Tail Risk in Hedge Funds: Evidence from Portfolio Holdings

Transcription

1 Tail Risk in Hedge Funds: Evidence from Portfolio Holdings Vikas Agarwal, Stefan Ruenzi, and Florian Weigert This Version: December 1, 2014 Abstract This paper develops a tail risk measure for hedge funds to examine if tail risk can explain the cross-section of hedge fund returns and to identify the sources of tail risk. We find that tail risk predicts next month s returns of hedge funds. We find that tail risk is positively related to fund s incentive fee, lockup period, and past year s performance, and is negatively related to the fund size and presence of high watermark provision. Using data on hedge funds long equity positions as revealed in their mandatorily disclosed quarterly holdings, we find that crash risk of equity holdings on average explains more than 30% of hedge funds overall tail risk. This relationship holds even after controlling for (a) different stock characteristics, and (b) hedge funds exposure to an out-of-the-money put option factor as in Agarwal and Naik (2004) and factors that proxy for dynamic trading strategies as in Fung and Hsieh (2004). Keywords: Hedge Funds, Crash Risk, Tail Risk, Equity Holdings JEL Classification Numbers: G11, G23 Vikas Agarwal is from Georgia State University, J. Mack Robinson College of Business, 35 Broad Street, Suite 1234, Atlanta GA 30303, USA. [email protected]: Fax: Vikas Agarwal is also a Research Fellow at the Centre for Financial Research (CFR), University of Cologne. Stefan Ruenzi is from the University of Mannheim, L9, 1-2, Mannheim, Germany. [email protected]. Tel: Florian Weigert is from the University of St. Gallen, Swiss Institute of Banking and Finance, Rosenbergstrasse 52, 9000 St. Gallen, Switzerland. [email protected]. Tel: We thank Martin Brown, John Cochrane, Andre Güttler, Juha Joenväärä, Gunter Löffler, George Panaytov, Paul Söderlind, and Fabio Trojani for their helpful comments and constructive suggestions. We benefited from the comments received at presentations at the 6th Annual Conference on Hedge Funds in Paris, the University of Mannheim, the University of St. Gallen, and the University of Ulm. 1

2 Tail Risk in Hedge Funds: Evidence from Portfolio Holdings Hedge funds are often described as pursuing trading strategies that generate small positive returns most of the time before incurring a substantial loss akin to picking up pennies in front of a steam roller or selling earthquake insurance (Duarte, Longstaff, and Yu, 2007; Stulz, 2007). Hedge funds are therefore exposed to substantial tail risk, i.e., hedge funds incur substantial losses in times when investors marginal utility is very high. However, there is limited research on how hedge funds trading strategies contribute to their overall tail risk. Our paper fills this gap in the literature by using the mandatorily reported 13F quarterly equity holdings of hedge funds from 1994 to 2007 to better understand the sources of tail risk in hedge funds. In particular, we address two research questions. First, is tail risk a priced factor in explaining the cross section of hedge fund returns? Second, what are the determinants of the tail risk of hedge funds? We make several contributions to the literature. First, we derive a new measure for hedge funds tail risk. Second, we are the first to use the mandatory 13F portfolio disclosures of hedge fund firms to analyze the tail risk that can potentially emanate from the long equity positions of hedge funds (as opposed to from their dynamic trading strategies or from their derivatives positions). We start by deriving a new non-parametric estimate for hedge funds overall tail risk based on their reported returns. This tail risk measure is based on the lower tail dependence of hedge funds returns and the market return. It is defined based on the conditional probability that an individual hedge fund has its worst individual return realizations exactly in the same months in which the market also has its worst return realizations. We show that such a tail risk measure has predictive power for the cross section of hedge fund returns. We find that hedge funds with high overall tail risk have higher future returns than hedge funds with low 2

3 overall tail risk. The return spread amounts to more than 4% p.a. in terms of the Fung and Hsieh (2004) 7-factor model and is particularly strong for equity-oriented hedge funds styles. Next, we investigate the determinants of the overall tail risk of hedge funds, i.e., why some funds are more exposed to tail risk than others and which fund characteristics are associated with strong tail risk. We document several findings. First, we observe that fund size is negatively related to fund s tail risk, suggesting that smaller funds are more exposed to extreme risk in the equity markets. 1 Second, we find that incentive fees are positively related to hedge funds tail risk, consistent with the risk-inducing behavior associated with the call option feature of the incentive fee contract (Brown, Goetzmann, and Park, 2001; Goetzmann, Ingersoll, and Ross, 2003; Hodder and Jackwerth, 2007; Aragon and Nanda, 2012). Third, we observe that high watermark provisions are negatively related to tail risk, which is consistent with the intuition that the inclusion of a high watermark in the fee contract reduces fund managers propensity to take risk as they are induced to care about the future sequence of options (Panageas and Westerfield, 2009). Finally, tail risk is positively related to a fund s lockup period and to a fund s past year returns. Tail risk being positively associated with past performance is consistent with better performing fund managers responding to the greater implicit incentives from the convexity in the flow-performance relation for hedge funds (Agarwal, Daniel, and Naik, 2003). The lockup period being positively related to tail risk suggests that funds that make more long-term and relatively illiquid investments are more likely to take extreme state-contingent bets leading to higher tail risk. There are different potential sources of hedge fund s tail risk. In particular, tail risk can be driven by: (i) writing out-of-the-money puts on the equity market (Agarwal and Naik, 2004), (ii) dynamic trading strategies of hedge funds e.g., trend-following strategies (Fung and Hsieh, 2004), and (iii) investments in equity long positions that are crash sensitive 1 This finding is different from findings for the stock market for which Chabi-Yo, Ruenzi, and Weigert (2014) document large stocks being more crash-sensitive. 3

