Assessing Market Risk for Hedge Funds :
Nonlinear Risk Exposures to the Market
著者名(英)
Midori Munechika
journal or
publication title
The economic review of Toyo University
volume
34
number
1・2
page range
185-213
year
2009-03
URL
http://id.nii.ac.jp/1060/00002333/
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http://creativecommons.org/licenses/by-nc-nd/3.0/deed.ja
東洋大学「経済論集」
34巻1・2合併号 2009年3月
Assessing Market Risk for Hedge Funds
一Nonlinear Risk Exposures to the Market
Midori Munechika
Abstract This article analyzes the hedge hmd index retUrns from January l 994 to July 2008 to characterize the systematic risk exposures of hedge fUnd strategies． Our results indicate that an asymmetric sensitivity of their returns to the equity market returns is pronounced in certain strategies such as a family ofEvent Driven， Managed FutUres， and Emerging Markets． In particular， Merger Arbitrage and Managed Futures exhibit contrastive option−like payoffs． Merger Arbitrage index retUms bear a close resemblance to a payoff from selling a European put option， that is， they are positively correlated with market retums in down−markets while uncorrelated with market retums in up−markets． On the other hand， Managed Futures index retums are very much like a payoff from buying a European put option， that is， they are negatively correlated with market returns in down−markets while uncorrelated with market retUrns in up−markets． We also found that the asymmetric sensitivity of the hedge fUnd industry as a whole to the market was considerable under the bullish markets whereas it shaq）ly declined in the bearish markets． The sub−period analysis suggests that there is a possibility ofchanging the nonlinear natures ofhedge fUnd retUrns from July 2007 downward． Contents l．Introduction 2．Hedge Fund Indices and Sector Weights 3．Statistical Properties ofHedge Fund lndex Returns 4．Piecewise Linear Regressions 5．Stability Tests 6．Sub−period Analysis7．Concluding Remarks
1．lntroduction
Hedge fUnds are of interest not only to investors and academics， but also to policy makers． They have remarkably increased both in terms of assets under management and number of fUnds over the last two decades． The hedge fUnd industry has emerged as one of the crucial parts of the modem financial system． Now a large number of hedge fUnds face adverse market conditions and a tuming point under the current intemational financial crises triggered by the US． subprime market downtum in June 2007． The hedge血nd industry as a whole has experienced net outflows in 2008． The te㎜“hedge fUnd”is applied to any pooled investment vehicle that is privately organized， and administered by investment managers． Due to their private nature， hedge fUnds have fewer restrictions on their investment strategies than conventional investment nmds such as mutual fUnds and pension fUnds． MutUal fUnds typically use a long−only buy−and−hold−type strategy on traditional asset classes， whereas hedge fUnds can take more dynamic trading strategies， such as long as well as short positions in securities and often use derivative instruments． At the begiming of the 1990s main investors to hedge fUnds were high net worth individuals． The fbcus has mainly shifted to institutional investors including endowments， foundations， pension血nds， insurance companies， banks and co叩orations since the burst of the IT bubble in 2000． Their main o句ectives are to diversify traditional investment portfblios and improve overall risk−retUrn profile based on the general lack of correlation of hedge fUnd returns with stock and bond markets． Although it is recognized that their low correlations are attractive featUres fbr investors， a major source of risk fbr hedge fimds is still market risk、 It is not easy fbr institutional investors to identifシthe role of hedge fUnds in their portfolio and to determine the appropriate amount for their investment． Market risk is the risk of loss（or gain）arising from unexpected changes in market prices such as security or commodity prices， or market rates such as interest or exchange rates． Using leverage and reducing hedging strategies can not only escalate market risk but also result in non−linear risk exposures to the markets． This in tum， poses the issue of how to capture complicated characteristics of risk fbr hedge 血nds． Alarge number of studies have investigated the unique risk−retum profiles of hedge fimds， often arguing thaUheir retums tend to indicate an asymmetric sensitivity to the market For instance， Mitchell and Pulvino［2001］， Agarwal and Naik［2004］， and Chan， Getmansky， Hass， and Lo［2005］fbund that the hedge fUnd retums were related to market retums in a nonlinear way． This article updates and extends their analysis based on the piecewise linear regression model used in Mitchell and Pulvino［2001］ノ In general， measuring market risk can be examined by regression analysis of a linear factor model． A IMitchell and Pulvino ［2001］investigated the strategy of risk arbitrage and found option like features of the payoff of risk arbitrage．Assessing Market Risk f（）r Hedge Funds−Nonlinear Risk Exposures to the Market linear factor model relates to the return on an asset to the values of a limited number of factors such as market indices， which is common in investment analysis． However， the linear factor model can not capture non−1inear risk exposures to the markets． The purpose of this study is to consider the nonlinear risk exposures of the hedge fUnd strategies to the equity market by performing the piecewise linear（i．e．， spline） regression． This article is organized as follows． Section 2 describes the classification of hedge fUnd indices and the trend of sector weights． Section 3 provides statistical properties ofhedge fund index retUrns． Section 4 presents our regression model using a linear spline with one knot and reports the estimated results． Section 5 performs the stability tests for examining the possibility of structural change of the hedge fund industry． Section 6 carries out the sub−period analysis fbr the two broad−based indices and Fund of Hedge Funds lndex． Concluding remarks are presented in Section 7．
2．Hedge Fund lndices and Sector Weights
