The Gross Truth About Hedge Fund Performance and Risk: The Impact of Incentive Fees

Transcription

1 The Gross Truh Abou Hedge Fund Performance and Risk: The Impac of Incenive Fees Chris Brooks, ICMA Cenre, Universiy of Reading, Reading. Andrew Clare, Faculy of Finance, Cass Business School, London. Nick Moson, Faculy of Finance, Cass Business School, London. Absrac Facor models are frequenly applied o hedge fund reurns in an aemp o separae he reurn from idenified risk facors (bea) and from manager skill (alpha). More recenly, hese same echniques have been used o replicae he reurns from hedge fund sraegies wih varying degrees of success. In his paper, we show ha due o he paricular naure of hedge fund incenive conracs, he use of ne of fee reurns can lead o considerably biased esimaes of facor exposures which can disor he picure of fund manager performance. The soluion we propose is o model he gross reurns of hedge funds and he incenive fees independenly, which gives a ruer represenaion of he underlying reurn generaing process. Using a large sample of hedge funds, we quanify he effec of his bias on boh performance aribuion and replicaion. We find ha using ne of fee reurns undersaes he reurn aribuable o bea by up o 58 basis poins per annum. Following from his we find ha some of he addiional bea exposure can be capured by basing replicaion on gross raher han ne reurns. We also invesigae he risk aking behaviour of fund managers condiional upon he dela of heir incenive opion and find ha conrary o previous sudies, here does appear o be evidence of increased risk aking for hose managers who find hemselves significanly below heir high waer mark. Keywords: hedge fund, reurns, alpha, bea, fees, performance JEL Classificaions: G1, G2 Elecronic copy available a: hp://ssrn.com/absrac=

2 Inroducion Invesors in hedge funds are generally charged an annual managemen fee ha can range anywhere from 1% o 3% of asses under managemen, and also an incenive fee which is ypically beween 10% and 30% of annual profis, based upon he fund s overall performance. I is argued ha he annual managemen fee is designed o cover he fund s operaing coss while he incenive fee incenivizes he manager o produce absolue reurns. 1 This incenive fee is ypically subjec o wo consrains: a hurdle rae and a high-waer mark. The hurdle rae is a benchmark reurn ha mus be exceeded before he performance incenive fees are payable. In pracice, his hurdle rae is ofen se a zero, alhough benchmarks such as LIBOR are also common. The high-waer mark means ha each invesor only pays performance fees when he value of heir invesmen is greaer han is previous highes value, which ensures ha an invesor only pays an incenive fee for posiive performance once any previous underperformance has been recouped. The exisence of such incenive fees and high-waermark provisions means ha hedge fund fees are boh ime-varying and pahdependen, and herefore ha he relaionship beween gross and ne of fee reurns is nonlinear. Figure 1 illusraes his via a Mone Carlo simulaion of 5,000 funds over a 100 year hisory, assuming ha he underlying gross reurns are 1% per monh wih a 5% sandard deviaion (comparable o hisorical equiy marke reurns). For funds ha charge only an annual managemen fee (for example, muual funds), he disribuion is simply moved o he lef by 0.17% per monh wih all oher momens unchanged. However, inroducing a 20% annual incenive fee ha is accrued monhly and paid annually wih a high-waer mark provision, leads o a more significan change in he disribuion. Firs, he mean ne reurn is 0.70%, implying ha he mean incenive fee payable is 0.13% per monh, which is clearly less han 20% of he 0.83% reurn ne of managemen fees because fees are only payable on posiive reurns above he high-waer mark. Second, he sandard deviaion of ne reurns is 4.67%, which is lower han he 5% for gross reurns. This is because he fees ac o smooh reurns over ime. So if, for example, he reurns ne of managemen fees bu before incenive fees for wo consecuive monhs are +1% and -1%, he ne reurns will be +0.8% and -0.8%. Third, he ne reurns exhibi negaive skew because incenive fees will be charged on posiive bu no on negaive reurns. Finally, ne reurns exhibi excess kurosis since he incenive fees 1 Kahn, Scanlan and Siegel [2006] provide an exensive discussion and analysis of hedge fund fees. 1 Elecronic copy available a: hp://ssrn.com/absrac=

3 have he impac of pushing he disribuion away from he shoulders ino he cenre, and he sandard deviaion is lower. Figure 1 Mone-Carlo Simulaion of he Effec of Incenive Fees 2% Annual Managemen Fee Only 2% Annual Managemen Fee + 20% Incenive Fee wih High-Waer Mark -15% -10% 5% 0% 5% 10% 15% Gross Reurn Ne Reurn -15% -10% -5% 0% 5% 10% 15% Gross Reurn Ne Reurn Summary Saisics Summary Saisics Gross Reurn Ne Reurn Gross Reurn Ne Reurn Mean 1.00% 0.83% Mean 1.00% 0.70% Sandard Deviaion 5.00% 5.00% Sandard Deviaion 5.00% 4.67% Skew Skew Kurosis Kurosis Performance aribuion and he effec of incenive fees on he risk exposures of an invesor Mos of he empirical work on he effec of marke or risk facors on hedge fund reurns builds upon he work of Sharpe [1992]. His framework for he analysis of muual funds involved he developmen of an asse class facor model o deermine risk exposures of he form: R n = α + β i, Fi, + ε (1) i= 1 where R represens he reurn on he fund a ime, F i, represens he reurn on facor F i a ime, β i, represens he sensiiviy of he fund o facor F i a ime and α is he value added by he manager. 2

