then mostly consist of only two words; first name and family name. The names in the FSA Register appear to be the full legal names. While they do not contain any titles or nick names, they mostly consist of three words; including a second given name. First, we require the family names to match. Further, we require every given name from RF to be included in the given names from FSA. Here, initials and full names are treated equally and the order of the given names does not matter. Since a manual check follows anyway, this assures that we do not exclude any potential matches due to abbreviations or differential ordering of given names. 36 E.g. PriceWaterhouseCoopers classifies all employees under the same CF Code. 142

Chapter 3 Audit Experts 3.A.2 Differences Among Firms With and Without an Audit Expert Table 3.9 does not indicate any obvious differences between firms that appoint an audit expert in our observed period and firms without an appointment. But note that the descriptive statistics for the firms with an audit expert in the observed period include observations before and after the appointment of the expert to the board. A comparison of firms without an expert and observations from firms with an expert but only before the appointment of the expert shows that there are only minor differences between the two groups. We conduct t-tests on mean differences for each variable for the two pooled samples. In this comparison firms that will appoint an audit expert in the future are significantly smaller with respect to total assets (p-value 0.063) and total current assets (p-value 0.049) and, which is related to the size, have less often an audit firm from the Big4 group (p-value 0.019), slightly lower audit fees (p-value 0.053), and lower reporting lags (p-value 0.095). Furthermore we observe significant differences for the share of firms with fiscal year-end in the busy season (lower for firms that will appoint an audit expert with p-value 0.014), the Tobin s Q (higher for firms that will hire an audit expert with p-value 0.093), and, due to differential time periods, a lower IFRS share (p value 0.000) for firms that will appoint an audit expert. However, there are no differences with respect to firm characteristics related to client risk (leverage ratio, current ratio, return-on-assets, and accruals). Apart from the characteristics related to size, there is no pattern visible in the differences. 143

Chapter 3 Audit Experts Table 3.9: Regression Variables Statistics - Splitted Sample Column (I) Column (II) only firms without an audit expert on the board only firms that appoint an audit expert variable mean std dev median 1% 99% mean std dev median 1% 99% audexp 0.734 0.442 1 0 1 ln(audit fees) 4.739 1.507 4.605 1.792 8.748 4.639 1.301 4.58 1.792 7.741 lnta 11.302 2.329 11.312 6.192 17.081 11.198 2.095 11.208 7.224 15.825 lntca 10.355 2.301 10.435 4.988 15.855 10.236 1.937 10.169 6.321 14.445 loss 0.346 0.476 0 0 1 0.388 0.488 0 0 1 levratio 0.493 0.277 0.491 0.012 1.315 0.519 0.258 0.519 0.032 1.258 curratio 3.602 18.062 1.429 0.213 39.359 2.187 3.498 1.321 0.258 22.263 roa -0.033 0.275 0.035-1.175 0.348-0.054 0.251 0.024-1.062 0.36 ifrs 0.784 0.411 1 0 1 0.671 0.47 1 0 1 tobin 1.904 1.993 1.41 0.419 8.699 1.833 1.973 1.299 0.42 10.26 acc 0.103 0.16 0.06 0.001 0.783 0.116 0.167 0.064 0.002 0.814 lnnaf 4.043 2.215 4.248 0 8.703 3.999 2.016 4.103 0 8.319 initial 0.062 0.24 0 0 1 0.07 0.255 0 0 1 big4 0.605 0.489 1 0 1 0.542 0.499 1 0 1 busy 0.72 0.449 1 0 1 0.643 0.479 1 0 1 lag 88.223 38.955 77 29 185 83.551 30.986 77 0 181 dacc -0.009 0.125-0.006-0.518 0.377-0.025 0.154-0.01-0.642 0.346 cfo 0.058 