EVALUATION OF FINANCIAL RISK OF HEDGE FUNDS AND FUNDS-OF-HEDGE FUNDS

Transcription

1 EVALUATION OF FINANCIAL RISK OF HEDGE FUNDS AND FUNDS-OF-HEDGE FUNDS Hee Soo Lee A thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy Discipline of Finance, Business School The University of Sydney July, 2011

2 Statement of Originality This is to certify that to the best of my knowledge, the content of this thesis is my own work. This thesis has not been submitted for any degree or other purposes. I certify that the intellectual content of this thesis is the product of my own work and that all the assistance received in preparing this thesis and sources have been acknowledged... Hee Soo Lee 2011 i

3 Dedication To my beloved husband, To my dear son, and To my precious daughter. ii

4 Acknowledgement It is with immense gratitude that I acknowledge the support and help of my supervisor, Dr. Maxwell Stevenson, who gave me confidence and guidance to carry out a PhD. His sage advice, insightful criticisms, and patient encouragement aided the writing of this thesis in innumerable ways. I deeply appreciate his kindness throughout the entire process. I would also like to thank my associate supervisor, Dr. Juan Yao, whose generous support, helpful comments and new data supply were absolutely invaluable to my work. Thank you. I would thank Associate Processor Graham Pardington for his helpful advice and kind support. I also gratefully acknowledge Professor Giorgio Valente for his constructive comments and ideas on my research presentation at The Fifth Annual Conference on Asia- Pacific Financial Markets of the Korean Securities Association. I am also pleased to acknowledge helpful comments provided by Dr. Abhishek Das at the Finance and Governance Conference, This thesis was also benefited from the assistance of Michael Siu Fung Ng in collecting data. I would like to thank The University of Sydney for giving me the opportunity to commence a PhD course and for providing a wonderful research environment. I am also grateful to the Discipline of Finance, Business School at The University of Sydney for their funding support throughout my doctoral studies. I owe my deepest gratitude to my family, who have always been with me. My beloved husband always stood by me and I could always rely on him for everything. My only son and lovely daughter are the reason for my life. Indeed, I would like to express my sincere appreciation to my parents and parents in law for their endless prayer and genuine love. I am also grateful to my sisters, brothers and my lovely nieces and nephews for their constant love. This thesis would not have been possible without dedicated love and constant support from my family. Thank you indeed. Lastly, I thank my heavenly Father. Father, I have so much to be thankful for, things unseen and seen, that You have done in my life. I give You all the glory. iii

5 Table of Contents Statement of Originality i Dedication..ii Acknowledgement...iii Table of Contents..iv List of Figures....x List of Tables..xi Abstract....xiv Chapter 1 Introduction Motivation and Objectives of the Thesis Background of Hedge Funds The Unique Environment of Hedge Funds Growth of the Hedge industry Hedge Fund Industry in Australia Structure and Contents of the Thesis...11 Chapter 2 - Literature Review Introduction Study of Hedge Fund Survival Survival Analysis Qualitative Response Model Study of Hedge Fund Performance Strategy and Performance Fund Size and Performance Fee structure and Performance Study of Hedge Fund Data Biases Conclusion...49 iv

6 Chapter 3 Data and Methodology Introduction Data Data Delineation Administrative Table Time-Series Data Table Normality Test for HF and FOHF Returns Data Biases The Estimation and Holdout Sample Methods Used to Estimate and Test the Cross-Sectional Relation between HF and FOHF Risk Measures Estimation of Risk Measures Standard Deviation (SD) Semi-Deviation (SEMD) Value- at Risk (VaR) Expected Shortfall (ES) Tail Risk (TR) Test at the Portfolio Level of HFs and FOHFs: Fama and French Method Test at the Individual Level of HFs and FOHFs: A Cross-Sectional Regression Survival Analysis and Cox Proportional Hazard (CPH) Model Introduction to Survival Analysis Describing Survival Distributions Censoring The Time Origin Cox (1972) Proportional Hazard Model with Fixed Covariates Partial Likelihood Estimation Estimating Survivor Functions Assessing Predictive Accuracy v

7 3.5.1 Survival Function Signal Detection Model Relative Operating Characteristic (ROC) Curve and AUROC Chapter 4 - Risk and Return in Hedge Funds and Funds-of-Hedge Funds: A Cross-Sectional Approach Introduction Empirical Results Results at the Portfolio Level of HFs and FOHFs Results at the Individual Level of HFs and FOHFs:A Cross-sectional Regression Conclusion..110 Chapter 5 - Modelling and Evaluating Predictive Accuracy of Financial Distress in Hedge Funds and Funds-of-Hedge Funds: A Cross-Sectional Approach Introduction Covariates Performance Measures Mean Return Winning Ratio Return Risk Measures Fund Size Measures Assets under Management (AUM) Minimum Investment Liquidity Lockup Period Redemption Frequency Notice Period Leverage vi

8 5.2.6 Fee Structure Management Fee Incentive Fee High Water Mark Hurdle Rate Strategy Domicile Description of Approach Classifying Funds Failures Preliminary Examination of the HFs and FOHFs Testing for Difference in the Survivor Functions between HFs and FOHFs Estimating the Survivor Functions of HFs and FOHFs: The Life-Table Method Risk Measures Explaining Survival of HFs and FOHFs Estimating the Risk Measures Comparison of the Risk Measures Model Construction for HFs and FOHFs Survival Multicollinearity Examination Estimating Cox (1972) Proportional Hazard Model for HFs and FOHFs Empirical Results Failed Funds Identification Preliminary Analysis for HFs and FOHFs Test of Difference in the Survival Functions between HFs and FOHFs Nonparametric Survival Functions of HFs and FOHFs: The Life-Table Method Risk Measures Comparison Correlation Matrix Cox (1972) Proportional Hazard Model Global Null Hypothesis Test.148 vii

9 Construction of Cox (1972) Proportional Hazard Model for HFs Construction of Cox (1972) Proportional Hazard Model for FOHFs Testing the Forecast Accuracy Signal Detection Model Relative Operating Characteristic Curve and AUROC Conclusion.163 Chapter 6 - The Effect of the GFC on Modelling and Predicting Financial Distress in Hedge Funds and Funds-of-Hedge Funds: A Time-Varying Approach Introduction Data Description of Approach Mixed Cox Proportional Hazard Model Partial Likelihood Estimation for Mixed CPH Model Estimating Baseline Hazard Function Estimating Survivor Probabilities Limitations and Benefits of the Time-Varying and Mixed CPH Model Development of SAS Macro Program Empirical Results Construction of Three Cox Proportional Hazards Models Dynamic Prediction of Survival Probabilities for HFs and FOHFs Model Validation Conclusion Chapter 7 Conclusions and Contributions Summary of findings Contributions Limitations and Suggestions for Future Research viii

10 References 217 Appendices 224 Appendix 3.A Summary of Investment Strategy Dummy Variables for HFs Appendix 3.B Summary of Investment Strategy Dummy Variables for FOHFs. 225 Appendix 4.A Results at the Portfolio Level of HFs and FOHFs Appendix 4.B Figures for the Returns of Portfolio Sorted by Alternative Risk Measures.230 Appendix 4.C Results at the Individual Level of HFs and FOHFs Appendix 6.A SAS Macro Program 248 Appendix 6.B AUROC Statistics ix

11 List of Figures Figure 1.1: Estimated Growth of Assets under Management of Hedge fund Industry: (Source: HFR)...8 Figure 1.2: Estimated Total Number of Hedge Funds and Fund-of-Hedge Funds: (Source: HFR) 9 Figure 3.1: Hypothetical Censored Funds from the Live Fund Database..78 Figure 3.2: Hypothetical Censored Funds from the Dead Fund Databse Figure 3.3: Observations Arranged in Event Time.. 80 Figure 3.4: Observations Arranged in Calendar Time Figure 3.5: Calculation of the Likelihood for Failure in a Fixed Covariate Model. 84 Figure 3.6: Signal Detection Model Figure 3.7: Relative Operating Characteristic Curve Figure 4.1: Returns of Portfolios Sorted by 95% ES_cf: January, 1995 to December, Figure 5.1: Survival Curves of HFs and FOHFs Figure 5.2: Hazard Function of HFs and FOHFs Figure 5.3: Signal Detection Model of HFs.159 Figure 5.4: Signal Detection Model of FOHFs 160 Figure 5.5: ROC Curve of HFs and FOHFs.162 Figure 6.1: Calculation of the Likelihood Function for Failure in a Mixed CPH Model..177 Figure 6.2: Survival Time for Seven Hypothetical Funds..180 Figure 6.3: Survival Curves for Non-Failed and Failed Funds..201 Figure 6.4: ROC Curves of Mixed Models for HFs and FOHFs Figure 4.B.1: Returns of Portfolio Sorted by SD: January, 1995 to December, Figure 4.B.2: Returns of Portfolio Sorted by SEMD: January, 1995 to December, Figure 4.B.3: Returns of Portfolio Sorted by 95% VaR_np: January, 1995 to December, Figure 4.B.4: Returns of Portfolio Sorted by 95% VaR_cf: January, 1995 to December, Figure 4.B.5: Returns of Portfolio Sorted by 95% ES_np:January,1995 to December, Figure 4.B.6: Returns of Portfolio Sorted by 95% TR_np:January,1995 to December, Figure 4.B.7:Returns of Portfolio Sorted by 95% TR_cf:January,1995 to December, x

12 List of Tables Table 1.1: Growth of the Australian Hedge Fund Industry: Table 1.2: Size of the Hedge Fund Industry in Asia in Table 2.1: Literature on Survivorship and Backfill Biases in Hedge Funds Table 3.1: Summary Statistics for Administrative Data Table 3.2: Summary Statistics for Return and Size Time Series Data Table 3.3: Normality Test for HF and FOHF Returns. 59 Table 3.4: Returns and Standard Deviations by Investment Strategy Table 3.5: Backfill Biases by Investment Strategy.. 61 Table 3.6: Survivorship Biases by Investment Strategy..61 Table 4.1: Average Returns of HF and FOHF Portfolios Formed According to a 95% Cornish- Fisher Expected Shortfall: January, 1995 to December, Table 4.2: Test for Average Return Differential between the Most Risky Portfolio and the Least Risky Portfolio...98 Table 4.3: Univariate Cross-Sectional Regressions of HF and FOHF returns on Age, Size and Liquidity: January, 1995 to December, Table 4.4: Average Values of the 180 Regression Slopes from the Month-by-Month Regressions of HF and FOHF Returns on 95% Cornish-Fisher Expected Shortfall, Age, Size and Liquidity: January, 1995 to December, Table 4.5: Average Values of the 180 Regression Slopes from the Month-by-Mont Regressions of HF and FOHF Returns on Eight Risk Measures: January, 1995 to December, Table 5.1: The List of Covariates Table 5.2: HFs Classification Table 5.3: FOHFs Classification Table 5.4: Testing Homogeneity of Lifetime Monthly Returns for Fund Classification..139 Table 5.5: Testing Homogeneity of Survival Curves for HFs and FOHFs Table 5.6: Survival and Hazard Estimates of HFs and FOHFs: Life-Table Method.142 Table 5.7: Summary of Estimation Sample Table 5.8: Univariate Cox Proportional Hazard Model for HFs..144 Table 5.9: Univariate Cox Proportional Hazard Model for FOHFs.145 Table 5.10: Rank Correlation Coefficients for Covariates of CPH Model for HFs xi

13 Table 5.11: Rank Correlation Coefficients for Covariates of CPH Model for FOHFs..147 Table 5.12: Global Null Hypothesis Tests of CPH Models for HFs..149 Table 5.13: Global Null Hypothesis Tests of CPH Models for FOHFs Table 5.14: Three Specifications of the Proportional Hazard Model for HFs Table 5.15: Three Specifications of the Proportional Hazard Model for FOHFs Table 5.16: AUROC Statistics of Corresponding Models for HFs and FOHFs 163 Table 6.1: Statistics for Fixed-time and Time-varying Covariates Table 6.2: Three Specifications of the Cox Proportional Hazard Model for HFs January, 1990 to December, Table 6.3: Three Specifications of the Cox Proportional Hazard Model for HFs January, 1990 to July, Table 6.4: Three Specifications of the Cox Proportional Hazard Model for FOHFs January, 1990 to December, Table 6.5: Three Specifications of the Cox Proportional Hazard Model for FOHFs January, 1990 to July, Table 6.6: The Predicted Survival Probabilities of Twenty HFs Randomly Selected from the Sample Period from January, 1990 to December, Table 6.7: The Predicted Survival Probabilities of Twenty HFs Randomly Selected from the Sample Period from January, 1990 to July, Table 6.8: The Predicted Survival Probabilities of Twenty FOHFs Randomly Selected from the Period January, 1990 to December, Table 6.9: The Predicted Survival Probabilities of Twenty FOHFs Randomly Selected from the Period January, 1990 to July, Table 6.10: Summary of AUROC Statistics for HFs and FOHFs.204 Table 4.A.1: Average Returns of Hedge Fund and Fund-of-Hedge Fund Portfolios Formed According to Standard Deviation: January, 1995 to December, Table 4.A.2: Average Returns of Hedge Fund and Fund-of-Hedge Fund Portfolios Formed According to Semi-Deviation: January, 1995 to December, Table 4.A.3: Average Returns of Hedge Fund and Fund-of-Hedge Fund Portfolios Formed According to 95% Nonparametric VaR: January, 1995 to December, Table 4.A.4: Average Returns of Hedge Fund and Fund-of-Hedge Fund Portfolios Formed According to 95% Cornish-Fisher VaR: January, 1995 to December, Table 4.A.5: Average Returns of Hedge Fund and Fund-of-Hedge Fund Portfolios Formed According to 95% Nonparametric Expected Shortfall: January, 1995 to December, xii

14 Table 4.A.6: Average Returns of Hedge Fund and Fund-of-Hedge Fund Portfolios Formed According to 95% Nonparametric Tail Risk: January, 1995 to December, Table 4.A.7: Average Returns of Hedge Fund and Fund-of-Hedge Fund Portfolios Formed According to 95% Cornish-Fisher Tail Risk:January, 1995 to December, Table 4.C.1: Average Values of the 180 Regression Slopes from the Month-by-Month Regressions of HF and FOHF Returns on Standard Deviation, Age, Size and Liquidity: January, 1995 to December, Table 4.C.2: Average Values of the 180 Regression Slopes from the Month-by-Month Regressions of HF and FOHF Returns on Semi-Deviation, Age, Size and Liquidity: January, 1995 to December, Table 4.C.3: Average Values of the 180 Regression Slopes from the Month-by-Month Regressions of HF and FOHF Returns on 95% Nonparametric VaR, Age, Size and Liquidity: January, 1995 to December, Table 4.C.4: Average Values of the 180 Regression Slopes from the Month-by-Month Regressions of HF and FOHF Returns on 95% Cornish-Fisher VaR, Age, Size and Liquidity: January, 1995 to December, Table 4.C.5: Average Values of the 180 Regression Slopes from the Month-by-Month Regressions of HF and FOHF Returns on 95% Nonparametric Expected shortfall, Age, Size and Liquidity: January, 1995 to December, Table 4.C.6: Average Values of the 180 Regression Slopes from the Month-by-Month Regressions of HF and FOHF Returns on 95% Nonparametric Tail Risk, Age, Size and Liquidity: January, 1995 to December, Table 4.C.7: Average Values of the 180 Regression Slopes from the Month-by-Month Regressions of HF and FOHF Returns on 95% Cornish-Fisher Tail Risk, Age, Size and Liquidity: January, 1995 to December, Table 6.B.1: The AUROC Statistics of Three Models for HFs at Every Failure Time: January, 1990 December, Table 6.B.2: The AUROC Statistics of Three Models for FOHFs at Every Failure Time: January, 1990 December, Table 6.B.3: The AUROC Statistics of Three Models for HFs at Every Failure Time: January, 1990 July, Table 6.B.4: The AUROC Statistics of Three Models for FOHFs at Every Failure Time: January, 1990 July, xiii

15 Abstract The primary objective of this thesis is to provide models capable of predicting financial distress in individual hedge funds (HFs) and funds-of-hedge funds (FOHFs). Two approaches were used to build these models. The first approach was based on a cross-sectional model while the second one was on a time-varying model. Using a survival analysis technique known as the Cox Proportional Hazards (CPH) model, the first study not only established a survival/hazard model to determine the factors which contributed most to the survival and failure probabilities, but also provided a forecast of survival probability until a specific failure time for HFs and FOHFs. It focused on the comparison between the financial distress forecasting models of HFs and FOHFs under three alternative risk measures of fund failure. Following the estimation of the model, an out-of-sample forecast for both the HFs and the FOHFs was conducted and the predictive accuracy of the estimated CPH models was tested and compared by using Signal Detection Model, Relative Operating Characteristic (ROC) curve and Area under ROC curve (AUROC). According to the test results of the predictive accuracy of the models, the estimated models exhibited satisfactory accuracy in forecasting the most likely failed funds in an out-of-sample test. The second approach used the CPH model incorporating both time-varying factors and fixed factors. After establishing survival/hazard models with time-varying and fixed covariates under three specifications of CPH model (mixed model, fixed model and time-varying model), the study used the mixed CPH model to predict dynamic changes of survival probabilities over the lifetime of HFs and FOHFs. In an effort to identify the effect that the recent Global Financial Crisis (GFC) has had on the financial distress experienced by hedge funds, modelling and prediction was firstly confined to the pre-gfc period. Further analysis xiv

16 that included data post-gfc, allowed for the evaluation of model stability through the identification of significant predictors that held across both the pre-and post-gfc periods, as distinct from those predictors that were significant in only one of these time periods. A SAS Macro program was developed for generating survival probabilities predicted by the mixed CPH model. Following the generation of survivor curves for all companies during the period that included the GFC, the resulting ROC curves and AUROC statistics confirmed the ability of the dynamic CPH models to provide early warning signals to investors about possible fund failures. The secondary objective of this thesis is to examine whether the available data on HFs and FOHFs can reveal the risk-return trade-off and, if so, to find the best risk measure that captured the cross-sectional variation in HF and FOHF returns. With the Live Funds and the Dead Funds datasets provided by Hedge Fund Research Inc. (HFR), alternative risk measures such as semi-deviation, value at risk, expected shortfall and tail risk were concentrated and compared with standard deviation in terms of their ability to describe the cross-sectional variation in expected returns of HFs and FOHFs. Firstly, the risk measures were analysed at the portfolio level of HFs and FOHFs by adopting the Fama and French (1992) approach. Secondly, the various estimated risk measures were compared at the individual HF and FOHF levels by using univariate and multivariate cross-sectional regressions. The results showed that the available data on HFs and FOHFs exhibited different risk-return trade-offs. The Cornish-Fisher expected shortfall or Cornish-Fisher tail risk could be an appropriate risk measure for HF return. Although appropriate alternative risk measures for the HFs were found, it was difficult to determine the risk measures that best captured the cross-sectional variation in FOHF returns. xv