Much of the recent debate has been around the importance of greater transparency and includes 廿equent calls fbr policy makers to regulate hedge fUnds． A major problem with transparency， that is， the availability of infbrmation about hedge fUnds comes originally from the facts that they are o債en private partnerships and not obligated to report their results to the public． Consequently， it is inevitable to some extent that hedge fUnd indices suffer statistical imperfections arising not only from the general secrecy and selfLreporting natUre but also from biases which are peculiar to the hedge fUnd industry， such as selection bias， survivorship bias， and so on． In spite of these imperfections， it seems that an analysis of the hedge fUnd indices is usefU1 to consider the dynamism of the hedge fund industry as a whole． More than 20 hedge fUnd indices have emerged over the last 15−20 years． Among of them， two leading hedge fUnd index providers， Hedge Fund Research（HFR）and Credit Suisse／Tremont（CSff）have received wide recognition as relatively good proxies fbr the representation ofthe hedge filnd universe． The two main providers use different calculation methods． The HFR indices are calculated by the equally weighted method， which takes the arithmetic mean of the individuahmderlying fUnds． It means that every fUnd， independent of its size， is weighted equally， and thus， the perfbrmances of small fUnds are given relatively more weight than those of large fUnds． The CS／T indices utilize a value weighted（i．e．， weighted by assets under management）method， which accounts fbr the size of the倉mds． Hence， the CS／T indices give relatively more weight to the performance of larger hedge fUnds．2 For the sake of robustness， we use 2Hedge fUnd retUrns based on the value weighted calculation method can hardly be replicated since larger hedge funds are often closed｛br new investments． The equally weighted calculatien method is used most index providers． See Casa and Rechesteiner［2001］．both the HFR and the CS／T indices fbr the period from January 1994 to July 2008 in our empirical investigation， This means that the data set includes the Mexican peso crisis of l 994−95， the Asian crisis of l997， the Russian−and the LrCM crises of 1998， the IT bubble burst of 2000 as well as the credit crunch after the sub−prime meltdown of 2007． Most hedge fUnd index providers calculate on overall or aggregate（broad−based）index as well as a number of sub−indices， corresponding to the various types of hedge fUnd strategies or geographical destinations． First， the HFRI Monthly Perfbmlance Indices has constructed the hedge fUnd indices derived from the HFR Database consisting of information on over 11，000 hedge血nds and血nd of血nds worldwide， which are classified by fbur primary strategies：Equity Hedge， Event Drlven， Macro， and Relative Value． The fbur primary strategies are fUrther subdivided into sub strategies． The broad−based index is Fund Weighted Composite Index which includes over 2000 constituent fUnds with a minimum of US＄50 million under management and more than a l 2−month track record except fbr Fund of Funds． Emerging Markets Index is a fUnd−weighted composite ofall Emerging Markets血nds， which has no investment strategy criteria． Fund of Funds Composite Index includes over 800 constituent Fund of Funds． Next， the CS／T Hedge Fund indices consist of a composite index（the CS／T Hedge Fund Index）and ten strategy style−based indices derived from the CS／T database including more than 5000 fUnds：Convertible Arbitrage， Dedicated Short Bias， Emerging Markets， Equity Market Neutral， Event Driven， Fixed Income Arbitrage， Global Macro， Long Sho牡Equity， Managed Futures， and Multi−Strategy． The CS／T Hedge Fund Index includes more than 900 fUnds with a minimum of US＄50 million under management and more than a 12−month track record． Figure l shows capital allocations of investors to hedge fUnd strategies based upon the CS／T ten sub−indices from January l 994 to July 2008． It indicates that investors’capital allocations have been diversified among the investment strategies over the last fifteen years． In the early part of l 994， a number of hedge hmds recorded substantial losses by abruptly rising US interest rate． The LrCM crisis in 1998 caused substantial volatility to hedge血nd retums．3 During the period between 1994 and l 998， Global Macro was the largest strategy whose share was more than 60％in the hedge且md industry． It recorded the highest mean monthly retum，1．29％among ten sub−divided indices of the CS／T． Global Macro fUnds exploit any opportunity that they can find in the market． Their investment approach relies on market timing skills， taking aggressive and purely market directional bets with no particular hedging policy． They fbcus on identifying extreme price movements and leverage is often applied． Profits arise from correctly 3Cross−sectional volatility of the hedge fUnd industry peaked in Augus口998， the month in which the Russian default caused the LrCM crisis． The cross−sectional correlation and the volatility among hedge fund strategies from January 1994 to July 2008 based on the CSfT hedge fUnd indices are discussed in Munechika［2009］．
Assessing Market Risk for Hedge Funds−Nonlinear Risk Exposures to the Market Figure 1：Sector Weights among Hedge Fund Strategies 100S 90、 80％ 70、 60％ 50％ 40㌔ 30％ 20％ 10％ 0％ ∂＼
vドずみ㌦ぷ心ドぷぴ轟“♂ぽぷ・㌔．㌔“」㌔∨」’W“右ぽ宙へ♂心○