0.183 0.081-0.742 0.352 0.035 0.175 0.06-0.777 0.36 cta 0.254 2.361 0.067-0.481 2.576 0.232 1.217 0.058-0.548 3.915 lloss 0.244 0.43 0 0 1 0.304 0.46 0 0 1 The table reports descriptive statistics for the variables included in the main regressions introduced in Section 3.5. The underlying sample is divided in 3 268 (2 235) firm-year observations from 938 (617) firms without an audit expert used in the audit fee (discretionary accruals) regression and 474 (369) firm-year observations from 104 (79) firms that appoint an audit expert in our observed period in Panel A and B. The sample is explained in Section 3.4. Brief descriptions of the variables are given in Table 3.2. 144

Chapter 3 Audit Experts 3.A.3 Univariate Analysis Table 3.10: Univariate Analysis of Audit Fees and Discretionary Accruals Audit Fees Discretionary Accruals firms (pairs) 50 45 firm-years before the appointment 139 114 firm-years after the appointment 181 158 paired t-test two-sided 0.011 ** 0.05 ** paired t-test one-sided 0.005 *** 0.025 ** signed rank test 0.000 *** 0.025 ** The table reports results (p-values) from a univariate analysis of the audit fees and discretionary accruals. We use paired difference tests to compare the audit fees and discretionary accruals of one and the same firm without the former audit firm employee on the board to periods with the expert. The tests and the underlying samples are described in Section 3.5.2. The numbers show the p-values and ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively. Table 3.11: Univariate Analysis of Audit Fee Dynamics Panel A: One year before the appointment vs. years after the appointment t-1 to t t-1 to t+1 t-1 to t+2 t-1 to t+3 t-1 to t+4 firms (pairs) 49 39 29 20 9 paired t-test two-sided 0.226 0.100 * 0.078 * 0.097 * 0.729 paired t-test one-sided 0.113 0.050 ** 0.039 ** 0.048 ** 0.364 signed rank test 0.000 *** 0.001 *** 0.049 ** 0.161 0.952 Panel B: Two years before the appointment vs. years after the appointment t-2 to t t-2 to t+1 t-2 to t+2 t-2 to t+3 t-2 to t+4 firms (pairs) 36 30 22 17 8 paired t-test two-sided 0.081 * 0.000 *** 0.022 ** 0.053 * 0.250 paired t-test one-sided 0.040 ** 0.000 *** 0.011 ** 0.026 ** 0.125 signed rank test 0.000 *** 0.000 *** 0.012 ** 0.079 * 0.292 The table reports results (p-values) from a univariate analysis of the audit fees. We use paired difference tests to compare the audit fees of one and the same firm from one year (Panel A) and two years (Panel B) before the appointment of an audit expert to the years with the expert on the board. The tests and the underlying samples are described in Section 3.5.2. The numbers show the p-values and ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively. 145

Chapter 3 Audit Experts Table 3.12: Detailed Univariate Analysis of Audit Fees and Discretionary Accruals Column (I) Column (II) Column (III) execu non-execu small board large board non-indep. board indep. board Panel A: Results Paired Difference Tests (p-values): Audit Fees firms (pairs) 29 21 28 22 23 27 paired t-test two-sided 0.072 * 0.012 ** 0.003 *** 0.056 * 0.014 ** 0.021 ** paired t-test one-sided 0.036 ** 0.006 *** 0.001 *** 0.028 ** 0.007 *** 0.011 ** signed rank test 0.001 *** 0.001 *** 0.000 *** 0.006 *** 0.001 *** 0.002 *** Panel B: Results Paired Difference Tests (p-values): Discretionary Accruals firms (pairs) 25 20 24 21 19 26 paired t-test two-sided 0.066 * 0.221 0.04 ** 0.294 0.122 0.252 paired t-test one-sided 0.033 ** 0.110 0.020 ** 0.147 0.061 * 0.126 signed rank test 0.116 0.121 0.063 * 0.204 0.126 0.137 The table reports the results (p-values) from a univariate analysis of the audit fees (Panel A) and the discretionary accruals (Panel B). We use paired difference tests to compare the audit fees of one and the same firm without the former audit firm employee on the board to periods with the expert. The tests and the underlying samples are described in Section 3.5.2. The numbers show the p-values and ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively. 146