17 Chapter 1 Introduction 1.1 Motivation and Objectives of the Thesis The role of hedge funds in the financial markets has become a controversial issue since the 1997 Asian financial crisis, due to large losses by some high profile hedge funds such as the Long-Term Capital Management in 1998, the Soros Fund in 2000 and Amaranth in More recently, it has been claimed that hedge funds contributed to the financial market crisis in Undoubtedly, hedge funds have become an influential force in financial markets. While most academic literature has recognized that the hedge funds industry provides risk sharing and liquidity to the financial market, there is also an opposite view that increased systemic risk of the financial system and associated financial instability could result from the nature of funds exposure to risk. A large part of growth in the hedge fund industry was derived from growth in funds-of-hedge funds (FOHFs). Most investors increasingly adopted FOHFs as the preferred investment vehicles, which were estimated to account for 20% to 25% of global hedge fund industry assets at the end of 2009 [HFR Industry Report]. The significant influence of individual hedge funds (HFs) and funds-of-hedge funds (FOHFs) on the financial market motivated this research on the financial distress of HFs and FOHFs and the search for the most appropriate risk measure that would capture the cross-sectional variation in these types of funds The primary objective of this thesis is to provide models capable of predicting financial distress in HFs and FOHFs. In order to develop these models, two approaches were used. The first approach was based on a cross-sectional model (Chapter 5) while the second one 1 These three funds made a loss of 3,600 million, 5,000 million and 6,400 million US dollars, respectively, due to excess leverage during the Russian default crisis, the internet and technology bubble and energy price shocks. 1

18 was on a time-varying model (Chapter 6). In the first approach, by using a survival analysis technique known as Cox Proportional Hazards model, a survival/hazard model was produced to determine the factors which contributed most to the survival and failure probabilities. A forecast of survival probability up to a specific failure time for HFs and FOHFs, is also provided in the study. The study focused on a comparison among the financial distress forecasting models of HFs and FOHFs under three alternative risk measures of fund failure. By applying a filter criteria based on returns and assets under management of funds, the groups of failed funds were firstly distinguished from the funds that ceased to report to the data vendors. The Cox Proportional Hazards (CPH) model, based on cross-sectional analysis, was estimated for HFs and FOHFs by incorporating covariates suggested from previous literature [Gregoriou (2002), Baba and Goko (2009), Chapman et al. (2008) and Ng (2008)]. Additionally, the effects of three alternative risk measures, namely, standard deviation, Cornish-Fisher Value at Risk and Cornish-Fisher expected shortfall, on a fund s survival were compared by estimating the corresponding three models for HFs and FOHFs. Following an estimation of the model, an out-of-sample forecast for both the HFs and the FOHFs were conducted. The second approach to modelling failure probabilities of HFs and FOHFs used the CPH model, but incorporating both time-varying and fixed factors. After survival/hazard models with time-varying and fixed covariates under three specifications of CPH model (mixed model, fixed model and time-varying model) were estimated, the study predicted the dynamic changes in survival probabilities over the lifetime of HFs and FOHFs using the mixed CPH model. In an effort to identify the effect that the recent Global Financial Crisis (GFC) has had on the financial distress experienced by hedge funds, modelling and prediction was firstly confined to the pre-gfc period. Further analysis that included data post-gfc, allowed for evaluation of model stability through the identification of significant predictors that held 2

19 across both the pre-and post-gfc periods, as distinct from those predictors that were significant in only one of these time periods. A SAS Macro program was developed for generating survival probabilities predicted by a CPH model which incorporated fixed and time-varying covariates. In addition, the forecast performance of the three specifications of the model was evaluated by using AUROC (Area under Relative Operating Characteristic curve) statistics. A secondary objective of this thesis is to examine whether the available data on HFs and FOHFs can reveal the risk-return trade-off and, if so, to find the best risk measure that captures the cross-sectional variation in HF and FOHF returns (Chapter 4). With the dramatic growth of HFs and FOHFs, it is essential to find the most appropriate risk measures that capture the cross-sectional variation in these types of funds. Due to the nature of negative skewness and excess kurtosis in HF and FOHF returns [Fung and Hsieh (1997), Agarwal and Naik (2001), Amin and Kat (2003), Huston, Lynch and Stevenson (2006) among others], any risk estimation which assumed a normal distribution of returns severely underestimates the actual risk exposure. Traditional risk management such as mean-variance analysis, the Sharpe ratio and Jensen's alpha assumed a normal distribution measure of returns. As a consequence, the traditional measures of returns incorporated the standard deviation. This would appear to be inappropriate for risk measures of HFs and FOHFs. In order to overcome this problem, alternative risk measures such as semi-deviation, Value at Risk (VaR), expected shortfall and tail risk were examined. They were compared with those measures dependent on the standard deviation in terms of their ability to describe the cross-sectional variation in expected returns of HFs and FOHFs. Hedge fund investors are challenged with large information asymmetries and high search costs. Furthermore, both entry into and exit from active management involve non-trivial costs. 3

20 The results of this thesis will allow investors to better estimate the expected lifetime of a HF, or a FOHF, before any funds are allocated to it. They will also provide better warning signals about possible fund liquidation to investors already committed. In addition, understanding the risk-return relationship in HFs and FOHFs will be invaluable to investors in building more profitable investment strategies. 1.2 Background of Hedge Funds Alternative Investment Management Association (AIMA) defined a hedge fund as A hedge fund constitutes an investment program whereby the manager or partners seek absolute returns by exploiting investment opportunities while protecting principal from potential financial loss [AIMA (2008), p. 10]. Two prominent features of hedge funds implicit in this definition are the attempt to generate positive absolute returns by taking risk while trying to control losses so as to avoid negative compounding of capital. Moreover, McNally categorically stated that There is no standard definition of a hedge fund; the name is typically applied to managed funds that use a wider range of financial instruments and investment strategies than traditional managed funds, including the use of short selling and derivatives to create leverage, with the aim of generating positive returns regardless of overall market performance [McNally (2004), p. 57]. As indicated in these definitions, hedge funds have unique characteristics compared to the other investment vehicles and it can be inferred that the investment philosophy of a hedge fund manager is different from that of a manager who is confined to a market benchmark. The first hedge fund was managed by Alfred Winslow Jones in Employing a primary strategy of long-short equity position and leverage, he achieved returns net of fees significantly higher than the best performing mutual funds. In 1966 his achievement story 4

21 was published in the article by Carol Loomis with the title The Jones Nobody Keeps Up With, where the term hedge fund originated. Published in Fortune, the article shocked the investment community and invoked substantial interest in hedge funds. In spite of the rapid growth during 1967 and 1968, the hedge fund industry suffered losses and capital withdrawals (like many other funds) during the bear market periods of and In 1986, however, the article with the tile The Red-Hot World of Julian Robertson in Institutional Investor reported that the Tiger Fund run by Julian Robertson achieved compounded annual returns of 43% (net of all fees) during its first six years of existence. This rekindled interest in hedge funds, ultimately leading to the formation of numerous new funds. The global hedge fund assets under management achieved high levels of growth until 2007, after which they declined drastically in 2008 in the wake of the Global Financial Crisis (GFC) The Unique Environment of Hedge Funds It is well known that hedge funds have unique features. The key characteristic of hedge funds is that they are exempt from many investment protection and disclosure requirements. While mutual funds, being one of the equity investment alternatives like hedge funds, are controlled by strict investment regulations in order to protect investors, hedge funds are exempted from most of those regulations. Due to this limited regulatory oversight, hedge funds report their information only on a voluntary basis. Banned from advertising publicly, hedge funds report fund information voluntarily to data collection agencies in order to attract potential investors. This makes the comprehensive nature and integrity of hedge fund data questionable. However, there are numerous recent calls for the regulation of hedge funds to be tightened following the Global Financial Crisis (GFC) of

22 The unregulated environment surrounding hedge fund helps managers to implement flexible investment strategies in the global markets. They can adopt short selling, leverage, derivatives and highly concentrated investment positions to increase returns or decrease systematic risk. This enables them to achieve returns irrespective of market conditions. Thanks to the flexibility in investment options, although hedge funds are expected to provide positive absolute returns in all market conditions, they deliver wide dispersion in investment returns, volatility and risk. Hedge funds are also characterized by their unique fee structure. Hedge fund managers receive not only an annual management fee, but also an incentive fee which is based on a percentage of a hedge fund s capital gains and capital appreciation. On average, the management fee charged by individual hedge funds is 1.5% of assets under management, and an incentive fee of 19% of excess return above a prescribed benchmark. 2 The majority of individual hedge funds incentive fees are paid out according to a high water mark provision. A fund with a high water mark provision allows managers to earn the incentive fee only after they recoup all past losses. In some cases, hedge funds include hurdle rate provision in their fee structure. The hurdle rate refers to the minimum return, such as the Treasury Bill rate or LIBOR, which ought to be achieved for fund managers to earn incentive fees. For a fund with a hurdle rate provision, incentive fees can be charged on the basis of the profit from investment in excess of the hurdle rate. Since the onset of the GFC, the hedge fund industry has been confronted with increased requests for tightened regulation. It was claimed that hedge funds had contributed to financial market volatility in 2008 through short selling transactions and massive selling of shares due to deleveraging and redemptions. In April 2009, G20 finance ministers announced proposals for extending the supervision to all financial institutions including large hedge funds. They 2 According to the data from Hedge Fund Research Inc. (HFR) used in this study. 6

23 proposed that the hedge fund industry be regulated by a proposed Financial Stability Board made up of members of G20 and European Commission. Three major European and US hedge fund groups the Alternative Investment Management Association, the President s Working Group and the Managed Fund Association announced that they were working towards worldwide best practice standards. These organisations revisited a global standard on such issues as disclosure, risk management, dealing with conflicts of interest within organisations and statements about operation and business controls [IFSL Research of Hedge Funds 2009]. With a new environment looming on the horizon, regulation of the hedge fund industry is likely to change Growth of the Hedge Fund Industry The hedge fund industry has grown rapidly over the past 60 years. It expanded dramatically during the period of 1980s through the early 2000s extending from US based investments to Europe, Asia and Australia. This rapid growth was achieved through an increased number of new financial instruments and improved technology which helped to develop sophisticated investment strategies during the same period. In addition, the performance based incentive fee structures attracted high-skilled professionals to invest in hedge funds. Both assets under management (AUM) in hedge funds and the number of funds increased from around US$39 billion with 610 funds in 1990 to US$1,900 billion with 10,100 funds in [HFR Industry Report, Year End 2010]. The rapid growth in the hedge fund industry over the 18 years until 2007 is evident from Figure 1.1 which shows the growth in the size of hedge funds since Estimates on the size of the hedge fund industry vary due to exemption from disclosure requirements. 7

24 Following a decade of notable growth, assets under management (AUM) of the hedge fund industry decreased remarkably in 2008 due to the Global Financial Crisis (GFC). The International Financial Services London (IFSL) estimated that AUM would decline by more than 20% to US$1,500 billion in Being the biggest on record, the decrease was caused by the combination of negative performance, the rush in redemptions and liquidations of fund [IFSL Report 2009]. Figure 1.1 Estimated Growth of Assets under Management of Hedge fund Industry: (Source:HFR) $2,000,000 $1,800,000 $1,600,000 $1,400,000 AUM (In $MM) $1,200,000 $1,000,000 $800,000 $600,000 $400,000 $200,000 $ According to the data released in March, 2009 by HFR, the total number of liquidations in 2008 was 1,471, showing a 70 percent increase from the previous full year record of 848 liquidations set in Furthermore, only 659 new funds were launched in 2008, which was the lowest since 2000 when 328 funds were launched. Figure 1.2 clearly presents the remarkable growth in the number of hedge funds until The number of hedge funds fell by 9% in 2008 to 9,284. This decrease resulted from the funds closed due to losses, a lack of liquidity and redemptions as investors looked for safer investments [IFSL Report 2009]. 8

25 Around three quarters of funds were individual hedge funds and the remainder were funds-ofhedge funds that provided a combined investment in individual hedge funds. Figure 1.2 Estimated Total Number of Hedge Funds and Fund-of-Hedge Funds: (Source: HFR) Number of Funds 11,000 10,000 9,000 8,000 7,000 6,000 5,000 4,000 3,000 2,000 1, Hedge Fund Industry in Australia Australia is the largest centre of hedge fund industry in Asia. The AUM of the Australian hedge fund industry multiplied quickly with a seven-fold increase between 2002 and The number of managers and funds also increased significantly. The number of individual hedge funds (HF) as well as funds-of-hedge funds (FOHF) tripled between 2002 and Table 1.1 indicates the growth of the Australian hedge fund industry during the period from 2002 to

26 Table 1.1 Growth of the Australian Hedge Fund Industry: (Source: Austrade 2008) Year AUM (A$Billion) No. of HF No. of FOHF No. of HF Managers No. of FOHF Managers Of the A$70.3 billion of AUM in 2007, around two thirds (A$45.5bn) were included in HFs while the remainder (A$24.8bn) were in FOHFs. Table 1.2 clearly shows that Australia was the largest centre of hedge funds in Asia in Australian hedge fund managers managed around 35 percent more AUM than managers in Hong Kong and around 130 percent more than managers in Singapore. Table 1.2 Size of the Hedge Fund Industry in Asia in (Source: Austrade 2008) Location of Hedge Fund Managers Operating in Asia AUM in US$ Billion Australia 38.6 Japan 17.3 Hong Kong 28.3 Singapore 16.5 Other 5.0 Subtotal UK [managers with Asian strategies] 22.9 US [managers with Asian strategies] 39.1 Total The rapid growth of hedge fund industry in Australia was fuelled by the Australian regulatory environment. Australia was rated as having one of the most financially sound markets in the 4 The data reported excludes FOHF. 10

27 world by the International Monetary Fund (IMF). Australia s regulatory system was also regarded as the world s best [Austrade (2008)]. There are no specific regulations of hedge funds in Australia. Hedge funds fall under the scope of the Corporations Act 2001, as do other types of managed funds. Australian hedge funds usually take the form of trusts, while company structures are also used. The provisions in the Corporations Act 2001 are applied according to whether funds are structured as trusts or companies [Reserve Bank of Australia (2004)]. Accordingly, Australian hedge fund managers have to comply with the same licensing, ongoing compliance and governance standards as do traditional investment managers. This results in a high level of transparency in fund management. Mr Ivey, chairman of the Australian chapter of Alternative Investment Management Association (AIMA) has been quoted as saying, All investors, wholesale, retail and international, can draw assurance that Australian hedge fund managers operate in a competitive industry that is well regulated. He also acknowledged that other factors supporting the rapid growth of hedge fund industry in Australia included the deep talent pool of investment management expertise, a sound regulatory framework for alternative investment strategies, Australia s mandatory pension fund scheme and the desire of local investors to diversify their investments. 1.3 Structure and Contents of the Thesis This thesis proceeds as follows. Chapter 2 - Literature Review This chapter reviewed research literature relevant to the hedge fund industry. Firstly, studies on Hedge Fund Survival were examined. Secondly, research into Hedge Fund Performance was discussed in three categories: i) Strategy and Performance, ii) Fund Size and 11

28 Performance, and iii) Fee Structure and Performance. Thirdly, hedge fund data biases were discussed. Chapter 3 Data and Methodology The first part of this chapter describes data, descriptive statistics and results of normality testing of HF and FOHF returns. The second part contains details of methods used to estimate the risk measures and to test the cross-sectional relation between hedge fund returns and risk measures. Survival analysis and the Cox (1972) Proportional Hazards model, along with forecast evaluation metrics are discussed. Chapter 4 - Risk and Return in Hedge Funds and Funds of Hedge Funds: A Cross- Sectional Approach The objective of this chapter is to examine whether the available data on individual hedge funds (HFs) and funds-of-hedge funds (FOHFs) can reveal the risk-return trade-off and, if so, to find the best risk measure that captures the cross-sectional variation in HF and FOHF returns. Using the Live Funds and the Dead Funds datasets provided by Hedge Fund Research Inc. (HFR), alternative risk measures such as semi-deviation, VaR, expected shortfall and tail risk were compared with traditional risk measures that incorporated the standard deviation in terms of their ability to describe the cross-sectional variation in expected returns of HFs and FOHFs. Firstly, the risk measures were analysed at the portfolio level of HFs and FOHFs by adopting the Fama and French (1992) approach. The results were then compared with the findings of Liang (2007) for HF data, as well as with those in Hutson et al. (2006) for FOHFs. Secondly, the various estimated risk measures were compared at the individual HF and FOHF levels by using univariate and multivariate cross-sectional regressions. Additional independent variables were incorporated into the analysis in order to 12

29 distinguish liquidity, age and size effects from the relationship between risk and expected return. Chapter 5 - Modelling and Evaluating the Predictive Accuracy of Financial Distress in Hedge Funds and Funds-of-Hedge Funds: A Cross-Sectional Approach This chapter investigated the failure probability of individual hedge fund (HFs) and fund-ofhedge funds (FOHFs). The research was performed through the adoption of the semiparametric survival analysis approach known as the Cox (1972) Proportional Hazard (CPH) Model using fixed covariates. To begin with, the financially failed HFs and FOHFs were selected from the Dead Fund database for the purpose of this chapter. As a preliminary analysis, the difference in the survivor functions between HFs and FOHFs was tested and the survivor functions of HFs and FOHFs estimated by employing the Life-Table Method. Prior to constructing the survival forecasting models for HFs and FOHFs, three risk measures, standard deviation, Cornish-Fisher VaR and Cornish-Fisher expected shortfall, were compared in terms of their ability to explain failures of HFs and FOHFs. Lastly, predictive accuracy of the estimated CPH models for HFs and FOHFs was tested and compared by using measures derived from Signal Detection Theory, namely, the Relative Operating Characteristic (ROC) curves and the Area under the ROC (AUROC). Chapter 6 The Effect of the GFC on Modelling and Predicting Financial Distress in Hedge Funds and Funds-of-Hedge Funds: A Time-Varying Approach The aim of this chapter is to identify the effect that the recent Global Financial Crisis (GFC) has had on the financial distress experienced by individual hedge funds (HFs) and funds-ofhedge funds (FOHFs), along with the reliability of accepted models to predict financial distress across a time horizon that included such a tumultuous financial event. With the development of a SAS Macro program for generating survival probabilities, dynamic changes in survival probabilities were predicted over the lifetime of HFs and FOHFs after the estimation of baseline hazards by using a mixed CPH model that incorporated time-varying 13

30 and fixed covariates. After identifying those funds in financial distress, the covariates that lost and gained importance in the prediction of failure for both HFs and FOHFs as a result of the GFC were identified. Following the generation of survivor curves for all companies, the resulting ROC curves and AUROC statistics confirmed the ability of the dynamic CPH models to provide investors with early warning signals indicating possible fund failures. Chapter 7 Conclusions and Contributions This chapter presents a brief summary of chapter 4, 5 and 6 and concludes the thesis with the key findings. Thesis contributions are presented in this chapter. The limitations of this thesis and the direction for future research are also provided in this chapter. 14