田ConverUble Arbltrage ■Dedlcated Short Bias 口Emerging Merkets 口Equlty Markθt Neutrei ■E＞ent Driven 口FI×ed lncome Arbitrage■Global Macro 口Leng／Short Equ：ty ■Managed Futures ■Multl−Stretegy Source：Author’s compilation based on data from Credit Suisse／Tremont． anticipating Price movements in global markets． Thereafter， Long／Short Equity has increased， and acc皿nted fbr more than 50％oftotal weight in 2000． The IT bubble ended around March 2000． During the period between January 1999 and March 2000， its mean monthly retum was 3．20％， which was the highest one among the CS／T ten sub−indices． Long／Short Equity funds rely on a strategy combining of rong positions in undervalued stocks and short positions in overvalued stocks， which is known as the long／short strategy．4 The purposes of selling stocks short are to hedge a portfolio’s market exposure（and／or sector exposure）， to make profits from stock price declines， and to capture relative value． The traditional long−only buy−and−hold type strategy has only one source of retum， which is the appreciation ofthe purchased stock． A source of retUrn in long／short strategies is the spread in performance between the long position and the short position． The spread makes profits when the stocks on the long side appreciate㎞value while the shorted stocks depreciate in value． The short position represents abet on an overvalued stock that should decrease in value in the near fUtUre， which in tUrn can be served as hedging the market risk of the long side． Therefbre， the payoff arises from relative mispricings of securities rather than the movement of the market as a whole． After the IT bubble burst in March 2000， the equity markets tumed into a bearish environment． In 2001，the markets were hit by the disruption event of 9−ll，followed by the events at Enron and Worldcom in 4The original Alfred Winslow Jones hedge fUnd model was mainly based on this strategy． More specialized strategies， such as arbitrage and relative value are formed on the basis of long／short strategies． Lhabitant［2002］， pp．9−10．2002．The share of Event Driven has grown rapidly from l 4」0％in March 2000 to 26．80％in June 2002． In 2008， the sum of the top two strategies， Long／Short equity and Event Driven， represents more than half of the hedge fUnd industry． The payoffs of both strategies arise primarily from relative mispricings of securities rather than the movement of the market as a whole．
3．Statistical Properties of Hedge Fund lndex Returns
Table l provides the descriptive statistics fbr the monthly retums of individual indices of the HFR （Panel A）and the CS／T（Panel B）． For comparison， statistics fbr the S＆P 500， the Russel12000， the NASDAQ， and the Dow Jones Industrial Average are included in Panel C， The perfbrmance statistics suggest the fbllowing points． First， the historical retum characteristics vary widely across hedge fUnd investment styles while the risk levels measured by standard deviations are considerably lower than those of the stock market index retums． Consequently， on the Sharpe ratio basis， most of the hedge fUnd strategies yield a better perforrnance than do the stock market indices except for Short Bias（the HFR）and Dedicated Short Bias（the CS／T）．5 1t is interesting to note that the estimated Sharpe ratio of Fund of Funds Composite was O．07， which value is not better than those of stock market indices． The concept behind fUnd of f廿nds is that an investment manager evaluates many hedge血nds’performances， and maintains a portfolio composed of the best of them， charging a fee in exchange for the potential to deliver high performance． Theoretically， well−designed and well−managed fUnds of hedge fUnds are supposed to deliver better performance than other s仕ategies since they can offer efficient risk diversi負cation， aff（）rdability， accessibility， professional management， and built−in asset allocation．6 Thus， institutional investors often prefer to invest fUnds of 五mds in their portfblios． However， the empirical evidence reveals that it is quite di伍cult to of飴r consistently be廿er performance in Fund of F皿ds Composite than other strategies on average as shown in Table l． Second， most hedge fUnd indices and the stock market indices indicate that the retums do not seem to be normally distributed． A normal distribution has a skewness of zero and a kurtosis of three． The skewness is a popular measure for the asymmetry of a distribution． A positively skewed distribution has a tail extending to the right；conversely a negatively skewed distribution has a tail extending to the lefL If the 5The Sharpe ratio is the most prominent risk−adjusted performance measurement， which is the difference between the mean fUnd retUrn and the mean risk−free rate divided by the standard deviation of the fUnd retUrns． 6For more detail explanations about Funds ofFunds， see Lhabitant［2002］， Chapter l 6．Assessing Market Risk for Hedge Funds−Nonlinear Risk Exposures to the Market
Table 1：Descriptive Statistics of Hedge Fund Index Returns
January 1994 to July 2008
Sample
S屹e
Mean
STD
Skew
Kurt Jarque−Bera Sharpe Ratio Panel A：Hedge Fund Research Fund Weighted Composite Equity Hedge Equlty Market Neu“al Energy／Basic Materials Technology／Healthcare Short Bias Quantitative Directional Event Drjven Merger Arbi廿age Distressed／Restnlcturing Privatelssue釆egulationD Macro Systematic Diversified Relative value FI−ConvertibleArbitrage FI−Asset Backed FI−Co【porate Yield Altematlve Multi−Strategy Emerging Markets Fund ofFunds Corn osite
555355555515555555555777677777757777777777111111111111111111111
010110100010000000000
851479986951745243969806822097818976757595
120555311122201111031
727040516211824238297958237880500191238996
46 Q5 Q2S4329450976417308161518107636259330
0000000−1100021410100
↑ 一 一 ’ ． 一 一 ≡ ≡ 一 ■ “ ， ．． 8・ ・ヂ ●● ■●■ ⇒‘■ ■■■ ．●■ ●■● ●右■ ■■写 ■■⑨ ・ ●■■ 1．●197063955028188048512877125641589832359684
543455370043265094676
11
1 3 亭寧 ウ．．’ヂ． ．・．ウ 皐・ ・ ・ ・ ・ 守，． ⑨◎．． ■十 ■． ．， 皐▼ ●■奉 ・ヂ・ ●季■ ■●． e■■ ．・・ ウ●■ ■■■ 63．64 25．25 5．76 13．40 42．81 48．95 9．44 179．64 463．50 467，73 34．15 7．11 1，02 1440．30 78．23 5924．29 401．89 32．38 142．77 193，94 87，72 吟● ◆ヂ．・ 皐●． か・ ●章．‘．・ ．● ・． ．． ■今 ．・ヂヂ．． ■■・ ■●● ■■■ ■●● ■●■ ヂ●■ 卓■右 ●●●133953082827306154427223210224341231201110
000000000000000000000
一 Pane旧l Credit Suisse／Tremont CS／T Hedge Fund［ndex Convertible Arbitrage Dedicated Short Bias Emerging Markets Equity Market Neutral Event Driven Fixed lncome Arbitrage Global Macro Long／Short Equity Managed Futures Multi−Strate 175 175 175 175 175 175 175 175 175 175 172 0．85 0．64 0．05 0．83 0．79 0．89 0．47 1，12 0．94 0，62 0．73 2．16 1．42 4、87 4．43 0．80 1．62 L17 3，00 2．84 3．45 L28 0．10 −1．50 0，78 −0．69 0，36 −3．Ol −3．11 0．02 0．19 0．00 −1．04 ■⑨● ・・■ ●⑨■ ● ヂ■■ 章●● ■■■ 5．35 6，87 4．77 8．08 3．52 23，13 18．14 6．19 6．76 3．IO 5．30 ■章● ・■． ■⑨‘ ●，■ ●⑨● ■ヂ・ ●毒参 ●●楡 40．53 174．91 4048 202、17 5．76 3219，52 1953，18 74，41 104．39 0，07 69．12 ・． ●． ・・ ・・ ・・・． ● ヂ．． 皐● ■‘ “● ● e ． ■●■ 0．25 0，23 −0．06 0．12 0．58 0．36 0．13 0．28 0．23 0．09 0．34 Panel C：Market lndex S＆P500 Russel12000NASDAQ
DJIA 175 175 175 175 0．65 0，72090