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Chapter 3 Audit Experts Beasley, M. S. (1996). An empirical analysis of the relation between the board of director composition and financial statement fraud. Accounting Review 71 (4), 443 465. Beattie, V. and S. Fearnley (2002). Auditor Independence and Non-audit Services: A Literature Review. London: Institute of Chartered Accountants in England & Wales. Beaulieu, P. R. (2001). The effects of judgments of new clients integrity upon risk judgments, audit evidence, and fees. Auditing: A Journal of Practice & Theory 20 (2), 85 99. Bedard, J. and Y. Gendron (2010). Strengthening the financial reporting system: Can audit committees deliver? International Journal of Auditing 14 (2), 174 210. Bedard, J. and K. Johnstone (2010). Audit partner tenure and audit planning and pricing. Auditing: A Journal of Practice & Theory 29 (2), 45 70. Bell, T. B., W. R. Landsman, and D. A. Shackelford (2001). Auditors perceived business risk and audit fees: Analysis and evidence. Journal of Accounting Research 39 (1), 35 43. Caramanis, C. and C. Lennox (2008). Audit effort and earnings management. Journal of Accounting and Economics 45 (1), 116 138. Carcello, J. V., D. R. Hermanson, T. L. Neal, and R. A. Riley Jr. (2002). Board characteristics and audit fees. Contemporary Accounting Research 19 (3), 365 384. Carcello, J. V., C. W. Hollingsworth, A. Klein, and T. L. Neal (2006). Audit committee financial expertise, competing corporate governance mechanisms, and earnings management. Working paper, University of Tennessee. Choi, J., J. Kim, X. Liu, and D. Simunic (2008). Audit pricing, legal liability regimes, and Big 4 premiums: Theory and cross-country evidence. Contemporary Accounting Research 25 (1), 55 99. Cohen, J., U. Hoitash, G. Krishnamoorthy, and A. M. Wright (2014). The effect of audit committee industry expertise on monitoring the financial reporting process. The Accounting Review 89 (1), 243 273. Craswell, A. T. and J. R. Francis (1999). Pricing initial audit engagements: A test of competing theories. Accounting Review 74 (2), 201 216. Craswell, A. T., J. R. Francis, and S. L. Taylor (1995). Auditor brand name reputations and industry specializations. Journal of Accounting and Economics 20 (3), 297 322. Daske, H., L. Hail, C. Leuz, and R. Verdi (2008). Mandatory IFRS reporting around the world: Early evidence on the economic consequences. Journal of Accounting Research 46 (5), 1085 1142. Davidson, R. and J. MacKinnon (1993). Estimation and Inference in Econometrics (1 ed.). New York: Oxford University Press. Davidson, R. A. and E. G. Willie (1996). Empirical evidence on the functional relation between audit planning and total audit effort. Journal of Accounting Research 34 (1), 111 124. 148

