- Email: [email protected]
Should hedge funds be cautious reporting high returns?
Research in International Business and Finance 30 (2014) 195–201
Contents lists available at ScienceDirect
Research in International Business and Finance j o ur na l ho me pa ge : w w w . e l s e v i e r . c o m / l o c a t e / r i b a f
Should hedge funds be cautious reporting high returns? Benjamin R. Auer ∗ University of Leipzig, Department of Finance, Grimmaische Str. 12, 04109 Leipzig, Germany
a r t i c l e
i n f o
Article history: Received 5 March 2013 Received in revised form 7 July 2013 Accepted 9 July 2013 Available online 20 July 2013 JEL classification: G10 G11 Keywords: Sharpe ratio Hedge funds Performance measurement Manipulation
a b s t r a c t In a recent article, Schuster and Auer (2012) show that fund managers with a certain positive performance need to be aware of the fact that too high prospective excess returns can lower the empirical Sharpe ratio of their funds. In this note, we investigate the empirical relevance of this effect. We analyse whether hedge funds being evaluated on the basis of the Sharpe ratio negatively influence their performance by reporting too high returns. Our results show that a economically significant number of hedge funds listed in the CISDM hedge fund database has at least once reported a high return causing this effect. © 2013 Elsevier B.V. All rights reserved.
1. Introduction In the last decades, the widespread belief that the best-known reward-to-risk ratio, the Sharpe ratio, is an inadequate performance measure in the case of non-normally distributed returns has led to an explosion in the development of alternative performance measures. The Sharpe ratio was discarded especially for the evaluation of hedge funds because their returns show asymmetry and fat tails. However, the recent contributions of Eling and Schuhmacher (2007) and Schuhmacher and Eling (2011, 2012) move an important step towards rehabilitating the Sharpe ratio. The authors show that (a) a comparison of the Sharpe ratio to twelve other performance measures results in almost identical rank ordering across hedge funds and emphasise that (b) normally distributed returns are not required
∗ Tel.: +49 341 97 33 672; fax: +49 341 97 33 679. E-mail address: [email protected] 0275-5319/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ribaf.2013.07.004
196
B.R. Auer / Research in International Business and Finance 30 (2014) 195–201
to justify the use of the Sharpe ratio to rank funds. Taking also into account that the Sharpe ratio can be used when a hedge fund represents the entire or only a portion of the investors risky investment (see Dowd, 2000), that the Sharpe ratio is a computational easy performance measure for which we already have sophisticated statistical tests (see Lo, 2002; Ledoit and Wolf, 2008) and that it is the standard measure used in most empirical studies (for recent applications, see Arnold et al., 2004; Huang and Lin, 2011; Hammami et al., 2013), it might be considered as the performance measure investors prefer from a theoretical as well as from a practical point of view. It is well-known that hedge fund managers do not have to provide information regarding a fund’s return and usually voluntarily report to hedge fund databases after an incubation period – a time lag between the inception date of the fund and the date the track record is included into a database (see Fung and Hsieh, 2000, 2006). As hedge funds are not allowed to attract investors through public advertisement (see Fung and Hsieh, 1999; Posthuma and Van der Sluis, 2003), they use the listings in the databases for marketing purposes. A fund with a successful incubation period will backfill the returns, whereas a fund with a negative performance will start reporting as soon as a good performance is achieved and will not backfill data. Thus, hedge funds only supply data on which they wish to be evaluated by investors. If investors evaluate the performance of funds on the basis of the Sharpe ratio, hedge fund managers may also have an incentive to take into account the recent findings of Schuster and Auer (2012) when reporting new returns to databases. The authors show that for funds whose performance exceed a certain limit, not only low (below a certain critical level) but also high (above a certain critical level) excess returns in a prospective period can result in a lower empirical Sharpe ratio. Therefore, good funds evaluated on the basis of the Sharpe ratio may negatively influence their performance by reporting too high returns. These findings are especially relevant for hedge funds because Brown et al. (1999) and Ibbotson et al. (2011) report that hedge funds have shown a persistent good performance in the last decades. Thus, they may often encounter situations where they might be tempted to shift payments between periods in order to avoid too high returns and a reduced empirical Sharpe ratio. There may even be an incentive to optimise (or manipulate) backfill data in order to fight negative effects on historic funds rankings and to make relative performance look more persistent. In this note, we analyse the hedge funds listed in the Center for International Securities and Derivatives Markets (CISDM) database. We focus on answering two research questions: How often were hedge funds in situations where reporting a too high return could have reduced their empirical Sharpe ratio? And, have managers actually negatively influenced their performance by reporting too high returns? The note is organized as follows: Section 4 briefly reviews the theoretical results of Schuster and Auer (2012). Section 3 describes the dataset. Section 4 presents the results of our empirical analysis. Finally, Section 5 concludes. 2. Critical excess returns Consider a fund for which we have a time series of n − 1 excess returns (over a riskfree rate) denoted n−1 r1 , . . ., rn−1 . Its sample average excess return for the first n − 1 periods is r n−1 = (1/(n − 1)) i=1 ri =: a
n−1
2 = (1/(n − 2)) i=1 (ri − a)2 =: b. Thus, the empirical Sharpe and the related sample variance is ˆ n−1 √ n−1 = r n−1 /ˆ n−1 = a/ b. ratio is given by SR Schuster and Auer (2012) show that for a fund fulfilling the four conditions n > 2, a > 0, b > 0 and n−1 > n−1/2 a prospective excess return rn below na2 − b > 0 ⇔ SR
l
r = a + n· or above ru = a + n ·
h−
h+
h2
ah + (n − 1)
ah h2 + (n − 1)
(1)
,
(2)
B.R. Auer / Research in International Business and Finance 30 (2014) 195–201
197