0．70 4．06 5．23 7．26 4，17 一〇，56 −0．45 −O．35 −0，52 ◎■’ ．・ ● ●■● 3．68 4．Ol 4．09 4．13 ●■● ●＄● ．皐写 12．65 13．29 1227 17，23 ●・ヂ ■■■ オ■・ ■●卑 0，09 0．07 0．08 0．10 Source：Author’s calculations， based on data from Hedge Fund Research， Credit Suisse／Tremont， and Yahoo！Finance． Notes：（1）＊，＊＊and＊＊＊denote significance at the 10％，5％， and l％levels， respectively． （2）The Jarque−Bera normality test is asymptotically distributed as a central Z2 with 2 degrees of freedom under the null hypothesis， with 10％，5％and l％critical values，4．61，5，99 and 9．21 for the sample size（n＝175）． retum distributions are negatively skewed， standard deviation will overestimate the proportion of retUrns above the mean and underestimate the proportion of retums below the mean．7 Akurtosis whose value is more than three is referred to‘excess’kurtosis． Positive excess kurtosis implies more weight in both tails of the distribution than in the normal distribution， that is， a‘fat tailed’distribution． This means that large negative and positive retUrns are much more likely than w皿ld be the case under a normal distribution． It is noteworthy that the skewness and the kurtosis are reflected in risk preferences of investors． 7For more on this see Feibel［2003］， p，149，Aretum distribution with negative skewness and positive excess kurtosis indicates le丘一tail risk exposure， which is an unattractive featUre for risk−averse investors． This is because large negative re加ms are much more likely than would be the case whose retums are nomally distributed． For example， the strategies that produced negatively skewed retum distributions（less than minus one）with positive excess kurtosis were Event Driven， Merger Arbitrage， Distressed Restructuring， Relative Value， Convertible Arbitrage， Asset Backed， and Multi−strategy in the HFR， and Convertible Arbitrage， Event Driven， Fixed Income Arbitrage， Multi−strategy in the CS／T． However， most of these strategies have relatively high Sharpe ratios． Conversely， Private lssue／Regulation D in the HFR and Dedicated Short Bias in the CS／T exhibit highly positive skewness and excess kUrtosis． Their return distributions have an attractive feature for investors since large positive retums are much more likely than would be the case whose retums are nomlally distributed． However， the Sharpe ratio of Dedicated Short Bias showed the smallest value ofnegative O．06 More precisely， the issue of whether the retum distributions are normally distributed can be examined by implementing the Jarque−Bera normality test． Under the hypothesis of nomlality， the JB−test statistic would be：
狙ヱタ2＋」！（k−3）2−5Z2［2］
24 6 where P is the sample skewness and 楡 is the sample kurtosis． ln large samples， the distribution of the JB−test statistic is asymptotically Chi−squared distributed， Z2 with two degree of freedom． The JB−test statistics are compared with the 90％，95％，99％−quantile of the Z2［2］distribution， which equal to 4・61， 5．99，and 9．21，respectively．8 As is evidenced by their significant JB−test statistics， it seems appropriate to conclude that most hedge fUnd index returns and all stock market index returns are not normally distributed． The statistical properties of non−normally distributed hedge fUnd index retUrns pose difficult problems fbr measuring risk． Traditional risk management based on the mean−variance approach only takes two parameters， mean retum and retum variance（and／or standard deviation）into account to specify the risk−retum pro丘le of the investor’s portfblio． The Sharpe ratio based on the M−V criterion therefbre only takes the first and second moments into account to specify the risk−retum profile of the investor’s portfblio． If the returns are normally distributed， the first two moments of the distributions are enough to characterize their risk−retUrn profile． However， in the case of non−normally distributed returns， skewness and㎞Hosis might play a significant role on risk perception fbr investors． 9For example、 we reject the hypothesis of normality if the value of JB−test statistic exceeds 9．21 and accept it otherwise at the significance level of 1％． See R．achev， Menn and Fabozzi［2005］， pp．ll6−117．Assessing Market Risk f（）r Hedge Funds−Nonlinear Risk Exposures to the Market
Autoco「relation
The hedge fUnd index retums exhibit significant serial correlations compared to those of the stock market indices． The estimated autocorrelation coe伍cients fbr lag one to five together with the Ljung−Box （LB）statistics with five and ten autocorrelations are reported in Table 2． The勾ung−Box test examines the joint hypotheses． The null hypothesis is that all the五rst 〃1 autocorrelation coefflcients are jointly zero． For the test of significance of the autocorrelation coefflcients， confidence intervals f（）r the autocorrelations can be calculated under the assumption that returns are normally distributed． For a sample of this size （n＝175），an autocorrelation coefficient is defined as statistically significant at the l O％level if it lies outside 土0」24，significant at the 5％level if it lies outside±α148 and significant at the 1％level if it lies outside 土0．195．9 The relevant critical values to the LB statistic are丘om a z2distribution will〃1 degree of freedom at the 10％，5％， and l％［evels． Fifteen hedge fUnds indices in the HFR and six hedge fUnds indices show positive serial correlation at the first lag statistically significant at the 5％level while the stock market indices show very little evidence of autocorrelation．lo Significant serial coπelation in hedge五md index retums leads to underestimation of the standard deviation of retums． Consequently， the calculated Sharpe ratio is overestimated to its true value since the standard deviation ofretums is biased by positive serial correlation． As mentioned befbre， it is not reflected in the skewness and the kurtosis． The Sharpe ratios of hedge fUnds possibly underestimate their tail risk exposures． Tb sum up， our findings are that the monthly return distributions of hedge fund indices show significant degree ofskewed， fat tailed， as well as positive autocorrelated distributions． Correlation Structure to Markets The degree of systematic risk in hedge fUnds can be considered the correlation structure to the markets． Table 3 reports correlations of hedge fund index returns to the market index returns． As for the broad−based indices， the correlations of the HFR to the markets are much higher than those of the CS／T． It is clear that， most of strategies in the HFR are highly correlated to the Russell 2000（small−cap stocks）and the NASDAQ （small technology stocks）compared with the S＆P 500（large−cap stocks）and the DJIA． This featUre can be found to some extent in the CS／T． This implies that hedge funds were heavily．