31 Chapter 2 - Literature Review 2.1 Introduction Over the past decade, the hedge fund industry has attracted considerable attention from a wide range of academics and practitioners. A large part of growth in the hedge fund industry was derived from growth in funds-of-hedge funds (FOHFs). FOHFs are assumed to be less risky than individual hedge funds (HFs) because a portfolio of hedge funds must be less risky than holding only one or two hedge funds. While the growth in FOHFs has been phenomenal, their risk, return and survival characteristics were not well studied in the literature. To my best knowledge, no one but Gregoriou et al. (2008) has conducted research about survival of FOHFs. Most of hedge fund survival studies used hedge fund data without separating HFs and FOHFs while a few studies excluded FOHFs in their research. The existing evidence on FOHF performance is that they tend to underperform hedge fund indices by small but significant amounts. Brown et al. (2004) found that FOHFs offered consistently lower average returns and Sharpe ratios than HFs over the period They also found that FOHF returns were more left skewed (-0.307) relative to HF returns ( ). Amin and Kat (2003a), who examined the performance of 11 FOHFs as well as other categories of HFs, found significant underperformance of FOHFs. One explanation for the apparent underperformance of FOHFs is that their reported returns, in contrast to HFs, did not suffer to the same extent from the biases. Fung and Hsieh (2000a) estimated survivorship bias for FOHFs at 1.4 percent annually, and Amin and Kat (2003b) estimated it at only 0.63 percent over the period , compared to 1.89 percent for HFs. In addition, FOHFs reported more accurately than other categories of HFs, so the stale pricing bias was less in FOHFs relative to HFs [Liang (2003)]. For these reasons, FOHF data were less likely to 15

32 understate risk-adjusted performance, and so the apparent underperformance reported in studies such as Amin and Kat (2003a) was probably not explained simply by the double fee structure inherent in FOHFs. Research literature relevant to the hedge fund industry is reviewed in this chapter, beginning with an analysis of studies of hedge fund survival and performance. Firstly, studies of Hedge Fund Survival are examined in Section 2.2. The majority of the studies in this area have employed one of two statistical techniques to research hedge fund failure - survival analysis or qualitative response modelling. A number of studies using survival analysis and qualitative response modelling are reviewed in Section and Section 2.2.2, respectively. Secondly, research on Hedge Fund Performance is discussed in Section 2.3. This area of study is classified into three categories: i) Strategy and Performance, ii) Fund Size and Performance, and iii) Fee Structure and Performance. These studies analysed the characteristics of hedge funds that influence their performance. A number of studies related to the three categories are discussed in Section 2.3.1, Section 2.3.2, and Section 2.3.3, respectively. Lastly, studies of Hedge Fund Data Biases are discussed in Section 2.4. This section shows the summary of previous results for hedge fund survivorship and backfill biases. 2.2 Study of Hedge Fund Survival Many financial studies used qualitative response models with dichotomous dependent variables such as probit or logit models. These models have been used to examine research problems related to financial distress in several fields such as stocks, bonds and funds. Since 16

33 the publication of many works using qualitative response models, a substantial body of financial distress research employing survival analysis emerged. Survival analysis estimates the probability of the time to default and allows the production of profiles of default probabilities of funds. In default modelling of hedge funds, the outcome variable of interest is failure due to poor performance. The hedge fund survival literature can be divided into studies using survival analysis and those employing qualitative response models Survival Analysis Survival analysis has been widely used by academics and practitioners in a number of fields in finance. The objective of the survival analysis is to establish the relationship between an observation s characteristics and the timing of a particular event. An important study that employed the survival analysis for predicting a financial event is Wong, Pardington, Stevenson and Torbey (2007). The event of interest in this study was the exit from Chapter 11 protection with zero value being returned to shareholders. With the employment of a statistical method known as Cox (1972) proportional hazards model, the study developed a model for jointly predicting the duration of Chapter 11 bankruptcy and the payoff to shareholders. The study performed an additional test to verify two important assumptions of proportional hazard and independent censoring underlying the use of the Cox proportional hazards model. With the models being built for predictive, rather than explanatory purpose, the study evaluated predictive power of the estimated model within a holdout sample by using the Signal Detection Model (SDM) and the Relative Operating Characteristic (ROC) curve. In contrast to the results of chapter 4 in this thesis, the out-of-sample evaluation lent no support to the modelling as being useful for forecasting. This study did not use hedge fund 17

34 data, but it is important to the current thesis because a near identical method used in chapter 4. However, the study did not incorporate time-varying parameters. The first known study to use the Cox (1972) proportional hazards model to analyse hedge fund survival was Brown, Goetzmann and Park (2001). This study aimed to investigate the volatility of hedge funds in light of managerial career concerns. They used proportional hazards methods to examine the association between the past performance and the risk level of funds, and factors associated with funds and managers exiting the industry. They used the Trading Advisers Selection System (TASS) Hedge Fund Database, manually augmented to include missing data, for the period 1989 to First, they examined funds volatility strategies by presenting figures that showed the change in volatility for funds as a function of relative performance. For both hedge funds and commodity trading advisors (CTAs), they found that the decrease in volatility was most significant in the highest decile of performance whereas the greatest increase in volatility was found among the median performers rather than the poor performers. Brown et al. (2001) s findings ran contrary to the simple theory that hedge fund managers have a strong incentive to take extreme risks when their incentive fee, which usually incorporates high water marks and hurdle rates, is out of the money. This led them to suggest that there must be another factor limiting any increase in volatility in the case of poor performers. This hypothesis was confirmed by a contingency table test showing that sometimes losers decreased volatility and winners increased it. The study concluded that the volatility strategy was associated with performance relative to other funds but not performance relative to the high water mark. To pursue the matter of fund volatility further, Brown et al. (2001) examined the influence of performance and risk of fund termination using both the Cox (1972) proportional hazard and the Probit regression models. Relative and absolute performance over multiple periods, volatility and seasonality of returns were employed as covariates in the regression models. 18

35 They found that hedge funds with relatively poor performance or higher risk were more likely to terminate. The authors noted that the relationship between volatility and termination from the reporting system provided a disincentive for hedge fund managers to gamble excessively when they performed below their high water mark. They concluded that manager risk choice appeared to be more strongly affected by industry benchmarks than the high water mark threshold. They explained this obvious contradiction as being related to managers concerns about their reputation in the industry. Although the purpose of Brown et al. (2001) s analysis was different from that of the current study, their results provided useful background. They applied survival analysis techniques to hedge fund data, but their analysis contained a critical defect in that they regarded all funds in the Dead Fund database as failures. As a result, the event examined was not hedge fund failure but discontinuation of reporting to a hedge fund data vendor. In hedge fund databases, Dead Funds are funds which have discontinued reporting to a particular hedge fund data vendor. The problem with Brown et al. (2001) s method was that the Dead Fund database included funds which stopped reporting in spite of good performance, as well as funds suffering from poor performance. That is, all funds in the Dead Fund database had not failed due to the poor performance. For example, some funds stopped reporting to vendors because they had reached their target asset size and did not need to attract new investors while continuing to operate. The relationship between fund managers style consistency and their funds survival probability was assessed by Bares, Gibson and Gyger (2001), who applied cluster analysis to Financial Risk Management (FRM) hedge fund data that had a performance track record of at least 36 months at the end of April They showed that the investment strategy of a manager may depart over time from a strategy he or she has reported. In addition, they examined fund survival probabilities using the nonparametric Kaplan-Meier estimator. 19

36 Recognising the error of treating all funds that have discontinued reporting as failed funds, they differentiated failed funds from funds that became dead for other reasons by applying the Sharpe ratio 5 criteria. Monthly average Sharpe ratios over the last and the last two years of activity were calculated for all Dead Funds. If at least one of these ratios was below 0.2 for any fund, it was presumed that the fund s manager had ceased activity due to poor performance. To investigate factors contributing to the fund survival probability, Bares et al. (2001) made the survival function conditional on variables of interest including the major strategies, the asset under management, the beta 6 and the strategy inconsistency. They showed that the funds with the strategy of Relative Value were more likely to vanish than the others, while managers who were more flexible and changed their strategy were less likely to cease their activity. They also found that the funds with a smaller size of assets under management as well as a higher beta exhibited a significantly higher probability to disappear. Boyson (2002) examined the effects a of manager s characteristics on hedge fund performance, volatility and survival. The study used a sample from the TASS database consisting of the funds which provided returns for the period of twenty-four consecutive months and at least $1 million in assets during the period January 1994 to December The author constructed proxy variables for manager skill, experience and training that contained manager age, CFA, MBA, PhD, JD and other advanced degree (0,1) indicator variable, a number of years experience variable and an SAT variable. 7 Boyson (2002) first examined the cross-sectional relationship between manager characteristics and hedge fund performance, controlling for fund characteristics and systematic market exposure and concluded that manager tenure and having an MBA was negatively related to performance. Boyson (2002) regressed standard deviations of fund returns and Sharpe ratios against 5 The risk free interest rate is set at 0. 6 The beta is the linear coefficient of the regression of manager s net monthly return on the Russel 2000 index return over the last 12 months of activity and measures the directional exposure. 7 The SAT variables represented the average SAT score from the manager s undergraduate institution. 20

37 manager characteristics to investigate the general relationship between volatility and manager attributes. Interestingly, this analysis showed that while there was some relationship between hedge fund manager characteristics and hedge fund risk-adjusted performance, there was a much more significant relationship between hedge fund manager characteristics and volatility. Both managers with MBAs and managers with longer tenure had returns with low volatility, leading to Sharpe ratios similar to those of managers with short tenures and without MBAs. Finally, Boyson (2002) investigated the relationship between manager characteristics and fund failure using a time-varying proportional hazard model. Using the funds reasons for leaving the database, the author estimated an initial model by defining only the liquidated funds as failures and a second model by labelling all the funds that had exited as failures. The results were little different. The author explained these similar outcomes as implying that those funds exiting the database were underperforming and perhaps in danger of failure. Manager and fund characteristics and market indices were incorporated in the model to investigate causal factors impacting on the hedge funds survival. The result of Boyson s analysis implied a negative relationship between return volatility and manager tenure. That is, the probability of survival increased significantly with manager tenure and manager age, suggesting that older and longer-tenured managers took on less risk than their shorter tenured counterparts in order to survive, even at the cost of lower returns. The study concluded that the threat of failure impacted more significantly on the behaviour of older and longer tenured managers than the increased financial reward from realizing high returns. Gregoriou (2002) focused directly on hedge fund survival using the Product-Limit estimator, Life Table method, Accelerated Failure Time Model and Cox Proportional Hazard models. The effects of a wide range of covariates on a fund s survival lifetime - including leverage, average millions managed, management fee, performance fee, minimum purchase, mean 21

38 monthly returns, redemption period and fund style - were investigated in this study. The author argued that failing to include Live Funds in the estimation process would result in a downward bias of their survival lifetime due to the contribution of the Live Funds to the overall survival lifetime of the funds. As a consequence, Gregoriou (2002) incorporated both Live and Dead Fund data in his survival analysis. The dataset included information about 1,503 Live and 1,273 Dead Funds which was sourced from the Zurich Capital Markets database spanning the period January 1990 to December By including a range of covariates to explain a fund s survival lifetime, the study found that fund size had an important impact on survival time with those funds above the median size being associated with longer survival times. Low leverage funds were found to be more likely to survive longer than high leverage funds, while funds with higher minimum purchases tended to fail faster. Notably, funds with annual redemptions were inclined to have longer survival times. Another interesting finding was that investment in funds-of-hedge funds was an ideal strategy due to their higher survival time and to diversification effects. However, the results obtained by Brown et al. (2001) and Gregoriou (2002) were questionable due to their categorisation of all Dead Funds as failures. It is well known that funds are included in the Dead Fund database because of poor performance as well as other reasons. As a consequence, the focus of these studies was the explanation of the survival characteristics of funds which had discontinued reporting, but had not necessarily failed. Rouah (2005) aimed to reconcile important issues about the treatment of all funds that exited the database as failed funds. Rouah s study applied a competing risks model to account for the different reasons hedge funds ceased reporting, rather than aggregating all the reasons into a single homogeneous group. The author argued that separately treating exit type, or the reason for discontinuing reporting, was essential in order to avoid blurring the effect of predictor variables on fund s survival. Another improvement in the analytical method offered 22

39 by this study was incorporating time-varying covariates in the standard Cox (1972) proportional hazard model. Predictor covariates with values that changed over time, such as returns and volatility, were included in the regression model as time-varying variables rather than as fixed variables. As the impact of time-varying predictor variables were measured at many points in a fund s lifetime, the model with time-varying covariates provided investors with better warning signals about possible fund failure. Rouah (2005) used data about 2,371 Live Funds and 1,224 Dead Funds sourced from the Hedge Fund Research (HFR) database for the period January, 1994 to December, The HFR database provided information about funds exit reasons classified into three groups: i) liquidated, ii) closed to new investors, or iii) simply stopped reporting to HFR. A range of the predictor variables representing performance measures, general features, trading parameters and fund age were incorporated in the regression model. Variables representing returns, assets under management and volatility were treated as time-varying covariates. The study fitted the Cox (1972) proportional hazard model for each exit type separately in a competing risks framework and extended the model employed by Brown et al. (2001) by allowing for competing risks and time dependent predictor variables. Several interesting findings were uncovered in the Rouah (2005) research. He found that funds that had simply stopped reporting for no identified reason had reported good returns and large assets under management. As such, they resembled Live Funds more than they did liquidated funds. Return volatility was identified as an important predictor of fund liquidation, while funds with high water mark provision 8 were more likely to be liquidated. The author also found that the predictive power of the explanatory variables found to be significant in the Brown et al. (2001) model changed when competing risk and time-varying covariates were 8 A fund with high water mark allows the manager to earn the incentive fee only after all past losses are recouped. 23

40 incorporated. Interestingly, it was revealed that isolating liquidation caused funds expected survival times to be approximately twice as long as those estimated when exits were aggregated. Rouah (2005) concluded that aggregation of the exit type into a single group blurred the effect of performance and size predictor variables in the survival models. The reasons why hedge funds stop reporting their performance were investigated by Grecu, Malkiel and Saha (2007). They also compared the characteristics of funds which stopped reporting their performance with those that continued to report. The authors used hedge fund data from the TASS database for the period January 1996 to April They first analysed the returns of funds in the Dead Fund database, then examined the fund s time to failure and changes in the hazard rate using both the Cox (1972) proportional hazard model and loglogistic survival model. The survival analysis models incorporated covariates including Sharpe ratio, volatility, assets under management, performance relative to funds in the same category and performance relative to all funds in the database. Grecu et al. (2007) s analysis showed that the returns of funds which stopped reporting were significantly lower at the end of their reporting lives. The authors explained this result by suggesting that the majority of funds stopped reporting because of poor performance. They also found that the possibility that a fund will stop reporting reached a high point at around five and a half years of operation, and then decreased gradually over time. In addition, the estimated coefficients of the survival analysis models suggested that better-performing funds, larger funds, and funds that outperformed their peers were less likely to stop reporting their performance. Their debatable conclusion was that the majority of funds stopped reporting because they failed. Chapman, Stevenson and Hutson (2008) made an important contribution to the hedge fund survival literature by focusing on the causal factors and the prediction of financial distress of 24

41 hedge funds. Whilst previous researchers confined themselves to explaining the factors impacting on the survival time of hedge funds, Chapman et al. (2008) were the first to develop a model to predict the occurrence and timing of a hedge fund s financial distress. They addressed an issue arising from the Baba and Goko (2009) study that used only those funds which stopped reporting due to liquidation as failure times in the estimation of the proportional hazards model. Chapman et al. (2008) claimed that using liquidation to define failure gave insufficient insight into the financial distress of the hedge funds. Accordingly, the authors filtered the Dead Fund database into two groups of survivors and failures on the basis of several criteria. Using the Live and the Dead Fund databases maintained by HFR for the period between January 1990 and July 2007, Chapman et al. (2008) applied the Cox (1972) proportional hazard model to analyse causal factors of financial distress in hedge funds. The authors examined a range of variables including return measures, fund size, leverage, fee structure, domicile, strategy, liquidity and managerial discretion, and minimum investment. The study exposed the significant effects of return properties such as mean, variance, win ratio and drawdown but also assets under management (AUM) on the fund s survival probabilities. Contrary to Baba and Goko (2009), Chapman et al. (2008) found that leverage was a significant factor in hedge fund survival. Their study also showed that funds with higher leverage were likely to survive longer. Having considered the deficiencies of examining fee structure in raw percentage, Chapman et al. (2008) transformed management fees and incentive fees to dollar value prior to estimation. However, these variables were not found to be significant. The authors also found the high water mark provision to be a weakly significant predictor. Interestingly, the particular strategy of fund-of-hedge funds was consistently found to exhibit longer duration times. 25

42 After estimating the coefficients of covariates that significantly predicted fund failure using the proportional hazard model, Chapman et al. (2008) tested the forecasting accuracy of their model. Survival curves were fitted to each fund in the holdout sample which consisted of 100 survivors and 100 failures, and the time series of the survival probabilities for each fund was obtained. A cut-off threshold to convert the survival probability into a state-based prediction of survivor or failure was determined at the 120 th month after the fund s inception. Each fund in the holdout sample obtaining a survival probability greater than the cut-off threshold was predicted as a survivor and each fund below was predicted as a failure. The true state of each fund in the holdout sample was then compared against its predicted state. Chapman et al. (2008) s results showed that it was possible to predict failures in hedge funds by combining the Cox (1972) proportional hazard model and the forecasting theory of the Signal Detection Model. 9 The two empirical survival probability distributions of survivors and failures from the hedge fund failure forecasting model were capable of differentiating between survivors and failures, with higher probabilities of survivors than failures in the holdout sample. Additionally, the Relative Operating Characteristic (ROC) Curve 10 of the forecasting model showed that the hit rate was always above the false alarm rate across the range of cut-off probabilities. This implied that the forecasting models of hedge fund failure developed in Chapman et al. (2008) s study offered a relative high level of skill in predicting the occurrence of failures in hedge funds. Ng (2008) aimed to build a system that was able to provide a forecast for the time varying likelihood of failure in individual hedge funds using publicly available data. Based on Chapman et al. s (2008) modelling procedure, Ng (2008) conducted a comprehensive sensitivity analysis. He estimated 31 proportional hazard models by changing parameters in each specification. One of them was nominated as a base model to which the remaining 30 9 The Signal Detection Model is explained in Section The ROC curve is a further application of Signal Detection Model and explained in Section