n < SR n−1 . Only for new excess returns where h = ab/(na2 − b), causes a lower empirical Sharpe ratio SR n > SR n−1 . rl < rn < ru we get SR These results highlight that a fund with a sufficient number of excess return observations, positive average and standard deviation of excess returns in period n − 1, and an empirical Sharpe ratio in period n − 1 greater than n−1/2 encounters the effect that a high prospective excess return rn > ru lowers its empirical Sharpe ratio. Henceforth, we call the situation where the above mentioned four conditions are fulfilled critical situation and the case of an actual reduction of the empirical Sharpe ratio because of a high excess return high return effect. As we can see from (2), this effect has special (but not exclusive) relevance in the early years of a fund’s existence because for funds with very high n the excess return ru can (but must not) become large and virtually unreachable. 3. Data In our study, we use the same dataset as in Auer (2013). We obtained hedge fund data from the CISDM hedge fund database being one of the oldest and most commonly used hedge fund databases in the market (see Ding and Shawky, 2007; Eling, 2009). As of November 2009, it contained return data for a total of 6854 individual hedge funds (not including funds of hedge funds) reporting monthly net-of-fee returns for the time period from January 1972 to November 2009. Like other popular hedge fund databases (e.g. MAR, HFR, TASS; see Amin and Kat, 2003), the CISDM database offers additional information on each fund, such as company name, strategy description, and net asset value (for further details, see www.isenberg.umass.edu/CISDM/). The database includes 2353 (34.33%) surviving and 4501 (65.67%) dissolved funds. Our findings were generated on the basis of a reduced sample resulting from an exclusion of all funds that did not report at least a one year return history to the database, funds with only quarterly returns and funds with obviously faulty return entries. This screening procedure results in a sample of 6377 remaining funds. Following Eling and Schuhmacher (2007), a rolling monthly riskfree rate corresponding to the interest rate on 10-year US Treasury bonds (extracted from Thomson Reuters Datastream) was used to calculate the excess returns of these funds. Alternatively, a constant riskfree rate equal to the average interest rate for the period under consideration or the interest rate at the beginning of the investigation period could be used. However, all three approaches yield virtually identical results as far as the high return effect is concerned. Table 1 describes major characteristics of the 6377 funds in our sample. It shows the numbers of funds that follow specific investment strategies and invest with particular geographical focuses. Furthermore, it reports the mean net asset value and the mean fund age in the dataset. As we can see, most funds are attributed to the strategy “Equity Long/Short” (2415) and the geographical focus “Global” (1364). “Market Timing” (3) and “Australia/New Zealand” (16) subsume the lowest numbers of funds. There is also a considerable number of funds (2537) that do not disclose their geographical focus of operations. The mean net asset value amounts to about 30 million US Dollars. The mean fund age is about 64 months or roughly 5 years. 4. Empirical analysis In a first step of our empirical analysis, we check in which periods of an individual fund’s history the conditions stated in Section 2 were fulfilled. We find that for only 883 funds the conditions were never met resulting in a smaller sample of 5494 funds that encountered our critical situation at least once. For each fund in the reduced sample, we then calculate the fraction of critical periods to total observation periods. Fig. 1 plots the distribution of those fractions and shows that for a considerable number of funds the critical periods account for more than 90% of the entire return history. 1182, 902, 1138 and 2272 funds yield fractions in the intervals W =]0 % , 25 %], X =]25 % , 50 %], Y =]50 % , 75 %] and Z =]75 % , 100 %], respectively. Before continuing with our main analysis, it is instructive to have a look at the time series evolution of the number of critical situations across all funds. For each month in our sample period, we count the number of funds in a critical situation and plot the resulting time series in Fig. 2. It reveals a
198
B.R. Auer / Research in International Business and Finance 30 (2014) 195–201
Table 1 Dataset characteristics. Hedge fund strategy Capital structure arbitrage Convertible arbitrage Distressed securities Emerging markets Equity long only Equity long/short Equity market neutral Event driven multi strategy
22 219 179 531 205 2415 347 254
Fixed income Fixed income MBS Fixed income arbitrage Global macro Market timing Merger arbitrage Multi strategy Option arbitrage
186 90 199 342 3 118 360 43
Other relative value Regulation D Relative value multi strategy Sector Short bias Single strategy Undisclosed
Geographical focus Asia/Pacific Asia/Pacific (excl. Japan) Australia/New Zealand Eastern Europe Global
140 195 16 108 1364
Japan Latin America Middle East/Africa North America North America/Europe
175 94 43 561 57
UK United States Western Europe Undisclosed
Other characteristics Mean net asset value Mean age
32 16 100 449 54 139 74
67 633 387 2537
29.56 64.13
For our sample of 6377 hedge funds, this table shows the numbers of funds that follow specific investment strategies and operate with certain geographical focuses. It also reports the mean net asset value (in millions of US Dollars) and the mean age (in months) of the funds in the dataset.
sharp rise in the number of critical situations as we move from 1972 to 2008. This observation can be explained as follows. First, the hedge fund market has experienced enormous growth in our sample period leading to a significant extension of the number of funds listed in the CISDM database (see Fung and Hsieh, 1999; Ding and Shawky, 2007). Second, as a critical situation is accompanied by a positive Sharpe ratio, the sharp rise also implies that a large number of funds entered the market that deliver desirable investment performance in excess of a riskfree rate (see Ibbotson et al., 2011). The decline in 2009 can be explained by the turbulences related to the recent financial crisis that led to
250
200
150
100
50
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Fig. 1. Distribution of the fraction of critical periods in hedge funds’ return histories. For 5494 hedge funds, this figure shows the distribution of the individual fraction of periods in which a high prospective excess return can result in a lower empirical Sharpe ratio to the total number of return observations. The sample period spans from January 1972 to November 2009.
