Bond Fund Risk Taking and Performance

Bond Fund Risk Taking and Performance Abstract This paper investigates the risk exposures of bond mutual funds and how the risk-taking behavior of these funds affects their performance. Bond mutual funds often outperform their respective benchmark bond indexes, but underperform after controlling for bond market risk factors. We show that risk-taking behavior helps to explain the different performances of funds. Risk taking leads to higher returns relative to benchmarks in normal credit risk periods, but lower returns in high credit risk periods. Further, fund risk taking is found to be persistent and is primarily driven by poor long-term past performance. Our analysis also shows no evidence that risk-taking funds attempt to conceal their risky bets at mandatory disclosure and that fund investors show no ability to differentiate the skill and risk components of fund performance in their investment decisions. Keywords: Bond Funds, Incentives, Risk Taking, Performance, Fund Flows JEL Classification Number: G11, G23, G32

Last year, 79% of intermediate-term bond funds which hold a mix of government and corporate bonds maturing in five to 10 years beat the comparable bond index. Over the past 12 months, investment-research firm Morningstar estimates, intermediate bond funds have surpassed the indexes against which they measure themselves by an average of 1.8 percentage points; long-term government bond funds have beaten their chosen benchmarks by 2.5 points. Wall Street Journal, April 13, 2013. 1 1 Introduction Can bond mutual funds easily beat their benchmarks? Empirical findings in the extensive literature on mutual fund performance seem to suggest that bond fund managers, like their equity fund counterparts, are unable to outperform the benchmarks. However, the above quote from the Wall Street Journal indicates that many bond mutual funds do beat their benchmark indexes, at least for some specific time periods. While bond funds in the U.S. are about 60% as large as domestic equity funds, 2 there is relatively little research on bond fund risks and performance. The few studies that have examined bond fund performance find that, after controlling for bond market and economic risk factors, bond funds generally do not yield positive alphas. In this paper, we examine the risk exposures of bond funds and how their different risk exposures affect performance. Existing studies on bond funds examine fund performance by specifying and explicitly controlling for bond market risk factors. Blake, Elton, and Gruber (1993) find that on average, bond funds underperform their benchmarks after controlling for multiple bond risk factors (as proxied by bond indexes). Elton, Gruber, and Blake (1995) conclude that the magnitude of bond fund underperformance, after controlling for fundamental economic risk factors, is approximately equal to the fund expense ratio. Consistent with these two studies, Ferson, Henry, and Kisgen (2006) 1 The Bond Market Can t Be This Easy to Beat Can It?, Wall Street Journal, April 13, 2013 2 As of 2013 year end, the total net asset value of bond funds was 22% of the $15 trillion worth of U.S. mutual fund assets, and that of equity funds was 38%. See Investment Company Fact Book, 2014. 1

show that the risk-adjusted pre-expense excess return of bond funds is just enough to cover the expenses. Chen, Ferson, and Peters (2010) find that, even though bond funds exhibit some market timing ability, they still underperform after expenses. Employing fund holdings data, Cici and Gibson (2012) find no evidence of selection ability and weak evidence of timing ability in corporate bond funds. Our study evaluates bond fund performance by assessing the risk exposure of bond funds relative to their benchmarks and examining the effects of risk exposure on fund performance. Each fund is classified by its investment objective, and its performance is compared with that of a matched bond index benchmark (index-adjusted performance) and is also evaluated in a multi-factor setting (risk-adjusted performance). This approach allows us to evaluate bond fund performance with and without explicitly controlling for additional bond risk factors beyond their respective bond index benchmarks and to assess how differences in risk exposures between bond funds and bond indexes affect fund performance. We further develop methodologies to evaluate risk taking by bond funds and explore the determinants of their risk-taking decisions. We start by examining bond fund performance relative to an index benchmark. Based on annual fund returns, our results indicate that most bond funds outperform their matched benchmark indexes after the 2008 financial crisis and that a substantial number of bond funds outperform their benchmarks over different time periods during the full sample period of 1993 to 2013. More important, across different investment objectives, performances of bond funds relative to their respective benchmarks vary substantially over the sample period and are negatively correlated with levels of credit risks in the financial market. We employ multi-factor models to assess bond fund performance and find that bond funds on average generate significantly negative risk-adjusted alphas over the full sample period. In contrast to their time-varying index-adjusted outperformance, results from rolling-window multi-factor regressions reveal that risk-adjusted bond fund returns do not vary substantially over time and are consistently negative. These findings suggest that bond mutual funds exhibit different risk characteristics from their matched bond indexes. We next examine how the risk characteristics of bond funds differ from those of their bench- 2