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Zusammenfassung (Summary in German) Diese Dissertation ist eine Sammlung von drei Forschungspapieren die während meines Promotionsstudiums im Doctoral Programme in Quantitative Economics and Finance an der Universität Konstanz entstanden sind. Die erste Studie beschäftigt sich mit der Risikonahme von Hedgefondsmanagern. Die typischen Kompensationsverträge von Hedgefondsmanagern bieten diesen Anreize, das Risiko ihrer Fonds dynamisch zu steuern. Die Studie deckt die dadurch entstandene empirisch Risikonahme im Zeitablauf auf und analysiert mögliche Erklärungsansätze für die gewonnene Struktur. Die zweite Studie analysiert ob Hedgefondsfirmen Aktien unabhängig voneinander handeln, oder ob sie gemeinsam kaufen und verkaufen, ähnlich einer Herde. Nachdem eine generelle Tendenz zu herdenähnlichem Handelsverhalten dieser Firmen aufgezeigt wird, beschäftigt sich eine detaillierte Analyse mit möglichen Erklärungsansätzen und Implikationen. Die letzte Studie analysiert den Effekt auf den Prüfungsaufwand und die Qualität der Finanzberichterstattung, wenn Unternehmen frühere Mitarbeiter von Wirtschaftsprüfungsgesellschaften ins Board of Directors berufen. Da beide Variablen von Interesse nicht direkt beobachtbar sind, wird der Verlauf von geeigneten Proxies an deren Stelle betrachtet, nachdem ein solcher Prüfungsexperte berufen wurde. Die Dissertation ist in drei Kapitel unterteilt, wobei jedes Kapitel eines der Forschungspapiere beinhaltet. Im Folgenden wird eine Zusammenfassung jeder Studie gegeben. Kapitel 1 (Hedge Fund Risk Taking) ist eine gemeinsame Arbeit mit Olga Kolokolova, in der wir die empirische Risikonahme von Hedgefondsmanagern aufdecken. Dafür benutzen wir eine Stichprobe von 714 Hedgefonds, die tägliche Fondsrenditen an Bloomberg berichten im Zeitraum von 2001 bis 2011. Während der Großteil der empirischen Hedgefondsliteratur auf monatliche Fondsrenditen zurückgreift, benutzen wir diese Stichprobe täglicher Renditen, die bisher in der Literatur keine Beachtung fand. Die tägliche Frequenz der Beobachtungen erlaubt es uns, eine Zeitreihe von monatlichen Risikomaßen (monatliche Standardabweichung täglicher Renditen) für jeden Fonds zu konstruieren. Mittels des so gewonnenen Paneldatensatzes identifizieren wir die dynamische Risikonahme der Manager in einem zweistufigen Verfahren. In einem ersten Schritt regressieren wir die monatlichen Risikomaße auf eine Reihe von erklärenden Variablen, welche sehr wahrscheinlich die aktuelle Ausprägung des Risikomaßes beeinflussen, aber keinen Zusammenhang zur Risikonahme der Manager aufweisen. Die Risikonahme ist dann in den Residuen dieser dynamischen Panelregression enthalten. In dem zweiten Schritt analysieren wir dann den 164

Zusammenfassung (Summary in German) Zusammenhang zwischen der Risikonahme (Residuen) und der Wertentwicklung der Fonds zu unterschiedlichen Zeiten im Kalenderjahr. Die theoretische Literatur sagt einen nichtlinearen Zusammenhang vorher, daher schätzen wir diesen mit nichtparametrischen Kernelregressionen und parametrischen stückweise linearen Regressionen. Unsere Ergebnisse zeigen in der Tat einen deutlich nichtlinearen Zusammenhang und eine starke saisonale Struktur in der Risikonahme. Zu Beginn eines Kalenderjahres reduzieren Fonds mit einer schlechten Wertentwicklung ihr Risiko. Gegen Ende des Jahres jedoch spekulieren sie auf ein Wiedererwachen indem sie das Risiko erhöhen. Beide genannten Risikoanpassungen sind statistisch und ökonomisch signifikant und wir analysieren die zugrundeliegenden Anreize indem wir experimentelle Variablen in die stückweise lineare Regression einbauen. Dabei zeigen wir, dass die Risikoreduktion für Fonds mit höheren Managementgebühren, kürzeren Ankündigungsfristen für den Anteilsrückkauf und kürzlich schlechter Wertentwicklung stärker ist. Diese Beobachtung ist konsistent mit einer Aversion der Manager gegen frühe Fondsliquidation und den Verlust zukünftiger Managementgebühren. Der Risikoanstieg ist nicht ausschließlich von der Existenz einer High-Water Mark und fondswertabhängiger Anreizgebühren getrieben, was auf die Präsenz anderer Anreize hindeutet, wie