4 (Chabi-Yo, Ruenzi, and Weigert, 2014; Kelly and Jiang, 2014). To understand which of these channels explain the tail risk of hedge funds, we first regress individual hedge funds returns on the Agarwal and Naik (2004) put option factor and call option factor (as representatives of the derivative strategies of a hedge fund), and on the Fung and Hsieh (2004) trend-following factors (as representatives of dynamic trading strategies), and on the Chabi-Yo, Ruenzi, and Weigert (2014) crash risk factor based on common equities (which proxies for tail risk stemming from long equity positions). This provides us the hedge fund return exposures (betas) with respect to this group of factors. We then analyze how the cross-sectional differences in hedge funds overall tail risk can be explained by the funds exposures to these three factors. We find that hedge funds overall tail risk is negatively related to the Agarwal and Naik (2004) put option factor, and positively related to the Chabi-Yo, Ruenzi, and Weigert (2014) equity crash risk factor. The two sensitivities together explain more than 40% of the variance of overall tail risk in the cross section of hedge fund returns. Ceteris paribus, a one standard deviation decrease (increase) in the put option beta (LTD beta) is associated with an increase of overall tail risk by 0.22 (0.11). This translates into an increase of 92% and 46% in the tail risk for put option beta and LTD beta, respectively, as the average tail risk of hedge funds is 0.24 (see Table 1). Finally, motivated by the strong exposure to the equity crash risk factor, we directly analyze the relationship between the overall tail risk of hedge funds and the characteristics of their long positions in common equity. To do so, we merge the hedge fund returns reported in the commercial hedge fund databases to the reported 13F equity portfolio holdings of hedge funds. We find that there is a positive and highly significant relationship between the overall tail risk of hedge fund firms and the crash risk of their individual long equity positions. Overall, these findings show that the tail risk of hedge funds seems to be mainly driven by put writing strategies and by investments in stocks that are crash sensitive. 4

5 Our study relates to the broad literature on the risk characteristics of hedge funds. Agarwal and Naik (2004) and Fung and Hsieh (2001, 2004) show that hedge fund returns can be described by non-standard factor models. Furthermore, Agarwal, Daniel, and Naik (2009) and Aragon and Nanda (2012) show certain hedge fund fee structures can have an impact on performance and risk taking, respectively. Closely related to our paper, Jiang and Kelly (2012) show that hedge fund returns are exposed to an equity-based crash-risk factor. Although we find results similar to theirs using an alternative method to measure tail risk, the focus of our paper is different as we investigate the determinants and sources of crosssectional variation in tail risk across hedge funds. Our results also contribute to the emerging literature on the pricing implications of crash risk in stock returns. Chabi-Yo, Ruenzi, and Weigert (2014), and Kelly and Jiang (2014) show that stocks with strong crash sensitivity deliver higher returns than stocks with weak crash sensitivity. The structure of this paper is as follows. Section 1 describes the data used in this study. Section 2 presents results on the tail risk of hedge funds. Section 3 sheds light on the impact of fee structures and other hedge fund characteristics on their tail risk as well as possible sources of tail risk. Section 4 explicitly looks at the crash risk characteristics of reported hedge fund portfolio holdings. Section 5 concludes. 1. Data Our dataset comes from two distinct sources. Our first source of self-reported hedge fund returns is created by merging five commercial databases. We refer to the merged database as Union Hedge Fund Database. Our second source is the 13F equity portfolio holdings database from Thomson Reuters (formerly the CDA/Spectrum database). The Union Hedge Fund Database consists of a merge of five different major commercial databases: CISDM, Eureka, HFR, MSCI, and Lipper TASS and includes data from 11,417 hedge funds (6,245 equity-oriented funds). The use of multiple databases to 5

6 achieve a comprehensive coverage is important since 71% of the funds only report to one database (e.g., CISDM has 25.8% unique funds). 2 Since commercial hedge fund databases started tracking defunct hedge funds since 1994, to eliminate survivorship bias we start our sample period in Moreover, we eliminate the first 12 months of each fund s return series to avoid backfilling bias, which leaves us with a final sample of 7,694 distinct selfreporting hedge funds. We use this sample in Sections 2 to 4 when investigating the pricing of tail risk in the cross section of hedge fund returns and the determinants of tail risk. The 13F Thomson Reuters Ownership database consists of quarterly equity holdings of 5,188 institutional investors during the period from 1980 (when Thomson Reuters data starts) to Unfortunately, hedge funds are not separately identified in this database. Hence, we follow Agarwal, Fos, and Jiang (2013) to manually classify a 13F filing institution as a hedge fund firm if it satisfies at least one of the following five criteria: (i) it matches the name of one or multiple funds from the Union Hedge Fund Database, (ii) it is listed by industry publications (e.g., Hedge Fund Group, Barron's, Alpha Magazine) as one of the top hedge funds, (iii) on the firm s website, hedge fund management is identified as a major line of business, (iv) Factiva lists the firm as a hedge fund firm, and (v) if the 13F filer name is one of an individual, we classify the name as a hedge fund if the person is the founder, partner, chairman, or other leading personnel of a hedge fund firm. Applying these criteria provides us with a dataset of 1,199 unique hedge fund firms among the 13F filing institutions. 4 Since our main focus in this analysis is on long equity positions of hedge funds, it is comforting to notice that the largest percentage (38.4%) of our sample funds belongs to the Equity category. Next, we merge the 1,199 hedge funds in the 2 Agarwal, Daniel, and Naik (2009) show that there is only limited overlap between different commercial databases. For a visualization of this overlap, see Figure A.1 in the Appendix which shows a Venn diagram of the five databases employed in this study. 3 Quarterly equity positions have to be disclosed by institutional investors that exercise investment discretion over $100 million of assets in 13F securities that include common stocks, convertible bonds, and options. 4 This number might seem low at first glance but is significant when considered in the context of the size of the industry. The total value of equity positions held by 13F hedge funds is $1.25 trillion which is equivalent to 83% of the size of the hedge fund industry in 2008 according to Credit Suisse/Tremont. 6