marks. We first compare bond fund index-adjusted performance across normal and high credit risk episodes over the sample period. The results show that fund performance differs substantially between normal and high credit risk periods, and that fund returns are significantly lower during high risk periods. We then decompose the index-adjusted performance of bond funds into a risk component and a non-risk or skill component that is based on the risk-adjusted return. We exploit the financial crisis of 2008 to 2009 as a natural experiment to determine the contribution of the two components to fund performance. Our analysis suggests that the return due to the risk component reverses from the normal credit risk period to the high credit risk period, while the skill component remains stable. Taken together, these results suggest that fund risk taking (i.e., funds have greater risk exposure than their bond index benchmarks) drives the different results on bond fund performance with and without controlling for risk factors. Why do bond funds take excessive risk relative to their benchmarks? Several studies on equity mutual funds provide evidence that, because mutual funds are often evaluated annually, poor performing funds in the early part of the year may have an incentive to shift risk by investing in more risky assets in order to improve performance prior to year end. To examine such short-term risk-shifting behavior, we follow Brown, Harlow, and Starks (1996) and classify funds into winner and loser funds based on their performance during the early part of the year (over the six- or ninemonth period). We then compare the frequency distribution of increasing risk between winner and loser funds in the later part of the year. We find that loser funds are not more likely to increase their risk levels than winner funds. These findings indicate that short-term risk shifting is unlikely the main explanation for the observed risk-taking behavior of bond funds. Instead, our evidence suggests that fund risk taking seems to be persistent over the short term, at least within a calender year. We consider another possibility that bond fund managers may decide to take greater risks and such risk-taking behavior could be more persistent than observed in equity mutual funds. Unlike equity fund risk taking, bond fund risk taking, in the form of increasing credit risk (lower credit quality) and/or increasing interest risk (longer maturity), can more reliably generate higher returns 3

during normal market conditions. Competition pressure may motivate bond fund managers to assume greater risks compared with their benchmarks. In this case, longer-term poor performance may drive risk taking. To test this hypothesis, we examine the relation between fund risk taking and longer-term fund performance over two- to three-year periods. We find that funds that have performed poorly over longer periods in the past tend to take greater risks these funds have higher returns in normal credit risk periods but lower returns during high credit risk periods. Competition induced risk-taking behavior could persist for longer periods and could permeate the bond fund industry. For example, some poorly performing funds may decide to take greater risks in order to improve their relative performance. The increased competition pressure could subsequently lead to more funds taking risks or lead to greater risk taking among funds that already are in riskier positions. The evidence we document across most bond fund styles and the quote from the Wall Street Journal article, mentioned earlier, indicate that bond fund risk taking is likely to be pervasive. Two mechanisms could help deter risk taking by bond funds. First, mutual funds are required to report their holdings on a quarterly basis. Such required portfolio disclosure can prevent bond funds from taking risks or can increase the cost of risk taking if funds have to conceal their risktaking behavior prior to disclosing their portfolio positions. We investigate the effectiveness of the first mechanism by analyzing bond fund returns just before the required portfolio disclosure date and fund returns during other days of the quarter. We compute daily return differences between bond funds and their benchmarks over 5-day and 10-day periods prior to the quarter end and compare these differences with those computed over the remaining days of the quarter. For risktaking funds, if bond fund managers hide their risk taking by quarter ends, the return differences between the funds and their benchmarks should be smaller at quarter ends than during the other days of the quarter. Our results, however, show that the return differences to be larger at quarter ends than non-quarter ends for both high risk-taking and low risk-taking bond funds. The second mechanism rests on the investment decisions of fund investors. If fund investors can distinguish between the performance generated by skills and the performance due to risk taking, and 4

make investment decisions based on skill-generated (or risk-adjusted) rather than raw performance (i.e., performance relative to a bond index), such investment behavior can diminish the incentive for fund managers to take risk. We investigate the effectiveness of the second mechanism by analyzing fund flows in relation to risk-adjusted and benchmark-adjusted fund performances. We find that investors respond positively to both risk-adjusted returns and benchmark-adjusted returns. In particular, bond fund raw returns are significantly positively related to subsequent fund flows even after controlling for the effects of risk-adjusted returns. These results suggest that bond fund investors may reward rather than penalize bond fund managers for taking risks if such behavior can help deliver higher returns. The rest of this paper is organized as follows. Section 2 describes the bond mutual fund sample and bond indexes used in the study. Section 3 presents empirical results on bond fund performance and risk taking. Section 4 explores potential causes of risk taking in bond mutual funds, while Section 5 examines the effectiveness of two market mechanisms that could discourage bond funds from risk taking. Section 6 offers some concluding remarks. 2 Data 2.1 Bond Mutual Funds The bond mutual fund data are from CRSP Survivor-Bias Free U.S. Mutual Fund Database. We use the sample period from 1993 to 2013 since detailed classifications of bond funds (Strategic Insight objective codes) became available from 1993 onwards. We form the initial broad sample of bond funds by including funds with CRSP objective codes of IC, IG and I but excluding municipal bond funds and mortgaged-backed funds. Based on Lipper objective codes, along with Strategic Insight objective codes, we classify bond funds into 11 investment styles: government bond funds (i.e., general, short maturity, intermediate maturity government bond funds), corporate bond funds (i.e., general,short maturity, intermediate maturity, high quality, BBB-rated, and high yield corporate bond funds), government and corporate bond funds, and index bond funds. Appendix A provides 5