43 models were compared for robustness. Each model was specified according to the variations in covariate definition, evaluation timing, data filtering as well as the thresholds used to identify failure times. Although Ng (2008) used the same databases as Chapman et al. (2008), his method of compiling the estimation sample was different. The author corrected the timing mismatch and double counting issues of Chapman et al. (2008) by examining the time period covered by both the Live and the Dead fund databases and removing the funds common to both databases from the Dead fund database. 11 The author also eliminated all funds-of-hedge funds from the dataset due to the fundamental differences between individual hedge funds and funds-of-hedge funds. 12 In contrast to previous studies, 13 Ng (2008) applied six different scenarios of the failure criteria using three figures of AUM depletion in the last 24 months, the average monthly fund return in the last 24 months and 12 months. Ng s (2008) models incorporated a range of covariates including fund size, return measures, leverage, strategy, liquidity, minimum investment, fee structure and domicile. The evaluation procedure for the model s forecasting power was similar to that of Chapman et al. (2008) except for the evaluation time. Ng (2008) evaluated the base model s forecasting ability at the 60 th month after the fund inception. The evaluation procedure showed that the Cox (1972) proportional hazard model incorporating fixed factors provided predictive ability for forecasting the occurrence of failure in individual hedge funds. Ng (2008) calculated the area under the ROC curve (AUROC) to quantify the predictive ability of the forecast model and the base model ascertained an AUROC of The model was robust against 11 The Live Fund database began in January 1992 and ended at April 2006, whilst the Dead Fund database began in January 1990 and ended at July As such the Dead Fund database began earlier and ended later than the Live Fund database. 12 A fund-of-hedge fund is a portfolio of individual hedge funds. 13 Liang and Park (2010) and Chapman et al. (2008) applied one set of failure criteria. 14 A perfect forecasting model provides AUROC of 1, while a model which has accuracy equal to that of chance represents AUROC of

44 modifications in covariate definition, evaluation time, data filtering and the thresholds for identifying failure times. Gregoriou, Kooli and Rouah (2008) investigated the causal factors driving the funds-of-hedge funds survival. After noting the dramatic growth of the funds-of-hedge funds between early 2000 and December 2005, the authors focused on four sub-categories - Strategic, Market Defensive, Diversified and Conservative fund-of-hedge funds. The authors argued that fundsof-hedge funds had become accepted as proven diversifiers of traditional investment portfolios, while the attrition rate of the individual hedge funds was troubling to investors 15. Also they suggested that if funds-of-hedge funds were to continue to be acceptable to institutional investors and high net-worth individuals, their attrition rate and expected lifetimes should be estimated accurately. Using information from HFR s Live and Dead fund databases from January 1994 to December 2005, Gregoriou et al. (2008) used the Kaplan- Mier method, a Weibull model and a Cox (1972) proportional hazard model to estimate the survival lifetime of funds-of-hedge funds. All funds in the Dead fund database were treated as being discontinued operations: that is, the funds-of-hedge funds that had failed due to poor performance were not differentiated from the funds-of-hedge funds that had simply stopped reporting and exited the Live Fund database voluntarily. Gregoriou et al. (2008) investigated the impact of different predictor variables on the survival lifetime of funds-of-hedge funds, such as average millions managed, management fee, minimum purchase and redemption period. To test whether funds that were not correlated with market funds survived longer, the authors incorporated the funds market beta in the survival models. The fund s market beta was calculated using a factor model that included the monthly return on the S&P 500 index, the Centre for Research in Securities Prices (CRSP) value weighted index, the Morgan Stanley World Capital Index (MSCI), and the Salomon 15 In 2005, approximately 1000 individual hedge funds disappeared. 28

45 Smith Barney World Government Bond Index. They also included an efficiency predictor variable which was quantified in terms of a score produced by data envelopment analysis (DEA) 16 to test whether the efficiency of a fund had a positive impact on its survival, even after controlling for other variables known to affect survival. Gregoriou et al. (2008) s analysis demonstrated that the Conservative sub-category was characterised by the lowest attrition. Small funds-of-hedge funds were less likely to live longer, while funds-of-hedge funds without a hurdle rate were more likely to survive longer. The study also found that the DEA score was significant and pointed to increased survival for efficient funds-of-hedge funds. Additionally, funds-of-hedge funds with high exposure to bond indices, but low exposure to equity indices were more likely to live longer, especially for the Market Defensive and Diversified sub-categories. Gregoriou et al. (2008) concluded that the fundsof-hedge funds were not a homogeneous group of funds, but rather constituted four distinct management styles. Further insight into the factors impacting on hedge fund liquidation was provided by Baba and Goko (2009). The authors avoided the problems caused by categorising all Dead Funds as failures. As mentioned above, the results from the Brown et al. (2001) and Gregoriou (2002) studies were questionable due to this problem. In an effort to overcome this issue, Baba and Goko (2009) treated only those funds which had reported their exit reason as liquidated as failed funds. This method was a more effective approach than that adopted in the two previous study of Brown et al. (2001) and Gregoriou (2002). However, they did not differentiate the funds that had failed due to poor performance from the funds that were liquidated due to other reasons, including returning capital to the investors. This point was discussed by Liang and Park (2010) 17 who showed that the funds that had reported 16 Liang, B., 2000, Hedge funds: The living and the dead, Journal of Financial and Quantitative Analysis, 35, Liang and Park (2010) used the same database as used in Baba and Goko (2009). 29

46 liquidated were not necessarily failures. Liang and Park (2010) gave an example of a liquidated fund from the Dead Fund database that had not experienced a single negative return for the 44 consecutive months prior to the liquidation, and generated a cumulative rate of return of 1,139% during its entire life of 67 months. Liang and Park (2010) argued that it was unreasonable to treat this fund as a failed fund just because it had been liquidated. Accordingly, the empirical results reported by Baba and Goko (2009) should be interpreted as being about the factors impacting on the liquidation of hedge funds as defined by the data vendors, not necessarily failure. Baba and Goko (2009) utilised the TASS databases of the Live and the Dead hedge funds for the period January 1994 to December Their sample consisted of 952 Live Funds and 270 liquidated funds from the Dead Fund database. To assess the effects of both fund-specific characteristics and dynamic performance properties on hedge fund survival probability, they applied three different survival analysis techniques, including the non-parametric Kaplan- Meier analysis, the semi-parametric Cox proportional hazard analysis and the discrete-time hazard Logit analysis. The Cox (1972) proportional hazard model incorporated a wide range of fixed as well as time-varying covariates including return properties, asset under management (AUM), leverage, fee structure, liquidity and minimum investment. Baba and Goko (2009) s analysis revealed the significant effects of return properties such as mean, variance and skewness, and AUM on the funds survival probabilities. The effect of recent fund flows was found to be important to hedge fund survival. They showed that higher survival probability of funds was associated with higher recent fund flows. Interestingly and contrary to previous studies, Baba and Goko (2009) did not find a significant effect of leverage on hedge fund survival. As for the fee structure, they found that funds with higher incentive fee had lower survival probability, while funds with a high water mark had higher survival probability. They also found that the funds with a longer redemption notice period 30

47 and a lower redemption frequency tended to survive much longer. They explained this result by suggesting that lower liquidity which was in the form of strict redemption qualification, made funds more stable and led to longer survival time. Liang and Park (2010) inspired numerous methodological specifications employed in this thesis and provided many useful insights. The purpose of Liang and Park s study was to compare downside risk measures which consider higher moments of funds return with standard deviation in predicting hedge fund failure. They implemented a survival analysis using a Cox (1972) proportional hazard model under a calendar time construction. 18 Having recognised the potential problem of using all Dead Funds or even just liquidated funds as failures, Liang and Park argued that liquidation did not automatically mean failure in the hedge fund industry as profitable hedge funds can be liquidated voluntarily in order to return capital to investors. They suggested simple criteria to define real failure of the hedge funds as follows: i) once listed in a database but stopped reporting, ii) negative average rate of return for the last six months, and iii) decreased AUM for the last twelve months. The study applied these criteria to the entire Dead Fund database, in order to determine not only those funds offering liquidation as an exit reason, but to identify funds that failed due to poor performance. This was intended to select all funds which had exhibited symptoms of poor performance from the sample. Following Liang and Park s example, most subsequent studies have acknowledged that liquidation does not automatically mean failure in the hedge fund industry. Like Baba and Goko (2009), Liang and Park (2010) utilized the TASS databases of the Live and the Dead hedge funds for the period January 1995 to December Using the Cox (1972) proportional hazard model, the study examined the effects of historical risk patterns, prior performance, size, age, leverage, style, high water mark, personal investment and 18 The calendar time model is explained in Section

48 lockup provision on fund survival. The risk measures incorporated in the model to compare with the standard deviation included semi-deviation, nonparametric Value-at-Risk (VaR), Cornish-Fisher VaR, nonparametric expected shortfall, Cornish-Fisher expected shortfall, nonparametric tail risk and Cornish-Fisher tail risk. Liang and Park (2010) estimated six models based on different definitions of failure. Liang and Park s study produced three major findings. Firstly, the downside risk measures such as expected shortfall and tail risk were superior to the standard deviation in terms of predicting hedge fund failure. Secondly, in line with previous research, liquidation did not necessarily mean failure in the hedge fund industry. Finally, the effects of performance, age, size, high water mark and lockup provision on hedge fund failure were clarified. Performance and high water mark were identified as significant determinants of fund failure irrespective of the failure definition, while the impact of age, size and the lockup provision changed depending on the definition of failure Qualitative Response Model The logit model is a well-known form of a qualitative response model. The logit model can be regarded as a generalisation of the linear regression model to a situation in which the dependent variable takes on only a finite number of discrete values. The logit model can be expressed as the following formula with an unobserved continuous dependent variable Y * and observed independent variables X: Y it = X it β + ε it X it and β are vectors of covariates and unknown parameters, respectively, and ε it is assumed to follow a logistic distribution. Although Y * is unobserved, it is associated with an 32

49 observable discrete random variable Y, whose values are determined by Y *. That is, a binary random variable Y can be modelled as an indicator variable that takes on the value 0 representing the Live Funds whenever Y it 0 and 1 indicating the liquidated funds whenever Y it > 0: Y it = 0 if Y it = X it β + ε it 0 Y it = 1 if Y it = X it β + ε it > 0, where Y it = 0 corresponds to a Live Fund and Y it = 1 corresponds to a liquidated fund. The probability of Y it = 1 conditional on the covariates is given by Pr(Y it = 1 X it ) = Pr(Y it > 0 X it ) = Pr X it β + ε it > 0 = F(X it β), where F( ) denotes the logistic cumulative distribution function: F X it β = exp( X it β) The unknown parameters β are estimated using the method of maximum likelihood. In an effort to estimate the influence of various hedge fund characteristics in the likelihood of liquidation, Chan, Getmansky, Haas and Lo (2005) adopted a logit analysis of liquidation. They attempted to quantify the potential impact of hedge funds on systematic risk by establishing new risk measures for hedge funds and applying them to individual and aggregate hedge fund return data. One of the risk measures was the hedge fund liquidation probability based on the logistic regression. Using the TASS database for the period from January 1994 to August 2004, the authors considered several methods examining liquidation probability, including a review of hedge fund attrition rates and a logit analysis of hedge fund liquidation. Although the TASS database provided one of seven distinct reasons for each fund 33

50 assigned to the Graveyard database, the authors argued that using the entire Graveyard database might be more informative. They did not have detailed information about each fund, therefore making it difficult to determine how any particular selection criterion would affect the statistical properties of the remainder. Their purpose was to develop a broader perspective of the dynamics of the hedge fund industry. As a result, Chan et al. (2005) included the entire set of Graveyard funds in their analysis and advised readers to keep in mind the composition of the sample when interpreting their empirical results. The sample for estimating the logit model of liquidation included 2,771 Live Funds and 1,765 funds in the Graveyard database. The authors adopted a set of explanatory variables including age, asset, return and flow variables. The flow variable 19 was inspired by the return chasing phenomenon in which investors flock to funds showing good recent performance and leave funds exhibiting underperformance. By adding indicator variables for the calendar years and hedge fund style categories to these covariates, Chan et al. (2005) specified five different models and estimated coefficients. The empirical results of the logit model estimates and implied probabilities suggested that several factors impacted on the likelihood of a hedge fund s liquidation including past performance, AUM, age and fund flows. All these factors were negatively associated with the probability of liquidation. Given these factors, the average liquidation probability for funds in 2004 was over 11%. This was higher than the historical unconditional attrition rate of 8.8%. A probit model is another form of qualitative response model and is a popular specification for a binary response model. The probit model differs from the logit model in that the probit model is essentially a function of the normal distribution and as such it is more limited in its 19 The flow variable was calculated as the fund s current year-to-date total dollar inflow divided by previous year s assets under management. Dollar inflow in month t is defined as FLOW t =AUM t -AUM t-1 (1+R t ) and AUM t is the total assets under management at the beginning of month t, R t is the fund s net return for month t, and year-to-date total dollar inflow is simply the cumulative sum of monthly inflows since January to the current year. 34

51 application. That is, the probit model assumes the standard normal distribution of the error term, while the error term in the logit model is assumed to follow the logistic distribution. Therefore, the probability of Y it = 1 conditional on the covariates is given by Pr(Y it = 1 X it ) = Pr(Y it > 0 X it ) = Pr X it β + ε it > 0 = Φ(X it β), where Φ( ) denotes the standard normal cumulative distribution function. The unknown parameters β are estimated using the method of maximum likelihood. Baquero, Horst and Verveek (2005) employed a probit model for studying hedge fund survival. They analysed the performance persistence in hedge funds, taking into account the level of bias, and modelled liquidation of hedge funds focusing on historical performance in order to correct for biases in the data. The funds which had been liquidated were modelled against the remaining funds in the Dead Fund database as well as the Live Fund database. Using the TASS database for the period 1994 to 2000, Baquero et al. (2005) adopted a longitudinal probit analysis to model hedge fund survival and its relationship with historical performance. Baquero et al. (2005) classified funds in the Dead Fund database into three groups. Of 612 Dead Funds, 316 funds were classified as liquidated and 219 funds were categorised as a self-selected group. This last group referred to cases where the fund continued to exist but stopped reporting to TASS. For the remaining 77 hedge funds, the exit reason was unknown. The authors tried to make an assessment of exit reasons for the funds where the exiting reason was unknown. This assessment was made by examining these funds money flows in the four quarters prior to disappearing from the database. If the money flows were negative in the final year of reporting, the fund was classified as liquidated and included in their sample of failures, otherwise the funds were considered to be self-selected. The model employed explanatory variables including historical returns over several previous quarters, fund size, 35

52 fund age, fund risk, an underwater indicator reflecting negative returns over a predetermined period, and the fund s investment strategy. The Baquero et al. (2005) s probit model analysis revealed a negative and significant relationship between the historical returns and the probability of the hedge fund s liquidation. That is, the funds with high returns were more likely to survive than the funds with low returns. As expected, the impact of the underwater indicator on fund survival was negative and significant. The authors also found that funds with higher incentive fees were more likely to be liquidated, while older funds were less likely to be liquidated. As far as investment styles were concerned, funds with an Event- Driven strategy showed the highest survival probability, while the funds employing Equity Market Neutral strategy had the shortest survival lifetime. Another study using a probit model was conducted by Malkiel and Saha (2005) who investigated the abnormal characteristics and biases in reported hedge fund returns. They also examined the determinants of hedge fund demise and investigated return persistence. Using the TASS database for , the authors performed a probit regression analysis to determine the factors impacting on the probability of a fund s demise. They employed four explanatory variables - the fund s return in each quarter for the most recent four quarters, the standard deviation of the fund s return for the most recent year, the fund s most recent performance relative to all other funds in the same primary category, and the fund s size in the most recent month. Malkiel and Saha (2005) s analysis suggested that a fund s recent performance was an important influence on the probability of its demise. However, the effect on the probability of the fund s demise relative to the performance of peers was found to be statistically insignificant. Higher return volatility increased the probability of the fund s exiting, with a lower the probability of demise for larger funds. Accordingly, the authors concluded that the funds exiting from the TASS database were likely to be the poor 36

53 performers rather than funds that were large enough that they no longer needed to attract new investors. 2.3 Studies of Hedge Fund Performance The literature includes several studies that examined hedge fund performance in terms of fund characteristics. Most of the studies provided insight into the investment strategy, fund size and fee structure that influenced hedge fund performance Strategy and Performance The effect of investment style on hedge fund performance is one of the most significant issues in the hedge fund industry. Many studies have examined the sources of hedge fund returns in terms of various investment strategies adopted by hedge fund managers. In an early study of hedge fund performance, Fung and Hsieh (1997) analysed investment management styles by focusing on hedge fund managers and commodity trading advisors (CTAs). They extended Sharpe s (1992) asset class factor model, which was used by mutual fund managers for fund style analysis, to accommodate the different approaches of hedge fund managers and CTAs. Fung and Hsieh (1997) added three new style factors to Sharpe s (1992) model and obtained significant improvement in the model s performance. In contrast to the qualitative method of classifying trading strategies, which was based on the description in the disclosure documents of hedge funds, they used quantitative methods to define investment style. They factor analysed the 409 hedge funds as a single group and extracted five mutually orthogonal principal components, explaining approximately 43% of the crosssectional return variance. Fung and Hsieh (1997) constructed five style factors whose 37

54 returns were highly correlated to the principal components. Having examined the disclosure documents of the hedge funds in each style factor, they associated the five style factors with qualitative style categories used by the hedge fund industry. They were System/Opportunistic, Global/Macro, Value, System/Trend Following, and Distressed. Although Fung and Hsieh (1997) found five dominant strategies, the hedge fund returns were statistically different in all of the standard markets in the world. Accordingly, they concluded that what drove hedge fund performance was not investment strategy but the manager s skill. A similar early study was conducted by Brown, Goetzmann and Ibbotson (1999) who examined the performance of off-shore hedge funds over the period 1989 through Using a database that included both defunct and surviving funds, they estimated basic risk and return characteristics of hedge funds and developed some broad stylistic classifications which they compared with self-reported stylistic descriptions. Also they examined evidence for performance persistence in the hedge fund industry. Due to a limitation of public information about investment strategies with off-shore hedge funds, they used self-reported managers activity to classify The U.S Offshore Directory universe into 10 basic styles. They used a value-weighted return for the performance of each style by estimating fund value at the beginning of each year. The results revealed that the individual style categories provided positive value-weighted risk-adjusted performance, and that no particular strategy outperformed others except for the global strategy which was dominated by the Soros funds and was not representative of the strategy. Agarwal and Naik (2000) studied hedge fund performance persistence across a range of investment strategies. Using databases provided by HFR which covered returns of hedge funds from January 1982 to December 1998, they classified investment strategies into two broad categories: Non-Directional and Directional. Strategies which exhibited low 38