7 13F filings to the hedge fund firms listed in the Union Hedge Fund Database following Agarwal, Fos, and Jiang (2013). The merging procedure is applied on the hedge fund firm level and entails two steps: First, we match institutions by name allowing for minor variations. Second, we compute the correlation between returns imputed from the 13F quarterly holdings and returns reported in the Union Database. We eliminate all pairs with negative correlations or matches where correlation is not defined due to lack of overlapping periods of data from both data sources. Finally, we end up with 396 hedge fund firms with 1,491 distinct hedge funds during the period from 1994 to We use this sample in Section 4 when investigating the proportion of a fund s tail risk stemming from the crash risk of their long equity positions. 2. Pricing of Tail Risk in the Cross-Section of Hedge Fund Returns We start our empirical analysis by investigating whether differences in a hedge fund's tail risk are associated with differences in their average returns. To evaluate individual hedge fund s tail risk, we measure the extreme dependence between hedge fund s self-reported returns and the value-weighted CRSP equity market return. In particular, we define a hedge fund's tail sensitivity (TailSens) via the lower tail dependence of its return r i and the CRSP value-weighted market r m return using 1 1 lim q 0 i i m m T a ils en s P r F q r F q, where F ( F ) denotes the marginal distribution function of the returns of hedge fund i, r i m i (the market return r m ) in a given period and q (0,1) is the argument of the distribution function. Hence, hedge funds with strong TailSens are likely to have their lowest return 7

8 realization at the same time when the equity market realizes its lowest return, i.e., these hedge funds are particularly sensitive to market crashes. 5 TailSens measures the likelihood that a hedge fund realizes its worst return exactly at the time when the market realizes its worst return. However, it does not take into account how bad the worst return realization of the hedge fund really is. To account for the severity of poor hedge fund returns, we define a hedge fund s tail risk () as T a ilr is k ri T a ils e n s., rm where r i denotes the volatility of the hedge fund return and r m is the volatility of the market return. We estimate TailSens and for hedge fund i in month t based on a rolling window of 24 monthly returns. The estimation is performed non-parametrically purely based on the empirical distribution function with a cut-off of q = We report the summary statistics of the TailSens and measure in Table 1. [Insert Table 1 here] Table 1 documents that average TailSens is 0.23 and is 0.24 over all hedge funds in the sample. A TailSens of 0.23 means that the probability that an individual hedge fund return is among the lowest 5% in a two-year period (given its marginal return distribution) exactly in those months when the market return in among the lowest 5% in the same period amounts to 23%. TailSens is weakest for Short Bias, Global Macro, and CTA hedge funds and strongest for Equity, Funds-of-Funds, and Event Driven hedge funds. is weakest for Short Bias, Fixed Income, and Equity Neutral hedge funds and strongest for Emerging Market, Equity, and Sector hedge funds. 5 Longin and Solnik (2001) and Rodriguez (2007) apply the lower tail dependence coefficient to analyze financial contagion between different international equity markets. Chabi-Yo, Ruenzi, and Weigert (2014) use lower tail dependencies to analyze extreme dependence structures in the bivariate distribution of a single stock return and the market return. 6 We obtain similar results when we apply different cut-off points of q=0.01, q=0.02, and q=

9 We also investigate the time series behavior of aggregate TailSens and. Aggregate TailSens () is defined as the monthly cross-sectional, equally-weighted average of TailSens () over all hedge funds in the sample. Figure 1 plots the time series of aggregate TailSens and aggregate. [Insert Figure 1 here] Figure 1 confirms the validity of the tail risk measures as occasional spikes in aggregate TailSens and aggregate correspond to different crisis events in financial markets. The first spike occurs in 1998, the year of the Russian financial crisis and the collapse of Long Term Capital Management (LTCM). Furthermore, we see an increasing trend in aggregate TailSens and aggregate in 2006 and 2007 that denotes the start of a worldwide financial recession triggered by the U.S. subprime mortgage crisis. To evaluate the predictive power of differences in hedge fund s tail risk on the crosssection of average hedge fund returns, we relate hedge fund returns in t+1 to hedge fund TailSens and at time t. We first look at univariate portfolio sorts. For each month t, we sort hedge funds into tercile portfolios based on TailSens (). We then compute monthly average excess returns of these portfolios at time t+1. We report the results in Table 2. [Insert Table 2 here] Panel A shows the results of equally-weighted univariate tercile portfolios sorted on TailSens. We report the monthly equally-weighted average excess return over the risk-free rate for the different portfolios as well as differences in returns between tercile portfolio 3 (strong TailSens) and tercile portfolio 1 (weak TailSens). Our results show that hedge funds with strong TailSens have significantly higher future returns than those with weak TailSens. Hedge funds in the tercile with the weakest (strongest) TailSens earn a monthly excess return of 0.50% (0.81%). The return spread between tercile portfolios 1 and 3 is 0.31%, which is 9