more details on the objective codes used to classify these funds. Since the CRSP mutual fund dataset reports fund characteristics based on the fund class level instead of the fund level, we combine the different fund classes into a single fund. Table 1 reports the number of funds in our sample for each fund style classification by year. The total number of bond funds is stable over the sample period and reaches its peak in 1999 and 2000. High yield corporate bond funds and government/corporate bond funds experience dramatic increases from 1993 to 2013. Table 2 reports the time series averages of monthly fund returns, expense ratios, and total net assets (TNA) for each fund investment objective. We first compute the cross-sectional average of these fund characteristics within a year and then compute the time-series average over the sample period. Returns and expenses for a specific fund are computed as value-weighted returns and expenses of various classes within the fund. As shown in Table 2, mean returns range from 0.315% to 0.574% per month with high-yield bond funds generating the highest returns. The standard deviation of returns is between 0.481% and 2.223% per month. Expenses vary according to different investment types and the passively managed index funds charge the lowest monthly expense of 0.05%. Corporate bond funds generally are larger in terms of size compared with government bond funds. 2.2 Bond Index Benchmarks Most bond mutual funds use Barclays bond indexes as their benchmarks. We obtain these indexes from DataStream and compute the monthly returns of the bond indexes based on the total return index. We select the following 10 Barclays bond indexes for bond mutual funds based on their respective investment objectives: Barclays U.S. aggregate index (LHAGGBD), Barclays U.S. credit 1-3y index (LHGC1T3), Barclays corporate intermediate index (LHCCRIN), Barclay corporate long-term index (LHCCRLG), Barclay U.S corporate high-yield index (LHYIELD), Barclays government 1-3Y index (LHGV1T3), Barclays US government intermediate index (LHGOVIN), Barclays US government long-term index (LHGOVLG), and Barclays US mortgage-backed security (LHMNBCK). Appendix A provides the link between each fund objective and the corresponding 6

benchmark bond index. 2.3 Other Variables The following analysis employs credit spreads as measures for high credit risk periods. Monthly data are obtained from Federal Reserve s website s H.15 historical data. We compute both long-term and short-term credit spreads. The long-term credit spread is measured as the yields of AAA or BAA corporate bond minus 10-year Treasury constant maturities. We take the difference between the yield of 3-month financial or nonfinancial commercial paper and 3-month T-bill rate to construct the short-term credit spread. Figure 1 displays the changes over the sample period. In addition, we construct several risk factors for subsequent analyses. Agg proxies for the average return of the aggregate bond market and captures the marketwide risk, Def is the difference in returns between the high-yield index and intermediate government index, T erm is the return spread between the intermediate- and short-term government bond indexes, and S&P 500 is a proxy for equity market performance. 3 Bond Fund Performance and Risk Taking In this section, we examine bond fund performance based on two vastly different approaches. The first approach is widely employed in the mutual fund industry, where it reports bond fund returns relative to a bond index benchmark. The other method is mainly adopted in academic research, where fund performance is evaluated while explicitly controlling for bond market risk factors. We then investigate whether different risk exposures between funds and their index benchmarks are the causes in the differences of the two performance results. 3.1 Bond Fund Returns Relative to Comparable Bond Index Benchmarks We first compare bond fund returns within each investment objective with their corresponding index benchmarks. We match each actively managed bond fund classification with the Barclays bond index. For each fund, we compute its annual return within a calender year and then compute 7

the average return of funds within each classification type. Table 3 reports the difference between the equal-weighted fund return of each fund classification and its corresponding bond index return and also the percentage of bond funds that outperform their benchmarks by year. Panel A of Table 3 shows that bond funds generally exhibit significantly negative relative returns across the sample period, except in recent years. We observe a majority of the funds turned around in 2009 from poor performance in prior years, especially in the 2008 financial crisis period. However, high yield and BBB corporate bond funds still underperform their respective benchmarks substantially by 13.972% and 13.615%. In comparison, intermediate government bond funds outperform their benchmarks by 5.486% in 2009, which is significantly larger than their past highest return difference of 0.713%. Consistent with the abovementioned the Wall Street Journal article, the intermediate government bond funds show outperformance of 1.41% after expenses in 2012. In addition, the percentage of outperforming funds also has increased dramatically from 2009 onwards with many fund classifications having over 50% outperforming funds. Panel B provides the counterpart results with expenses added back and hence, shows more increases in the percentage of outperforming funds. Evidence of outperformance in recent years is even more striking in Panel B, consistent with prior evidence that expenses contribute to a large amount of underperformance. In our analysis, we also compute year by year return differences between fund returns and index fund returns. Our untabulated results show that, except for several major financial and debt crisis years, most classification types show positive return differences and the percentage of outperforming funds, especially corporate bond funds, is over 60%. Since index funds passively invest in a variety of bonds, it is reasonable for government bond funds to yield relative lower returns. Additionally, more funds outperform index funds and the outperformance is more prevalent and larger in terms of magnitude in recent years. The percentage of outperforming high-yield funds is nearly 100% since 2009. The table also depicts a significant variation in the relative performance of bond funds over the sample period. During major financial market downturns, most bond fund classifications, as well as their comparable benchmarks, exhibit significantly lower returns. Still, the funds relative 8