etwa gute Ergebnisse am Jahresende vorzulegen. Darüber hinaus zeigen wir, dass das Fondsrisiko persistent ist und die Manager dies bei ihrer dynamischen Risikosteuerung berücksichtigen. Obwohl dies nicht der Fokus unsere Arbeit ist, ergänzen wir eine Querschnittsanalyse im Appendix und vergleichen unsere Ergebnisse mit den Resultaten früherer Studien für monatlich berichtende Fonds. Dabei zeigen wir, dass die Fonds in unsere Stichprobe diesen sehr ähnlich sind, was bedeutet, das zukünftige Forschung ebenfalls von den hochfrequenten Renditedaten profitieren kann. Dieses Forschungspapier ist in der akademischen Gemeinde auf positive Resonanz gestoßen und eine frühere Version hat einen Best Paper Award auf der FRAP Konferenz in Cambridge in 2013 erhalten. Im Kapitel 2 (Hedge Fund Herding) analysiere ich den Handel in großen U.S. Aktienpositionen einer Stichprobe von 748 Hedgefondsfirmen über den Zeitraum 1995 bis 2009. Die Daten über gehaltene Aktienpositionen kommen von regulatorischen Meldungen großer institutioneller U.S. Anleger, welche verpflichtet sind, solche Aktienpositionen quartalsmäßig zu berichten. Um daraus Hedgefondsfirmen zu identifizieren, die keine anderen Geschäftsbereiche als Hedgefondsmanagement betreiben, benutze ich Daten von kommerziellen Hedgefondsdatenbanken und einen Websuchalgorithmus. Ich konstruiere meinen neuen Datensatz indem ich weitere Informationen über die Aktien aus mehreren Quellen hinzufüge. Die Analyse beginnt damit den Handel innerhalb eines Quartals auf Aktienniveau zu untersuchen. Dabei folge ich der Methode von Lakonishok, Shleifer, and Vishny (1992) und finde einen Herdeneffekt. Das bedeutet, dass die Hedgefondsfirmen eine Tendenz aufweisen, gemeinsam in Aktienpositionen hinein und hinaus zu gehen, ähnlich einer Herde. Die Stärke des Herdenverhaltens ist in etwa mit der zu vergleichen, die in früheren Studien für Publikumfonds gemessen wurde, schwankt aber erheblich für Firmen die unterschiedliche Investitionsstrategien verfolgen. Eine detaillierte Analyse zeigt, dass das beobachtete Herdenverhalten konsistent ist mit den möglichen Erklärungen, dass die Firmen unabhängig voneinander auf die gleichen Signale handeln, oder, dass die Firmen 165

Zusammenfassung (Summary in German) dem Handel anderer, vermutlich besser informierter, Kollegen folgen. Eine klare Zuordnung zu den beiden Erklärungsansätzen ist nicht möglich, wenn das Herdenverhalten auf Aktienniveau untersucht wird. Aggregierte Zu- und Abflüsse von Investorengeldern in die Hedgefondsindustrie kann ich als mögliche Erklärung jedoch ausschließen. Ebenso kann ausgeschlossen werden, dass Zukäufe von Gewinneraktien und Verkäufe von Verliereraktien kurz bevor die Aktienpositionen gemeldet werden um Investoren zu beeindrucken (window dressing) als Erklärung dienen. Eine gemeinsame Handelsstrategie bei welcher frühere Renditen als Handelssignal dienen (feedback trading) kann ich ebenso wenig erkennen. Im Gegenteil dazu haben frühere Studien für Publikumsfonds einen Teil des Herdenverhaltens dieser durch gemeinsame Momentum-Strategien (positive-feedback trading) erklärt. Meine Ergebnisse deuten darauf hin, dass sich Hedgefondsherden auf profitablen Gelegenheiten bilden und die Aktienpreise nicht destabilisieren. In einem weiteren Schritt entwickle ich ein Maß für das Herdenverhalten auf Firmenniveau, welches auf einem bereits früher vorgeschlagenem Maß basiert. Ergebnisse von dynamischen Panelregressionen zeigen, dass das gemessene Herdenverhalten von Firmen auch keinen Zusammenhang zu individuellen Zu- und Abflüssen von Investorengeldern in die Fonds aufzeigt. Jedoch zeigt sich ein Zusammenhang zur kürzlich