B.R. Auer / Research in International Business and Finance 30 (2014) 195–201
199
3000
2500
2000
1500
1000
500
0 1972
1984
1992
2008
Fig. 2. Number of hedge funds in critical situations. This figure plots the time series that results from counting the number of hedge funds in critical situations for each month in our sample period.
a negative performance of many hedge funds. It is also attributable to a return reporting lag in the CISDM database. In the second step of our analysis, we seek to answer the question of whether the returns reported by hedge fund managers caused their empirical Sharpe ratio to rise or to fall in the identified critical situations. In the case of a falling Sharpe ratio, we are especially interested in whether the return responsible for the reduction was one associated with an excess return above the critical value ru . Table 2 documents our results separately for the four intervals mentioned above. For each interval, Panel A reports the number of critical situations as well as the numbers of cases in which the reported return led to an increase or a decrease of the empirical Sharpe ratio. The latter number is split up into the two possible causes for reduction (an excess return below rl or above ru ). As we can see, within each interval hedge funds reported too high returns in about 1% of the detected critical situations leading to a lower empirical Sharpe ratio. To get a more detailed picture on the fund level, Panel B gives the number of hedge funds that lowered their Sharpe ratio at least once by reporting a too high return. We see that about 8%, 14%, 15% and 32% of the funds in the intervals W, X, Y and Z, respectively, have this property. To show that our results are not only relevant in the early return history of a hedge fund, we take a more detailed look at the length the return history of a fund had reached in the period it experienced the high return effect. Some authors suggest that 24 monthly returns are the minimum for calculating meaningful performance measures (see for example Ackermann et al., 1999; Gregoriou, 2002; Capocci and Hübner, 2004; Liang and Park, 2007; Eling, 2009). Therefore, we also calculate the numbers of situations and funds where the empirical Sharpe ratio was lowered by a high return in the presence of a reported return history of at least 24 months (see Table 2). Our results show that in the most interesting interval Z about 26% of the high return effects occurred when the corresponding funds had a reported return history of at least 24 months. In fund numbers this means that within this interval we can identify 171 hedge funds that have experienced high return effects even in their late return history. Finally, in order to shed some light on the characteristics of funds that have experienced high return effects, Table 3 classifies these funds in a manner similar to Table 1. Clearly, high return effects are not limited to funds with a certain investment strategy or geographical focus. In comparison to the values in Table 1, the mean net asset value of funds with high return effects is somewhat lower, while the mean age is quite similar. However, these results are not surprising because the high return effect is a phenomenon related to specific return properties. If a fund invests in, for example, US stocks only, this does not necessarily mean that these particular properties are more or less likely.
200
B.R. Auer / Research in International Business and Finance 30 (2014) 195–201
Table 2 Main results.
Panel A: Number of critical situations Higher Sharpe ratio (rl < rn < ru ) Lower Sharpe ratio (rn < rl ) Lower Sharpe ratio (rn > ru ) Return history ≥ 24 month Panel B: Number of hedge funds Higher Sharpe ratio (rl < rn < ru ) Lower Sharpe ratio (rn < rl ) Lower Sharpe ratio (rn > ru ) Return history ≥ 24 month
Interval W ] 0%, 25%]
Interval X ] 25%, 50%]
Interval Y ] 50%, 75%]
Interval Z ] 75%, 100%]
6903 2509 (36.35%) 4279 (61.99%) 115 (1.67%) 1 (0.87%)
19,296 8707 (45.12%) 10,434 (54.07%) 155 (0.80%) 1 (0.65%)
47,565 23,415 (49.23%) 23,945 (50.34%) 205 (0.43%) 4 (1.95%)
172,468 85,300 (49.46%) 85,860 (49.78%) 1308 (0.76%) 344 (26.30%)
1182 742 (62.77%) 1175 (99.41%) 96 (8.12%) 1 (1.04%)
902 869 (96.34%) 899 (99.67%) 124 (13.75%) 1 (0.11%)
1138 1138 (100.00%) 1137 (99.91%) 174 (15.29%) 4 (0.35%)
2272 2272 (100.00%) 2269 (99.87%) 724 (31.87%) 171 (7.53%)
Panel A of this table reports the number of critical situations (defined in Section 2) that can be assigned to hedge funds whose fraction of critical situations to the total number of return observations lies within the intervals W, X, Y or Z. Furthermore, for each interval the numbers (and percentages in parentheses) of critical situations are given where rl < rn < ru , rn < rl and rn > ru . Panel B shows the numbers of funds within each interval and the numbers (and percentages in parentheses) of funds that experienced rl < rn < ru , rn < rl and rn > ru at least once. Furthermore, the Panels A and B reveal the numbers (and percentages of the numbers in the lines rn > ru ) of situations and funds in each interval where the Sharpe ratio was lowered because of rn > ru and the return history of the individual funds covered at least 24 months. Table 3 Characteristics of high return effect funds. Hedge fund strategy Capital structure arbitrage Convertible arbitrage Distressed securities Emerging markets Equity long only Equity long/short Equity market neutral Event driven multi strategy Geographical focus Asia/Pacific Asia/Pacific (excl. Japan) Australia/New Zealand Eastern Europe Global Other characteristics Mean NAV Mean age
7 64 42 78 22 394 40 55
Fixed income Fixed income MBS Fixed income arbitrage Global macro Market timing Merger arbitrage Multi strategy Option arbitrage
39 28 56 43 0 19 55 9
23 31 4 28 200
Japan Latin America Middle East/Africa North America North America/Europe
33 18 12 112 19
Other relative value Regulation D Relative value multi strategy Sector Short bias Single strategy Undisclosed
UK United States Western Europe Undisclosed
8 11 16 83 4 31 14
10 125 51 452
18.14 68.97
Constructed in analogy to Table 1, this table describes major properties of the 1118 hedge funds where the high return effect could be observed at least once.