performance covaries with broad bond market conditions. For example, the recent financial crisis contributes to the annual underperformance of government and corporate bond funds by -10.566%, but their relative performance rebounded in 2009 when the credit market conditions improved. The variation of bond fund relative performance exhibited throughout the sample period is not unique to the financial crisis period. Similarly, the percentage of outperforming funds also varies significantly over time, ranging from 10.99% to 53.45% from 1993 to 2013. The comparison of actively managed bond funds with comparable benchmarks shows strong evidence of outperformance over the recent few years and significant time variation in relative performance. The results are robust before and after expenses. One possible explanation is that bond fund managers exhibit significant skills. If managerial skills contribute to the performance results, the return differences should be stable and persistent over time. Thus, managerial skills alone may not be able to explain the relative performance of bond funds, the significant variations of bond relative performance and the high correlation between fund relative performance with bond market conditions. 3.2 Bond Fund Risk-Adjusted Returns In this section, we evaluate bond fund performance based on multi-factor models that are standard in the mutual fund performance evaluation literature. Blake, Elton, and Gruber (1993) adopt a six-factor models to measure bond funds performance. Elton, Gruber, and Blake (1995) add two fundamental variables. Chen, Ferson, and Peters (2010) develop a model to measure bond fund market timing. We evaluate bond fund performance by employing the most commonly used multi-factor model constructed based on Elton, Gruber, and Blake (1995). Since we do not include government mortgage backed securities funds in our sample, we exclude the mortgage related factor and the fundamental variables used in their paper. Our model specification is as follows. r i,t r f,t = α i +β 1,i (Agg t r f,t )+β 2,i Def t +β 3,i T erm t +β 4,i (SP 500 t r f,t )+β 5,i (HY ld t r f,t )+ɛ i,t, (1) 9

where r i r f is the return on a bond fund in excess of a risk free rate, r f, Agg proxies for the average returns of the aggregate bond market and captures the market wide risk, Def is the difference in returns between the high-yield index and the intermediate government index, SP 500 is a proxy for the returns of the equity market, T erm is the return spread between intermediate term government bond index and short term government bond index and HY ld is a proxy for returns of holding high yield in other words low grading bonds. Two indexes used to construct Def perfectly captures default risk since the coefficient in regressions between these two indexes is close to one according to Elton, Gruber, and Blake (1995). Blake, Elton, and Gruber (1993) and various studies on bond mutual funds find that the bond market risk factors in the above model are adequate to capture risks faced by bond funds. Base on the model, α can be interpreted as the portion of the return that cannot be explained by these risk factors. We thus employ this multi-factor model to investigate the risk-adjusted returns of the bond funds in our sample. We first examine fund performance based on the multi-factor model over the full sample period for each type of funds. We first run time series regression at the fund level for the sample period and then take the average of the α estimates within a classification type. To ensure the robustness of the results, we delete funds that do not have at least 24 monthly observations from the sample for the regressions. Table 4 reports the average of the α coefficients using time-series fund level multi-factor regression within each classification type along with the percentage of positive and negative α. In Panel A, column 2 and column 3 show that all the risk adjusted returns are significantly negative ranging from -0.083% to -0.047% per month. The average of the percentage of significantly negative α is 46.04% more than significantly positive abnormal returns. Meanwhile, the percentage of significantly negative α are larger than the percentage of significantly positive α implying after adjusting for risks, more funds reveal negative performance. The percentage of non-significant α shows similar pattern. Panel B shows similar results where the expenses are added back to net returns. Only the risk adjusted return of high yield corporate bond funds now becomes 0.028% per 10