invested in the 9According to the analysis presented in Table l， the normality assumption is extremely dubious． However、 the confidence intervals which shall be used nonetheless provide a general idea about each of the autocon−elation coefficients for significance． See more detail fbr significance tests in this context in Brooks and Katz［2001］and Brooks［2002］， pp．232−234． Lo @Getmansky， Lo and Makarov［2004］point out that the most plausible explanation among several potential sourccs f（）r serial correlation of hedge fiエnd retums is illiquidity expose and smoothed returns．Table 2：Autocorrelation in Hedge Fund lndex and Stock lndex Returns
January 1994 to July 2008
Monthly Return
・ρ
2
＾ρ ・ρ 3 ・ρ 4 ・ρ 5 ALB−（es ALB一ρ，。
Panel A：Hedge Fund Research Fund Weighted Composite Equity Hedge Equity Market Neutral Energy／Basic Materials Technology／Healthcare Short Bias Quantitative Directional Event Driven Merger Arbitrage Distressed／Restructuring Private lssueRegulation D Macro Systematic Diversified Relative Value FI−Convertib］e Arbitrage FI−Asset Backed FI−Corporate Yield Altemative Multi−S甘ategy Emerging Markets Fund ofFundS Com osite ●■ 0．192 ■■ 0．170 0．054 0．141’ ■■ 0．161 0．095 ，■ 0．153 ■■■ 0．272 ■■． 0．214 右■■ 0．411 ●●● 0．374 0．102 0．008 ■■● 0，286 ■，● 0．486 ●●■ 0．395 ■■● 0．337 0．031 ■●■ 0．291 ■■⑨ 0．282 ■●◆ 0．282 0．031 0．080 0．097 0，074 0．108 −0．107 −0．081 0．064 ヂウ0．161 ●●0．149 ●・・0．277 −0．046 −0．046 ●・0．181 舎e●0，207 ■⇒●0．261 0．142’ −0．032 0．119 0．079 0，094 一〇．052 0．028 0．ll2 −0．089 0．008 −0．040 −0、089 0．000 0．122 0．026 0．145⑨ 一〇．018 −0．049 0．026 0．116 0，145’ 0，006 0．116 −0，008 0，029 ．0，027 一〇．040 −0．016 0．143’ −0，060 0．037 −0．089 −0．093 0．OlO O．004 0．075 ●■0．171 −0．019 0．038 0，029 0．139’ 0．131’ 0，066 −0．006 0．072 0．006 −0．045 一〇．054 −0．060 0．023 −0，033 −0．021 ．0．114 −0．041 0．049 0，130 0，029 ■■吟0．205 0．020 0．029 −0．010 0．034 0．024 0．064 0．024 0，003 −0．014 ．0．070 8．045 7．153 8．274 6．373 7．073 7．737 8．692 琴ヂ14．346 念⑨■ 18．547 ■●， 35．355 ●ヂ● 48，013 2．424 1．253 ヂ■● 20．762 ヂ・● 55．881 ヂ■■ 46．875 ●●● 25．347 2．865 プ●■ 18．582 舎◆■ 15，499 ■■■17．103 12．078 14．646 ■■● 34．701 寧．23．152 ■18．285 12．455 12．617 ⑨●17．660 ■専●29．730 ■ヴ■ 35．985 ■●± 68．765 6．581 4．806 ●吟■ 23．225 ●ヂ●65275 ⑨●■ 51．096 ■●■ 27．068 ！3，387 ■●■25，676 ■・18．980 ●●● 19．612 Panel B：Credit Suisse／Tremont CS／T Hedge Fund Index Convertible Arbitrage Dedicated Short Bias Emerglng Markets Equity Market Neu仕al Event Driven Fixed Income Arbitrage Global Macro Long／Sho宜Equity Managed Fu仙es Multi，Strate ｛3） 0．lll ●■■ 0．501 0．101 ●●・ 0．277 ●●琴 0．286 ・・◆ 0．294 ●■● 0．288 0，056 ●・ 0．154 0．057 0，073 0．023 ■■● 0．288 −0．055 0．017 ■● 0．155 0．136ヂ ー0．007 0，014 0．044 ●● −0．168 0．051 一〇．015 0．146’ −0．053 −O．005 0．104 0．021 0．032 0．085 ．0．067 −0．080 0．098 一〇．058 ■■0．195 ．0．110 −0．060 0．047 0．030 0．094 −0．063 −0．086 0．002 0．000 0．038 0．049 −0．107 −0．081 0．026 0．002 −0，031 ■●■ 0．214 ・． −0．159 −0，016 −0．064 3．205 ヂ●● 70．680 7．151 ■，■ 15．524 ●●ψ 21、368 ●●ψ18，991 ■・・ 16，715 ●10．938 ■■ll．333 6，824 3．821 8．790 ●●● 76．227 7．967 ●■■ 24．129 ■■● 33．147 ■■ 21．934 ⑨■ 21．460 ■■ 22333 ●● 21．406 ■●19．768 5．989 Panel C：Market lndex S＆P500 Russell 2000
NASDAQ
DJIA 0．014 0．061 0．056 −0．039 一〇，042 −0．047 −0．OI6 −0，044 0．037 ■ −0．148 −0．024 −0，038 一〇，055 −0．107 −0．032 −0．048 0．095 −0．080 −O．034 0．047 2，787 8，214 5．326 1，713 7．669 13．277 9．949 4．402 Source：Author’s calculations， based on data廿om Hedge Fund Research， Credit Suisse／Tremont and Yahoo！Finance． Notes：（1）＊，＊＊and＊＊＊denote significance at the 10％，5％， and 1％levels， respectively． （2）The Ljung−Box Q5 （QlO）test for autocorrelation of order up to 5（10）is asymptotically distributed as a central X2 with 5（10）degrees of freedom under the null hypothesis， with 10％critical value 9．24（15．99），5％critical value l l．1（18．31）， and l％critical value 15．09（23．21）． smal1−cap stocks and small technology stocks． The portfblio of Long／short Equity hedge fUnds actually may not always have zero market risks， most 6mds have a long bias． Even though the fUnd manager make err in his choice of securities， the fUnd may still be profitable when the long position outperfbms the short position on a relative basis． This is a remarkable property of a long／short strategy， which explains why it has the ability to perfbrm well in both bear and bull markets．11 For example， the correlations of Long／Short Equity to the S＆P 500（0．60）and the 11 ree more detail in Lhabitant【2002］， pp．78−79．Assessing Market Risk for Hedge Funds−Nonlinear Risk Exposurcs to the Market
Table 3：Correlations between Hedge Fund lndex Returns and Market lndex Returns
January l 994 to July 2008
S＆P500
Russell 2000NASDAQ
DJIA
Panel A：Hedge Fund Research Fund Weighted Composite Equity Hedge Equity Market Neutral Energy／Basic Materials TechnologyfHealthcare Short Bias Quantitative Directional Event Driven MergerArbitrage DistressedfRestructUring Private lssue／Regulation D
Macro
Systematic Diversified Relative Value FI−Convertible Arbitrage FI−Asset Backed FI−Corporate Yield Alternative Multi−Strategy Emerging Markets Fund of Funds Composite197549973916993472283761366765433543044455
コ コ コ ロ コ ロ コ コ コ ロ ロ の コ ロ ロ000000000000000000000
一
444073111215135142135882478986644653155566
や サ ロ コ コ コ リ ロ ロ コ ロ シ コ コ00000000000000①000000
一
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ロ ロ コ ひ コ コ コ コ ロ コ ロ お①00000000000000000000
一
270508710501050662976651355665423543044354
ロ ロ コ ロ ロ ロ ロ コ コ ロ ロ ヒ ロ ふ00000000①000000000000
一