5. Conclusion Reporting returns signaling a good performance is a hedge fund’s most important marketing strategy. However, if investors evaluate a hedge fund on the basis of its Sharpe ratio listing too high returns can result in a lower empirical Sharpe ratio and therefore cause an unfavorable signal. In this note, we show that an economically significant number of funds listed in the CISDM hedge fund database historically has at least once suffered from this kind of effect. Taking into account that private investors
B.R. Auer / Research in International Business and Finance 30 (2014) 195–201
201
typically use easily obtainable measures like the Sharpe ratio when choosing the best fund from a set of given alternatives, the effect highlighted by Schuster and Auer (2012) may thus have influenced historical investment decisions in a negative way. In the light of this evidence, one can take several different positions. First, one might advise hedge fund managers to reconsider reporting exceptionally high returns, unless they are certain that investors use performance measures that do not show a high return effect. One example for such a measure is the Calmar ratio (average excess return divided by the maximum drawdown) proposed by Young (1991). Second, the risk of actually encountering the high return effect could be regarded as not very high. Even though the high return effect arose for a large number of funds, it occurred only in about 1% of the time. Thus, fund managers might just tolerate this risk because it would probably be more cost intensive to consequently monitor how performance measures react to reported returns. Third, a manager’s strategy in a certain period may not even be to attract new investors by controlling his Sharpe ratio but to maximise his managerial (incentive) fees. In this case, the manager would prefer reporting a high return and tolerate a decreasing Sharpe ratio. Acknowledgement The author thanks an anonymous referee for very useful comments and suggestions. References Ackermann, C., McEnally, R., Ravenscraft, D., 1999. The performance of hedge funds: risk, return, and incentives. Journal of Finance 54 (3), 833–874. Amin, G., Kat, H., 2003. Hedge fund performance 1990–2000: do the “Money Machines” really add value? Journal of Financial and Quantitative Analysis 38 (2), 251–274. Arnold, T., Nail, L., Nixon, T., 2004. Do ADRs enhance portfolio performance for a domestic portfolio? Evidence from the 1990s. Research in International Business and Finance 18 (3), 341–359. Auer, B.R., 2013. The low return distortion of the Sharpe ratio. Financial Markets and Portfolio Management, forthcoming. Brown, S.J., Goetzmann, W.N., Ibbotson, R.G., 1999. Offshore hedge funds: survival and performance 1989–95. Journal of Business 72 (1), 91–117. Capocci, D., Hübner, G., 2004. Analysis of hedge fund performance. Journal of Empirical Finance 11 (1), 55–89. Ding, B., Shawky, H., 2007. The performance of hedge fund strategies and the asymmetry of return distributions. European Financial Management 13 (2), 309–331. Dowd, K., 2000. Adjusting for risk: an improved Sharpe ratio. International Review of Economics and Finance 9 (3), 209–222. Eling, M., 2009. Does hedge fund performance persist? Overview and new empirical evidence. European Financial Management 15 (2), 362–401. Eling, M., Schuhmacher, F., 2007. Does the choice of performance measure influence the evaluation of hedge funds? Journal of Banking and Finance 31 (9), 2632–2647. Fung, W., Hsieh, D.A., 1999. A primer on hedge funds. Journal of Empirical Finance 6 (3), 309–331. Fung, W., Hsieh, D.A., 2000. Performance characteristics of hedge funds and commodity funds: natural vs. spurious biases. Journal of Financial and Quantitative Analysis 35 (3), 291–307. Fung, W., Hsieh, D.A., 2006. Hedge funds: an industry in its adolescence. Federal Reserve Bank of Atlanta Economic Review 91 (4), 1–33. Gregoriou, G., 2002. Hedge fund survival lifetimes. Journal of Asset Management 3 (2), 237–252. Hammami, Y., Jilani, F., Oueslati, A., 2013. Mutual fund performance in Tunisia: a multivariate GARCH approach. Research in International Business and Finance 29, 35–51. Huang, M., Lin, J., 2011. Do ETFs provide effective international diversification? Research in International Business and Finance 25 (3), 335–344. Ibbotson, R.G., Chen, P., Zhu, K.X., 2011. The ABCs of hedge funds: alphas, betas, and costs. Financial Analysts Journal 67 (1), 15–25. Ledoit, O., Wolf, M., 2008. Robust performance hypothesis testing with the Sharpe ratio. Journal of Empirical Finance 15 (5), 850–859. Liang, B., Park, H., 2007. Risk measures for hedge funds: a cross-sectional approach. European Financial Management 13 (2), 333–370. Lo, A., 2002. The statistics of Sharpe ratios. Financial Analysts Journal 58 (4), 36–52. Posthuma, N., Van der Sluis, P., 2003. A reality check on hedge fund returns. Free University of Amsterdam, Unpublished Manuscript. Schuhmacher, F., Eling, M., 2011. Sufficient conditions for expected utility to imply drawdown-based performance rankings. Journal of Banking and Finance 35 (9), 2311–2318. Schuhmacher, F., Eling, M., 2012. A decision-theoretic foundation for reward-to-risk performance measures. Journal of Banking and Finance 36 (7), 2077–2082. Schuster, M., Auer, B.R., 2012. A note on empirical Sharpe ratio dynamics. Economics Letters 116 (1), 124–128. Young, T., 1991. Calmar ratio: a smoother tool. Futures 20 (1), 40.