10 statistically significant at the 5% level. We also compute alphas for the tercile portfolios and the difference (31) portfolio based on the one-factor CAPM, the three-factor model of Fama and French (1993), as well as the Fung and Hsieh (2004) seven-factor model. We find that the spread between portfolios 1 and 3 is positive in each case; however, the spread is not statistically significant at the 10% level. In Panel B, we report the results of equally-weighted univariate tercile portfolios sorted on. Hedge funds with strong have significantly higher future returns than hedge funds with weak. Hedge funds in the tercile with the weakest (strongest) earn a monthly excess return of 0.50% (1.05%). The return spread between tercile portfolios 1 and 3 is 0.55%, which is statistically significant at the 1% level. In contrast to Panel A, alphas for the difference (31) portfolio based on the single-factor CAPM, the threefactor Fama and French (1993), as well as the Fung and Hsieh (2004) seven-factor model are all positive and statistically significant at the 10% level or better. Controlling for the seven factors in the Fung and Hsieh (2004) model, we observe a premium of 0.34% per month which translates into an annual spread of 4.08%. Panel C further corroborates the findings in Panel B as we obtain similar results using value-weighted sorts on. Hedge funds in the tercile with the weakest (strongest) earn a monthly excess return of 0.32% (0.73%). The return spread between tercile portfolios 1 and 3 is 0.41%, which is statistically significant at the 5% level. Our results are robust when we estimate alphas using the CAPM, Fama and French (1993) three-factor model, as well as the Fung and Hsieh (2004) seven-factor model. The spreads between portfolios 1 and 3, ranging between 0.30% and 0.37% per month, are all positive and statistically significant at the 10% level or better. Finally, Panel D presents the results of time-series regressions. Each month we regress the monthly excess return in month t+1 on the strong minus weak factor and on the 10

11 factors in the Fung and Hsieh (2004) seven-factor model. 7 We find that the factor has a positive coefficient of 0.13 for the hedge fund returns in our sample with a t-statistic of When investigating different hedge fund styles, our results show that is positive and significant for equity-oriented hedge fund strategies: equity, arbitrage, distressed, emerging markets, funds of funds, and sector hedge funds. In summary, we find that has a strong predictive power for the cross-section of hedge fund returns, in particular for hedge funds with equity-related investment styles. Hedge funds with strong tail risk outperform funds with weak tail risk by around 4.0% to 4.5% p.a. after adjusting for other risk factors in the Fung and Hsieh (2004) seven-factor model. 3. Determinants of Tail Risk 3.1 Tail Risk and Fund Characteristics Section 2 documents that tail risk is an important factor to explain the cross-section of hedge fund returns. We now investigate which fund characteristics are associated with strong tail risk. Besides fund characteristics like size, age and location, we mainly focus on a fund s fee structure that has been shown to relate to the risk-taking behavior of fund managers (Brown, Goetzmann, and Park, 2001; Goetzmann, Ingersoll, and Ross, 2003; Hodder and Jackwerth, 2007; Aragon and Nanda, 2012). We estimate panel regressions of tail risk of hedge fund i in month t+1 on fund i s characteristics measured in month t. Table 3 reports the results. [Insert Table 3 here] 7 We construct the strong minus weak factor by going long in funds in tercile 3 and going short in funds in tercile 1 during each month t in our sample period. We acknowledge that this factor is not investable though as it is not feasible to short hedge funds. Our objective here is to show that the tail risk factor is also important in time-series regressions. 11

12 In model (1), we include the time-invariant fund characteristics that include indicator variables for offshore hedge funds, funds with high watermark provision, and leverage. We also include management and incentive fees as well as lockup and redemption periods. We find that a hedge fund s tail risk is higher when the fund does not have a high watermark, when the fund charges a higher incentive fee, and when the fund has a longer lockup period. These findings are consistent with the predictions from the prior theoretical and empirical literature on the contractual features of hedge funds. For example, Panageas and Westfield (2009) show in their theoretical work that inclusion of a high watermark in the fee contract should reduce fund s propensity to take risk as the manager is induced to care about the future sequence of options. This would suggest that high watermark provisions should be negatively related to tail risk, which is confirmed in the results from model (1). We also observe a significantly positive relation between a fund s tail risk and three other variables: incentive fee, lockup period, and past year s fund returns. Incentive fees being positively related to funds tail risk is consistent with the risk-inducing behavior associated with the call option feature of the incentive fee contract (Brown, Goetzmann, and Park, 2001; Goetzmann, Ingersoll, and Ross, 2003; Hodder and Jackwerth, 2007; Aragon and Nanda, 2012). In model (2), we only include time-variant fund characteristics such as fund size (measured as the log of assets under management), age, and past year s returns as independent variables. We observe a significantly negative relation between tail risk and fund size, and a positive relation between tail risk and past year s returns. This evidence suggest that smaller funds are more exposed to extreme risk in the equity markets. Tail risk being positively associated with past performance is consistent with better performing fund managers responding to the greater implicit incentives arising from the convexity in the flowperformance relation for hedge funds (Agarwal, Daniel, and Naik, 2003). 12

13 Finally, in model (3), we include both the time-invariant and time-variant fund characteristics together, and continue to find results consistent with those in models (1) and (2). Taken together, the findings from our analyses of tail risk and fund characteristics are intuitive and broadly consistent with the predictions based on the prior literature. 3.2 Tail Risk and Portfolio/Trading Strategies So far we have investigated which fund characteristics are associated with a hedge fund s tail risk. In this Section, we take a closer look and examine the channels through which hedge funds may be exposed to tail risk. We focus on three distinct trading strategies that can potentially contribute to a hedge fund's overall tail risk: (i) Agarwal and Naik (2004) and Jurek and Stafford (2011) show that an investment strategy of writing put options on the market return matches the risk profile of a wide class of hedge funds. Hence, tail risk can be potentially generated by trading strategies involving derivatives or taking state-contingent bets that give risk to such an exposure. (ii) Fung and Hsieh (2004) document that dynamic, leveraged trading strategies lead to nonlinearities in hedge fund returns. This implies that tail risk can possibly be induced by dynamic trading strategies. (iii) Chabi-Yo, Ruenzi, and Weigert (2014) and Kelly and Jiang (2014) show that the crash risk of individual stocks shows a pronounced cross-sectional dispersion. Thus, tail risk in hedge funds can be due to the crash risk of equity holdings of the funds. 8 As a first step towards identifying the sources of tail risk, we estimate a hedge fund s exposure to the: 8 Jiang and Kelly (2012) show that a tail risk factor derived from the cross section of stock returns has explanatory power for the cross section of hedge fund returns. 13