4 Sharpe regressed muual fund reurns agains welve asse class reurns and inerpreed he resuling beas as represening he muual funds hisoric exposures o he asse classes. Sharpe s resuls showed ha only a limied number of major asse classes were required o successfully replicae he performance of he universe of U.S. muual funds. Sharpe s model is he building block of mos risk-reurn research in hedge funds. This approach was firs used in he hedge fund arena by Fung and Hsieh [1997], who applied Sharpe s asse class facor model o a sample of hedge funds and muual funds using eigh asse classes. The resuls were srikingly differen for hedge funds compared o muual funds: 47% of he muual fund regressions had R-squared values higher han 75%, and 92% had R-squared figures higher han 50%. For he hedge fund regressions, 48% had R-squared values below 25%. Subsequen work by Fung and Hsieh and oher auhors has aemped o improve upon he explanaory power of he models using differen ses of independen variables, sample periods and hedge fund daabases. Mos of his work has been conduced wihin Sharpe s general framework. Some have concenraed on he addiion of non-linear facors such as opions (Agarwal and Naik [2000]) while ohers have esimaed ime-varying beas using eiher rolling window regressions (Fung and Hsieh [2004]), or by using saisical echniques such as he Kalman filer (Gehin and Vaissie [2006]). However, all of his work has been underaken using ne of fee reurns and linear regression echniques, where he resuling beas are inerpreed as represening he exposure of he invesor o a specific source of sysemaic risk. For muual funds, he only difference beween ne and gross reurns is he managemen fees ha are a fixed percenage of he asses under managemen. As equaion (2) illusraes, in his case he bea is he same for boh he invesor and he fund because he fees are independen of he fund reurn, and so he fees affec only he fund s alpha. R GROSS n, FEES = α + β F + ε (2) i= 1 i, i, However, because hedge funds also charge incenive fees which are a fixed percenage of he profis above a cerain hreshold, he fees are no independen of he fund s reurn. For his reason, he bea of he fund and he bea of he invesor can be differen depending upon he performance of he fund, as shown by equaion (3). 3

5 β Invesor = β β (3) Fund InceniveFee The incenive fee can be hough of as a call opion on a percenage of he performance of he fund. The invesor is shor his opion while he fund manager has he corresponding long posiion. Armed wih his informaion, i is relaively simple o calculae β InceniveFee from equaion (4), where δ is he dela of he incenive opion, InceniveF ee% is he InceniveOpion percenage fee charged by he fund and β Fund is he bea of he fund calculaed by regressing he gross reurns agains he risk facor/facors. β = δ * InceniveFee% * β (4) InceniveFee InceniveOpion Fund If, for example, he fund charges a 20% incenive fee, hen he boundary condiions are as follows: i) when he fund is a long way below he high-waer mark - all gains and losses from he fund will accrue o he invesor wih no incenive fees payable. δ InceniveOpion will be close ii) o zero and he exposures of he invesor are he same as he exposures of he fund; when he fund is a long way above he high-waer mark - all gains will resul in furher incenive fees being payable and losses will resul in a reducion in he fees. δ InceniveOpion will be close o 1, and hence he exposure of he invesor will be 20% smaller han he exposure of he fund. I is clear, hen, ha using ne of fee reurns o calculae beas will lead o biased esimaes. The correc approach would be o model he gross reurns of he fund and incenive fees separaely. The possible consequences of modelling ne raher han gross incenive fees is bes illusraed wih a sylised example. A sylised example of he problem: Bea Parners Suppose ha a hypoheical hedge fund called Bea Parners was esablished in January 1975, and unbeknown o is invesors, he fund simply invesed 100% of is asses on a passive basis in he S&P 500 index. Bea Parners charges he sandard 2% managemen fee, a 20% performance fee wih a hurdle rae of 0% and a high-waer mark provision. 4

6 Applying he approach suggesed by Ibboson and Chen [2006] o separae he sources of reurn ino alpha, bea and coss (or fees) by a saic linear regression of he ne reurns from Bea Parners agains he S&P500 index yields a slope coefficien of 0.91 and an alpha esimae of -0.23% per monh. This implies ha over he 31 year period, he compound annual reurns of Bea Parners comprise an alpha of -2.67%, a bea of 11.95% and fees of 4.32%. However, in his sylized example we know ha all of Bea Parners reurns are driven by bea and i is he incenive fees ha disor he picure. The correc approach is o use he gross reurns o calculae he alpha and bea esimaes before subracing he fees. This approach, as one would expec, yields an alpha esimae of zero and a slope coefficien of 1. Thus he compound annual reurns comprise an alpha of 0%, a bea of 13.45% and fees of 4.03%. Using reurns ne of fees undersaes boh he alpha and bea componens of he reurn of he fund. While i is clear ha he invesor does no receive all of hese reurns due o he fee srucure, separaing ou he effec of fees from he fund reurns gives he invesor a far ruer represenaion of he underlying reurn generaing process of he fund and of he performance of he fund manager. If an invesor were o follow he mehodology of Fung and Hsieh [2004] in an aemp o analyse he exposure of Bea Parners o he S&P 500 using a 24- monh rolling window regression on he ne of fee reurns, he resuls would be as shown in Figure 2. Figure 2 Bea Parners Rolling Window Regression Bea SP500 Using Ne Reurns 0.95 BETA S&P