55 correlation with the market were included in the non-directional group, while those which showed high correlation with the market were classified as directional. They further divided these two main groups into ten popular strategies and analysed the performance persistence of hedge funds following each of these strategies. They found that directional and nondirectional hedge funds showed similar degrees of persistence. That is, performance persistence of hedge funds was not related to the type of strategy adopted by the hedge funds. Interestingly, Agarwal and Naik (2000) found evidence of a few good managers who clearly outperformed their peers over long periods. This implied that, as indicated in Fung and Hsieh (1997), manager skill is more strongly associated with performance persistence than investment strategy. Results similar to those reported by Agarwal and Naik (2000) were obtained by Brown and Goetzmann (2003), who used monthly return histories of hedge funds from the TASS database over the period 1989 to January, 2000 to examine stylistic differences across hedge funds. They implemented a systematic quantitative approach to both the return history and the self-reported style information to comprehend and identify the major categories of hedge fund styles. They found that differences in style accounted for significant differences in hedge fund performance and in risk-taking by fund managers. Brown and Goetzmann (2003) also found that differences in investment strategies contributed to about 20% of crosssectional variability in hedge fund performance. However, they pointed out that although a particular style of hedge fund could outperform other strategies in any given year, this provided no evidence that the strategy would achieve higher performance in future years. Given the significant association of hedge fund style with determining performance and risk exposure, they concluded that appropriate style analysis and style management were critical to success for hedge fund investors. 39

56 More recent studies have distinguished some particular hedge fund strategies outperforming other strategies with a greater degree of accuracy. This improvement stemmed from the fact that more hedge fund data were now available and alternative return measures were more capable of evaluating hedge fund performance. Ding and Shawky (2005) proposed a new hedge fund performance measure that adjusted for hedge fund skewness. The new performance metric was the Skewness Adjusted Information Ratio in which they incorporated the excess skewness of returns into the excess volatility of returns. Using information from the Centre for International Securities and Derivatives Markets (CISDM) database for over March 1972 to December 2003, they examined hedge fund performance in relation to hedge fund categories. With the new performance measure, Ding and Shawky (2005) found that all hedge fund categories achieved above average performance when measured against the S&P 500 or the Vanguard Total Bond Market Index. Additionally, the performance of Equity, Futures and Global hedge funds were found to be significantly better than that of Funds-of-Hedge Funds (FOHFs) and Fixed Income strategies. Another new hedge fund performance measure was proposed by Eling (2006), who argued that a true evaluation of hedge fund performance needed consideration of autocorrelation, bias, and fat tails of returns. Eling (2006) conducted an evaluation using those variables, and showed that the majority of hedge funds lost their attractiveness except for funds adopting Equity Market Neutral, Distressed, or Global Macro strategies. These were the only three strategies that exhibited higher performance than stocks and bonds. Eling (2006) concluded that when autocorrelation, bias, and fat tails of hedge fund returns were taken into account, few hedge fund strategies appeared to be attractive investment options. Using the same dataset as in their 2005 study, Ding and Shawky (2007) examined hedge fund performance with respect to fund strategies with more reliable performance modelling. They first analysed the distributional properties of monthly returns for all of the hedge fund 40

57 categories. The mean and standard deviation of the hedge fund returns were found to have similar characteristics to those of stock and bond market indexed returns, while the skewness and kurtosis of the hedge funds presented different characteristics. They found that returns from hedge funds which invested in Equity, Futures, and Global securities were positively skewed, while Fixed Income hedge funds and Funds-of Hedge Funds had higher levels of kurtosis than the market indexes. In their 2007 study, Ding and Shawky found that the performances of Equity, Futures and Global hedge funds were better than those of other strategies, and argued that hedge fund strategy producing positive levels of skewness provided greater performance. They also estimated four different models to measure the performance of equity hedge funds and found that all equity fund categories provided above average performance when measured against the Wilshire 5000 index. Also they found strong evidence showing that Event Driven, Distressed Securities and Merger Arbitrage strategies significantly outperformed other strategies including Emerging Markets, Equity Hedge and Global Macro. The findings of Ding and Shawky (2007) and other recent studies with respect to hedge fund performance and strategy emphasize the importance of an accurate model for performance measurement in hedge fund data Fund Size and Performance Numerous authors have examined the relationship between hedge fund size and performance. In an early study of hedge fund performance, Liang (1999) produced empirical evidence indicating a positive relationship between fund size and performance. Using the hedge fund database maintained by HFR, he analysed the performance of hedge funds and compared them with mutual funds by discussing hedge fund features and evaluating hedge fund 41

58 performance using the asset-class factor model. To further examine the factors impacting on hedge fund performance, Liang (1999) ran a cross-sectional regression of average monthly returns on fund characteristics such as incentive fees, management fees, and fund assets and obtained a significant positive coefficient for the fund asset variable. This suggested that larger hedge funds outperformed small hedge funds. However, the author measured fund size only at one point, at the end of the period. Therefore, the study did not necessarily show the impact of fund size on fund performance, but equally, the impact of fund performance on fund size. Liang (1999) explained this result by suggesting that successful funds attracted more money. Other recent studies produced contradictory results regarding hedge fund size and performance. Hedges (2003) examined whether the portfolio size of hedge funds was linked to diminishing returns. The author was motivated by his observation that top hedge fund managers, such as Tiger and Soros, were successful even with far smaller fund sizes than the funds with which they began their careers. Using funds that stopped reporting and funds that started operation between January 1995 and December 2002, Hedges (2003) provided empirical evidence indicating that smaller funds outperformed larger funds and, moreover, showed that mid-sized hedge funds performed worst. In relation to the latter result, the author hypothesised that hedge fund managers may experience a mid-life crisis. He argued that smaller funds could invest all of their money into their best idea, while larger funds often found it difficult to invest continued inflows due to the constraints of internal asset allocation guidelines and policies. Hedges (2003) also identified liquidity cost as one of the disadvantages of a large asset hedge fund. Herzberg and Mozes (2003) obtained similar results to those of Hedges (2003). They analysed the persistence of hedge fund performance focusing on four parameters that were anticipated to impact on it. They were the length of fund history, AUM, the seasonality of 42

59 returns and the redemption policy. Using data provided by Hedge Fund.Net, Altvest and Spring Mountain Capital over the period from 1990 to 2001, they found that smaller funds exhibited marginally better performance than large funds, with significantly higher Sharpe ratios. Herzberg and Mozes (2003) also performed Chi-square tests to examine whether changes in assets under management (AUM) predicted changes in returns and the Sharpe ratio. They found that an increase in AUM was associated with reduced future performance. In contrast to Herzberg and Mozes (2003) findings, Gregoriou and Rouah (2003) found no correlation between the size of hedge funds and their performance. They studied the performance of 203 hedge funds and 72 funds-of-hedge funds over the period from January 1994 to December The geometric mean return, the Sharpe ratio and the Treynor ratio were used as performance measures. The Pearson correlation measures and Spearman rank correlation measures were employed to test the relationships. The most extensive study of the effect of fund size on hedge fund performance was carried out by Ammann and Moerth (2005). Using the TASS databases, they first analysed the difference between asset-weighted and equally weighted returns and the resulting difference in survivorship bias. In the second step, they estimated several different multi-asset class factor models to derive an alpha 20 of hedge fund returns using excess returns. Lastly, crosssectional regressions were used to identify the impact of fund size on excess returns, standard deviations, Sharpe ratios and alphas. The Ammann and Moerth (2005) results showed a negative relationship between fund size and returns. They also found that funds with little assets under management underperformed on average. They suggested that the underperformance of these very small funds was due to higher expense ratios. However, it was understandable that small funds relative to large funds were more readily able to invest 20 An alpha is the return in excess of the compensation for the risk borne, and thus commonly used to assess active managers' performances. 43

60 their capital into their best positions due to their increased flexibility and thus earned considerably higher returns Fee structure and Performance Hedge funds typically use innovative fee structures, so the effect of the fee structure on hedge fund performance is an issue frequently explored in the literature. The fee structures of the hedge funds usually include four essential components: management fee, incentive fee, high water mark, and hurdle rate. Most hedge funds charge a management fee of one to two percent of fund assets to cover administrative expenses. In contrast to the management fee, incentive fees are only imposed on funds with good performance, and are highly variable across hedge funds. Most funds apply an incentive fee with a high water mark or hurdle rate provision. The incentive fee is intended to encourage higher returns to investors by relating managerial compensation to fund performance. A fund with a high water mark allows managers to earn the incentive fee only after they recoup all past losses. The hurdle rate represents the minimum return, such as the Treasury Bill rate or LIBOR, which should be achieved by fund managers in order to earn an incentive fee. For funds with a hurdle rate provision, the incentive fees are charged on the basis of the profit from investment above the hurdle rate. The impact on hedge fund volatility from incentive fees which are subject to a high water mark provision is a controversial issue. Brown et al. (1999) argued that the typical fee structure of hedge funds had an impact on their volatility and survivability due to the fact that a manager who is out of the money (below the high water mark) may increase the volatility of returns. In addition, the more the manager is out of the money, the less incentive he or she may have to accept new funds and the less new investors are willing to invest. Therefore, 44

61 funds with poor performance may have high probability of decreasing in size and no longer continuing their business. However, this argument was not supported by Ackermann, McEnally and Ravenscraft (1999). They used a broader dataset which included databases from Managed Account Reports, Inc. (MAR) and HFR, and a wider set of metrics than that used by Brown et al. (1999). Ackermann et al. (1999) explained the superior performance of hedge funds by relating the incentive fee to their performance. In their empirical results, the incentive fee was found to be the most important and significant determinant of risk-adjusted returns. They showed that as the incentive fee increased from zero to the median value of 20 percent, the Sharpe ratio increased 66 percent on average. They explained this result by suggesting that the incentive fee was effective at aligning manager and investor, or attracting top managers. Interestingly, the coefficient on incentive fee in the Ackermann et al. (1999) total risk regression was always insignificant and did not exhibit a consistent sign. This suggested that, contrary to the theoretical arguments advanced by Brown et al. (1999), a higher incentive fee did not encourage managers to take excessive risk. Liang (2001) examined the relationship between fee changes and hedge fund performance. Using the TASS database, he studied hedge fund performance and risk between 1990 and Liang (2001) examined data from 1998 in detail because hedge funds were excessively affected by global financial market crisis in that year. In investigating the association between incentive and management fee changes and hedge fund performance, he found that the funds which performed substantially worse in 1997 reduced fees in The author suggested that, in line with the intended purpose of the incentive fee, poor performance was a critical motivation for funds to reduce incentive fees. The most comprehensive study to date of the effect of fee structure on hedge fund performance was undertaken by Agarwal, Daniel and Naik (2009). Using an extensive dataset created by the union of four large hedge fund databases - CISDM, HFR, MSCI and TASS - 45

62 they examined the role of managerial incentives and discretion in hedge fund performance. In analysing these issues, Agarwal et al. (2009) made important innovations in hedge fund research. They hypothesised that the incentive fee does not fully capture managerial incentives, as two different managers charging the same incentive fee rate could be facing different dollar incentives depending on the timing and magnitude of investors capital flows, the funds return history, and other contractual features [Agarwal et al. (2009)]. In order to overcome these limitations, they considered the incentive-fee contract as a call option written by the investors on the assets under management. The strike price was determined by the hurdle rate, high water mark and the net asset value (NAV) at which investor entered the fund. As a result, they empirically quantified the delta 21 of the manager s call-option-like incentive fee contract, which was referred to as the manager s option delta. This value represented the total expected dollar increase in the manager s compensation as the fund s net asset value increased one percent. In the Agarwal et al. (2009) analysis, several funds imposing the same percentage of incentive fee were found to have significantly different option deltas. This suggested that the option delta was an effective measure of the full value of managerial incentives. The main contribution provided by this study was to empirically demonstrate that hedge funds with greater managerial incentives, as measured by option delta, were associated with superior performance, while the incentive fee rate did not show explanatory ability for future returns. They also found that funds with high water mark provisions provided higher returns and so did funds with hurdle rate provisions though this relation was not statistically significant. 21 The delta of an option is defined as the rate of change of the option price with respect to its underlying asset's price. 46

63 2.4 Study of Hedge Fund Data Biases It is widely recognized that hedge funds are subject to several potential data biases associated with reported hedge fund returns. Most of these biases are due to the limited regulatory oversight. As indicated in Section 1.2.1, hedge funds are exempted from most of the regulations that are applied to mutual funds. Accordingly, hedge funds report their information only on a voluntary basis to several commercial hedge fund data vendors such as CSFB/Tremont, Hedge Fund Research (HFR), Managed Account Reports (now Zurich Capital Markets), MSCI, and Van Hedge Fund Advisors. After a hedge fund joined a hedge fund data vendor, it often reported its past unrevealed return history as well as returns on a going forward basis. These backfilled returns were found to cause an upward return bias because most funds reported only favourable return history and joined a database only after a period of good performance. This is called backfill bias. Since hedge funds are not permitted to advertise publicly, they report fund information voluntarily in order to attract potential investors and stop reporting fund information at their will. When a fund stops reporting its information, the fund is deleted from the live fund database with its information history and transferred to the dead fund database. The live fund database tracks only the funds that are currently reporting information. The main reason, among others, for exiting from the database was found to be the fund s poor performance [Grecu et al. (2007)]. Accordingly, survivorship bias occurs upward in the live fund database because the performance of a fund that stops reporting tends to be much lower than that of a live fund. Liquidation bias occurs when underperforming funds such as Long Term Capital Management (LTCM) the Soros Fund and Bear Stearns Hedge Funds withdraw from reporting in the lead up to their liquidation. The effect of this bias is clearly to overestimate hedge fund returns and underestimate their risk. When hedge funds disappear through mergers and reorganisations, hedge fund returns lead to either underestimation or overestimation of returns. This is referred to 47

64 termination bias. Self-selection bias is caused by funds that cease reporting voluntarily because they have reached capacity and no longer need the publicity associated with reporting performance, or funds that choose not to report at all. The effect of this bias is to underestimate hedge fund returns. Liquidation, termination and self-selection biases are generally grouped under the heading survivorship bias. Survivorship and backfill biases were examined in this thesis and hedge fund return data in the HFR database was found to exhibit large biases. These biases need to be corrected before analysing hedge fund data in order to avoid overstated results. The survivorship bias was corrected by including both live and dead funds in the sample while the backfill bias was fixed by removing hedge fund data before the initial date of joining the HFR databases. A number of previous studies reported survivorship and backfill biases of hedge funds and the results varied due to the use of different databases and sample periods. Table 2.1 shows the summary of previous results for hedge fund survivorship and backfill biases. 48

65 Table 2.1 Literature on Survivorship and Backfill Biases in Hedge Funds Study Analysis Period Database Survivorship Bias Backfill Bias Brown et al. (1999) TASS 3% N/A Ackermann (1999) HFR/MAR 0.16% N/A Fung nd Hsieh (2000a) TASS 3% 1.4% (omitting the first 12 months of each fund's reported returns) Liang (2000) HFR 0.60% N/A TASS 2.24% N/A Edward and Caglayan (2001) MAR 1.85% 1.17% Barry (2003) TASS 3.80% N/A Posthuma and Sluis (2003) TASS N/A 4% Malkiel and Saha (2005) TASS 4.42% (without Backfill Data) 7.31% (Difference in Mean) 5.74% (Difference in Median) Agarwal and Jorion (2010) TASS 5.23% (with Backfill Data) 6.70% (without Backfill Data) 1.48% N/A Ibbotson et al. (2011) TASS 3.16% (with Backfill Data) 5.13% (without Backfill Data) 2.05% (Live Funds) 4.02% (Live+Dead) 2.97% (Live+dead, Equal lweighted) 0.27% (Live+Dead, Value weighted) 2.5 Conclusion In this chapter, the three main topics of Hedge Fund Survival, Hedge Fund Performance and Hedge Fund Data Biases covered in the literature relevant to this thesis were reviewed. Studies in these areas uncovered several interesting issues. 49

66 Due to large losses sustained through the collapse of high profile hedge funds since 1998, hedge fund survival has become one of the most important topics in the hedge fund literature. The majority of hedge fund survival studies to date used one of two statistical techniques - survival analysis or qualitative response modelling. These studies identified many significant factors impacting on hedge fund survival, although there is disagreement about the importance of some covariates. In reviewing studies in this area, two distinct advances were identified in the literature. Firstly, it is obvious that researchers have begun to distinguish genuine failed hedge funds from those that have exited the database for other reasons. It is essential to identify real failure in order to avoid the confounding effect of predictor variables on hedge fund s survival lifetime. Secondly, recent studies have developed models capable of forecasting hedge fund failure rather than just explaining factors influencing hedge fund s survival time. In regard to hedge fund performance, the studies of investment strategies used by fund managers, the fund s assets under management and fee structure were discussed. The more recent studies of fund strategies found that some fund styles outperformed others, while earlier studies did not find significant effects of fund strategies on performance. The improvement in the results achieved by the more recent studies stems from the fact that more hedge fund data is now available and, as a consequence, updated return measures are more capable of evaluating hedge fund performance. Fund size was generally found to have a negative effect on hedge fund performance, although Gregoriou et al. (2003) found no correlation between the two. In addition, previous studies justified positive relationship between the incentive fees of hedge funds and fund performance. As shown in a number of previous studies, one of the major problems in conducting research on hedge funds is potential biases. Therefore, it is needed to correct these biases before analysing hedge fund data to avoid overstated results. 50

67 Chapter 3 Data and Methodology 3.1 Introduction The first part of this chapter describes data used in this thesis. This thesis employs a survival analysis framework [Allison (1984)] and the Cox (1972) Proportional Hazards (CPH) model to estimate the survival probability of individual hedge funds (HFs) and funds-of-hedge funds (FOHFs). As a preliminary analysis, risk-return trade-offs in HFs and FOHFs were examined and the risk measure that best captured the cross-sectional variation in HF and FOHF returns was identified in Chapter 4. As mentioned in Chapter 1, the main purpose of this thesis is to provide the survival forecasting models for HFs and FOHFs. This was performed by using the semi-parametric survival analysis approach with the incorporation of the risk measures estimated from Chapter 4 into the CPH models. As a last step, the predictive accuracy of the estimated CPH models was tested and compared using the Signal Detection Model and the Relative Operating Characteristic (ROC) curves. The remainder of this chapter is arranged as follows: Section 3.2 describes the data, descriptive statistics and results of normality testing of HF and FOHF returns. Section 3.3 presents the methods used to estimate risk measures and to test the cross-sectional relation between hedge fund returns and risk measures. Survival analysis incorporating the CPH model is discussed in Section 3.4, with the forecast evaluation metrics presented in Section