Panel B：Credit Suisse／Tremont CSIT Hedge Fund Index Convertible Arbitrage Dedicated Short Bias Emerging Markets Equity Market Neutral Event Driven Fixed Income Arbitrage Global Macro Long／Short Equity Managed FutUres Multi−Strategy 0．49 0．19 ・O．76 0．48 0．36 0．S6 0．09 0．21 0．60 −O．13 0．16 0．56 0．24 −0．82 0．53 0．24 0．62 0．11 0．20 0．76 −0．08 0．22 O．53 0．18 −0．81 0。49 0．25 0．52 0．07 ①．17 0．75 −0．15 0．19 0．41 0．15 −0．66 0．47 0．36 0．52 0．09 0．18 0．47 −0．14 0．08 Source：Author’s calculations， based on data from Hedge Fund Research， and Credit Suisse／Tremont and Yahoo！Finance． Note：Correlations significant at the significance level of5％are shown in bold type． Dow Jones Industrial Average（O．47）are lower than those of the Russell 2000（0．76）and the NASDAQ（0．75）． It is evidence that long／short equity funds are persistent net exposures to the spread between small versus large cap stocks in addition to the overall market． This means that Long／Short Equity hedge fUnds’retums arise from market directional as well as spread bets on the stock market． Consequently， they havesignificant correlation with equity markets as shown in Table 3． The majority of strategies exhibit positive correlations to the market indices except fbr Short Bias， Dedicated Short Bias， and Managed Futures． The estimated Sharpe ratios of all of the three negatively correlated strategies were much lower than other hedge fUnd strategies． ln particular， two of the three strategies were negative estimates in the Sharpe ratio． However， it is worth noting that these strategies can yield greater diversification benefits in consisting ofaportfolio・ The correlations of hedge fUnd strategies can valy over time． Figure 2 depicts the backwards 12−month rolling correlations betWeen the broad−based index retUrns and the market index returns， shown in the HFR Fund Weighted Composite in Panel A， the CS／T Hedge Fund lndex in Panel B， and both of indices to the S＆P 500 in Panel C． The correlations of the CS／T Hedge Fund Index were more volatile than those of the HFR Fund Weighted Composite over the sample period． The levels of correlation ranged from−0．19 with S＆P 500 in December l 995 to more than O．91 in April I 997． The CS／T showed very low correlations to the market indices in the early period from the end of l 994 to the middle of l 996． On the contrary， it exhibited higher correlation than the HFR in the subsequent tWo years． During the bear market condition from March 2000 to 2003， the correlation to the market was much higher in the HFR than the CS／T． The trend of correlations ofboth indices to the S＆P 500 has been almost the same since the end of2004．
4．Piecewise Linear Regressions
Hedge fund returns may relate to the stock market returns in a nonlinear way such as asymmetric sensitivity to the equity markets， which is not captured by correlation coe缶cients discussed in the previous section． The asymmetric sensitivity of hedge fUnd returns to the market implies that there are different beta coefflcients fbr down−markets versus up−markets． It can be considered by implementing the fbllowing 「eg「eSSIOnS・ Tb begin with our empirical testing， we estimate the Market Model：R、−Rノ＝α汁β（R． −Rf）＋・、， （1）
where R， is the monthly hedge fUnd index retum to the i th strategy， Rf is the monthly risk−free rate， RM is the monthly retum on the stock market index． Here， we use the monthly retum of the 3−month t・ea・ury・b・nd・・th・・i・k・f・ee・et・m Rf，・nd th・S＆P 500 i・d・x・・R．・121fα， i・z・…th・CAPM i・ 12 ve con丘rmed that the monthly retums on all hedge fUnd indices and the S＆P 500 index， and the 3−month TB are stationary based on conducting the unit root tests（i．e．， the DF test， the ADF test， and the Phillip−Perron test）with and without trend at l％signi丘cance leveLAssessing Market Risk for Hedge Funds−Nonlinear Risk Exposures to the Market Figure 2： 12−month Rolling Correlations between Hedge Fund lndex and Market lndex Returns Panel A：HFR Weighted Composite vs． Market lndices 2 1 1 8 0 6 0 4 0 2 0 0 NF＼藁一
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S＆P500 DJIA−．・Russetl2000 NASDAQcomposite Panel B：CS／T Hedge Fund lndex vs． Market lndices競
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S＆P500−≡ −Russell2000 NASDAQcempeslte DJIA Panel C：HFR and CS／T to S＆P 5001ndex ｝ 一 一 1 「 ｝ ﹁° 1 卜゜ へートwt’ー、Lξ゜︾＄∼︾トー° 2 0 § 、 敬竃
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⋮ W ⋮ °︷i°°ー﹁°C 8 0 6 0 4 0 2 0 一 4 0 一The HFR W81ghted Composite lndex Return−The CS／T Hedgo Fund Indox Return Source：Author’s calculations、 based on data from Hedge Fund Research， and Credit Suisse／Tremont and Yahoo！Finance．expected to be hold．13 To characterize the systematic risk exposures of hedge fUnds， the CAPM−type model can be used since it separate the retum of hedge fUnds into two parts：systematic and idiosyncratic． Beta coefflcient fii can be seen as systematic risk exposure to the market， alpha coefficientαi is the excess retUrn generated by the hedge fUnd strategy， and the error teml ui represents the portion of the index retum not related to the market， that is， idiosyncratic risk． Next， we estimate the piecewise linear CAPM−type model： R，−R∫一（1一δア）［αi・βL・（R。−R，）］・δア［α獅・β”・（RザRf）］・u、’ （2） wh・・eα『・ndβ㌔・e th・i・tercept・nd th・・1・pe c・・伍・i・nt・wh・n the excess m・・k・t・e加m i・less than th・t㎞・・h・ld l・v・1τ，andαζ・ndβ”・・e th・i・t・・cept・nd the s1・pe c・・ff1・i・nt・wh・n the excess market retum is greater than the threshold levelτ．δτis a dummy variable： δ・一
o1・RM＞T・ （30， RM≦T．）
Figure 3 provides a graphical description of the model specified by equation（2）assuming a negative threshold． The horizontal axis is the excess monthly retum ofthe S＆P 500 index and the vertical axis is the excess monthly retum of a hedge fUnd strategy． However， such a regression model would neglect the continuity of the fUnction just by dividing tWo linear pieces． The result we estimate would apPear more like the broken lines than the continuous fUnction we had expected as shown in the solid line．14@Restricted
regression is required to gain the desired effect． To insure continuity， the fbllowing restriction is imposed on the model：15α『＋βL・τ＝α獅＋β”・r． （4）