7 The rolling regression resuls show how he bea varies beween a maximum of 1 and a minimum of 0.82 over he sample period. On he basis of his informaion an invesor migh conclude ha Bea Parners is varying is exposure o he marke over ime bu by consrucion, he acual bea of he fund is 1.0 a all imes. All of he variaion in exposure is acually coming from he change in he dela of he incenive fee opion. We know ha he bea of he invesor can easily be calculaed from equaions (3) and (4) once we have idenified he dela of he incenive opion. In his example, he incenive opion is simply a 1-monh call opion on he S&P 500 wih a srike se a he curren high-waer mark, and hus he dela can easily be calculaed using he Black-Scholes equaion. Figure 3 shows how he bea of he invesor evolves over ime. As one would expec, he invesor s bea is always beween 0.8 and 1. When he incenive opion has zero dela, he invesor and fund beas are he same. When he incenive opion has a 100% dela, hen he invesor bea is 20% lower han ha of he fund. The evoluion of he invesor s exposure is far less smooh using his procedure compared o using ne reurns; par of he reason for his is he re-seing of he high-waer mark each January afer incenive fees are paid. In fac, using ne reurns simply resuls in a moving average of he rue invesor bea. Figure 3 Bea Parners Invesor Bea 1.05 Bea SP500 Using Ne Reurns Bea SP500 Using Gross Reurn + Incenive Opion BETA S&P

8 Empirical Analysis of Ne and Gross Hedge Fund Reurns We now propose a echnique for recovering gross of fee hedge fund reurns and apply his o individual hedge fund performance daa. The hedge fund reurn daa are exraced from he TASS live and graveyard daabases from January 1994 hrough o December More specifically, we exrac monhly Ne Asse Values (NAV) for all hedge funds ha are denominaed in US Dollars, ha repor monhly and ha have a leas 37 daa poins. This crierion resuls in a oal sample of 2,837 funds of which 1,433 are currenly reporing and 1,404 are no longer reporing. We recognise ha his daa will be subjec o he various biases described by Fung and Hsieh [2002] and ohers, namely survivorship, insan hisory and selecion bias. We minimise survivorship bias by using boh he live and graveyard daabases, and by using daa only from January 1994 when TASS began collecing daa on graveyard funds. Insan hisory bias has been esimaed by Fung and Hsieh a approximaely 1.4% pa. We esimae he size of he selecion bias by comparing he reurn on he equally weighed reurn of our sample o he equally weighed reurn on all funds in he daabase. We esimae his o be 0.83%pa. Using hese NAVs we calculae monhly ne and gross reurns using he following procedure. All hedge fund daabase providers (and indices) repor monhly ne, raher han gross, performance figures. However, all of hese providers also repor NAVs as well as ne performance figures, and by using a number of realisic assumpions i is relaively sraighforward o esimae gross reurns from hese NAV numbers. To do his, assumpions abou he following issues are required: i. Managemen fees are calculaed and paid on a monhly basis ii. Incenive fees are accrued on a monhly basis, bu are only paid a he end of he calendar year iii. Unless specified oherwise, he fund applies a high-waer mark provision iv. The fund implemens an Equalisaion Credi /Coningen Redempion approach o calculaing he NAV 2 such ha i is he same for all invesors. 2 For a more horough explanaion see McDonnell [2003]. 7

9 The ne hedge fund reurn for period is calculaed using expression (5): R NET = ( NAV NAV ) NAV 1 1 (5) The gross reurn calculaion is calculaed as follows: R GROSS = ( NAV NAV 1) + MgFee + ( AccruedIncenFee AccruedIncenFee 1) ( NAV + AccruedIncenFee ) 1 1 (6) where and 1 MgFee = NAV 1 (7) 1 MgmFee% AccruedIncenFee = max{ 0, NAV HighWaerMark} 1 (8) 1 InceniveFee% a he end of each year, he accrued incenive fee is rese o zero and if necessary, he highwaer mark moved upwards o reflec his. By applying his echnique o he daa, we can consruc equally weighed indices for he en sraegies repored in he TASS daabase as well as a broad index of all hedge funds in our sample. The Saisical Properies of Ne and Gross Reurns Table 1 conains he summary saisics for he ne and gross reurns in he sample. Clearly, by consrucion, he compound annual, gross reurns are higher han he ne reurns wih he difference beween he wo being he fees. For our sample, he average fee charged has been 5.15% p.a., ranging from 2.57% for dedicaed shor bias o 6.07% for managed fuures. 8