14 (i) Agarwal and Naik (2004) out-of-the-money put and call option factors (as a proxy for hedge funds tail risk due to their derivative positions and state-contingent bets). The put (call) out-of-the-money option factor consists of a trading strategy of writing out-of-themoney put (call) options on the equity market. (ii) Fung and Hsieh (2004) trend following factors (as a proxy for tail risk due to dynamic trading strategies). (iii) Chabi-Yo, Ruenzi, and Weigert (2014) strong minus weak LTD-risk factor (as a proxy for crash risk induced by equity holdings). The strong minus weak LTD-risk factor consists of a trading strategy going long in stocks with strong crash risk exposure and going short in stocks with weak crash risk exposure. We estimate hedge fund i s exposures to these factors for month t based on a rolling window of 24 monthly returns. We next estimate Fama and MacBeth (1973) regressions at the individual hedge fund level of tail risk in month t (as defined in Section 2) on the exposures to the Agarwal and Naik (2004), Fung and Hsieh (2004), and Chabi-Yo, Ruenzi, and Weigert (2014) factors in month t. We report the results of this regression in Table 4. [Insert Table 4 here] In models (1) and (2), we regress a hedge fund s tail risk on a fund s exposure to the Agarwal and Naik (2004) out-of-the-money (OTM) put and call option factors ( Put-OTM and Call-OTM). We find that tail risk is strongly negatively related to Put-OTM with a coefficient of 9.881, which indicates that tail risk is related to a trading strategy of writing out-of-the-money put options on the equity market index. This relationship is statistically significant at the 1% level. As expected, we do not find a significant relationship between tail risk and Call-OTM. 14

15 Models (3) and (4) display the results of regressions of tail risk on a fund s exposure to the Fung and Hsieh (2004) trend-following factors ( PTFSSTK, PTFSB, PTFSFX, PTFSCOM, and PTFSIR). We do not find a statistically significant relationship between tail risk and PTFSSTK, a trend-following factor in the U.S. stocks. 9 In model (5), we investigate the relationship between tail risk and LTD-Risk, the sensitivity to the Chabi-Yo, Ruenzi, and Weigert (2014) strong minus weak LTD-Risk factor. We find a strong positive relation between tail risk and LTD-Risk (coefficient of 0.482), which indicates that tail risk is related to a trading strategy of buying stocks with strong LTDrisk and selling stocks with weak LTD-risk. The positive relationship is statistically significant at the 1% level. Finally, in model (6), we regress tail risk on the complete set of hedge fund return sensitivities. We continue to find that tail risk is positively related to LTD-Risk and negatively related to Put-OTM. A one standard deviation increase in LTD-risk increases a fund s tail risk by A one standard deviation decrease in Put-OTM increases a fund s tail risk by The R-squared of the regression is which documents that almost one half of a hedge fund s tail risk can be explained by its exposure to a trading strategy involving writing put options on the equity market ( Put-OTM) and investing in stocks with strong crash risk ( LTD-risk). As a side note, we also investigate the impact of Put-OTM and LTD-risk on the cross section of hedge fund returns. Panel A of Table A.1 reports the results of equallyweighted univariate portfolio sorts based on LTD-risk. We find that hedge funds with strong LTD-risk have significantly higher future returns compared to funds with weak LTD-risk. Hedge funds in the tercile with the weakest (strongest) LTD-risk earn a monthly 9 However, we find weakly significant relation between tail risk and trend-following factors in currency and interest rates ( PTFSFX and PTFSIR). 15

16 excess return of 0.49% (0.96%). The return spread between tercile portfolios 1 and 3 is 0.47%, which is statistically significant at the 1% level. We also compute alphas for the tercile portfolios and the difference (3 1) portfolio based on the CAPM, Fama and French (1993) three-factor model, as well as the Fung and Hsieh (2004) seven-factor model. We find that the spread between portfolios 1 and 3 is positive in each case; however, the spread is not statistically significant at conventional levels. A similar picture emerges based on Put- OTM. Hedge funds with weak Put-OTM have significantly higher future returns than funds with strong Put-OTM. Hedge funds in the tercile with the weakest (strongest) Put-OTM earn a monthly excess return of 0.93% (0.48%). The return spread between tercile portfolios 1 and 3 is 0.45%, which is statistically significant at the 1% level. We again compute alphas for the tercile portfolios and the difference (31) portfolio based on the CAPM, Fama and French (1993) three-factor model, and the Fung and Hsieh (2004) seven-factor model. As before, we find that the spread between portfolios 1 and 3 continues to be negative in each case; however, the spread is not statistically significant at conventional levels. 4. Tail Risk induced from Equity Portfolio Holdings Our results so far indicate that crash risk induced by equity holdings seems to be an important component of the overall hedge fund tail risk. According to model (5) of Table 4, LTD-risk explains more than 30% of the variation in the tail risk across hedge funds. To establish direct evidence between crash risk induced by equity holdings and overall hedge fund tail risk, we use the Thomson Reuters 13F database providing common stock holdings of more than 5,000 institutional managers with 100 million or more in 13F securities (i.e., equities, convertible bonds, and options). The database provides long equity holdings of 1,199 manually classified hedge fund firms. The merge between the Union Hedge Fund Database and the 13F Portfolio Holdings follows Agarwal, Fos, and Jiang (2013) and is explained in 16