Since RM＝（1一δ「）・1∼〃＋δ「・1∼M，the standard linear model（1）in which fUnd i’s market betas are identical in up and down markets is a special case of the piecewise linear specification（2）， the case where βL＝β”． Table 4 reports the results of the linear and piecewise linear regressions， in which the threshold level of excess market retum（in excess of the risk−free rate）is zero，16 First， the results of the CAPM type linear regression show significant Jensen’s alphas in the most part of hedge fund strategies， which can be 13α：is called Jensen’s Alpha， which can be inte中reted as the risk−a（加sted value added by active fUnd management See Feibel［2003］， p」95． 14 eor example， the non−restricted piecewise linear regression on the HFR Weighted Composite Index retum at the th，e、h。ld l，vel。f ze，。 excess m、，k，t，etu。，・h。、 th・劔1・wi・g・e・ult・・c・・ff1・i・nt・・fα『，βL，αζ，・ndβH・・e O．45， 038，091，and O．21，respectively． It is clear that continuity was not satisfied． 15The piecewise linear regression model can be formulated as a linear spline fUnction with one knot． For more detail discussion about the spline function， see Ruppert［2004］， pp．405−406， and Greene［2000］， pp．322−325． 16We detennine the significance using heteroscedasticity and autocorrelation−consistent standard errors・Assessing Market Risk for Hedge Funds−Nonlinear R．isk Exposures to the Market Figure 3： Piecewise Linear Model
Excess Retum
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’ βL ’ ’、 Source：Author’s compilation based on Figure 2 in Mitchell and Pulvino［2001］， p．2143． considered as the major fbrce behind a big boom in the financial sector during the last decade． Second， according to the piecewise linear regression estimates， overall the evidence illustrates that most HFR and more than half of CS／T strategies indicate a nonlinear risk−retUrn relation as manifested through significant betas． For example， the indices whose down−market betas are much greater than their up−market betas （among the indices that both betas are statistically significant at l O％1evel）are Fund Weighted Composite （the broad−based index）， Equity Hedge， Technology Healthcare， Quantitative Directional， Event Driven， Emerging Markets in the HFR， and Emerging Markets， Long／Short Equity in the CS／T． Conversely， the indices whose do㎜一market betas are much smaller than their up−market betas are Energy Basic Materials， Systematic Diversified in the HFR． The asymmetric sensitivity to the market can be tested by perforrning the Wald tests of restrictions on th・p・・am・t・・s b・・ed・・th・F−stati・ti・． Th・hyp・th・・i・i・th・n t・・t・d by th・・e・tri・ti・n・βL＝β”． lf th・ restriction is valid， there should be little difference in the two residual sum−of−squares computed with and without the restrictions imposed and the F−value should be small、 The idea of this test is to see whether the unrestricted parameter estimates by the piecewise regression based on equation（2）and（4）are significantly different from their restricted values． When the unrestricted estimates fail to satisfy the restrictions， then doubt is cast on the validity of the restrictions． Based on the Wald test reported in Table 4， the F−statistics of Quantitative Directional， Event Driven， Merger Arbitrage in the HFR， and Managed Futures in the CS／T can．。象；る］；旨コ。﹄名 ξ。壱。旨ま2旨ξ゜・吟ヱ。。・。s。工三コs°・♂エ8象＝＝賞・。壱。力ξ。書二・ξ窃口▽一g。‘こ8工宰﹂▽。至亘巴。己︵い︶．。9弓三三き壱。﹂三。﹀。一嵩皇烏§N§ど§老一で 含§旦曇・・芭‖§エ︵寸︶．言≧り8§・ぎ・。ま［§義ざo［皇⋮。§已一昼・8。喜⋮▽旨．‡．“e．・・﹂。ヒ3・閃喝§・・盲膓・8き亘巨8。§で旨訟日・・で。§5皇 ・。 E嘱旨萱冨賃ξ。苔倫・；。・8頃葛朋［昌亘§。自︵N︶．毒。﹂昌o盲E§二。着∈⋮。8×。唱［￡・。﹄二巨匂8⊂。・。。己。お・・已2・⋮。﹂・。。﹂。・。写8畳⑪エこ。・，三・，尼︵一︶二g。z ．oO口司ロ一］一〇〇￡ぷ匂＝口↑口o已o﹂﹂い＼O。‘。ー咽コoり一一勺o宍︶ ▽已恒．調o﹄do。う⇔匡唱已コ﹂obo▽o＝已◎頃5ω力己o℃ogり句工．のロo⋮↑旦コ⇔言o。◎“﹂o日コ＜︰oo﹄コooり
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ω∈ヨΦ匡xΦ℃三〇8島oり2ω∈3Φ匡×8三盲⊃﹂Φ習Φ三〇ω⊂Ω切・。Φ﹂OΦ匡﹂8⊂コΦω言Φ8圧で編﹂＄⊂コ⋮寸Φ五巴 ゜。WNエコ﹃εマひひ［拾雲旨hAssessing Market Risk for Hedge Funds−Nonlinear Risk Exposures to the Market decisively reject the null hypothesis of symmetric sensitivity at the 5％level of significance， and the F−statistics of Distressed／Restructu血g and Systematic Diversified， and Yield Altemative in the HFR r《jected the null hypothesis at the 10％level of significance． The reported probability is the marginal significance level of the F−test． For example， the reported probability of the HFR Fund Weighted Composite was O．109． R《乖cting the null hypothesis that the aggregate hedge fUnd index’s market betas are identical in up and down markets would be wrong in less than l O9％observations， To gauge the sensitivity of the results to the choice of threshold， the estimates of the selected indices at the thresholds倉om−1 percent to−5 percent are presented in Table 5． Event Driven in the HFR is the
primary strategy index composed of Merger Arbitrage， Distressed／Restructuring， and Private
Issue／Regulation D， whose comparable index is Event Driven in the CS／T． The estimates of both Event Driven show that the increase in their down−market betas is much greater than those in their up−market betas as the threshold drops， and the threshold minimizing the sum ofsquared residuals is−5％of the excess market retum． Event Driven strategy fbcuses on events such as mergers， takeovers， and reorganizations． The fUnd managers are required special㎞owledge of a broad range of corporate events and shi恒heir portfblios during different parts of the business cycle in the investment process． They seek to profit from potential mispricing of securities related to a丘㎜一speci丘c or market event， such as mergers， ban㎞ptcies， restructuring and so on． Source of retum comes from fUtUre valuation of the company’s debt or equity instnlments and is less dependent on overall stock market gains． The risk arises倉om the nonrealization of such events． This is more likely to occur during do㎜一market conditions． Event Driven fUnds invest in various asset classes including derivatives．17 Merger arbitrage fUnds trade securities of companies involved in a merge or acquisition Typically， they buy the stock of a company being acquired at a discount to the takeover price， and sell short the stock of the acquirer at the current price with a goal ofextracting a small profit when the deal closes． The strategy is event driven rather than market driven． Merger arbitrage fUnds are exposed to significant event risk due to the fim−specific positions they take． A large proportion of deals go through during up−market condition， and they make profits， which are unrelated to the degree of up−market condition． Individual deal risks are idiosyncratic and can be diversified away． They are therefbre less exposed to market risk under normal market conditions． However， the deals often fail during down−market conditions， the fUnds incurs large 17 Pnvestment strategies with derivatives are designed to create asymmetric， non−normal return distributions． For example， strategies with purchasing put options reduces the risk of losses， while leaving the potential for rcturns、 in exchange fbr a lower average retum due to the cost ofthe put options． Conversely， written call options have the opposite effect．Table 5：Piecewise Linear Regressions of Se｜ected Hedge Fund lndices to S＆P 5001ndex Returns January l 994 to July 2008