68 3.2 Data Data Delineation It is difficult to identify a representative hedge fund database among a number of hedge fund databases. It is well known that hedge funds report their information only on a voluntary basis due to limited regulatory oversight. Since hedge funds are not permitted to advertise publicly, they report fund information voluntarily to a data collection agency in order to attract potential investors. As a result, conflicting results of studies based on different databases have been produced [Ackermann, McEnally, and Ravenscraft (1999), Malkiel and Saha (2005), Brown et al. (1999) among others]. This makes the comprehensive nature and integrity of hedge fund data questionable. This study adopted the Hedge Fund Research (HFR) database, which is a database that is commonly used by academics and practitioners. There are three major hedge fund databases employed in the literature, namely the HFR, Lipper TASS and CISDM (Centre for International Securities and Derivatives Markets) databases. Each database supplies its own family of indices. HFR provides two separate databases. One is the Dead Fund Database, while the other is called the Live Fund Database. As indicated in the name, the Live Fund database includes information about all hedge funds which are currently reporting to HFR, while the Dead Fund database consists of information regarding all hedge funds which have discontinued reporting to HFR. It has been acknowledged in the literature that hedge fund databases have trouble with several biases [Ackermann et al. (1999), Brown et al. (1999), Malkiel and Saha (2005), among others]. The sample of HFR data adopted in this study included Dead Funds as well as Live 52

69 Funds in order to moderate survivorship bias. The Dead and Live Fund databases used in this study covered the period from each fund s initial date of joining the HFR up to December, The backfilled return and AUM data which covered the period before each fund s initial date of joining the HFR were removed from the databases due to the backfill bias 22. The sample of funds from the raw database was filtered as the first step of the analysis. This initial filtering included restricting the funds to those with a minimum of 36 months of data 23 to guarantee a sufficient number of observations for the estimation process. Also, this ensured that all funds in the sample were hedge funds which did not seek short term and high risk objectives 24. To ensure data consistency, those funds that did not report returns net of all fees to HFR on a monthly basis, or had missing data, were deleted. For the purpose of this research the hedge fund database was divided into two classes. One class contained the HF data, while the other was comprised of the FOHF data. The Live Fund database included 2003 HFs and 879 FOHFs, while the Dead Fund database contained 2303 HFs and 816 FOHFs. HFs were categorized into 4 classes according to their investment strategies. They were Equity Hedge, Event Driven, Macro, and Relative Value. Two index funds were deleted from the HF sample to make HFs distinct from portfolio hedge funds. The FOHFs adopted one of the four strategies including Conservative, Diversified, Market Defensive and Strategic. After the removal of funds which did not meet the data requirements of this research, 1484 HFs and 627 FOHFs remained in the Live Fund database, while 1329 HFs and 535 FOHFs comprised the Dead Fund database. A number of hedge fund 22 The backfill bias is caused by including a hedge fund s previously unreported performance history with its first monthly report to data collectors. 23 The same analysis in this thesis was conducted with funds having a minimum of 24 months of data to check the sample selection bias and no bias was found. 24 Gregoriou (2002), Chapman et al. (2008), Ng (2008), Baba and Goko (2009) and Liang and Park (2010) applied similar minimum observation requirements and reported no resulting sample selection biases. 53

70 characteristics are included in three information tables available from the HFR databases, namely, the administrative table, the performance table and the assets table Administrative Table The administrative table contains a variety of information about each fund. Among them are minimum investment, redemption policy, fee structure, leverage and domicile. The minimum investment is a restriction imposed by a fund on new investors. The redemption policy includes lockup period, redemption frequency and notice period. The lockup period is the length of time in which a new investor is restricted from redeeming assets, while the notice period is the number of days in advance investors should notify before redeeming their assets. The redemption frequency indicates the frequency at which the investors can redeem their assets. The fee structure is represented by management fee, incentive fee, high water mark and hurdle rate. The management fee and incentive fee are the percentage rate charged by fund managers. A fund with a high water mark provision allows managers to earn the incentive fee only after they recoup all past losses. For a fund with a hurdle rate provision, the incentive fee can be charged on the basis of the profit from investment above the hurdle rate. The domicile indicates whether a fund is an offshore vehicle or not. The HFR database also provides leverage information as to whether a fund is allowed to use leverage and if so, whether this leverage is limited with a maximum ratio. Table 3.1 presents summary statistics of these fund characteristics provided in the sample in the Live Fund database, the Dead Fund database and the Combined Fund database which includes both of the Live and Dead Fund databases. 54

71 Table 3.1 Summary Statistics for Administrative Data The statistics of minimum investment, management fee, incentive fee, redemption frequency, notice period, and lockup period are average values for each fund group. The dollar value of the management fee obtained by a fund manager was calculated by multiplying the percentage by the average asset under management of the fund s entire life. The incentive fee was firstly calculated by multiplying the fund s average monthly return by the average monthly asset under management to evaluate the profit per month over the fund s lifetime. This figure was then multiplied by the percentage of incentive fee to calculate the dollar value of the incentive fee obtained by a fund manager. The statistics of leverage, high water mark, hurdle rate and domiciled offshore are the percentage of funds within each group. Live Dead Combined HF FOHF HF FOHF HF FOHF Number of Funds Minimum Investment (US$) 1,249, , , ,197 1,087, ,366 Leverage (%) Management Fee (US$) 3,271,953 2,651,206 1,186,203 1,648,298 2,286,542 2,189,454 Incentive Fee (UD$) 368,513 51, ,424 60, ,272 55,272 High Water Mark (%) Hurdle Rate (%) Redemption Frequency (days) Notice Period (days) Lockup Period (days) Domiciled Offshore (%) As expected, the amount of minimum investment of FOHFs was significantly lower than that of HFs. This may be the main reason why FOHFs have become more favoured by various investors. The leverage was a contrasting characteristic between HFs and FOHFs. A significantly higher proportion of HFs (70.92%) included in the Combined database levered up their investment capital than did FOHFs (43.03%) in order to achieve greater exposure to their investment position. The proportion of FOHFs (49.16%) using leverage in the Dead Fund database was marginally higher than that of FOHFs (37.52%) in the Live Fund database. It is interesting to note that the incentive fee imposed by the FOHFs was less than a third of that charged by HFs in the Combined database. This may be due to the different fee structures between HFs and FOHFs. While a HF charges a management and incentive fee, a FOHF charges extra fees at the underlying hedge fund level, as well as management and 55

72 incentive fees at the FOHF level. The proportion of HFs having the high water mark provision was higher than that of FOHFs in both the Live and the Dead Fund databases, while the ratio of FOHFs applying hurdle rate provision was greater than that of HFs Time-Series Data Table The HFR offers each fund s monthly returns. The monthly return represents the change in the net asset value (NAV) of each fund during the month, compared to the NAV at the beginning of the month. In addition, monthly data is provided in regard to the asset under management (AUM) of each fund. Monthly returns were calculated as the difference in the NAV during the month divided by the NAV at the beginning of the month. Returns were net of all fees including management fee, incentive fee and other fund expenses. In reality, the actual returns that investors received differed from the reported returns owing to factors such as redemption fee and the bid-ask spread offered by the fund. Nevertheless, the reported returns were the basis for actual returns investors obtain in practice. Table 3.2 presents the descriptive statistics for the return and size time series data that was sourced in this study from the Live Fund database, the Dead Fund database and the Combined database (of the other two). The duration indicates the average number of months over the lifetime of a class of funds. For the Dead Funds it was measured as the difference between the fund s initial date of joining the HFR and the last reporting date. For a Live Fund s duration, the calculation was the number of months from the fund s initial date of joining the HFR to December, The winning ratio was the ratio of the number of positive monthly returns divided by the total number of monthly returns. 56

73 Table 3.2 Summary Statistics for Return and Size Time Series Data The numbers reported were obtained on the basis of the average values for each fund included in each database. The statistics of return and assets under management (AUM) are monthly averages. The winning ratio is the ratio of the number of positive monthly returns divided by the total number of monthly returns Live Dead Combined HF FOHF HF FOHF HF FOHF Number of Funds Duration (months) Mean Return (%) Standard Deviation Skewness Kurtosis Mean AUM ($'000') Standard Deviation Skewness Kurtosis Winning Ratio The average duration of Live Funds was longer than that of Dead Funds in each group of HFs and FOHFs, and the HFs showed longer average duration than the FOHFs. As can be observed from the Table 3.2, the average monthly return of the HFs was higher than that of the FOHFs. The returns for HFs were more volatile than those for the FOHFs, and the FOHFs had thicker tails in their return distributions than was the case for the HFs. The skewness statistics indicated negative values across the Live, Dead and Combined categories for both HFs and FOHFs. It was also noticeable that the average standard deviation of the Live HF returns, while greater than that of the Dead HF returns, was a relatively large number compared to the average mean return. This implied that the standard deviation may not be an appropriate risk measure for HFs. The most distinct difference was found between the average monthly AUM of the Live and the Dead Funds. The average AUM of the Live Funds was notably greater than that of the Dead Funds in each group of HFs and FOHFs. As expected, funds that maintained reporting showed a higher winning ratio, with the higher 57

74 ratio for FOHFs indicating that they had a greater frequency of positive monthly returns than the HFs Normality Test for HF and FOHF Returns It has been well established in the literature that the reported returns of HFs and FOHFs are not normally distributed and exhibit excess kurtosis and negative skewness [Fung and Hsieh (1997), Lo (2001), Brooks and Kat (2001), Amin and Kat (2003), Agarwal and Naik (2004), Brown et al. (2004), among others]. Previous studies found that there was an important difference between average skewness for individual hedge funds and skewness for portfolios of hedge funds, including funds of hedge funds. In an analysis of optimal portfolios of hedge funds, Amin and Kat (2002) found that as the number of funds increased, standard deviation fell, but median skewness became more negative. Kat and Lu (2002) found that amongst individual hedge funds, funds in most strategy categories were associated with negative skewness, and all had excess kurtosis. Using hedge fund indices Brook and Kat (2001) found evidence of hedge fund non-normality with very strong excess kurtosis and negative skewness. They also found statistically significant negative skewness for the convertible arbitrage, risk arbitrage, distressed and emerging markets strategies, while equity market neutral, long-short equity and macro strategies are generally not significantly skewed. Table 3.3 presents the proportion of rejection in the Jarque-Bera and Lilliefors normality test 25 for HF and FOHF returns. 25 The Lilliefors test is more appropriate when the sample size is small. The Lilliefors test was conducted as the number of funds in several strategies, such as Conservative and Market Defensive, is small. 58

75 Table 3.3 Normality Test for HF and FOHF Returns This table presents the proportion of rejections using the Jarque-Bera and Lilliefors normality tests. Fund Group HF FOHF All Hedge Funds Investment Strategy % rejection in J-B test % rejection in Lilliefors test % rejection in J-B test % rejection in Lilliefors test % rejection in J-B test % rejection in Lilliefors test Equity Hedge 69% 57% 56% 49% 62% 52% Event Driven 84% 78% 72% 66% 78% 72% Macro 57% 45% 54% 48% 55% 47% Relative Value 85% 84% 77% 71% 80% 77% Conservative 96% 93% 80% 76% 88% 84% Diversified 83% 77% 67% 58% 75% 68% Market Defensive 63% 48% 60% 48% 61% 48% Strategic 74% 64% 67% 66% 71% 65% All Fund-of-Hedge Funds Live Fund Dead Fund Combined Fund 71% 62% 61% 55% 66% 58% 82% 76% 70% 64% 76% 70% As expected, rejection rate in the J-B test (Lilliefors test) was high, showing 66% (58%) on average in the Combined HFs and 76% (70%) in the Combined FOHFs. The average rejection rate of FOHFs was higher than that of HFs, but there was a great fluctuation across investment strategies. Among the strategy classes in the Combined HFs, Relative Value and Event Driven showed high J-B test rejection rate of 80% and 78% respectively, while Macro yielded lower rejection rate of 55%. The strategy of Conservative in the Combined FOHFs showed high J-B test rejection rate of 88%, while Market Defensive presented rejection rate of 61%. It is interesting to note that the rejection rates for Live Funds are higher than those for Dead funds Data Biases As mentioned in Chapter 2, one of the major problems in conducting research on hedge funds is potential data biases associated with reported hedge fund returns. Backfill and survivorship biases in the sample are reported in this section. Table 3.4 shows compounded annual returns 59

76 and standard deviations for i) Combined funds, ii) Live funds, as well as iii) Dead funds in the equal-weighted portfolio by investment styles. The information in this table was used to estimate backfill and survivorship biases for the sample of this thesis. Table 3.4 Returns and Standard Deviations by Investment Strategy This table presents returns and standard deviations for fund groups (Combined, Live and Dead Funds) by investment strategy with backfilled data and without backfilled data. With Backfill Data Without Backfill Data Compound Annual Return (%) Standard Deviation (%) Compound Annual Return (%) Standard Deviation (%) Combined Funds Live Funds Dead Funds Equity Hedge Fund-of-Funds Macro Relative Value Event Driven All Funds Equity Hedge Fund-of-Funds Macro Relative Value Event Driven All Funds Equity Hedge Fund-of-Funds Macro Relative Value Event Driven All Funds The backfill biases were calculated as the difference between the performance of funds with backfill data and that of funds without backfill data. Table 3.5 presents estimated backfill biases for i) Combined funds, ii) Live funds, as well as iii) Dead funds in the equal-weighted portfolio by investment style. 60

77 Table 3.5 Backfill Biases by Investment Strategy Combined Live Dead Equity Hedge 6.08% 3.73% 7.68% Fund-of-Funds 3.55% 2.88% 4.09% Macro 7.44% 6.24% 8.40% Relative Value 2.88% -0.07% 4.91% Event Driven 3.79% 1.11% 5.80% All Funds 5.06% 3.21% 6.42% As shown in the Table 3.4, the equal weighted portfolio of combined funds with backfill data returned 9.29% a year, while the combined funds without backfill data returned 4.23%. As a result, the backfill bias reported in Table 3.5 was estimated at 5.06% (9.29% %) a year for the combined funds. With the same method of estimating backfill bias for the combined funds, the live and dead funds presented the backfill biases of 3.21% and 6.42%, respectively. It should be noted that the dead fund database exhibited notably higher backfill bias than live funds. This result was caused by the fact that most dead funds performed poorly and voluntarily exited the database. Therefore, it is understandable that the performance of the dead funds without backfill data was relatively lower than their past unrevealed return history. As in previous studies, the survivorship bias was calculated as the difference between the performance of live funds and that of combined funds of live and dead funds. Table 3.6 shows survivorship biases calculated with backfill data and without backfill data. Table 3.6 Survivorship Biases by Investment Strategy With Backfill Data Without Backfill Data Equity Hedge 0.36% 2.71% Fund-of-Hedge Funds -0.09% 0.57% Macro 1.04% 2.24% Relative Value 1.24% 4.19% Event Driven 0.29% 2.97% All Funds 0.39% 2.24% 61

78 When backfill return data was included, combined funds generated compounded annual return of 9.29%, while only live funds showed a slightly higher return of 9.68% a year. This return difference of 0.39% (9.68% %) reported in the second column of Table 3.6 was the estimated survivorship bias per year for all funds with backfill data. On the other hand, funds excluding the backfill data were found to have greater survivorship biases. Combined funds without backfill fund data accomplished only a return of 4.23% a year, while live funds provided a greater return of 6.47% a year. As a result, an estimated survivorship bias for all funds without backfill data was 2.24% (6.47% %). For the funds without the backfill data, the survivorship bias estimate was higher than the bias estimated by funds with backfill data. This result was due to the fact that backfill bias in the Dead Fund database (6.42%) was higher than the bias estimated in the Live Fund database (3.21%). When investment strategies were examined separately, funds with the strategy of Relative Value were found to have the highest survivorship bias while Funds-of-Hedge Funds showed the lowest. After comparing the results with those of previous studies, we found that the survivorship bias in the HFR database was relatively lower than that in the TASS database. As indicated in Table 2.1, survivorship bias in the TASS database ranged from 2.24% to 6.70% while the survivorship bias in the HFR database was found to be only 0.60% by Liang (2000). When the current study estimated survivorship bias in the HFR database after excluding the backfill data, it increased from 0.39% to 2.24%. However, it was still lower than that of 5.13% estimated with the TASS database without the backfill data [Ibbotson et al. (2100)]. As Liang (2000) explained, the reason that the survivorship bias in the HFR database was lower than that in the TASS database was due to the relatively lower number of dead funds collected in the HFR. 62

79 3.2.2 The Estimation and Holdout Sample Given the purpose of this study was forecasting failures of HFs and FOHFs, it was essential to select an appropriate holdout sample on which to test the model s forecasting accuracy. The holdout sample consisted of funds not used in the estimation process, but which were representative of the mix of failed and non-failed funds in the estimation sample. For the purpose of this study, the Dead Funds were classified into failed funds and likely survivor funds prior to holding out funds from the Dead Fund database. It was performed by applying failure criteria 26 to the Dead HFs and FOHFs. Once the Dead HFs and FOHFs were classified into failed funds and likely survivor funds, it was possible to select the holdout sample. The likely survivor funds were considered as alive to differentiate them from the failed funds which had exited the database due to their poor performance. For a true test of predictive ability, the same proportion of failed funds as was the case in the estimation sample was selected for the holdout sample. This was also the case for the funds that survived which included live and likely survivor funds. Due to data limitations with the FOHFs, 40% of funds from each fund group were included in the holdout sample. 27 After fund allocation to the holdout sample, the estimation sample included 1688 HFs and 698 FOHFs, while the holdout sample contained 1125 HFs and 464 FOHFs. 26 The failure criteria are presented in Section With 40% of funds in each fund group being used as holdout sample, the number of failed FOHFs in holdout sample was

80 3.3 Methods Used to Estimate and Test the Cross-Sectional Relation between HF and FOHF Risk Measures Estimation of Risk Measures All the risk measures studied in this chapter were estimated in order to test cross-sectional variation in HF and FOHF returns. Eight risk measures including the standard deviation, semi-deviation, nonparametric VaR, Cornish- Fisher VaR, nonparametric expected shortfall, Cornish- Fisher expected shortfall, nonparametric tail risk and Cornish- Fisher tail risk were estimated using the same procedure. Monthly returns over the previous 36 to 60 months (as available) were used to estimate risk measures for each month within the test period. The test period started from January, 1995 and the estimation window started from January, That is, monthly returns between January, 1990 and December, 1994 were used to estimate risk measures as of January, This calculation was repeated by rolling the sample forward by one month ahead until the risk measure for December, 2009 was calculated. As a consequence, 180 months of timeseries data for each risk measure was obtained. As the number of funds at each month and their available return history were different across the sample, the number of estimated risk measures at each month was not identical. Funds having a return history of less than 36 months at a particular month were excluded from the estimation sample for that month Standard Deviation (SD) The standard deviation was firstly estimated to compare with other risk measures in terms of their ability to describe the cross-sectional variation in expected returns of HFs and FOHFs. Traditional risk management measures that include mean-variance analysis, the Sharpe ratio 64