month with t-statistic of 2.35. However, the risk adjusted returns for the other classification types are all insignificant varying from -0.02% to 0.011% per month. The coefficients of risk factors do not change as much from Panel A to Panel B since expenses contribute largely to the underperformance. As stated in Elton, Gruber, and Blake (1995), There is no evidence that managers, on average, can provide superior returns on the portfolios they manage, even if they provide their services free of cost. Table 4 provides evidence of bond funds significant underperformance over the sample period which is consistent with the previous literature. Table 3 shows that bond funds exhibit strong variation in raw return differences year by year. Results in Table 4 show that risk adjusted returns are significantly negative over the full sample period. In order to compare the raw return differences and risk-adjusted returns more directly over the sample period, we also examine year by year risk-adjusted returns. We run a 3-year monthly multi-factor rolling window regression at fund level and α are averaged for each year for each classification type. Table 5 reports the rolling-window results for each year. Staring from 1996, all the bond funds exhibit significantly negative α every year. The average of the time-series rolling α varies from -0.08% to -0.04% per month significant at 1% level. The positive raw return differences in recent years can be well explained by these risk factors and now become significantly negative implying that after adjusting for risk factors, fund managers do not deliver abnormal returns. Compared with Table 3, risk-adjusted α in Table 5 exhibit consistently negative values for every period starting from 1996 with few exceptions. There is evidence that risk-adjusted returns do not show significant variation which is inconsistent with the fact that raw return relative to benchmark indexes exhibit significant variation from 1993 to 2013. The two different fund performance evaluation approaches yield drastically different results. If we measure bond fund performance relative to their index benchmarks, many bond funds outperform their index benchmarks even after fund expenses. Moreover, such outperformance varies over time and correlates with bond market conditions. However, if we evaluate bond fund performance based on the standard multi-factor models, bond funds show reliably negative risk-adjusted returns, the negative risk-adjusted returns are largely stable and persist over the sample period. Clearly, 11

the risk exposures of bond funds differ substantially from their bond index benchmarks. 3.3 Risk Taking and Bond Fund Performance Are the different risk exposures of bond funds and bond index benchmarks we documented above due to measurement errors, fund manager skills including both security selection and market (risk) timing skills, or risk taking? In this subsection, we assess the robustness of the results of and the possible causes of the different risk exposures. Two risk factors play a predominant role in bond returns, unexpected changes in interest rates and default risk (Fama and French, 1993). Default risk arises when economic conditions worsen which in turn change the likelihood of default. During low credit risk period, higher risk assets on average enjoy higher returns. However, when financial market condition deteriorates, potential risks related with risky assets can be realized which lead to lower bond funds returns. In our first test, we use the relation between credit risk and risky asset return to distinguish the possible explanations of measurement errors, managerial skills and risk taking. We divide the full sample period into high and normal credit risk periods and assess fund returns and fund risk exposures under different market conditions. The intuition behind our test is straightforward. If measurement errors (or misclassification of fund objectives) drive the results, fund returns or fund risk exposures should not differ systematically across the different credit risk periods. Similarly, if fund managers exhibit security selection skills, they should be able to deliver positive risk-adjusted returns regardless of the credit risk periods. If fund manager market (risk) timing skills are responsible for the observed difference in risk exposures, risk-adjusted returns should be higher during high credit risk periods. If, however, fund manager risk taking is responsible for the different risk exposures, then fund returns will be lower during the high credit risk periods after adjusting for average fund risk exposure through the sample period. In the previous multi-factor model, we have shown that bond funds yield significantly negative risk adjusted returns over the full sample period. We now introduce a high credit risk indicator to differentiate risk adjusted performance between normal and high credit risk periods. We measure 12

credit risk as the difference between the yields of BBB rated corporate bonds and the yields on treasury maturities in both long term and short term. Figure 1 presents the credit spread plot over time. The most recent 2007 financial downturn displays the highest credit spread. Since Baa- Treasury generates the largest difference in yields, we construct the high credit risk indicator using 1 standard deviation within the mean of Baa measured credit spread. In our regression analysis, we set the high credit risk indicator equal to 1 if the credit spread of a specific month is above 1 standard deviation from the mean, otherwise the credit risk indicator equals 0. This method provides us with the monthly high credit risk indicator variable. The regression method in this subsection is exactly the same as the multi-factor model regression in the previous section except that we add the high credit risk indicator in the model. The average α s are shown in Table 6 along with the coefficients of the high credit risk indicator variable, along with the percentage of positive/negative α s. In Panel A, the intercept now stands for the relative performance during normal credit risk period. All classification types generate significantly negative risk-adjusted returns. Over the whole sample periods, bond funds significantly underperform risk benchmarks during the normal credit risk periods with a range of -0.076% to -0.031% per month. Most coefficients of high credit risk indicator are significantly negative, indicating that fund returns are further lower during high credit risk periods. The difference in the monthly return in the high credit risk periods and the normal credit risk periods ranges from -0.193% to -0.086%. We obtain qualitatively similar results from regressions based on bond fund pre-expense returns, and based on different specifications of the high credit risk periods, for example, when we use 0.5 standard deviation within the mean to define high credit risk indicator. The substantially lower returns during the high credit risk periods confirm the robustness of the results we document previously on the different risk exposures between bond funds and bond indexes. The evidence lends support for the risk taking based explanations on the different risk exposures. When bond funds take greater risks than contained in their benchmark index, they may outperform their index benchmark based on raw returns during normal credit risk periods, but will not outperform their risk benchmarks during the same periods. During high credit risk periods, 13