erzielten Wertentwicklung im Vergleich zu anderen Fonds. Die Firmen in meiner Stichprobe scheinen dem Aktienhandel anderer Fonds zu folgen, welche kurz zuvor eine überdurchschnittliche Wertentwicklung verzeichneten. Daher kann zumindest ein Teil des beobachteten Herdenverhaltens gegenseitiger Verfolgung im Handel zugeordnet werden. Weiterhin zeigen Querschnittsregressionen einen negativen Zusammenhang des Herdenverhaltens der Firmen zum Firmenrisiko und zur größenadjustierten Anzahl gehaltener Aktien, was konsistent mit beiden genannten Erklärungen ist. Insgesamt sind meine Ergebnisse konsistent mit früheren Nachweisen gemeinsamen Aktienhandels von Hedgefondsmanagern und bestätigen Besorgnisse über eine unnötige Erhöhung der Preisvolatilität nicht. Gleichzeitig ergeben sich aber einige neue Frage für die zukünftige Forschung. Insbesondere das starke Herdenverhalten von Fonds, deren Investitionsstrategie auf Fusions- und Übernahmeereignisse abzielt, provoziert die Frage nach der Rolle dieser (Herden von) Hedgefondsfirmen als Aktionäre bei solchen Ereignissen. Diese und weitere Fragen werden in laufenden Forschungsprojekten untersucht, die zwar nicht Teil dieser Dissertation sind, aber auf meinem hier entwickelten Datensatz aufbauen. Dieses Forschungspapier ist in der akademischen Gemeinde auf positive Resonanz gestoßen und eine frühere Version hat einen Best Paper Award auf der ACDD Konferenz in Strasbourg in 2012 erhalten. Kapitel 3 (Audit Experts) ist eine gemeinsame Arbeit mit Benjamin Hess. Wir analysieren den Effekt der Prüfungsexpertise ehemaliger Angestellter von Wirtschaftsprüfungsgesellschaften auf den Prüfungsaufwand und die Qualität der Finanzberichterstattung. Genauer gesagt betrachten wir die Entwicklung der Prüfungsgebühren und der diskretionären Periodenabgrenzungen nachdem ein solcher Prüfungsexperte ins Board of Directors einer Firma im U.K. gewechselt hat im Zeitraum zwischen 2002 und 2009. Die Prüfungsgebühren dienen hierbei als Proxy für den Prüfungsaufwand und die diskretionären Periodenabgrenzungen dienen als Proxy für die Qualität der Finanzberichter- 166

Zusammenfassung (Summary in German) stattung. Wir messen die Variation in diesen beiden Proxies innerhalb der Unternehmen über die Zeit mit Hilfe von Paneldatenregressionen. Das Schätzverfahren kontrolliert für allgemeine Unterschiede zwischen den Unternehmen und für übliche Determinanten von Prüfungsgebühren und diskretionären Periodenabgrenzungen. Es gewährleistet dadurch eine klare statistische Identifikation von Veränderungen, die aus der Berufung von Prüfungsexperten resultieren. Die Methode erfordert allerdings die Kenntnis der Zeitpunkte solcher Berufungen. Öffentlich verfügbare Daten über Anstellungsverhältnisse erlauben uns Mitarbeiter von Prüfungsgesellschaften zu identifizieren, die ohne große Zeitlücke in ein Board berufen werden. Wir konstruieren eine neue Paneldatenbank indem wir diese Daten mit Informationen aus anderen Quellen zur Zusammensetzung von Boards, Geschäftsberichtsdaten, Informationen zu Prüfungsgesellschaften und Finanzmarktdaten verknüpfen. Unsere Ergebnisse zeigen einen Anstieg der Prüfungsgebühren den ersten Jahren nach Berufungen von Prüfungsexperten. Wir ordnen diesen Gebührenanstieg Verbesserungen in der Finanzberichterstattung zu, welche geprüft werden müssen, d.h. höhere Prüfungsgebühren als Zeichen für mehr Prüfungsaufwand der mit einer höheren Qualität der Finanzberichterstattung einhergeht. Da aber ein Anstieg der Prüfungsgebühren ebenso das Ergebnis von internen Kontrollproblemen oder einer geforderten Risikoprämie des Prüfers sein könnten, analysieren wir zusätzlich die diskretionären