Contents lists available at ScienceDirect
Research in International Business and Finance j o ur na l ho me pa ge : w w w . e l s e v i e r . c o m / l o c a t e / r i b a f
Should hedge funds be cautious reporting high returns? Benjamin R. Auer ∗ University of Leipzig, Department of Finance, Grimmaische Str. 12, 04109 Leipzig, Germany
a r t i c l e
i n f o
Article history: Received 5 March 2013 Received in revised form 7 July 2013 Accepted 9 July 2013 Available online 20 July 2013 JEL classification: G10 G11 Keywords: Sharpe ratio Hedge funds Performance measurement Manipulation
a b s t r a c t In a recent article, Schuster and Auer (2012) show that fund managers with a certain positive performance need to be aware of the fact that too high prospective excess returns can lower the empirical Sharpe ratio of their funds. In this note, we investigate the empirical relevance of this effect. We analyse whether hedge funds being evaluated on the basis of the Sharpe ratio negatively influence their performance by reporting too high returns. Our results show that a economically significant number of hedge funds listed in the CISDM hedge fund database has at least once reported a high return causing this effect. © 2013 Elsevier B.V. All rights reserved.
1. Introduction In the last decades, the widespread belief that the best-known reward-to-risk ratio, the Sharpe ratio, is an inadequate performance measure in the case of non-normally distributed returns has led to an explosion in the development of alternative performance measures. The Sharpe ratio was discarded especially for the evaluation of hedge funds because their returns show asymmetry and fat tails. However, the recent contributions of Eling and Schuhmacher (2007) and Schuhmacher and Eling (2011, 2012) move an important step towards rehabilitating the Sharpe ratio. The authors show that (a) a comparison of the Sharpe ratio to twelve other performance measures results in almost identical rank ordering across hedge funds and emphasise that (b) normally distributed returns are not required
∗ Tel.: +49 341 97 33 672; fax: +49 341 97 33 679. E-mail address: [email protected] 0275-5319/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ribaf.2013.07.004
196
B.R. Auer / Research in International Business and Finance 30 (2014) 195–201
to justify the use of the Sharpe ratio to rank funds. Taking also into account that the Sharpe ratio can be used when a hedge fund represents the entire or only a portion of the investors risky investment (see Dowd, 2000), that the Sharpe ratio is a computational easy performance measure for which we already have sophisticated statistical tests (see Lo, 2002; Ledoit and Wolf, 2008) and that it is the standard measure used in most empirical studies (for recent applications, see Arnold et al., 2004; Huang and Lin, 2011; Hammami et al., 2013), it might be considered as the performance measure investors prefer from a theoretical as well as from a practical point of view. It is well-known that hedge fund managers do not have to provide information regarding a fund’s return and usually voluntarily report to hedge fund databases after an incubation period – a time lag between the inception date of the fund and the date the track record is included into a database (see Fung and Hsieh, 2000, 2006). As hedge funds are not allowed to attract investors through public advertisement (see Fung and Hsieh, 1999; Posthuma and Van der Sluis, 2003), they use the listings in the databases for marketing purposes. A fund with a successful incubation period will backfill the returns, whereas a fund with a negative performance will start reporting as soon as a good performance is achieved and will not backfill data. Thus, hedge funds only supply data on which they wish to be evaluated by investors. If investors evaluate the performance of funds on the basis of the Sharpe ratio, hedge fund managers may also have an incentive to take into account the recent findings of Schuster and Auer (2012) when reporting new returns to databases. The authors show that for funds whose performance exceed a certain limit, not only low (below a certain critical level) but also high (above a certain critical level) excess returns in a prospective period can result in a lower empirical Sharpe ratio. Therefore, good funds evaluated on the basis of the Sharpe ratio may negatively influence their performance by reporting too high returns. These findings are especially relevant for hedge funds because Brown et al. (1999) and Ibbotson et al. (2011) report that hedge funds have shown a persistent good performance in the last decades. Thus, they may often encounter situations where they might be tempted to shift payments between periods in order to avoid too high returns and a reduced empirical Sharpe ratio. There may even be an incentive to optimise (or manipulate) backfill data in order to fight negative effects on historic funds rankings and to make relative performance look more persistent. In this note, we analyse the hedge funds listed in the Center for International Securities and Derivatives Markets (CISDM) database. We focus on answering two research questions: How often were hedge funds in situations where reporting a too high return could have reduced their empirical Sharpe ratio? And, have managers actually negatively influenced their performance by reporting too high returns? The note is organized as follows: Section 4 briefly reviews the theoretical results of Schuster and Auer (2012). Section 3 describes the dataset. Section 4 presents the results of our empirical analysis. Finally, Section 5 concludes. 2. Critical excess returns Consider a fund for which we have a time series of n − 1 excess returns (over a riskfree rate) denoted n−1 r1 , . . ., rn−1 . Its sample average excess return for the first n − 1 periods is r n−1 = (1/(n − 1)) i=1 ri =: a
n−1
2 = (1/(n − 2)) i=1 (ri − a)2 =: b. Thus, the empirical Sharpe and the related sample variance is ˆ n−1 √ n−1 = r n−1 /ˆ n−1 = a/ b. ratio is given by SR Schuster and Auer (2012) show that for a fund fulfilling the four conditions n > 2, a > 0, b > 0 and n−1 > n−1/2 a prospective excess return rn below na2 − b > 0 ⇔ SR
l
r = a + n· or above ru = a + n ·
h−
h+
h2
ah + (n − 1)
ah h2 + (n − 1)
(1)
,
(2)
B.R. Auer / Research in International Business and Finance 30 (2014) 195–201
197