10 Table 1 Saisical Properies of Ne and Gross Reurns Sample Size Live Graveyard Toal Converible Arbirage Dedicaed Shor Bias Emerging Markes Equiy Marke Neural Even Driven Fixed Income Arbirage Global Macro Long Shor Equiy ,166 Managed Fuures Muli Sraegy All Hedge Funds 1,433 1,404 2,837 Ne Compound Annualised Annual Re Sd. Dev. Skewness Kurosis Jarque-Bera Probabiliy Converible Arbirage 10.38% 4.23% % Dedicaed Shor Bias -0.79% 18.06% % Emerging Markes 14.41% 15.50% % Equiy Marke Neural 11.01% 2.51% % Even Driven 12.91% 4.41% % Fixed Income Arbirage 9.16% 3.51% % Global Macro 9.18% 5.99% % Long Shor Equiy 16.29% 9.18% % Managed Fuures 9.83% 11.04% % Muli Sraegy 13.42% 4.70% % All Hedge Funds 13.17% 5.93% % Gross Compound Annualised Annual Re Sd. Dev. Skewness Kurosis Jarque-Bera Probabiliy Converible Arbirage 14.32% 4.81% % Dedicaed Shor Bias 1.77% 19.50% % Emerging Markes 19.86% 16.75% % Equiy Marke Neural 15.42% 2.96% % Even Driven 17.43% 5.07% % Fixed Income Arbirage 13.43% 3.83% % Global Macro 13.62% 6.92% % Long Shor Equiy 21.76% 10.47% % Managed Fuures 15.89% 12.59% % Muli Sraegy 18.45% 5.34% % All Hedge Funds 18.31% 6.72% % When examining he sandard deviaion of reurns, he empirical resuls are in line wih our earlier Mone Carlo simulaion, and in all cases he gross reurns exhibi higher annualised sandard deviaion han ne reurns wih he average difference being 0.78%. For skewness, he empirical resuls are also as expeced wih an average increase of Wih regard o kurosis he resuls are much less clear cu, wih increases for some sraegies and decreases for ohers. Overall, however, here is a reducion in kurosis of The combinaion of all of his means ha gross hedge fund reurns look far more normal han ne reurns and in fac, conrary o Brooks and Ka [2002], for our sample i would appear ha on average hedge fund reurns display posiive skewness and do no exhibi significanly excess kurosis. 9

11 Performance Aribuion In order o aribue hedge fund reurns beween alpha, bea and fees, Ibboson and Chen [2006] carry ou regressions on ne of fee hedge fund reurns, using S&P 500 oal reurns (including boh concurren and wih a one-monh lag), U.S. Inermediae-erm Governmen Bond reurns (including one-monh lag), and cash (U.S. Treasury Bills) as benchmarks. They consrain all syle weighs o sum o one, bu allow individual syle weighs o be negaive or above one o accoun for shoring and leverage. Once hey have calculaed alphas, hey deduced his from he ne reurn o give he reurn from bea. Then, using he median managemen and incenive fee levels, hey esimae wha he fees on his oal ne reurn would have been o gross i up. We replicae Ibboson and Chen s mehodology using he ne of fee reurns for our sample of hedge funds and he following risk facors: he oal reurn of he Wilshire 5000 composie index; he oal reurn of Lehman US Aggregae Index; and one monh USD LIBOR. We hen compare his o he resuls we obain by calculaing he gross reurn before performing he regressions. The resuls are presened in Tables 2 and 3 which are direcly comparable o Tables 5 and 6 and Figure 1 in Ibboson and Chen [2006]. By consrucion, he alpha esimae for gross reurns will be larger by a leas he managemen fees, alhough in all cases, he increase is much larger han his (he average increase being 4.51% p.a.). For our sample using gross reurns, alpha is significan a he 5% level for all 10 sraegies, whereas when using ne reurns i is only significan for 6 of hem. For all sraegies, he magniude of bea for he risky asses (socks and bonds) is greaer and consequenly he reurn aribuable o bea is also larger (he average increase being 0.64% p.a.). This implies ha alhough he major impac of fees is indeed on alpha, he effec on bea is no insignifican. 10