they are likely to underperform their index benchmark based on raw returns, and can significantly underperform after adjusting for average risk exposure. We further utilize the recent financial crisis of 2007-2009 as a natural experiment to investigate how risk taking by bond funds contribute to bond fund performance. Based on Figure 1, the highest credit risk during the most recent financial crisis is between from 2007:8 and 2009:7. To be consistent, we also define two normal risk periods of the same length ranging from 2003:5 to 2005:7 and 2005:8 to 2007:7, respectively. In the following analysis, we will address these three periods as pre-, during and post crisis period. Because the significantly higher credit risk during the financial crisis is largely unexpected and the large jump of credit risk significantly affected the bond market, we can more clearly identify risk taking and the effects of risk taking on bond fund performance. To start, we first run a time-series multi-factor model regression for each fund from 2003:5 to 2009:7. We define the α estimated from the whole period as the skill component of fund performance (Skill), as it captures the average risk-adjusted return over the three subperiods both during and surrounding the financial crisis. We then compute fund level average return difference relative to benchmark index for the pre-, during and post crisis periods to obtain the raw relative outperformance/underperformance. For each fund, we compute the differences between the raw relative performances over the three sub-periods and the α estimated over the whole period (2003:5-2009:7). We designate the three different values as the risk components of fund performance (Risk) during the three sub-periods. We thus decompose bond fund performance relative to the index benchmark into a skill component and a risk component. If bond fund managers do not take excessive risks and the performance is only attributed to managers skills, then the risk component of the performance or Risk is the residual that is not explained by fund manager skills specified in the model. Risk should be uncorrelated between the two contiguous periods or positively correlated if the model fails to capture fully fund manager skills. However, if performance is also attributed to risk taking, such risk component performance is more likely to reverse from normal to high credit risk period since potential risks are realized during the financial crisis period. Consequently, the higher performance during the pre-crisis period 14

reverses and predicts lower performance during the financial crisis period. We measure fund manager skills based on the α estimated over the full period surrounding the financial crisis as fund performance over the whole period provides a more reliable gauge on fund manager skills. Thus the skill component is a constant and is naturally persistent over the three sub-periods. In order to assess the validity of our approach and the robustness of the results we presented above, we also run the multi-factor model regression for each fund for each of the three sub-period and define the α estimated from the each sub-period as the skill component of fund performance (Skill). We report the skill component of fund performance in Panel B, following the same approach in Panel A in Table 7. The results show substantially different patterns than those reported in Panel A the skill component of fund performance exhibits persistence rather than reversal. We also examine the results on the risk component of fund performance based on the α estimated over the three sub-period. We find similar results as reported in Panel A. Overall, the results based on fund performance surrounding the recent financial crisis offer direct support for the risk-taking hypothesis. Funds that perform well pre-crisis due to greater risk exposure performed poorly during the financial crisis, and vice versa. In contrast, the estimated fund manager skills do not show patterns of reversal across the periods but exhibit some level of persistence. To sum up, the results in this section suggest that bond funds differ systematically from their index benchmarks in their risk exposure. The difference in risk exposure helps to explain the difference in raw fund performance relative to their index benchmarks and helps to reconcile the different results in fund performance evaluations with and without controlling for bond market risk factors. The generally greater risk exposure in bond funds increases fund returns during normal credit risk periods and reduces fund returns during high credit risk period. Such risk taking behavior helps to explain the time series variations in bond fund performance relative to their index benchmarks. 15

4 What Drives Bond Fund Risk Taking? We find in the previous section that on average, bond funds take greater risks than their index benchmarks. In this section, we explore potential causes of such risk-taking behavior. We focus on the following questions: What drives bond fund risk taking, and why do some fund managers decide to deviate from their proper risk benchmarks? 4.1 Short-term Risk Shifting Several studies on equity mutual funds (see, e.g., Brown, Harlow, and Starks (1996), Chevalier and Ellison (1997)) provide evidence that, because mutual funds are often evaluated annually, poor performing funds in the early part of the year may have an incentive to shift to higher risk assets in order to improve the performance within the year. This type of short-term risk shifting behavior may not explain completely the evidence of risk taking we documented in the previous section, but the existence of such risk-shifting behavior can at least help us to understand some of the motives behind bond fund risk taking. To examine such short-term risk-shifting behavior within a calender year, we follow Brown, Harlow, and Starks (1996) and classify funds into winner and loser funds based on their performance during the early part of the year (over the six- or nine-month period). We then compare the frequency distribution of increasing risk between winner and loser funds in the later part of the year. To start with, within each fund style classification, we form three groups based on a funds performance during the first M month of a year. For each fund j, the cumulative return over month M is computed as: M RT N j,m = (1 + r j,t ) 1 (2) t=1 where r j,t is the monthly return for fund j in month t. We rank each fund into 3 groups based on RT N in order to maintain enough observations within each classification type. We define winners as the top ranking group and losers as the bottom ranking group. We select the first half of each 16