n < SR n−1 . Only for new excess returns where h = ab/(na2 − b), causes a lower empirical Sharpe ratio SR n > SR n−1 . rl < rn < ru we get SR These results highlight that a fund with a sufficient number of excess return observations, positive average and standard deviation of excess returns in period n − 1, and an empirical Sharpe ratio in period n − 1 greater than n−1/2 encounters the effect that a high prospective excess return rn > ru lowers its empirical Sharpe ratio. Henceforth, we call the situation where the above mentioned four conditions are fulfilled critical situation and the case of an actual reduction of the empirical Sharpe ratio because of a high excess return high return effect. As we can see from (2), this effect has special (but not exclusive) relevance in the early years of a fund’s existence because for funds with very high n the excess return ru can (but must not) become large and virtually unreachable. 3. Data In our study, we use the same dataset as in Auer (2013). We obtained hedge fund data from the CISDM hedge fund database being one of the oldest and most commonly used hedge fund databases in the market (see Ding and Shawky, 2007; Eling, 2009). As of November 2009, it contained return data for a total of 6854 individual hedge funds (not including funds of hedge funds) reporting monthly net-of-fee returns for the time period from January 1972 to November 2009. Like other popular hedge fund databases (e.g. MAR, HFR, TASS; see Amin and Kat, 2003), the CISDM database offers additional information on each fund, such as company name, strategy description, and net asset value (for further details, see www.isenberg.umass.edu/CISDM/). The database includes 2353 (34.33%) surviving and 4501 (65.67%) dissolved funds. Our findings were generated on the basis of a reduced sample resulting from an exclusion of all funds that did not report at least a one year return history to the database, funds with only quarterly returns and funds with obviously faulty return entries. This screening procedure results in a sample of 6377 remaining funds. Following Eling and Schuhmacher (2007), a rolling monthly riskfree rate corresponding to the interest rate on 10-year US Treasury bonds (extracted from Thomson Reuters Datastream) was used to calculate the excess returns of these funds. Alternatively, a constant riskfree rate equal to the average interest rate for the period under consideration or the interest rate at the beginning of the investigation period could be used. However, all three approaches yield virtually identical results as far as the high return effect is concerned. Table 1 describes major characteristics of the 6377 funds in our sample. It shows the numbers of funds that follow specific investment strategies and invest with particular geographical focuses. Furthermore, it reports the mean net asset value and the mean fund age in the dataset. As we can see, most funds are attributed to the strategy “Equity Long/Short” (2415) and the geographical focus “Global” (1364). “Market Timing” (3) and “Australia/New Zealand” (16) subsume the lowest numbers of funds. There is also a considerable number of funds (2537) that do not disclose their geographical focus of operations. The mean net asset value amounts to about 30 million US Dollars. The mean fund age is about 64 months or roughly 5 years. 4. Empirical analysis In a first step of our empirical analysis, we check in which periods of an individual fund’s history the conditions stated in Section 2 were fulfilled. We find that for only 883 funds the conditions were never met resulting in a smaller sample of 5494 funds that encountered our critical situation at least once. For each fund in the reduced sample, we then calculate the fraction of critical periods to total observation periods. Fig. 1 plots the distribution of those fractions and shows that for a considerable number of funds the critical periods account for more than 90% of the entire return history. 1182, 902, 1138 and 2272 funds yield fractions in the intervals W =]0 % , 25 %], X =]25 % , 50 %], Y =]50 % , 75 %] and Z =]75 % , 100 %], respectively. Before continuing with our main analysis, it is instructive to have a look at the time series evolution of the number of critical situations across all funds. For each month in our sample period, we count the number of funds in a critical situation and plot the resulting time series in Fig. 2. It reveals a
198
B.R. Auer / Research in International Business and Finance 30 (2014) 195–201
Table 1 Dataset characteristics. Hedge fund strategy Capital structure arbitrage Convertible arbitrage Distressed securities Emerging markets Equity long only Equity long/short Equity market neutral Event driven multi strategy
22 219 179 531 205 2415 347 254
Fixed income Fixed income MBS Fixed income arbitrage Global macro Market timing Merger arbitrage Multi strategy Option arbitrage
186 90 199 342 3 118 360 43
Other relative value Regulation D Relative value multi strategy Sector Short bias Single strategy Undisclosed
Geographical focus Asia/Pacific Asia/Pacific (excl. Japan) Australia/New Zealand Eastern Europe Global
140 195 16 108 1364
Japan Latin America Middle East/Africa North America North America/Europe
175 94 43 561 57
UK United States Western Europe Undisclosed
Other characteristics Mean net asset value Mean age
32 16 100 449 54 139 74
67 633 387 2537
29.56 64.13
For our sample of 6377 hedge funds, this table shows the numbers of funds that follow specific investment strategies and operate with certain geographical focuses. It also reports the mean net asset value (in millions of US Dollars) and the mean age (in months) of the funds in the dataset.
sharp rise in the number of critical situations as we move from 1972 to 2008. This observation can be explained as follows. First, the hedge fund market has experienced enormous growth in our sample period leading to a significant extension of the number of funds listed in the CISDM database (see Fung and Hsieh, 1999; Ding and Shawky, 2007). Second, as a critical situation is accompanied by a positive Sharpe ratio, the sharp rise also implies that a large number of funds entered the market that deliver desirable investment performance in excess of a riskfree rate (see Ibbotson et al., 2011). The decline in 2009 can be explained by the turbulences related to the recent financial crisis that led to
250
200
150
100
50
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Fig. 1. Distribution of the fraction of critical periods in hedge funds’ return histories. For 5494 hedge funds, this figure shows the distribution of the individual fraction of periods in which a high prospective excess return can result in a lower empirical Sharpe ratio to the total number of return observations. The sample period spans from January 1972 to November 2009.