12 Regression Resuls: Table 2 Regression Resuls for Equally Weighed Hedge Fund Indices Compound Annual Reurn Annual Alpha Beas (Sum of Beas = 1) Socks Bonds Cash RSQ Using Ne Reurns 10.38% 3.87% ** % Converible Arbirage Using Gross Reurns 14.32% 7.38% ** % Using Ne Reurns -0.79% 4.10% % Dedicaed Shor Bias Using Gross Reurns 1.77% 7.89% ** % Using Ne Reurns 14.41% 4.27% % Emerging Markes Using Gross Reurns 19.86% 8.86% ** % Using Ne Reurns 11.01% 5.75% ** % Equiy Marke Neural Using Gross Reurns 15.42% 9.89% ** % Using Ne Reurns 12.91% 5.76% ** % Even Driven Using Gross Reurns 17.43% 9.64% ** % Using Ne Reurns 9.16% 3.84% ** % Fixed Income Arbirage Using Gross Reurns 13.43% 7.79% ** % Using Ne Reurns 9.18% 2.81% * % Global Macro Using Gross Reurns 13.62% 6.78% ** % Using Ne Reurns 16.29% 7.51% ** % Long/Shor Equiy Using Gross Reurns 21.76% 12.21% ** % Using Ne Reurns 9.83% 5.05% % Managed Fuures Using Gross Reurns 15.89% 10.88% ** % Using Ne Reurns 13.42% 6.91% ** % Muli-Sraegy Using Gross Reurns 18.45% 11.46% ** % Using Ne Reurns 13.17% 5.69% ** % All HF Using Gross Reurns 18.31% 10.20% ** % * Significan a a 10% confidence level ** Significan a a 5% confidence level Table 3 Analysis of Sources of Reurn for Equally Weighed Hedge Fund Indices Sources of Reurn: Alpha, Bea, and Cos Converible Arbirage Dedicaed Shor Bias Emerging Markes Equiy Marke Neural Even Driven Fixed Income Arbirage Global Macro Long/Shor Equiy Managed Fuures Muli-Sraegy All HF Pre-Fee Reurn Fees Pos-Fee Reurn Alpha Sysemaic Beas Using Ne Reurns 14.98% 4.60% 10.38% 3.87% 6.51% Using Gross Reurns 14.32% 3.94% 10.38% 7.38% 6.94% Using Ne Reurns 1.01% 1.80% -0.79% 4.10% -4.89% Using Gross Reurns 1.77% 2.57% -0.79% 7.89% -6.12% Using Ne Reurns 20.01% 5.60% 14.41% 4.27% 10.13% Using Gross Reurns 19.86% 5.46% 14.41% 8.86% 11.00% Using Ne Reurns 15.76% 4.75% 11.01% 5.75% 5.26% Using Gross Reurns 15.42% 4.41% 11.01% 9.89% 5.53% Using Ne Reurns 18.14% 5.23% 12.91% 5.76% 7.16% Using Gross Reurns 17.43% 4.52% 12.91% 9.64% 7.79% Using Ne Reurns 13.46% 4.29% 9.16% 3.84% 5.33% Using Gross Reurns 13.43% 4.26% 9.16% 7.79% 5.64% Using Ne Reurns 13.47% 4.29% 9.18% 2.81% 6.37% Using Gross Reurns 13.62% 4.45% 9.18% 6.78% 6.84% Using Ne Reurns 22.37% 6.07% 16.29% 7.51% 8.78% Using Gross Reurns 21.76% 5.47% 16.29% 12.21% 9.56% Using Ne Reurns 14.28% 4.46% 9.83% 5.05% 4.78% Using Gross Reurns 15.89% 6.07% 9.83% 10.88% 5.01% Using Ne Reurns 18.77% 5.35% 13.42% 6.91% 6.50% Using Gross Reurns 18.45% 5.03% 13.42% 11.46% 6.99% Using Ne Reurns 18.46% 5.29% 13.17% 5.69% 7.48% Using Gross Reurns 18.31% 5.15% 13.17% 10.20% 8.12% 11

13 Facor Model Specificaion and Replicaion Using gross raher han ne of fee reurns when aemping o duplicae hedge fund performance via facor replicaion should produce beer resuls for wo main reasons. Firs, as we have already demonsraed, he use of ne of fee reurns for performance aribuion leads o an underesimaion of he reurn ha is aribuable o bea, and hence i follows ha using gross reurns in aemping o replicae hedge fund reurns should produce beer resuls by capuring his addiional bea reurn. Second, he opion-like naure of incenive fees creaes a non-linear payoff o he facors which should be eliminaed by using gross reurns. In order o assess he difference beween replicaed ne and gross hedge fund reurns, we employ a mehodology similar o ha of Hasanhodzica and Lo [2007]. However, whereas Hasanhodzica and Lo and ohers have used he same small number of facors for every sraegy, we sar wih a large se of 11 candidae facors and underake a procedure o idenify he significan facors for each sraegy individually. This is because of he heerogeneous naure of hedge fund sraegies and he advanage is ha i avoids he use of superfluous facors in he regressions. Table 4 shows he se of 11 candidae facors. These facors were chosen because hey provide a broad cross secion of risk exposures which have all been idenified in previous sudies as significan. Imporanly, all of he facors are invesable via radiional funds, exchange raded funds or fuures which is essenial if hey are o be used for replicaion. We classify he facors ino wo groups: hose ha require invesmen and hose ha are cash neural. To ensure ha when we consruc clones and resric he sum of beas o be equal o one, his resricion only applies o facors ha require invesmen. In order o idenify he significan facors for each sraegy, we firs exrac monhly reurns for live and graveyard funds from he TASS daabase for January 1990 o December 1994 and consruc equally weighed sraegy indices. Alhough his sample will be severely affeced by survivorship bias, because we are only looking o idenify he facors ha drive reurns raher han making any judgemens abou performance, we feel ha his is an accepable approach. Nex we run regressions for all possible combinaions of one o eleven facors, a oal of 2 11 = 2,048 regressions, in order o idenify he mos parsimonious model, which we define as he one wih he lowes Akaike Informaion Crierion (AIC). The resuls are shown in Table 5. 12