T
αH t（∋ L β t（βL） β︸ t（βH） つ A（ij−R』 （％）SSR
Panel A：HFR Event Driven％4234δ
0．81 0．75 0．72 0．69 0．68 ■●． ■●■ ●●● ・■． ■●⑨ 5．32 5．75 6．16 6．15 6．08 ●■ヴ 0．41 ■●■ 0．44 ■・● 0．48 ■■■ 0．53 ■■・ e．sc 4．68 4．19 3．97 3．65 3．60 ■．．0．20 ■●●0．22 ・・． 0．23 ●■，0．23 ■傘■ 0，24359
4．41 5．20 5．77 6、23 46．12 46．11 46．58 46，78 47．28 Min Merger Arbitrage﹂234づ
0．60 0．55 0．53 0．52 0」50 ●■■ ・■・ ●●■ ■・■ ．◆■6498’3
10／0913
5556孟U
●●卓0．23 ■●● 0．25 ●■命 0．29 ●■⑨ 0．34 ψ・京 0．41 3．35 3．04 3．Ol 3，05 3．29 ・ 0，06 ■・ 0．07 ■■■ 0．08 ■■■ 0．08 ele8 “命 1．90 2．43 2．73292
3，14 31．81 31．763295
34．21 35．77Min
Distressed／RestructUring4234、連州
■治■ 0．84 ●●■ 0．76 ●■●0．70 ■■■0．66 σ●■ 醸64 4．90 5．35 5．38 5．19 5．09 ■●■ 0．33 ■■● 0．36 癖●● 0．40 ■■■ 0．44 ●愈喜 o．52 3．02 2，82 2，60 2．34 2、35 0．06 0．08 ● 0．10 ●■ 0．ll e。t2 脚 0．88 1．35 1．81 2．14 2．36 27．02 27．12 27．14 27．Ol 27、72Min
Short Bias234つ
OJ5
0．19 0．23 0．27 0．28 0．38 0．50 0．64 0．78 0．85 ‘●ザ ー1．④5 ■章■ −1．06 ●・● −1．07 ●守■ −LO5 ●■■ −1．05 ■■4 ・7．20 ・OS2 吟●皐 一6．22 −0．93 ●●● −5，34 −0．95 ，●・ −4，45 −0．96 ●■● −3．76 −0．97 ・6．97 −7，33 ．7，91 −8，54 −8，83 48、2韮 48．21 48．20 48．16 48．16Min
Emerging Markets﹂434
LO3
0．91 0．81 0．75031
●■● ●■● ●● ●● ・o 2．68 2．67 2，56 2．40 2．33 ■■■ 0．84 ■■■ 0．91 ●1●1．①0 4⑨■1．10 126 ‘“ 3．93 3，64 3，35 3，02 2．95 ●●楡 0．36 ●■■ 0．39 ■・， 0．41 ■■■ 0．43 “事 立44 2，85 3．60 4．25 4，72 5．21 35．19 35．40 35．68 35．80 36i24Min
Panel B：CS／「「 Event Driven％4234
●章■ 0．82 ●専●0．76 ，宇，0．72 ●傘● 0．69 ■ザ．儀67 4．20 5．15 6，10 6，49 6，6？ 1ウ， ①．36 1■， 0．41 ■■● O．47 ■●■ 0．55 0．66 ’“ 2．28 2．16 2．11 2．03 2，05 0．10 ●■ 0．11 ●● O．12 ■●● 0．13 ぴ13 “ L50 1．98 2．46 2．80 3，12 33．53 34．35 35，62 36．56 37，s7Min
Dedicated Short Bias 一1234
一 一 一 一〇，11 −0．09 ．0．07 −0．05 ゆ．04 一〇．32 −0．28 −0．24 −0．18 ・Oll6 ■⑨． −LOO ●■■ −LO2 ケ右■ −LO6 ⑨■● −1．09 カ●専 一1．16 ■■■ −5．98 −O．87 ■■● −5．19 −O．87 ●●■ −4．49 −OS7 ●●● −3．75 −0．88 ■■◆ −3・；30 ぷ．88 一8．41 −8．87 ．9．43 −10．05 −10．37 59，20 59．23 59．28 59．29 s／91135Min
Emerging Markets4234
0．92 0．81 0．73 0．67 0。“ 章ウ■θ章．．●・■ 2．03 2．12 2，09 2．OO 1．98 ■・i O．77 ■■■ ③．84 ●●癖 0．93 ■・■LO5
…1．23 2．76 2．58 2．39 2．18 2．16 ●ウ 0．31 ■● 0．33 ●■● 0．35 楡▼θ 0．36 ●ヴワ037
2．08 2．59 3．05 3，36 3．69 22，91 23，182349
23．68 24．23 Min Managed FutUres4234つ
．0．39 ．0．31 −O．19 ・0．ll −0．02 一1．29 −1．18 −0．78 0．45 −O．10 一〇．44 −0．58 −O．72 ・e．s7 −1．04 ■●章 ●■章 ●■● ・’炉 ●■● 一3．78 −5．08 ．5．98 −6．70 −6．60 0．16 0．15 0．12 0．10 0．07 1．12 L21 1．07 0．93 0，69 5．12 6．98 8．05 8．66 8．62Min
Source：Author’s calculations， based on data from Hedge Fund Research， and Credit Suisse／Tremont and Yahoo！ Finance． Notes：（1）Results fbr five thresholds excess market retums（from−1％to−5％）are presented．（2）The statistical significance is determined by using heteroscedasticity and autocorrelation−consistent standard errors．（3）＊，＊＊，and＊＊＊ denote significance at the 10％，5％and 1％levels， respectively．（4）Parameters significantly different from zero at the 5％level are shown in bold type． losses． The systemic risk that many deals are cancelled all at once emerges when the market declines sharply． As a result， Merger Arbitrage shows no correlation with the market during up−market conditions，Assessing Market Risk fbr Hedge Funds−Nonlinear Risk Exposures to the Market but large positive correlation during down−market conditions． This implies that the payoff of Merger Arbitrage has option−like featUres similar to a profit from writing（selling）aEuropean put option． Distresse（レRestruc加ring strategy invests in the securities of firms ln行nancial distress（te．， reorganization and／or bankmptcy）， ranging廿om senior debt to common stock． In depreciating markets， the probability of fims emerging f「om financial distress is lower． Therefbre， their do㎜一market betas increase dramatically during market downtums while up−market betas increase moderately． Similar to Merger Arbitrage， a strong nonlinear risk−retum trade−off is shown in Distressed／Restructuring． Emerging Markets in both of the HFR and the CS／T indicate not only strong asymmetric sensitivity to the market but also a property as an aggressive asset beyond the threshold of−4％ofthe excess market retum since their down−market beta coef臼cients are greater than one． Conversely， Short Bias and Dedicated Short Bias demonstrate strong negative sensitivity in both up−market and down−market conditions． Managed Future且mds are operated by commodity trading advisors using a trend fbllowing strategy， which is an investment strategy to derive the maximum benefit from large， directional moves in a variety of asset markets． Managed Futures presents the asymmetric sensitivity to contrast with Merger Arbitrage since the coefficients are of opposite sign， with an up−market beta of O．10and a do㎜一market beta of−0．87 at the threshold of−4％excess market retum minimizing the sum of squared residuals． The payoff of Managed Futures has option−like properties similar to a profit丘om buying a European put option． It seems to provide S＆P500 downside protection with little exposure on the upside． Investment in Managed Futures can yield greater diversification benefits than investment in traditional assets classes．
5．Stability Tests
To consider the possibility of structUral change of the hedge fUnd industry， we perform stability tests in the piecewise regression of the two broad−based indices． Figure 4 plots the residuals of piecewise Figure 4：Residuals of Piecewise Regressiorls8642024
Panel A HFR Weighted Composite lndex ：〈帖岬枇榊：
一8 −12 1994 1996 t998 2000 2002 2004 2006 2008 Panel B CSn Hedge Fund lndex 8404喝
0 1 5 0 5 ・ 0 1 一 1994 1996 1998 2000 2002 2004 2006 2008regressions for the HFR Weighted Composite Index（WCI）and the CS／T Hedge Fund Index（HFI）． The graph views both clearly show that the fits are particularly bad before the IT bubble burst in March 2000， First， to test the stability of this regression， we perform the Chow breakpoint test， in which the data was partitioned in March 2000 into two subsamples． Two test statistics fbr the Chow breakpoint test are presented as follows：