17 Section 1. Our final sample consists of 396 hedge fund firms with 1,491 distinct hedge funds in the period from 1994 to We start by aggregating the tail risk of hedge fund firm i in month t according to the value-weighted tail risk of the company s distinct hedge funds. Second, using the 13F portfolio holdings, we calculate the equity positions crash risk (LTD-risk). For this purpose, we use daily return data over the previous year to compute the lower tail dependence coefficients between a single stock s return and the CRSP value-weighted market return using copulas and extreme value theory (see Chabi-Yo, Ruenzi, and Weigert (2014) for a detailed explanation of the calculation of LTD-coefficients). 10 We then compute the LTD-risk of a hedge fund firm i in month t as the value-weighted LTD-risk of its equity positions. To analyze the relationship between overall hedge fund tail risk and equity LTD crash risk, we estimate panel regressions. We regress tail risk of hedge fund firm i in month t on hedge fund firm i s portfolio LTD-risk in month t after controlling for different risks and firm characteristics. Table 5 reports the results. [Insert Table 5 here] In model (1), we use LTD-risk as the only explanatory variable. It has a positive coefficient of and its impact is highly statistically significant at the 1% level. This finding provides direct evidence of a strong positive relation between a hedge fund s tail risk and crash risk induced by its equity holdings. 10 Similar to the relationship between and TailSens, we define LTD-risk as LTD risk LTD ri, rm where r i denotes the volatility of the stock return and r m the volatility of the equity market return and LTD is the lower tail dependence coefficient between individual stock returns and the equity market return. 17

18 In models (2) to (7), we expand our setup and control for different portfolio characteristics such as size, past yearly return, skewness, kurtosis, idiosyncratic volatility, and beta. We find that tail risk is positively related to idiosyncratic volatility and beta. More importantly, in all regressions, LTD-risk is significantly positively related to overall tail risk. A one standard deviation increase in equity LTD-risk increases a hedge fund firm s tail risk by 0.05, which is economically significant given the average level of tail risk of In summary, this section shows that tail risk of hedge funds is directly induced by the crash risk of their long equity positions. 5. Conclusion This paper shows that hedge funds with strong tail risk outperform funds with weak tail risk by 4 to 4.5% per annum in terms of the Fung and Hsieh (2004) 7-factor alpha. Moreover, it shows that tail risk is strongly related to a fund s exposure to a put writing strategy on the equity market as well as to an equity-based crash risk factor. Finally, using 13F portfolio disclosures, it provides evidence on a strong direct link between hedge funds tail risk and their investments in long equity positions that are crash sensitive themselves. Overall, these results offer first insights into the channels through which hedge funds are exposed to tail risk. 18

19 Appendix Figure A.1: Venn Diagram of the Union Hedge Fund Database The Union Hedge Fund Database contains a sample of 11,417 hedge funds by merging the following databases: CISDM, Eureka, HFR, MSCI, and Lipper TASS. This figure shows the percentage of funds covered by each database individually and by all possible combinations of multiple databases. The figure is taken from Agarwal, Fos, and Jiang (2013). 19

20 Table A.1: -LTD Risk and -Put OTM and the Cross-Section of Hedge Fund Returns This table reports results from the relationship between -LTD Risk and -Put OTM in month t and monthly excess returns in month t+1. Panel A shows the results from equal-weighted univariate portfolio sorts based on -LTD Risk in month t and (adjusted) returns in month t+1. In each month t, we rank hedge funds into terciles and and form equally-weighted portfolios at the beginning of the month. The column Return reports the average future monthly return of the tercile portfolios in excess of the one-month t-bill rate. The column labeled CAPM-Alpha t+1 ( FF-Alpha t+1, 7-Factor- Model t+1 ) reports the monthly alpha with regard to the Capital Asset Pricing Model (Fama and French (1993) s three-factor model, Fung and Hsieh s (2004) 7-factor model.). Panel B reports the results from equally-weighted univariate portfolio sorts based on -Put OTM in month t and (adjusted) returns in month t+1. The sample covers hedge funds from the Union Hedge Fund Database constructed from combining the CISDM, Eureka, HFR, MSCI, and Lipper TASS databases. The sample period is from January 1994 to December The t-statistics are reported in parentheses below the coefficients. Panel A: -LTD Risk and Future Returns: Equal-Weighted Portfolio Sorts Portfolio -LTD Risk Return t 1 CAPM- Alpha t 1 FF-Alpha t 1 7-Factor- Alpha 1 Weak -LTD Risk % 0.39% 0.41% 0.43% % 0.48% 0.58% 0.53% 3 Strong -LTD Risk % 0.63% 0.70% 0.70% t 1 Strong-Weak %** (2.13) 0.24% (1.41) 0.29% (1.39) 0.27% (1.51) Panel B: -Put OTM and Future Returns: Equal-Weighted Portfolio Sorts Portfolio -Put OTM Return t 1 CAPM- Alpha t 1 FF-Alpha t 1 7-Factor- Alpha 1 Weak -Put OTM % 0.71% 0.75% 0.71 % % 0.61% 0.62% 0.51% 3 Strong -Put OTM % 0.41% 0.48% 0.42% t 1 Strong-Weak %** (2.15) 0.30% (1.45) 0.27% (1.59) 0.29% (1.45) 20

21 References Agarwal, Vikas, and Narayan Y. Naik, 2004, Risks and Portfolio Decisions Involving Hedge Funds, Review of Financial Studies 17, Agarwal, Vikas, Naveen D. Daniel, and Narayan Y. Naik, 2003, Flows, Performance, and Managerial Incentives in the Hedge Fund Industry, Working Paper, Georgia State University and London Business School. Agarwal, Vikas, Naveen D. Daniel, and Narayan Y. Naik, 2009, Role of Managerial Incentives and Discretion in Hedge Fund Performance, Journal of Finance 64, Agarwal, Vikas, Vyacheslav Fos, and Wei Jiang, 2013, Inferring reporting-related biases in hedge fund databases from hedge fund equity holdings, Management Science 59, Aragon, George O., and Vikram Nanda, 2012, Tournament behavior in hedge funds: Highwater marks, fund liquidation, and managerial stake, Review of Financial Studies 25, Brown, Stephen J., William N. Goetzmann, and James Park, 2001, Careers and Survival: Competition and Risk in the Hedge Fund and CTA Industry, Journal of Finance 56, Chabi-Yo, Fousseni, Ruenzi, Stefan, and Florian Weigert, 2014, Crash Sensitivity and the Cross-Section of Expected Stock Returns, Working Paper, Ohio State University and University of Mannheim. Duarte, Jefferson, Francis Longstaff, and Fan Yu, 2007, Risk and Return in Fixed Income Arbitrage: Nickels in Front of a Steamroller?, Review of Financial Studies 20, Fama, Eugene F., and Kenneth R. French, 1993, Common risk factors in the returns on stocks and bonds, Journal of Financial Economics 33,