14 Table 4 Candidae Facors for Replicaion Facors Requiring Invesmen Cash Neural Facors Name Descripion Daasream Mnemonic Name Descripion Daasream Mnemonic MKT Dow Jones Wilshire 5000 Composie Toal Reurn WILEQTY SMB Dow Jones Wilshire Small Cap Minus Dow Jones Wilshire Large Cap (Boh WILDJSC & WILDJLC Toal Reurn) CMDTY GSCI Commodiy Toal Reurn GSCITOT USD Finex-US Dollar Index Reurn NDXCS00 BOND Lehman US Agggregae Toal Reurn LHAGGBD CREDIT Lehman US Credi Inermediae Bond Index Minus Lehman Governmen Inermediae (Boh Toal Reurn) EMERGING MSCI Emerging Markes Index Toal Reurn GLOBAL_STOCKS JP Morgan Global Broad Excluding U.S. Toal Reurn MSEMKFL SLOPE Lehman US Treasury: 20+ Year Index Minus Lehman Shor Treasury Index (Boh Toal Reurn) JPMBXUS LHCRPIN & LHGOVIN LHTR20Y & LHSHORT GLOBAL_BONDS MSCI World Excluding U.S. Toal Reurn MSWFXU DVIX Change In CBOE VIX Index CBOEVIX The findings are in line wih wha one would expec. Equiy based facors are idenified as significan for hose sraegies ha involve equiies such as long/shor equiy, dedicaed shor bias and even driven. Bond or credi facors are idenified as significan for fixed income sraegies such as converible arbirage and fixed income arbirage. The R-squared of he regressions ranges from 5.2% for managed fuures o 76.17% for long/shor equiy, showing ha facor models appear o perform much more saisfacorily for some sraegies han for ohers. Table 5 Resuls of Facor Selecion GLOBAL_ GLOBAL_ AIC R 2 MKT SMB USD CMDTY BOND CREDIT SLOPE EMERGING STOCKS BONDS DVIX Converible Arbirage % (0.0761) (1.1339) (0.1400) Dedicaed Shor Bias % (0.1512) Emerging Markes % (0.0895) (0.8859) (0.0465) Equiy Marke Neural % (0.0559) (0.0688) (0.0336) (0.0643) Even Driven % (0.0659) (0.0568) (0.1718) (0.5388) (0.0275) (0.0616) Fixed Income Arbirage % (0.1421) (0.0409) (0.6105) (0.1492) (0.0733) Global Macro % (0.1227) (0.7591) (0.0443) (0.0625) (0.1232) Long/Shor Equiy Hedge % (0.0457) (0.0582) (0.0895) (0.0248) (0.0719) (0.0219) (0.0297) (0.1116) Managed Fuures % (0.2274) (0.0737) (0.2698) Muli-Sraegy % (0.0940) (0.0542) (0.2531) (0.9248) (0.0431) 13

15 Having idenified he facors ha drive hedge fund reurns for each individual sraegy, we now aemp o consruc linear clones using rolling window regressions. In addiion o he facors idenified above, we also inroduce anoher facor, 1 monh U.S. Dollar LIBOR, o allow for leverage. Using he facors idenified above plus he LIBOR facor, for each individual hedge fund sraegy we run a rolling window regression using a 24 monh window from January 1995 o December 2006 as shown in equaion (9) R n = α + β i, Fi, + ε (9) i= 1 n subjec o β i, = 1 for hose facors classified as requiring invesmen plus LIBOR. i= 1 The esimaed regression coefficiens * β i are hen used as porfolio weighs o consruc simple clone reurns * R i using equaion (10) * R i = n i= 1 * β i, (10) In order o mach he volailiy of he clone reurns o he volailiy of he underlying hedge fund reurns, we calculae a leverage facor γ from equaion (11) 24 2 ( R = ) / 23 k 1 i k Ri γ i = (11) * 2 R ) / * ( R k= 1 i k i This leverage facor is hen used o calculae he clone reurns Rˆ i using equaion (12) ( γ i Ri) ( γ i) LIBOR ˆ * i R = 1 (12) This procedure was repeaed for he indices and individual funds using boh ne and gross reurns, which resuls in a clone series running for 10 years from January 1997 o December 2006, he resuls are presened in Tables 6 and 7. 14