B.R. Auer / Research in International Business and Finance 30 (2014) 195–201
199
3000
2500
2000
1500
1000
500
0 1972
1984
1992
2008
Fig. 2. Number of hedge funds in critical situations. This figure plots the time series that results from counting the number of hedge funds in critical situations for each month in our sample period.
a negative performance of many hedge funds. It is also attributable to a return reporting lag in the CISDM database. In the second step of our analysis, we seek to answer the question of whether the returns reported by hedge fund managers caused their empirical Sharpe ratio to rise or to fall in the identified critical situations. In the case of a falling Sharpe ratio, we are especially interested in whether the return responsible for the reduction was one associated with an excess return above the critical value ru . Table 2 documents our results separately for the four intervals mentioned above. For each interval, Panel A reports the number of critical situations as well as the numbers of cases in which the reported return led to an increase or a decrease of the empirical Sharpe ratio. The latter number is split up into the two possible causes for reduction (an excess return below rl or above ru ). As we can see, within each interval hedge funds reported too high returns in about 1% of the detected critical situations leading to a lower empirical Sharpe ratio. To get a more detailed picture on the fund level, Panel B gives the number of hedge funds that lowered their Sharpe ratio at least once by reporting a too high return. We see that about 8%, 14%, 15% and 32% of the funds in the intervals W, X, Y and Z, respectively, have this property. To show that our results are not only relevant in the early return history of a hedge fund, we take a more detailed look at the length the return history of a fund had reached in the period it experienced the high return effect. Some authors suggest that 24 monthly returns are the minimum for calculating meaningful performance measures (see for example Ackermann et al., 1999; Gregoriou, 2002; Capocci and Hübner, 2004; Liang and Park, 2007; Eling, 2009). Therefore, we also calculate the numbers of situations and funds where the empirical Sharpe ratio was lowered by a high return in the presence of a reported return history of at least 24 months (see Table 2). Our results show that in the most interesting interval Z about 26% of the high return effects occurred when the corresponding funds had a reported return history of at least 24 months. In fund numbers this means that within this interval we can identify 171 hedge funds that have experienced high return effects even in their late return history. Finally, in order to shed some light on the characteristics of funds that have experienced high return effects, Table 3 classifies these funds in a manner similar to Table 1. Clearly, high return effects are not limited to funds with a certain investment strategy or geographical focus. In comparison to the values in Table 1, the mean net asset value of funds with high return effects is somewhat lower, while the mean age is quite similar. However, these results are not surprising because the high return effect is a phenomenon related to specific return properties. If a fund invests in, for example, US stocks only, this does not necessarily mean that these particular properties are more or less likely.
200
B.R. Auer / Research in International Business and Finance 30 (2014) 195–201
Table 2 Main results.
Panel A: Number of critical situations Higher Sharpe ratio (rl < rn < ru ) Lower Sharpe ratio (rn < rl ) Lower Sharpe ratio (rn > ru ) Return history ≥ 24 month Panel B: Number of hedge funds Higher Sharpe ratio (rl < rn < ru ) Lower Sharpe ratio (rn < rl ) Lower Sharpe ratio (rn > ru ) Return history ≥ 24 month
Interval W ] 0%, 25%]
Interval X ] 25%, 50%]
Interval Y ] 50%, 75%]
Interval Z ] 75%, 100%]
6903 2509 (36.35%) 4279 (61.99%) 115 (1.67%) 1 (0.87%)
19,296 8707 (45.12%) 10,434 (54.07%) 155 (0.80%) 1 (0.65%)
47,565 23,415 (49.23%) 23,945 (50.34%) 205 (0.43%) 4 (1.95%)
172,468 85,300 (49.46%) 85,860 (49.78%) 1308 (0.76%) 344 (26.30%)
1182 742 (62.77%) 1175 (99.41%) 96 (8.12%) 1 (1.04%)
902 869 (96.34%) 899 (99.67%) 124 (13.75%) 1 (0.11%)
1138 1138 (100.00%) 1137 (99.91%) 174 (15.29%) 4 (0.35%)
2272 2272 (100.00%) 2269 (99.87%) 724 (31.87%) 171 (7.53%)
Panel A of this table reports the number of critical situations (defined in Section 2) that can be assigned to hedge funds whose fraction of critical situations to the total number of return observations lies within the intervals W, X, Y or Z. Furthermore, for each interval the numbers (and percentages in parentheses) of critical situations are given where rl < rn < ru , rn < rl and rn > ru . Panel B shows the numbers of funds within each interval and the numbers (and percentages in parentheses) of funds that experienced rl < rn < ru , rn < rl and rn > ru at least once. Furthermore, the Panels A and B reveal the numbers (and percentages of the numbers in the lines rn > ru ) of situations and funds in each interval where the Sharpe ratio was lowered because of rn > ru and the return history of the individual funds covered at least 24 months. Table 3 Characteristics of high return effect funds. Hedge fund strategy Capital structure arbitrage Convertible arbitrage Distressed securities Emerging markets Equity long only Equity long/short Equity market neutral Event driven multi strategy Geographical focus Asia/Pacific Asia/Pacific (excl. Japan) Australia/New Zealand Eastern Europe Global Other characteristics Mean NAV Mean age
7 64 42 78 22 394 40 55
Fixed income Fixed income MBS Fixed income arbitrage Global macro Market timing Merger arbitrage Multi strategy Option arbitrage
39 28 56 43 0 19 55 9
23 31 4 28 200
Japan Latin America Middle East/Africa North America North America/Europe
33 18 12 112 19
Other relative value Regulation D Relative value multi strategy Sector Short bias Single strategy Undisclosed
UK United States Western Europe Undisclosed
8 11 16 83 4 31 14
10 125 51 452
18.14 68.97
Constructed in analogy to Table 1, this table describes major properties of the 1118 hedge funds where the high return effect could be observed at least once.