81 and Jensen's alpha assume a normally distributed return and as such, incorporate standard deviation as a risk measure. However, it is well documented in the literature that hedge fund returns do not follow a normal distribution, which renders the standard deviation as an inappropriate risk measure for this type of fund. The standard deviation is defined as equation (3.1): SD t = 1 n t (R n t 1 i R 2 i=1 t ), R t = 1 n t R n i t i=1 (3.1) where n t is the number of returns in the estimation window at time t Semi-Deviation (SEMD) Compared to the standard deviation, semi-deviation is derived only from negative deviation from the mean. Intuitively, it is a plausible measure of downside risk and is calculated as follows: n t SEMD t = 1 Min{(R n t R ), t 0} 2 t t=1, R t = 1 R n i t i=1 (3.2) n t where n t is the number of returns in the estimation window at time t. This formula reveals that the semi-deviation gives a positive weight only to deviation below the mean return. That is, returns below the mean return increase semi-deviation, whereas returns above mean return do not. In effect, the semi-deviation defines risk as volatility below the mean return. Considering the fact that investors dislike low returns, a downside risk measure like semi-deviation is preferred especially when the return distribution is skewed negatively. 65

82 Value- at Risk (VaR) For some time, Value-at-Risk (VaR) was adopted as a main risk measurement in the investment industry. VaR was originally created to produce a single number that captures the total risk of a portfolio. For a given horizon time and confidence level of (1-α), VaR is defined as a threshold such that one can lose money greater than VaR with a probability α. Three essential decision variables are needed to estimate VaR. They are a confidence level, a set horizon and an estimation model. In this study, a 95% confidence level with a time horizon of one month and two different estimation models were employed. One of these estimation models is the nonparametric VaR, while the other is the Cornish-Fisher VaR Nonparametric VaR (VaR_np) As the name implies, nonparametric VaR does not impose any parametric assumption on the return distribution. It was estimated with reference to the lower tail of the empirical distribution. Put another way, nonparametric VaR 28 with 95% confidence level was calculated as the 5th percentile of all observations in an estimation window that included more than 36 observations Cornish-Fisher VaR (VaR_cf) This is a parametric VaR using the Cornish-Fisher (1937) expansion. In the traditional parametric VaR, returns are assumed to follow the normal distribution. This infers dependence on the mean and standard deviation of the returns. Under the normal distribution assumption, the critical value corresponding to a confidence level is determined from the distribution. That is, the 95% normal VaR is computed as in equation (3.3): VaR normal(95%) = (μ + z α σ) = (μ σ) (3.3) 28 It should be noted that nonparametric VaR calculated from 5th percentile should be multiplied by -1 to have the same direction of risk value as other risk measures. 66

83 where μ and σ are the sample mean and standard deviation of returns, respectively, and z α is the critical value from the standard normal distribution corresponding to the confidence level of (1 α) 100%. The returns of HFs and FOHFs do not all follow the normal distribution with negative skewness and leptokurtosis being a characteristic on the average 29. Therefore, another parametric VaR capturing higher-order moments was needed to explain nonnormality of HFs and FOHFs return. As a result, the Cornish-Fisher expansion was used in this study to correct the critical value. In practice, the Cornish-Fisher expansion computes the adjusted critical value through a function of the standard normal critical value, skewness and kurtosis of the return data. The Cornish-Fisher expansion was developed to obtain an approximation of any distribution using the moments of the distribution and a critical value from the standard normal distribution. That is, the α percentile of a return distribution is calculated by standardized moments of the distribution and the corresponding percentile of the standard normal distribution 30. The first four terms of the Cornish-Fisher expansion for the α percentile of the standardized return, R μ, are shown in equation (3.4): σ z α = z α (z α 2 1)S (z α 3 3z α )K 1 36 (2z α 3 5z α )S 2 (3.4) where S and K are the skewness and excess kurtosis of returns data, respectively, and z α is the critical value from the standard normal distribution with a (1 α) 100% confidence level. Like the normal VaR, the Cornish-Fisher VaR is computed from equation (3.5): VaR cf(95%) = (μ + z α σ) (3.5) As shown in equations (3.4) and (3.5), the Cornish-Fisher VaR incorporates higher-order moments (skewness and excess kurtosis) of the empirical return distribution. It follows that 29 See Fung and Hsieh(1999), Lo(2001), Agarwal and Naik(2001), Brown,Goetzmann and Liang(2002), Kat and Lo(2002) Amin and Kat(2003) among others. 30 See Jonson, Kotz and Balakrishnan (1994), Mina and Ulmer (1999) and Jaschke (2001) among others. 67

84 VaR cf(95%) equals to VaR Normal(95%) if the returns follow the normal distribution where skewness (S) and excess kurtosis (K) are zero Expected Shortfall (ES) Though it seems clear that VaR is employed as a useful measure of risk exposure in the investment industry, VaR has a number of limitations causing problems for hedge fund investors. VaR cannot completely capture the risk profile that hedge funds exhibit. This means that it does not give any information about the expected amount of loss when the return level breaches VaR and simply presents the starting point in the dangerous tail of the return distribution. That is, it does not tell anything about tail shape. It is also an unconditional measure of risk, which is less relevant than a conditional measure for investment strategies that react dynamically to changing market conditions. Furthermore, VaR is difficult to estimate without the assumption of the normal distribution of returns. Given the dynamic characteristics of HF and FOHF returns, it is reasonable to say that the standard VaR measures based on a simple and stationary distribution of returns do not seem to provide investors with a suitable insight to the risk of HF and FOHF investment. Artzner, Delbaea, Eber and Heath (1999) introduced coherent risk measures which fulfil the property of subadditivity. 31 This property is desirable for risk measures. However, various examples have shown that VaR lacks this desirable property of subadditivity. Furthermore, VaR provides information as to where the dangerous tail of return distribution starts, but it does not tell anything about tail shape. It fails to tell us how big the loss could be once it reaches VaR. In the case of heavy tailed distribution like those of HFs and FOHFs, losses much higher than VaR have to be taken into account in order to measure risk accurately. 31 It is also called monotonicity, translation invariance and positive homogeneity. 68

85 One of the noted members of coherent risk measures is expected shortfall (ES). ES considers losses above the VaR, and measures the expected loss greater than or equal to VaR. Hence, it is clear that ES is always greater or equal to VaR at a chosen confidence level. Liang and Park (2007) define ES as follows: ES t (α, τ) = E[R t+τ R t+τ VaR t (α, τ)] = VaR (α,t) v= vf R,t (v)dv F R,t [ VaR t (α,τ)] = VaR t (α,t) vf R,t (v)dv α (3.6) where R t+τ denotes the portfolio return during the period between t and t + τ, f R,t denotes the conditional probability density function (PDF) of R t+τ, F R,t denotes the conditional cumulative distribution function (CDF) of R t+τ conditional on the information available at time t, and VaR t (α, τ) denotes VaR during the period between t and t + τ at the confidence level of (1 α). In this chapter, both nonparametric and Cornish-Fisher ES were estimated as two measures. Once VaR_np (95%) was estimated within a monthly estimation window from January 1995 to December 2009, all returns less than or equal to VaR_np (95%) became the sample. ES_np (95%) was computed as the average of the new sample. ES_cf (95%) was calculated with the same method as ES_np (95%), except the returns from the estimation window were sorted on the basis of VaR_cf (95%) instead of VaR_np (95%) Tail Risk (TR) Tail risk (TR) was adopted in this study to capture the impact of extremely low returns. TR is derived from the deviation of returns from the mean return within each estimation window, for returns less than VaR. TR is defined in the following formula. TR t (α, τ) = E t [ R t+τ E t (R t+τ ) 2 R t+τ VaR t (α, τ)] (3.7) 69

86 As shown in the equation (3.7) above, TR is similar to semi-deviation except for being derived from returns below VaR rather than returns below the mean return. Both nonparametric TR and Cornish-Fisher TR were estimated. Nonparametric TR at the 95% confidence level (TR_np (95%)) was estimated with returns lower than VaR_np (95%), while Cornish-Fisher TR at 95% confidence level (TR_cf (95%)) used returns below VaR_cf (95%) Test at the Portfolio Level of HFs and FOHFs: Fama and French Method As mentioned above, the estimation period for risk measures started in January, 1990 and the test period was between January, 1995 and December, Having calculated risk measures for each month in the test period using the previous 36 to 60 monthly returns (as available), portfolios were formed on the each risk measure at each month. For each month, returns of HFs and FOHFs were ranked on the basis of their risk measure to construct 10 decile portfolios. Portfolio #1 contained the least average risk measure, while portfolio #10 included the highest average risk measure. This portfolio formation method is much the same as Fama and French (1992), with the exception that portfolios were updated on a monthly basis rather than yearly. For example, in January, 1995 risk measures for each fund were estimated by the return history from January, 1990 to December, 1994 and all funds were ranked into 10 equally weighted portfolios based on the rank of estimated risk measures. Once the portfolios were formed, the portfolio returns in January, 1995 (one month ahead estimation window) were calculated as the equal-weighted average of returns of individual funds in the same portfolio. By rolling over one month ahead, the risk measures were estimated for each fund and ranked according to the updated risk measures to form new portfolios. That is, the second estimation window for updating portfolios was from February, 1990 to January, 1995 and portfolios returns were computed in February, This 70

87 procedure was repeated until the 180th portfolio based on the estimation period between December, 2004 and November, 2009 was constructed. As a consequence, 180 time series of returns for the 10 equally weighted portfolios based on risk measures were obtained. These portfolios were generated and tested for i) Live HFs and Live FOHFs, ii) Dead HFs and Dead FOHFs, as well as iii) Combined HFs and Combined FOHFs. Then, as in the standard asset pricing literature, the difference between the returns of the most risky portfolio (portfolio #10) and the returns of the least risky portfolio (portfolio #1) were used in order to test the riskreturn trade-off for each risk measure Test at the Individual Level of HFs and FOHFs: A Cross-Sectional Regression The cross-sectional regression approach of Fama and Macbeth (1973) was used to test the risk-return trade off in HFs and FOHFs. The test period began in January, 1995 and finished in December, 2009 (180 months). Similar to Fama and French (1992), the cross-sectional one-month-ahead predictive regression was run to investigate the predictive power of risk measures at the individual fund level. The data from January, 1990 to December, 1994 was used to estimate the risk measures and then the January, 1995 cross-sectional returns were regressed on the lagged calculated risk measures. This procedure was repeated by rolling the sample forward by one month to generate risk measures and run the cross-sectional regressions until the whole sample was exhausted by December, For each month, the cross-sectional returns of the HFs and the FOHFs were separately regressed on the eight risk measures discussed above in order to compare their ability for describing the cross-sectional variation in expected returns. As a consequence, each fund had 180 sets of time series coefficient estimates of the eight risk measures which were used in the corresponding 180 cross-sectional regressions. 71

88 Univariate cross-sectional regressions were run for the 180 months using the following model: R it = α t + β t RM i,t 1 + ε it, (3.8) where R it is the realized return of fund i in month t and RM i,t 1 is the risk measure for fund i in month t-1. RM i,t 1 is specified by the standard deviation (SD), semi-deviation (SEMD), nonparametric VaR (VaR_np), Cornish-Fisher VaR (VaR_cf), nonparametric expected shortfall (ES_np), Cornish-Fisher expected shortfall (ES_cf), nonparametric tail risk (TR_np) and Cornish-Fisher tail risk (TR_cf) measures. Additional independent variables were incorporated into the analysis in order to distinguish age, size and liquidity effects from the relationship between risk and expected return. These characteristics of funds have been reported in the literature to be related to the cross-section of hedge fund returns. Ammann and Moerth (2005), Hedges (2003) and Herzberg and Mozes (2003) found that fund size impacted on hedge fund performance. Bali et al. (2007) and Liang and Park (2007) showed that fund age as well as size explained, to some extent, the expected return of a fund. Liang (1999), Liang and Park (2007) and Aragon (2007) found the liquidity premium in hedge fund returns using the lockup provision of the fund, so it was an another explanatory variable. Accordingly, monthly cross-sectional regressions were performed for the following univariate specifications to demonstrate the relationship between return and fund characteristics. R it = α t + β t Age i,t 1 + ε it (3.9) R it = α t + β t Ln(AUM) i,t 1 + ε it (3.10) R it = α t + β t Lockup i + ε it (3.11) 72

89 Age was calculated on a monthly basis. Fund size was measured by ln(aum), where AUM is fund s assets under management, and fund liquidity was measured by the lockup period on an annual basis. 32 Age, size and lockup effects were, therefore, controlled in order to study the relationship between expected return and risk measure for HFs and FOHFs. Multivariate cross-sectional regressions for 180 months were run using the following model. R it = α i,t + β 1t RM i,t 1 + β 2t Age i,t 1 +β 3t Ln(AUM) i,t 1 + β 4t Lockup i + ε i,t (3.12) For each risk measure, empirical tests were performed for i) Live HFs and Live FOHFs, ii) Dead HFs and Dead FOHFs, as well as iii) Combined HFs and Combined FOHFs using both the Live and Dead Fund databases. Following Fama and McBeth (1973), the time series of the parameter estimates from the cross-sectional regression were used to test the risk-return trade-off. That is, the time series means of the monthly regression slopes were used to determine which risk measures on average have non-zero expected premiums during the January, 1995 to the December, 2009 periods. Despite the fact that all funds in the database are regarded as a single asset class, the HFs and FOHFs are heterogeneous according to their strategies. Thus, the style effects were adjusted by adding strategy dummy variables to the univariate regression as well as multivariate regression. The univariate regression model for HFs and FOHFs with strategy dummy variables is as follows: R it = 4 s=1 D s α s,t + β t RM i,t 1 + ε i,t (3.13) The strategy dummy variables for HFs and FOHFs are presented in Appendix 3.A and 3.B, respectively. 32 The lockup period of fund without a lockup provision was set to zero. 73

90 In addition, univariate regression models for HFs and FOHFs with strategy dummy variables for age, size and liquidity effects are as follows. R it = 4 s=1 D s α s,t + β t Age i,t 1 + ε i,t (3.14) R it = 4 s=1 D s α s,t + β t Ln(AUM) i,t 1 + ε i,t (3.15) R it = 4 s=1 D s α s,t + β t Lockup i,t 1 + ε i,t (3.16) Similarly, the multivariate regression model for HFs and FOHFs with strategy dummy variables is specified below. R it = 4 s=1 D s α s,t + β 1t RM i,t 1 + β 2t Age i,t 1 +β 3t Ln(AUM) i,t 1 + β 4t Lockup i + ε i,t (3.17) 3.4 Survival Analysis and Cox Proportional Hazard (CPH) Model The objective of this study is to build powerful models for forecasting financial failure of individual hedge funds (HFs) and funds-of-hedge funds (FOHFs). This was achieved through the semi-parametric survival analysis approach known as the Cox (1972) Proportional Hazard Model. The concept of survival analysis and the Cox (1972) proportional hazard model is explained in the remainder of this section Introduction to Survival Analysis As noted by Kleinbaum and Klein (2005), Generally, survival analysis is a collection of statistical procedures for data analysis for which the outcome variable of interest is time until an event occurs. (p.4) That is, the objective of survival analysis is to establish the relationship between an observation s characteristics and the timing of a particular event. An 74

91 event is defined as a qualitative or a quantitative change that can be situated in time. The qualitative change refers to a transition from one discrete state to another, while the quantitative change means a quantitative variable crosses a predetermined threshold. Survival analysis is greatly useful for studying many different kinds of events Describing Survival Distributions The event of interest in this study is the financial failure of HFs and FOHFs. As such, the duration of a fund is the time period elapsed from a fund s inception date to its failure date. In survival analysis, the time at which events occur are assumed to follow some random process. The cumulative probability distribution of a fund s failure time, T, is thus given by: F(t) = Pr(T t) (3.18) where t is time, and Pr (T t) is the probability that a fund s failure time, T, is less than or equal to t. In survival analysis, however, it is usual to deal with the concept of a survivor function. The survivor function identifies the probability that a fund survives past time t and is expressed as: S(t) = Pr(T > t) = 1 F(t) (3.19) Another common way to describe a probability distribution of a continuous variable is the probability density function. In survival analysis, the probability density function can be defined as: f(t) = df(t) dt = ds(t) dt (3.20) 33 The survival analysis is also known by several different names across different fields: event history analysis (sociology), reliable analysis (engineering), failure time analysis (engineering), duration analysis (economics), and transition analysis (economics). 75

92 In the empirical estimation of the survivor function, the hazard function, h(t), is used as a way of describing distributions. The hazard function measures the risk that a fund will fail in a small interval of time between t and t + t, conditional on the fund surviving until time t. That is: h(t) = lim t 0 Pr (t T<t+ t T t) t (3.21) The hazard function is used to quantify the instantaneous risk that an event will occur at time t. It is a rate. By definition, the hazard function does not represent the instantaneous probability of an event time t, because it can be greater than 1. It is unobserved and is seen as a fund s characteristic. That is, each fund can be represented by its own hazard function which can be estimated from the fund s data. Having estimated the hazard function, the survivor function can be derived using the hazard function as follows: h(t) = lim t 0 Pr(t T<t+ t T t) t = lim t 0 F(t+ t) F(t) ts(t) = f(t) = 1 df(t) = 1 d(1 S(t)) = 1 ds(t) = dlns(t) S(t) S(t) dt S(t) dt S(t) dt dt (3.22) t h(u)du 0 = lns(t) (3.23) t 0 S(t) = exp h(u)du (3.24) The equation (3.24) above exhibits a probability of survival beyond time t, and can be used to generate a probability of a survival at particular duration time. Put another way, the hazard function makes it possible to predict the survival probability of a fund. It is clear that the central factor of an accurate funds failure forecasting model is an appropriate estimation of its hazard function. 76

93 Censoring The basic concept in survival analysis is the risk set which is defined as the set of all individuals who are at risk of the event occurrence at each point in time. At the end of each point in time, the risk set is adjusted by deleting the number of individuals who not only have experienced the event in that period of time, but also those who have been censored. The observations are called censored when information about the time they experience the event is not given. As pointed in Rouah (2005), it is essential to include the Live Funds as well as the Dead Funds in the risk set for this study. Inclusion of only the Dead Funds in the risk set would lead to downward bias of the funds survival time. This is because the lifetimes of the Live Funds (censored funds) also provide information about the survival time of the funds in the database. Censoring occurs in many forms and for many different reasons. An observation on a variable T, which is the time of occurrence for an event like fund failure, is right censored if all information about T is beyond some point in time. Symmetrically, left censoring occurs when all information about T is that prior to some point in time. The hedge fund sample for this study had only right censored funds which were found in the Dead Funds as well as the Live Funds. The time period for this study began at a fund s initial date of joining the HFR and ended for all remaining in the study at December, Hence, it was obvious that all Live Funds at the end of the time period were censored because all information about T was that it was sometime after December, In contrast, identifying censored funds in the Dead Fund database was not straightforward. Some funds may have exited from the database prior to the end of some time period because of their financial failure, while others for reasons other than the event. That is, the Dead Fund database included funds which stopped reporting in spite of satisfactory performance, as well as funds suffering from poor performance. That is, all funds in the Dead Fund database had certainly not failed due to poor 77