year as our performance evaluation period (i.e., M = 6). We then compute the ratio of volatility (RAR) based on fund return volatility after and before month M in order to examine changes in fund risk levels across the three performance groups. For each fund j at month M, RAR is calculated as: RAR j,m = 12 t=m+1 (r j,t r j,12 M ) 2 / (12 M) 1 M t=1 (r j,t r j,m ) 2 (M 1) (3) RAR is the ratio of fund return standard deviation after month M relative to return standard deviation before month M. Without risk-shifting behavior, the ratio of standard deviation of fund returns will be similar for the three groups of funds. If poor performing funds take greater risk during the second period of a year in order to catch up with other funds in the same style, the ratio will be higher for these loser funds. To examine the tendency of funds in the three performance groups to shift risks, we rank funds within each style classification into 3 groups based on the volatility ratio. We define the top ranking group as high RAR and bottom ranking group as low RAR. In the end, we will have a (RT N,RAR) pair for each fund and a 2x2 classification scheme based on performance and volatility ratio: High RT N, High RAR; High RT N, Low RAR; Low RT N, High RAR; Low RT N, Low RAR. The null hypothesis is that, without systematic risk-shifting, these two classification methods are independent thus the frequency of funds falling into one of the four categories is the same (25%). We employ a Chi-Square test to examine if the frequencies are significantly different across the four categories. Table 8 reports the results for the frequency distribution based on fund performance and volatility ratios in the first five columns. Among all the bond fund style classifications, only high yield corporate bond shows significantly higher frequencies for Low RT N, High RAR and High RT N, Low RAR which is 26.40% and 28.56%, respectively. This implies that for high yield corporate bond funds, loser funds shift to higher risk assets so as to improve performance in the second half of the year meanwhile winner funds exhibit a different pattern. Nevertheless, the rest of the classification types are either insignificant or exhibit significantly lower frequencies for Low RT N, High 17

RAR and High RT N, Low RAR. The results suggest, measured based on fund return volatility, loser bond funds do not increase risks and winner bond funds do not decrease risks over short term. In addition to examining fund risk shifting based on fund return volatility, we further utilize the performance decomposition methodology to directly assess changes in the risk component of fund performance during the calender year. Again, the skill portion of the performance is the riskadjusted return (α) from the multi-factor model and the risk component of fund performance(risk) is the difference between index-adjusted return and the risk-adjusted return. As such, the risk component of performance captures the portion of return explained by risk taking. The underlying arguments for our test based fund returns are the same as those for the volatility ratio tests in Brown, Harlow, and Starks (1996) and Busse (2001). If poor performing funds take more risks to improve performance after month M, the risk component of the performance of such funds should increases over the second part of a year. We thus can use the risk components of performance (Risk) in the two periods to examine the probability of funds moving from low risk taking to high risk taking or vice versa. The methodology of return based risk-shifting test follows closely the volatility ratio based test. We first sort funds within each classification category into 3 groups based on raw cumulative returns during the first M months of the year to obtain winner and loser funds. Then we compute the risk component of fund performance for winner and loser funds using the risk-adjusted returns from the rolling-window multi-factor regressions over the previous three-year period. We compute the risk component of fund performance for winner and loser funds in the two periods of the year: before and after month M based on the index-adjusted returns and the risk-adjusted returns. We sort winner and loser funds into 3 risk groups based on the risk component of fund performance during the first M months of the year, with the top ranking funds defined as High Risk 1st and the bottom ranking funds as Low Risk 1st. We similarly rank fund risks for the second part of the year and obtain funds with high ( High Risk 2nd ) and low risks ( Low Risk 2nd ). The above method also generates a 2x2 frequency table with the (Risk 1st, Risk 2nd ) pair. If poor performing bond funds take risk to improve performance, we expect to observe sig- 18