22 Fama, Eugene F., and James D. MacBeth, 1973, Risk, return, and equilibrium: empirical tests, Journal of Political Economy 81, Fung, William, and David A. Hsieh, 2001, The Risk in Hedge Fund Strategies: Theory and Evidence from Trend Followers, Review of Financial Studies 14, Fung, William, and David A. Hsieh, 2004, Hedge fund benchmarks: A risk-based approach, Financial Analysts Journal 60(5), Goetzmann, William N., Jonathan E. Ingersoll, and Stephen A. Ross, 2003, High-water Marks and Hedge Fund Management Contracts, Journal of Finance 58, Hodder, James E., and Jens C. Jacwerth, 2007, Incentive Contracts and Hedge Fund Management, Journal of Financial and Quantitative Analysis 42, Jiang, Hao, and Bryan Kelly, 2012, Tail Risk and Hedge Fund Returns, Working Paper, Erasmus University Rotterdam and University of Chicago Booth School of Business. Jurek, Jakub W., and Erik Stafford, 2011, The Cost of Capital for Alternative Investments, Working Paper, Harvard Business School. Kelly, Bryan, and Hao Jiang, 2014, Tail Risk and Asset Prices, Review of Financial Studies 27, Longin, Francois, and Bruno Solnik, 2001, Extreme correlation of international equity markets, Journal of Finance 56, Panageas, Stavros, and Mark Westerfield, 2009, High-water Marks: High-risk Appetites? Convex Compensation, Long Horizons, and Portfolio Choice, Journal of Finance 64, 136. Rodriguez, Juan C., 2007, Measuring Financial Contagion: A Copula Approach, Journal of Empirical Finance 14, Stulz, Rene, 2007, Hedge Funds: Past, Present, and Future, Journal of Economic Perspectives 21,

23 Figure 1: Aggregate Tail Risk Over Time This figure displays the evolution of aggregate TailSens and aggregate over time. Aggregate TailSens is defined as the monthy cross-sectional, equally-weighted average of the individual TailSens coefficients over all hedge funds in our sample. Aggregate is defined as the monthy crosssectional, equally-weighted average of the individual coefficients over all hedge funds in our sample. The sample covers hedge funds from the Union Hedge Fund Database constructed from combining the CISDM, Eureka, HFR, MSCI, and Lipper TASS databases. The sample period is from January 1994 to December

24 Table 1: Summary Statistics This table provides summary statistics for the average TailSens measure, the average measure, and the average monthly excess return. TailSens is defined as the lower tail dependence measure between a hedge fund's return and the value-weighted excess market return (see Section 2). is defined as return and r m ri T a ilr is k T a ils e n s. rm, where r i denotes the volatility of the hedge fund the volatility of the market return. Averages are taken first over the cross section of hedge fund returns and then over time. The sample covers hedge funds from the Union Hedge Fund Database constructed from combining the CISDM, Eureka, HFR, MSCI, and Lipper TASS databases. The sample period is from January 1994 to December Strategy Description Number of Funds Average TailSens Average Average Monthly Excess return All 7, % Not Assigned 1, % Equity 1, % Equity Neutral % Event Driven % Short Bias % Arbitrage % CTA % Distressed % Emerging % Markets Funds of Funds 1, % Fixed Income % Global Macro % Sector Funds % Others % 24

25 Table 2: Tail Risk and the Cross-Section of Hedge Fund Returns This table reports results from the relationship between TailSens and of hedge funds in month t and their monthly excess returns in month t+1. Panel A reports the results from equal-weighted univariate portfolio sorts based on TailSens in month t and (adjusted) returns in month t+1. In each month, we rank hedge funds into terciles and and form equal-weighted portfolios at the beginning of each month. The column Return t+1 reports the average return next month in excess of the one-month t-bill rate for each tercile. The column labeled CAPMAlpha t+1 ( FF-Alpha t+1, 7-Factor-Alpha t+1 ) reports the monthly alpha using the Capital Asset Pricing Model (Fama and French (1993) s threefactor model, Fung and Hsieh s (2004) 7-factor model.). Panels B and C report the results from equally-weighted (value-weighted) univariate portfolio sorts based on in month t and (adjusted) returns in month t+1. Panel D displays the results of time-series regressions. Each month we regress the monthly excess return in month t+1 on the strong minus weak factor in month t and the factors of the Fung and Hsieh (2004) 7-factor model. The sample covers hedge funds from the Union Hedge Fund Database from combining the CISDM, Eureka, HFR, MSCI, and Lipper TASS databases. The sample period is from January 1994 to December The t-statistics are reported in parentheses below the coefficients. Panel A: TailSens and Future Returns: Equal-Weighted Portfolio Sorts Portfolio TailSens t Return t 1 CAPM- Alpha t 1 FF-Alpha t 1 1 Weak % 0.45% 0.36% 0.43% TailSens % 0.53% 0.46% 0.54% 3 Strong TailSens % 0.61% 0.58% 0.63% t 1 Strong-Weak %** (2.02) 0.16% (1.12) 0.22% (1.44) 0.20% (1.32) Panel B: and Future Returns: Equal-Weighted Portfolio Sorts Portfolio t Return t 1 CAPM- Alpha t 1 FF-Alpha t 1 7-Factor- Alpha 7-Factor- Alpha 1 Weak % 0.45% 0.36% 0.43% % 0.58% 0.49% 0.53% 3 Strong % 0.72% 0.71% 0.77% t 1 Strong-Weak %*** (3.01) 0.27%* (1.89) 0.35%** (2.04) 0.34%** (2.18) 25