Periodenabgrenzungen als ein Maß für die Qualität der Finanzberichterstattung. Wir zeigen, dass der beobachtete Gebührenanstieg in der Tat mit einer permanenten Reduktion der diskretionäre Periodenabgrenzungen einhergeht. Detaillierte Ergebnisse zeigen ferner, dass beide Resultate getrieben sind von Experten die als Executive Directors berufen werden und von Unternehmen mit schwacher Corporate Governance und kleinen Boards. Dies entspricht einem stärkeren Effekt der Finanzberichterstattungsexpertise, wenn der Einfluss des bestellten Experten im Board groß ist, was wiederum den von uns dargelegten Wirkungszusammenhang bestätigt. Insgesamt zeigen unsere Ergebnisse, dass die Stakeholder der Unternehmen und andere Adressaten der Geschäftsberichte einen höheren Prüfungsaufwand und eine Verbesserung der Qualität der Finanzberichterstattung von der Berufung ehemaliger Wirtschaftsprüfungsangestellter erwarten können. Unsere umfassenden empirischen Belege sprechen für die Rationalität dieser fortwährenden Berufungspraxis, stehen jedoch im Widerspruch zu einigen früheren Ergebnissen zum Zusammenhang zwischen der Berufung von Prüfungsexperten und Bilanzpolitik. Darüber hinaus ziehen unsere Beobachtungen Fragen im Zusammenhang mit der Wahrnehmung der Finanzmärkten nach sich, da diese in früheren Studien keine signifikante Reaktion auf Expertenberufungen gezeigt haben. 167

Acknowledgments I would like to thank all those who supported and helped me during my years as a PhD student. Foremost, I thank my supervisor Jens Jackwerth for the knowledge, advice, and support that I received from him during this time. Also, I want to express my gratitude the rest of my dissertation committee: Axel Kind for acting as the second referee, and Günter Franke for chairing the committee and for his valuable feedback in seminars. I want to thank my coauthors Benjamin Hess and Olga Kolokolova for the pleasant and fruitful collaboration. I am especially grateful to Olga for being a great host in Manchester and making my time there so productive and joyful. My gratitude also goes to Bertrand Koebel, Heinrich Ursprung, Laurent Weill, and all others who made my time in Strasbourg a great experience. I gratefully acknowledge all funding sources that made this work and my research stays abroad possible. Many thanks to all my colleagues at the Institute of Finance, especially Marc Gerritzen and Anna Slavutskaya, for all the help and joy. I am very grateful to the secretary Monika Fischer for her permanent happiness and her support. Also, I thank all other colleagues from the PhD Program QEF in Konstanz and from the Augustin Cournot Doctoral School in Strasbourg who brought productivity, fun, and joy to the task. Last but not least, I thank my wife Christine and all the rest of my family for their unconditional and unlimited confidence, understanding, and support in all those years.

Record of Achievement Chapter 1 comes from joint work with Dr. Olga Kolokolova (Manchester Business School, University of Manchester). Parts of this work have been circulated as working paper with the same or a different title. My individual achievement in creating this work is 50% in the idea development and writing and 70% in the empirical part. Chapter 2 comes from my own work. Parts of this work have been circulated as working paper with the same or a different title. Chapter 3 comes from joint work with Benjamin Hess (Department of Economics, University of Konstanz). Parts of this work have been circulated as working paper with the same or a different title. My individual achievement in creating this work is 50%. Konstanz, 09.04.2014 (Achim Mattes)