16 Replicaion of Indices Converible Arbirage Dedicaed Shor Bias Emerging Markes Equiy Marke Neural Even Driven Fixed Income Arbirage Global Macro Long/Shor Equiy Managed Fuures Muli-Sraegy All HF Table 6 Replicaion of Indices Compound Annual Reurn Index Annual Sandard Deviaion Compound Annual Reurn Annual Sandard Deviaion Clone Correlaion Beween Clone & Index Mean R2 of Regression Using Ne Reurns 10.10% 4.27% 5.65% 4.64% 20.97% 29.15% Using Gross Reurns 14.03% 4.89% 5.95% 5.35% 20.01% 28.35% Using Ne Reurns -1.74% 18.80% -4.56% 20.88% 80.38% 87.91% Using Gross Reurns 0.64% 20.23% -5.71% 22.42% 81.19% 88.52% Using Ne Reurns 15.02% 16.12% 6.53% 16.38% 73.48% 83.28% Using Gross Reurns 20.66% 17.37% 6.47% 17.87% 72.91% 82.90% Using Ne Reurns 9.48% 2.25% 4.47% 2.61% 23.65% 41.88% Using Gross Reurns 13.46% 2.63% 4.61% 3.07% 23.28% 41.76% Using Ne Reurns 12.12% 4.65% 7.16% 4.72% 66.02% 71.21% Using Gross Reurns 16.55% 5.33% 7.78% 5.39% 64.67% 71.31% Using Ne Reurns 7.87% 3.34% 5.27% 3.71% 22.02% 50.36% Using Gross Reurns 11.75% 3.63% 5.48% 3.99% 23.70% 50.74% Using Ne Reurns 8.36% 5.28% 8.58% 6.89% 53.47% 61.82% Using Gross Reurns 12.68% 6.07% 9.25% 8.01% 53.30% 62.18% Using Ne Reurns 15.22% 9.73% 8.03% 10.79% 91.90% 90.55% Using Gross Reurns 20.51% 11.08% 8.64% 12.38% 90.70% 89.98% Using Ne Reurns 9.23% 10.70% 10.72% 12.39% 26.14% 32.30% Using Gross Reurns 14.98% 12.30% 11.75% 14.19% 26.50% 32.77% Using Ne Reurns 13.54% 4.87% 6.04% 5.12% 65.39% 69.49% Using Gross Reurns 18.54% 5.53% 6.34% 5.81% 63.67% 68.94% Using Ne Reurns 12.54% 6.20% 7.44% 6.91% 65.58% 86.69% Using Gross Reurns 17.51% 7.01% 7.68% 7.71% 64.85% 85.54% Replicaion of Funds Converible Arbirage Dedicaed Shor Bias Emerging Markes Equiy Marke Neural Even Driven Fixed Income Arbirage Global Macro Long/Shor Equiy Managed Fuures Muli-Sraegy All HF Table 7 Replicaion of Individual Funds Compound Annual Reurn Index Annual Sandard Deviaion Compound Annual Reurn Annual Sandard Deviaion Clone Correlaion Beween Clone & Index Mean R2 of Regression Using Ne Reurns 10.10% 4.27% 5.28% 4.75% % 29.40% Using Gross Reurns 14.03% 4.89% 5.59% 5.40% -4.21% 29.06% Using Ne Reurns -1.74% 18.80% -4.92% 25.54% 55.52% 88.55% Using Gross Reurns 0.64% 20.23% -6.17% 27.19% 56.29% 89.12% Using Ne Reurns 15.02% 16.12% 6.83% 21.07% 36.41% 83.43% Using Gross Reurns 20.66% 17.37% 6.82% 22.98% 36.22% 83.17% Using Ne Reurns 9.48% 2.25% 5.11% 3.10% 12.68% 40.15% Using Gross Reurns 13.46% 2.63% 5.27% 3.57% 13.00% 39.78% Using Ne Reurns 12.12% 4.65% 8.55% 5.50% 26.31% 65.45% Using Gross Reurns 16.55% 5.33% 9.41% 6.31% 26.02% 65.55% Using Ne Reurns 7.87% 3.34% 5.02% 4.26% 12.71% 51.08% Using Gross Reurns 11.75% 3.63% 5.20% 4.65% 13.18% 51.18% Using Ne Reurns 8.36% 5.28% 8.47% 8.59% 21.67% 57.04% Using Gross Reurns 12.68% 6.07% 9.04% 9.94% 21.75% 56.96% Using Ne Reurns 15.22% 9.73% 8.05% 13.07% 40.17% 90.14% Using Gross Reurns 20.51% 11.08% 8.77% 14.95% 39.90% 89.71% Using Ne Reurns 9.23% 10.70% 12.40% 13.45% 17.36% 34.25% Using Gross Reurns 14.98% 12.30% 13.36% 15.44% 17.66% 34.27% Using Ne Reurns 13.54% 4.87% 7.23% 6.56% 23.51% 69.29% Using Gross Reurns 18.54% 5.53% 7.61% 7.44% 23.51% 68.59% Using Ne Reurns 12.54% 6.20% 7.99% 8.46% 24.02% 86.53% Using Gross Reurns 17.51% 7.01% 8.35% 9.45% 28.75% 85.45% 15

17 In all cases, he reurn on he gross clones is greaer in magniude han for he ne clones (more negaive for dedicaed shor bias) alhough he sandard deviaion of he reurn is also slighly higher. The average improvemen in reurn for he gross clones over he ne clones is 0.24% for indices and 0.36% for individual funds. The improvemen in performance of he gross clones would appear o be proporional o he goodness of fi of he model. The bigges improvemen is seen in sraegies such as long/shor equiy and even driven where he R- squared values of he regressions are high and he smalles improvemen is for sraegies such as equiy marke neural and fixed income arbirage where he R-squared is much lower. The correlaion beween he clone and fund reurns is exremely high a over 85%, alhough here is no significan difference beween he ne and gross clones in eiher correlaion or R- squared. The Effec of Incenive Fees on he Risk Taking Behaviour of Funds We have already demonsraed how he payoff profile of hedge fund performance fees is idenical o a call opion on a percenage of he fund s performance. The raionale for his fee arrangemen is o incenivize he hedge fund manager o produce absolue reurns. However, he realiy is ha he arrangemen encourages managers o maximise he value of his fee opion; heir moivaions could be differen depending upon he dela of he opion. When he dela is high, he bulk of he value in he opion comes from is moneyness and lile from is volailiy. Bu when he dela is low, he reverse is rue. Auhors such as Scanlan and Siegel [2006] have suggesed ha managers who are significanly below heir high waer mark migh have an incenive o increase risk. This has been invesigaed for CTAs by Fung and Hsieh [1997a] and by Brown, Goezmann, and Park [2001], who boh find lile evidence of increased risk aking by managers below heir high waer mark. They hypohesise ha career and repuaion concerns as well as he increased risk of redempions offse he adverse risk-aking incenives creaed by he incenive fee conrac. In order o invesigae wheher his is he case for he hedge funds in our sample, we examine he disribuion of reurns condiional upon he dela of he incenive opion. Calculaion of he exac dela of he fee opion is problemaic because we do no have an appropriae model or a rue esimae of he implied volailiy, so insead we use he moneyness of he opion as a proxy for dela. Moneyness is defined as 16