26 Panel C: and Future Returns: Value-Weighted Portfolio Sorts Portfolio t+1 Return t 1 CAPM- Alpha t 1 FF-Alpha t 1 7-Factor- Alpha t 1 1 Weak % 0.29% 0.21% 0.23% % 0.40% 0.41% 0.41% 3 Strong % 0.59% 0.52% 0.60% Strong-Weak %** (2.16) 0.30%* (1.90) 0.31%* (1.92) 0.37%** (2.00) Panel D: and Future Returns: Time-Series Regressions Strategy Mktrf SMB Term Credit PTFSBD PTFSBD PTFSCOM Intercept All 0.13** 0.24*** 0.09*** 0.01*** 0.03*** *** 0.01** 0.63%*** (2.13) (8.25) (3.99) (2.72) (3.81) (0.12) (3.46) (2.45) (7.34) Strategy Not assigned 0.03 Equity 0.19*** Equity Neutral 0.08 Event Driven 0.01 Short Bias 0.10* Arbitrage 0.12* CTA 0.01 Distressed 0.22*** Emerging Markets 0.21** Funds of Funds 0.11* Fixed Income 0.05 Global Macro 0.01 Sector Funds 0.15** Others

27 Table 3: Tail Risk and Fund Characteristics This table reports the results of panel regressions with Newey-West corrected standard errors of in month t+1 on fund characteristics in month t. For fund characteristics, we include hedge fund size, age, an indicator variable that equals one if the fund is an offshore fund and zero otherwise, an indicator variable that equals one if the fund has a high water mark and zero otherwise, an indicator variable that equals one if the fund employs leverage and zero otherwise, management fee, incentive fee, the length of the redemption period, the length of lockup period, and fund s past year's return. The sample covers hedge funds from the Union Hedge Fund Database from combining the CISDM, Eureka, HFR, MSCI, and Lipper TASS databases. The sample period is from January 1994 to December The t-statistics are reported in parentheses below the coefficients. CrashRisk (1) CrashRisk (2) Offshore (1.10) High Watermark 0.015* (1.84) Leverage (0.56) Management Fee (0.91) Incentive Fee 0.172*** (2.53) Redemption Period (1.12) Lockup Period 0.001** (2.28) Size *** (2.81) Age (0.72) Past Year Return 0.251** (2.28) Constant 0.221** 0.254*** (2.03) (3.71) CrashRisk (3) (0.32) 0.020*** (3.84) (0.80) (0.71) 0.198*** (2.75) (0.71) 0.000* (1.74) *** (3.88) (0.70) 0.268*** (2.69) (1.03) N 220, , ,608 R

28 Table 4: Sources of Tail Risk This table reports the results of Fama and MacBeth (1973) regressions with Newey-West corrected standard errors of in month t+1 on a hedge fund s sensitivity to different risk factors that include the Agarwal and Naik (2004) out-of-the-money (OTM) put and call option factors, Fung and Hsieh (2004) trend-following factors, and Chabi-Yo, Ruenzi, and Weigert (2014) strong minus weak LTD-risk factor. We estimate a fund s sensitivity to the respective factor based on a rolling window of 24 monthly returns. The sample covers hedge funds from the Union Hedge Fund Database constructed from combining the CISDM, Eureka, HFR, MSCI, and Lipper TASS databases. The sample period is from January 1994 to December The t-statistics are reported in parentheses below the coefficients. (1) (2) (3) (4) (5) Put-OTM 9.881*** 10.29*** (10.66) (5.39) Call-OTM (0.53) PTFSSTK (1.26) (0.69) PTFSB (0.42) PTFSFX 0.501* (1.76) PTFSCOM (0.50) PTFSIR 1.141** (2.06) LTD-Risk 0.482*** (12.54) Constant *** *** 0.218*** 0.149*** *** (6.08) (5.72) (5.63) (5.59) (4.62) (6) 8.719*** (3.45) (1.19) 0.00 (0.00) (0.98) (0.22) (1.51) (0.47) 0.275*** (3.35) *** (5.97) Economic Significance N 298, , , , , ,717 R

29 Table 5: Tail Risk induced from Equity Portfolio Holdings This table reports the results of panel regressions with Newey-West corrected standard errors of of hedge fund firm i in month t on hedge fund firm s portfolio LTD-Risk in month t controlling for different risks and firm characteristics. The control variables include firm s size, its past return, return skewness, return kurtosis, idiosyncratic volatility of returns, and market beta. All risks and firm characteristics except firm size (which is measured at the end of last month) are estimated based on a rolling one-year horizon using daily return data. The sample covers hedge funds from the Union Hedge Fund Database constructed from combining the CISDM, Eureka, HFR, MSCI, and Lipper TASS databases. The sample period is from January 1994 to December The t-statistics are reported in parentheses below the coefficients. (1) (2) (3) (4) (5) (6) (7) LTD-Risk 0.608*** 0.637*** 0.612*** 0.591*** 0.583*** 0.320** 0.254** (3.95) (3.97) (3.72) (3.66) (3.63) (2.14) (2.08) Size *** (0.46) (0.34) (0.38) (0.60) (2.97) (1.20) Past Return (0.40) (0.57) (0.56) (0.25) (0.03) Skewness 0.090*** (2.61) (1.24) (1.13) (0.42) Kurtosis (0.25) (0.41) (0.77) Idio. Vol *** 8.848** (3.97) (1.99) Market Beta 0.184*** (5.52) Constant *** (0.24) (0.34) (0.26) (0.51) (0.84) (2.74) (1.32) Economic Significance N 13,500 13,500 12,926 12,926 12,926 12,926 12,926 R