5. Conclusion Reporting returns signaling a good performance is a hedge fund’s most important marketing strategy. However, if investors evaluate a hedge fund on the basis of its Sharpe ratio listing too high returns can result in a lower empirical Sharpe ratio and therefore cause an unfavorable signal. In this note, we show that an economically significant number of funds listed in the CISDM hedge fund database historically has at least once suffered from this kind of effect. Taking into account that private investors
B.R. Auer / Research in International Business and Finance 30 (2014) 195–201
201
typically use easily obtainable measures like the Sharpe ratio when choosing the best fund from a set of given alternatives, the effect highlighted by Schuster and Auer (2012) may thus have influenced historical investment decisions in a negative way. In the light of this evidence, one can take several different positions. First, one might advise hedge fund managers to reconsider reporting exceptionally high returns, unless they are certain that investors use performance measures that do not show a high return effect. One example for such a measure is the Calmar ratio (average excess return divided by the maximum drawdown) proposed by Young (1991). Second, the risk of actually encountering the high return effect could be regarded as not very high. Even though the high return effect arose for a large number of funds, it occurred only in about 1% of the time. Thus, fund managers might just tolerate this risk because it would probably be more cost intensive to consequently monitor how performance measures react to reported returns. Third, a manager’s strategy in a certain period may not even be to attract new investors by controlling his Sharpe ratio but to maximise his managerial (incentive) fees. In this case, the manager would prefer reporting a high return and tolerate a decreasing Sharpe ratio. Acknowledgement The author thanks an anonymous referee for very useful comments and suggestions. References Ackermann, C., McEnally, R., Ravenscraft, D., 1999. The performance of hedge funds: risk, return, and incentives. Journal of Finance 54 (3), 833–874. Amin, G., Kat, H., 2003. Hedge fund performance 1990–2000: do the “Money Machines” really add value? Journal of Financial and Quantitative Analysis 38 (2), 251–274. Arnold, T., Nail, L., Nixon, T., 2004. Do ADRs enhance portfolio performance for a domestic portfolio? Evidence from the 1990s. Research in International Business and Finance 18 (3), 341–359. Auer, B.R., 2013. The low return distortion of the Sharpe ratio. Financial Markets and Portfolio Management, forthcoming. Brown, S.J., Goetzmann, W.N., Ibbotson, R.G., 1999. Offshore hedge funds: survival and performance 1989–95. Journal of Business 72 (1), 91–117. Capocci, D., Hübner, G., 2004. Analysis of hedge fund performance. Journal of Empirical Finance 11 (1), 55–89. Ding, B., Shawky, H., 2007. The performance of hedge fund strategies and the asymmetry of return distributions. European Financial Management 13 (2), 309–331. Dowd, K., 2000. Adjusting for risk: an improved Sharpe ratio. International Review of Economics and Finance 9 (3), 209–222. Eling, M., 2009. Does hedge fund performance persist? Overview and new empirical evidence. European Financial Management 15 (2), 362–401. Eling, M., Schuhmacher, F., 2007. Does the choice of performance measure influence the evaluation of hedge funds? Journal of Banking and Finance 31 (9), 2632–2647. Fung, W., Hsieh, D.A., 1999. A primer on hedge funds. Journal of Empirical Finance 6 (3), 309–331. Fung, W., Hsieh, D.A., 2000. Performance characteristics of hedge funds and commodity funds: natural vs. spurious biases. Journal of Financial and Quantitative Analysis 35 (3), 291–307. Fung, W., Hsieh, D.A., 2006. Hedge funds: an industry in its adolescence. Federal Reserve Bank of Atlanta Economic Review 91 (4), 1–33. Gregoriou, G., 2002. Hedge fund survival lifetimes. Journal of Asset Management 3 (2), 237–252. Hammami, Y., Jilani, F., Oueslati, A., 2013. Mutual fund performance in Tunisia: a multivariate GARCH approach. Research in International Business and Finance 29, 35–51. Huang, M., Lin, J., 2011. Do ETFs provide effective international diversification? Research in International Business and Finance 25 (3), 335–344. Ibbotson, R.G., Chen, P., Zhu, K.X., 2011. The ABCs of hedge funds: alphas, betas, and costs. Financial Analysts Journal 67 (1), 15–25. Ledoit, O., Wolf, M., 2008. Robust performance hypothesis testing with the Sharpe ratio. Journal of Empirical Finance 15 (5), 850–859. Liang, B., Park, H., 2007. Risk measures for hedge funds: a cross-sectional approach. European Financial Management 13 (2), 333–370. Lo, A., 2002. The statistics of Sharpe ratios. Financial Analysts Journal 58 (4), 36–52. Posthuma, N., Van der Sluis, P., 2003. A reality check on hedge fund returns. Free University of Amsterdam, Unpublished Manuscript. Schuhmacher, F., Eling, M., 2011. Sufficient conditions for expected utility to imply drawdown-based performance rankings. Journal of Banking and Finance 35 (9), 2311–2318. Schuhmacher, F., Eling, M., 2012. A decision-theoretic foundation for reward-to-risk performance measures. Journal of Banking and Finance 36 (7), 2077–2082. Schuster, M., Auer, B.R., 2012. A note on empirical Sharpe ratio dynamics. Economics Letters 116 (1), 124–128. Young, T., 1991. Calmar ratio: a smoother tool. Futures 20 (1), 40.