18 Moneyness = NAV HighWaerMark (13) For our sample of 2,837 funds, we calculae he moneyness a each daa poin giving us a oal of 229,101 observaions. In order o invesigae he relaionship beween he dela of he incenive opion and he disribuion of reurns we divided he moneyness ino 3 sub-samples: - A The Money (ATM) where moneyness is greaer han 95% and less han 105% - In The Money (ITM) where moneyness is greaer or equal o 105% - Ou Of The Money (OTM) where moneyness is less han or equal o 95% Using hese sub-samples, we examine he properies of he disribuion of gross reurns a ime +1 condiional upon he moneyness a ime, he resuls are presened in Figure 4. Figure 4 The Effec of Incenive Fees on he Risk Taking Behaviour of Funds Summary Saisics ATM ITM OTM Whole Sample Mean 1.25% 1.71% 0.98% 1.38% Sandard Deviaion 4.94% 6.41% 8.51% 6.16% Skew Kurosis Observaions 109,813 84,608 34, ,101 Resuls of Kolmogorov-Smirnov Tes OTM ATM ITM OTM ATM ITM (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Probabiliy of acceping null hypohesis repored in parenheses The hree disribuions appear o be very differen. This is confirmed by he resuls of pairwise Kolmogorov-Smirnov ess, and in all cases we can rejec he null hypohesis ha he disribuions are he same. The sandard deviaion of he OTM sample is saisically larger han for eiher he ATM or he ITM samples, which appears o suppor he hypohesis ha hedge funds increase heir risk when hey are below heir high waer mark. However, i also appears ha ITM funds also increase heir risk, so i migh be ha funds who are ATM acually reduce heir risk. 17

19 Conclusions We have demonsraed ha esimaing he facor exposures of hedge funds using ne of fee reurns will lead o biased resuls due o he non-linear impac of incenive fees. We have proposed an alernaive procedure o esimae he exposures of he fund using gross reurns and he effec of fees independenly ha is simple o implemen. We have also illusraed, via a sylised example, ha he proposed procedure will lead o far more accurae esimaes of invesor exposures when he reurn generaion procedure is known. Using a large sample of hedge fund reurns, we have shown ha using ne of fee reurns undersaes he reurn aribuable o bea by up o 58 basis poins per annum. Following from his, we have demonsraed ha some of his addiional bea exposure can be capured by basing replicaion on gross raher han ne reurns. We have also invesigaed he risk aking behaviour of fund managers condiional upon he dela of heir incenive opion and found ha conrary o previous sudies, here does appear o be evidence of increased risk aking for hose managers who find hemselves significanly below heir high waer mark. 18

20 References Agarwal, V. and N.Y. Naik Performance Evaluaion of Hedge Funds wih Opion-based and Buy-and-Hold Sraegies", WP HF-003, London Business School (2000). Brooks, C. and H. Ka The Saisical Properies of Hedge Fund Index Reurns and Their Implicaions for Invesors. Journal of Alernaive Invesmens, Fall, (2002) pp Brown S. J., W. N. Goezmann, and J. Park Careers and survival: Compeiion and risk in he hedge fund and CTA indusry, Journal of Finance pp (2001). Fung W. and D. A. Hsieh. Survivorship bias and invesmen syle in he reurns of CTAs, Journal of Porfolio Managemen pp (1997a). Fung, W., and D.A. Hsieh. Empirical Characerisics of Dynamic Trading Sraegies: The Case of Hedge Funds, Review of Financial Sudies, 10, (1997b), pp Fung, W., and D.A. Hsieh. Exracing Porable Alphas from Equiy Long-Shor Hedge Funds, Journal of Invesmen Managemen, 2, (2004), pp Géhin, W and M. Vaissié The Righ Place for Alernaive Beas in Hedge Fund Performance: An Answer o he Capaciy Effec Fanasy, Journal of Alernaive Invesmens, Vol. 9, No. 1 (2006), pp Goezmann, W., Ingersoll J. and S. A. Ross. High-Waer Marks and Hedge Fund Managemen Conracs, Journal of Finance, 58, (2003), pp Hasanhodzica, J. and A. W. Lo. Can Hedge-Fund Reurns Be Replicaed?: The Linear Case Journal of Invesmen Managemen, Vol. 5, No. 2, (2007), pp Ibboson, R.G and P. Chen. The A,B,Cs of Hedge Funds: Alphas, Beas, and Coss, Yale ICF Working Paper No (2006). Kahn, R.N., Scanlan, M.H. and Siegel, L.B. Five Myhs abou Fees Journal of Porfolio Managemen Spring (2006). Ka, Harry M., "Alernaive Roues o Hedge Fund Reurn Replicaion: Exended Version", Cass Business School Research Paper No (April 2007). Ka, Harry M., "10 Things Tha Invesors Should Know Abou Hedge Funds," Journal of Wealh Managemen, (Spring, 2003) pp McDonnell, T. Performance Fee Equalisaion, AIMA Journal, Sepember Sharpe, W. F. Asse Allocaion: Managemen Syle and Performance Measuremen, Journal of Porfolio Managemen, 18, (1992), pp