nificantly higher than 25% frequency for Low Risk 1st /High Risk 2nd for these funds. Again, we employ a Chi-Square test to investigate the frequency of winning and losing funds in high/low risk taking category in the first M months moving into high/low risk taking category in the remaining 12-M months of the year. Unlike the volatility ratio based test, the return-based test can examine fund risk-shifting over a shorter window in the second part of the year. We report in Table 8 two evaluation periods based on the first 6- and 9-months, respectively: (6, 6) and (9, 3). From both panels, we find significantly lower than 25% frequency for loser funds to move from Low Risk 1st to High Risk 2nd, or for winner funds to move from High Risk 1st to Low Risk 2nd. In fact, low risk loser funds tend to stay in the low risk category in the second period and high risk winner funds tend to stay in the high risk category in the second period. The results indicate that winner and loser bond funds do not move to difference risk categories in the second part of the year. To sum up, the results from the standard volatility ratio tests and our return based tests provide no evidence that bond funds systematically shift risks during the year based on the prior performance within the year. Unlike equity funds, bond funds do not seem to shift risks frequently over short term. 4.2 Long-term Performance and Risk Taking We do not find significant short-term risk shifting in bond funds within a calender year. We now consider another possibility that bond fund managers may decide to take greater risks and such risk-taking behavior could be more persistent than observed in equity mutual funds. Unlike equity fund risk taking, bond fund risk taking, in the form of increasing credit risk (lower credit quality) and/or increasing interest risk (longer maturity), can more reliably generate higher returns during normal market condition period. Competition pressure may motivate bond fund managers to take greater risks than their benchmarks. In this case, longer term poor performance may drive risk taking. To test this hypothesis, we examine the relation between fund performance over two- and three-year periods and fund risk taking in the subsequent period. To measure fund risk-taking, we again employ the risk component of fund performance defined 19

by the difference between index-adjusted return and risk-adjusted return. We estimate the riskadjusted returns (α s) based on the rolling-window multi-factor regressions and then compute the risk component of fund performance for each month. Our main variable of interest is fund performance (index-adjusted return) over the past N-year period (N = 2, 3), and we intend to examine how fund performance over a longer period relates to fund risk-taking. We have shown previously that risk-taking can have distinctive impacts on fund performance during high and normal risk periods. Risk taking can lead to higher returns during normal credit risk period, but during high risk periods when the high risks are realized, risk-taking leads to lower returns. In order to identify and sharpen the test on the relation between fund past performance and fund risk-taking, we examine the relation separately for the high and normal risk periods. A month is classified as high credit risk month if the BAA-Treasury spread is above 0.5 standard deviation from the mean. We use the Fama-MacBeth methodology and run the cross-sectional regression month by month, but compute the mean and t-value for normal credit risk period and high credit risk period separately. The cross-sectional regression is specified as follows, Risk i,t = β 1,i + β 2,i P ast P erformance t 1 + β 3,i Exp t 1 + β 4,i F low Rate t 1 +β 5,i LogF amily T NA t 1 + β 6,i Bond T NA/F amily T NA t 1 + β 7,i LogAge t 1 +β 8,i LogT NA t 1 + ɛ i,t (4) where Risk is the risk component of fund performance and is defined as the difference between monthly index-adjusted return and its past N-year multi-factor model α, P astp erf ormance is the cumulative past relative performance relative to the benchmark indexes (index-adjusted return), Exp is the ratio of a bond s operating expenses borne by shareholders to the total investment value and is expressed in percentage, F lowrate is the ratio of fund flow at t and its TNA at t 1, Age is the number of years since the first formation date of a fund, F amilyt NA is defined as the total TNA of all the funds within a mutual fund management firm, BondT NA/F amilyt NA is the ratio of total TNA of the bond funds and the total TNA of all the mutual funds managed by a firm, 20

and T NA is the fund total net asset value. We include fund style classification dummies in the cross-sectional regressions. Table 9 reports the Fama-MacBeth regression results. To ensure the robustness of the results, we measure fund risk-taking based on α s from 2-year and 3-year rolling-window regressions. The measurement period of past fund performance corresponds to the estimation period of α. We compute the mean values of the estimation coefficients and the associated t-values for normal credit risk period and high credit risk period separately. As shown in the table, past performance is significantly negatively related with risk component performance in both panels for normal credit risk periods, indicating that underperforming funds tend to take more risks. For the high risk periods, past performance is positively related to fund risk-taking, suggesting a different relation between fund past performance and fund risk-taking than that shown in the normal credit risk period. While underperformance leads to greater risk-taking, such risk-taking leads lower returns in the higher risk period. The results are consistent across two assessment periods of α. The results show that older funds are inclined to take more risks with coefficient being significantly positive for both assessment periods during normal credit risk periods. In addition, bond funds in larger fund families take more risks than funds from smaller families measured by the relation for normal risk periods. Government bond funds may have different risk exposure than corporate bond funds. For example, interest rate risk can be particularly important for this type of funds. We also separately examine the relation between fund performance and fund risk-taking for government funds based on high and normal risk periods classified by term spread (10-year Treasury bond yield and 3-month T-bill yield), the results are similar. Overall, the results provide evidence on the relation between long-run fund performance and fund risk-taking. It is likely that bond fund managers may decide to increase fund risk exposures when fund performance lags their peers. Huang, Sialm, and Zhang (2011) find some evidence in equity funds that poor performing funds increase risks over time. However, unlike equity fund risk taking, bond fund risk taking, in the form of increasing credit risk (lower credit quality) and/or increasing interest risk (longer maturity), can more reliably generate higher returns during normal 21