94 performance. Therefore, the Dead Funds needed to be classified into censored and failed funds in order to construct more accurate prediction models for financial failure. Figure 3.1 and Figure show hypothetically censored and financially failed funds from the Live and Dead Fund databases, respectively, across the time period of this study. The funds entered the study at different times because each fund joined the HFR at a different date. The length of the line denotes the duration of the fund. An O marker indicates that the fund was censored at that point in time, while an X marker represents a fund that financially failed at that point in time. Figure 3.1 Hypothetical Censored Funds from the Live Fund Database Funds A B C D May 1996 Dec 2009 Time Period 34 The time horizon in the figures starts from May, 1996 which is the first initial date of funds joining the HFR for HFs and FOHFs. 78

95 Figure 3.2 Hypothetical Censored Funds from the Dead Fund Database Funds A B C D May 1996 Dec 2009 Time Period As mentioned above, all funds in the Live Fund database were censored at the end point of the time period (December, 2009), while for the Dead Fund database, some were censored and others experienced the event The Time Origin In survival analysis, the choice of origin time (0 point) can be problematic [Allison (1995)]. A fund s initial date of joining the HFR was determined to be its time origin in this study by considering backfill bias and following the criteria for choosing the time origin as the onset of continuous exposure to the risk of the event. The estimation model can be classified into two groups depending on the arrangement of the time origin. They are event time model and the calendar time model. Under the event time model, the time scale is defined as fund duration. Hence, all funds start at time 0 which is a fund s initial date of joining the HFR and finish at failure time or censoring time. In contrast, 79

96 the calendar time model establishes the time scale in chronological order starting from the first observation in the dataset. Figure 3.3 and Figure 3.4 present observations arranged in event time and calendar time, respectively. Figure 3.3 Observations Arranged in Event Time Funds A B C D E Event Time Figure 3.4 Observations Arranged in Calendar Time Funds A B C D E Calendar Time 80

97 When observations are arranged in calendar time and their duration is fully included in the time period, both the duration effect and calendar effect are reflected in the underlying hazard function. That is, it is no longer possible to establish the duration effect alone. Also, it seems to be clear that there is no need to incorporate economic indicators and other time dependent covariates that are specific to a particular time in a calendar time model. Given that the objective of this study is to forecast failure of funds outside the time period of the estimation sample, the calendar time model is seen to be inappropriate. This is because the calendar effects are only specific up to the time period of the estimation sample and, as such, fail to take advantage of information available from other time periods outside the specified time period. As a consequence, event time modelling was employed in this study Cox (1972) Proportional Hazard Model with Fixed Covariates A robust model for predicting financial distress in hedge funds is the semi-parametric survival analysis technique developed by Cox (1972) and known as the Cox Proportional Hazards (CPH) model. Survival analysis is concerned with predicting the probability and timing of a particular event. The event of interest in this study is the financial distress of hedge funds. The time until the occurrence of the event is best described by the hazard function. The hazard rate defines the instantaneous rate of change from a non-failed to failed state at time t, given survival until time t. It is often referred to as the instantaneous probability of failure. Fundamental to an accurate forecast model will be an appropriate estimation of the hazard function. This is achieved using the Cox Proportional Hazards (CPH) model. The basic CPH model does not incorporate time-varying covariates and is usually written as: 81

98 h i (t) = λ 0 (t)exp (β 1 x i1 + + β k x ik ) (3.25) This equation incorporates two factors in the hazard for a hedge fund, i, at time t. They are: (1) A baseline or underlying hazard function, λ 0 (t), which represents the hazard function for a hedge fund whose covariates all have values of zero. The baseline hazard function λ 0 (t) is left unspecified, except that it cannot be negative. (2) The exponential of a linear function of k fixed covariates. The hazard function given by equation (3.25) is called the proportional hazards model because the hazard for any hedge fund is a fixed proportion of the hazard for any other hedge fund. This is shown by equation (3.26) below: h i (t) = λ 0 (t)exp (β 1x i1 + +β k x ik ) = exp {β h j (t) λ 0 (t)exp (β 1 x j1 + +β k x jk ) 1 x i1 x j1 + + β 1 x ik x jk } (3.26) As can be seen from the equation (3.26), the baseline hazard function, λ 0 (t), cancels out, resulting in the ratio of the hazards for any two hedge funds being constant over time. In this model, λ 0 (t) needs not be specified. However, this implicitly assumes that the effect of the covariates on the risk of funds failure should be constant over time and that the log hazard functions of any two individuals should be strictly parallel. This allows for the estimation of the baseline hazard function, λ 0 (t). Given this feature, the coefficients of the proportional hazard model can be estimated through the partial maximum likelihood method Partial Likelihood Estimation Once the cross-sectional CPH model is specified, the coefficients of the model can be estimated by partial likelihood method. A partial likelihood is defined as a product of the 82

99 likelihoods for all the observed events. Thus, where I is the number of events, the partial likelihood function can be written as: I PL = i=1 L i (T i ) (3.27) L i (T i ) is the probability that an individual fund i has an event at time T i, conditional on its survival until T i. Put another way, it is the probability that at time T i the event occurred to fund i rather than to any of the other funds who had survived up to time T i. Therefore, the likelihood of the ith event, L i (T i ), can be given by the ratio of the fund i s hazard to the sum of the hazards for all other funds in the risk set at time T i, namely R(T i ). L i (T i ) is represented as: L i (T i ) = h i (T i ) h(t i ) j R(T i ) = λ 0 (T i )exp (β 1 x i1 + +β k x ik ) λ 0 (T i )exp (β 1 x j1 + +β k x jk ) j R(T i ) = exp (β 1 x i1 + +β k x ik ) exp (β 1 x j1 + +β k x jk ) j R(T i ) (3.28) In the case of equation (3.28) above, the underlying hazard function cancels. This enables the partial likelihood method to estimate the coefficients without the need to specify the underlying hazard function. Also, it should be noted that the risk set is adjusted at the end of each failure time by deleting the number of funds not only that have previously experienced the event in that period of time, but also that have been censored. Another interesting feature of the partial likelihood estimates is that, as a result of the elimination of the underlying hazard function, they depend only on the ranks of the event time and not the exact (calendar) time of each event. This also means that the partial likelihood method is valid only for data in which no two events occur at the same time. As it is quite general for data to have same event time, an alternative formulation should be applied to handle this situation. 35 Figure Most statistical programs handle tied data. The exact method of handling tied data was applied in this study. This method assumes that there is some underlying order in the events which have been aggregated into discrete event times. This method provides true partial likelihood estimates [Allison (1995)]. 83

100 illustrates how to calculate the likelihood for the failure of two hypothetical funds of A and C in a proportional hazard model with fixed covariates. Figure 3.5 Calculation of the Likelihood Function for Failure in a Fixed Covariate Model The length of the line denotes the duration of the fund. An O marker indicates that the fund is censored at that point in time, while an X marker represents that the fund financially failed at that point in time. The x i indicates a vector of covariate values of fund i and a marker represents applied covariate values. X A L A (1) = exp(β 1 x A1 + + β k x Ak ) j {A,B,C,D} exp β 1 x j1 + + β k x jk X B X C L C (3) = exp(β 1 x C1 + + β k x Ck ) j {C,D} exp β 1 x j1 + + β k x jk X D Event Time As shown in the above figure, the likelihood for a fund failure is calculated using covariate values at the beginning of the time period. That is, the same values of covariates are used to estimate the coefficients for each fund in the risk set regardless of the time. As a result, the hazard ratio is expected to be constant over the time. When the failure likelihood of fund C is calculated, the risk set includes only fund C and D because fund A and B have disappeared by failure and censoring, respectively. Given L i for all i, the partial likelihood can be expressed as: 84

101 I exp(β 1 x i1 + +β k x ik ) PL = i=1 (3.29) j R T exp β 1 x j1 + +β k x jk i Once the partial likelihood has been constructed, the coefficients, β, can be estimated by maximising the partial likelihood function with respect to β. As usual, it is more convenient to maximize the logarithm of the partial likelihood function, which is I I log PL = i=1(β 1 x i1 + + β k x ik ) i=1 log j R(T i ) exp β 1 x j1 + + β k x jk (3.30) The resulting estimates are consistent and asymptotically normal, but not fully efficient since some information about β is discarded in the partial likelihood function. In most cases, however, the loss of efficiency is quite small [Efron (1977)] Estimating Survivor Functions As revealed above, the proportional hazard model leaves the underlying hazard function unspecified and the partial likelihood method discards some information about the dependence of the hazard on time. Notwithstanding, it is possible to have nonparametric estimates of the survivor function based on a fitted proportional hazard model. The Cox survival model including only fixed covariates can be derived as follows: t S(t) = exp h(u)du 0 t = exp λ 0 (u) exp(β 1 x β k x k ) du 0 t = exp λ 0 (u)du {exp(β 1 x β k x k )} 0 = [S 0 (t)] exp(β 1x 1 + +β k x k ) (3.31) where S(t) is the survival probability at time t for a fund with covariate values of t 0 (x 1,, x k ), and S 0 (t) = exp λ 0 (u)du is the baseline survivor function which 85

102 represents the survivor function for a fund whose covariates all have values of zero. Once coefficients β have been estimated by partial likelihood, the baseline survivor function S 0 (t) can be estimated by a nonparametric maximum likelihood method. Then, the survivor function for any set of covariate values across the time period can be estimated by substitution in the survivor function formula. Once the baseline survivor function has been generated across the entire time period, it is possible to obtain predictions about survival time for particular sets of covariates. When predictions are generated, it is conventional to focus on a single summary measure rather than the entire distribution. The median survival time can be easily acquired by finding the smallest value of t such that S(t) Assessing Predictive Accuracy The main purpose of this study is to construct models capable of predicting failure of HFs and FOHFs. As such, it is essential to test the model s predictive power. The important process of testing for predictive accuracy involves fitting survival curves to each HF (or FOHF) from a holdout sample, selecting a point in time at which to evaluate the financial position of a fund, and then evaluating the ability of the models to predict financial distress in an ex-post fashion. That is, the probabilities of the survival curves are converted into a statebased prediction according to a cut-off probability. Above this cut-off probability funds are considered as survivors and failures otherwise. However, establishing an optimal cut-off probability is by no means a trivial task. The Relative Operating Characteristic (ROC) curve, derived from the Signal Detection Model (SDM), overcomes the problem of selecting an optimal cut-off probability. In the current study, each model s forecasting accuracy was quantified by calculating the area under the ROC curve (AUROC) for each forecasting model. 86

103 3.5.1 Survival Function Prior to assessing the predictive ability of the estimated models to forecast failure in HFs and FOHFs, it is necessary to generate survival probabilities at every failure time for all funds in the holdout sample. Once the hazard rate of each fund was estimated from the CPH model, the survival function of the fund was generated. The Cox (1972) survival model with fixed covariates can be written as equation (3.32). S(i t ) = [S 0 (i t )] exp(β x) (3.32) where S(i t ) is the survival probability at time t for a fund i with a vector of covariate values x, and S 0 (i t ) is the survivor function for a fund i whose covariate values are all zero. After estimating the vector of coefficients, β, by the partial likelihood method, the baseline survivor function, S 0 (i t ), can be estimated by a nonparametric maximum likelihood method. Following the estimation of the baseline survivor function, the estimated survivor function for any set of covariate value can be generated by substitution in the equation (3.32) Signal Detection Model The first step in assessing the predictive ability of the estimated models to forecast failure in hedge funds was to examine from a holdout sample the probability distributions at selected failure times, across groups of failures and survivors. By comparing the distributional characteristics of the two forecast groups, the forecast skill of the CPH models used in this study was ascertained. This was achieved by use of the Signal Detection Model (SDM) to determine the costs and benefits from different thresholds of cut-off probability that were used to identify hedge fund failure. A survival probability was generated for each fund from both the failed group and the 87

104 survivors in a holdout sample. In the SDM, the occurrence of an event (failure) was preceded by a signal in the data. A fund s estimated survival probability represented the signal, but it did not provide an obvious conclusion as to occurrence or non-occurrence of the fund s failure. The forecast of occurrence, or non-occurrence of the fund s failure was determined on the basis of a cut-off probability (s) such that, for a given failure time t, a fund was forecasted to fail when S(i t ) s, and not so otherwise. Figure 3.6 below is an idealized example of how the Signal Detection Model (SDM) distinguishes between the two states of failure and survival. Figure 3.6 Signal Detection Model The figure is an example of the Signal Detection Model. The horizontal axis represents the probability of survival, while the vertical axis is the density of forecasts corresponding to each point on the horizontal axis. The hit rate (H) is calculated as the area under the failures curve and to the left of the some nominated probability of survival, s. It is represented by a line vertical to the horizontal axis. The false alarm rate (F) is the area under the survivors curve and to the left of the same nominated probability of survival line. As expected, the probability density function of failures, f 1 (S, t), lies somewhere to the left of the probability density function of survivors, f 0 (S, t). 88

105 The forecasting ability is commonly evaluated by the hit rate, H. A hit (H) occurs when the occurrence of the event of financial distress is correctly predicted, given a nominated probability threshold level (the nominated cut-off probability for survival along the horizontal baseline). Thus, the hit rate (H) is the proportion of hedge funds experiencing financial distress that are correctly forecasted. So it is represented by the part of the failure s probability function, f 1 (S, t), lying to the left of the cut-off probability, s, and is given by: s H = f 1 (S, t)ds 0 (3.33) Alternatively, a false alarm is the occurrence of survival when failure is predicted. Accordingly, the false alarm rate (F) is the proportion of surviving hedge funds that are incorrectly forecasted as funds subjected to financial distress. It is represented the part of the survivor s probability density function, f 0 (S, t), lying to the left of the same cut-off probability, s, and is given by: s F = f 0 (S, t)ds 0 (3.34) The probability density of the two observed states (failures and survivors) was determined for all hedge funds in a holdout sample, producing a result corresponding to that in Figure 3.6 above. As shown in Figure 3.6, the hit rate and the false alarm rate vary as the cut-off probability changes because there is substantial overlap between the probability density functions for survivors and failures. That is, the selection of the cut-off probability entails a trade-off between the hit rate and the false alarm rate. As a consequence, it is impossible to separate completely the two groups on the basis of the cut-off probability as long as the probability density functions overlap. Accordingly, an optimal cut-off probability should be determined 89

106 by the combination of H and F that the decision maker is willing to accept on the basis of the relative cost of Type I error and Type II errors Relative Operating Characteristic (ROC) Curve and AUROC Once the probability distributions for failures and survivors have been determined, the Relative Operating Characteristic (ROC) curve can be plotted. As shown in Figure 3.7 below, the ROC curve is a representation of the hit rate, H (y-axis), against the false alarm rate, F (xaxis), as the probability threshold value, s, varies. Figure 3.7 is an example of a ROC curve generated by a typical SDM. As is evident from Figure 3.6, a low survival threshold, s, leads to low false alarm rates, but also small hit rates. As the decision threshold, s, decreases, H and F vary together according to the skill of the forecasting model. The dotted line running through the centre of the figure represents a forecast model with zero skill. A zero skill model would be represented by the linear ROC curve where H = F. A curve running up the y-axis to the point (0,1) and along the x-axis to the point (1,1) is a model with 100% forecast accuracy. High values of s will often result in high H and F rates. One would expect that a model offering predictive value would fall somewhere between these two boundaries. This process provided a robust method from a statistical standpoint for confirming that the model was able to predict financial distress for HFs and FOHFs. 90

107 Figure 3.7 Relative Operating Characteristic Curve The figure is an example of a ROC curve generated by a typical Signal Detection Model. As the decision survival threshold changes, hit rate and false alarm rate vary together according to the skill of the forecasting model. Importantly, it also makes it possible to quantify the predictive ability of a model by calculating the area under the ROC curve (AUROC). A perfect forecasting model provides AUROC of 1, while a model which has accuracy equal to that of chance represents AUROC of 0.5. The predictive ability of competing models can be evaluated by directly comparing the AUROCs. In the current study, several evaluation times were selected to assess forecasting accuracy and the results of predictive ability were compared across the different evaluation times and model specifications. 91

108 Chapter 4 - Risk and Return in Hedge Funds and Funds-of-Hedge Funds: A Cross-Sectional Approach Introduction The hedge fund industry has increased significantly over the past few years. Hedge Fund Research (HFR) Industry Report (Year End 2010) estimated that there were 9,237 hedge funds worldwide with at least US$1.9 trillion worth assets under management in Traditional investment strategies adopted by institutional investors had failed to satisfy their objectives in terms of return and risk, which had led investors to seek new ways of diversification. Many high-net-worth individuals, as well as institutional investors, have shown growing interest in hedge funds. With fund-of-hedge funds (FOHFs) being vehicles that provide combined investments in individual hedge funds (HFs), investment in them has been open to a wide range of investors. On the other hand, only institutions and high-networth individuals are allowed to invest in individual hedge funds (HFs). A large part of growth in hedge fund industry was due to an increase in the number of FOHFs. The HFR Industry Report in 2010 presented that most investors have increasingly adopted FOHFs as the preferred investment vehicles and they were estimated to account for 20% to 25% of global hedge fund industry assets at the end of FOHFs became more favoured by various investors given that FOHFs usually demand less initial investment than the HFs. As the name indicates, FOHFs invest in a number of HFs for the purpose of diversifying fund risk. This allows investors to allocate assets in dynamic market conditions. Additionally, FOHFs have a different fee structure from that of HFs. 36 This study was accepted for publication by The Australian Accounting Business and Finance Journal in May,

109 While a HF charges a management and incentive fee, a FOHF charges extra fees at the underlying HF level as well as management and incentive fees at the FOHF level. As a consequence, in some cases, FOHF investors might pay more fees than the total realized return in the investment. It is an interesting question as to whether it is worthwhile for investors to pay these extra fees. Theoretically, holding a portfolio of HFs must be less risky than investing in HFs. Despite the increasing significance of FOHFs in the development of the hedge fund industry, the risk and return characteristics of FOHFs are not well established in the literature. Most existing research on hedge fund performance showed that hedge funds exhibited better performance on a risk-adjusted basis relative to standard asset categories such as equity and bonds [Ackerman et al. (1999), Asness et al. (2001), Brown et al. (1999) among others]. On the other hand, the extant evidence on FOHF performance was that they had a tendency to underperform hedge fund indices by small but significant amounts [Brown et al. (2002), Liang (2004),]. Furthermore, a number of studies showed that the returns announced by HFs and FOHFs were not normally distributed with excess kurtosis and negative skewness [Fung and Hsieh (1997), Amin and Kat (2003), Agarwal and Naik (2004), Huston et al. (2006) among others]. Due to the nature of negative skewness and excess kurtosis in HF and FOHF returns, any risk estimation which assumes a normal distribution of returns would severely underestimate the actual risk exposure. Nevertheless, according to Amenc et al. (2004), only 2% of European multi-managers have paid attention to the skewness and kurtosis of the return distribution. Also, they revealed that most European multi-managers have continued to prefer the traditional mean-variance framework to monitor manager performance. This was confirmed by the fact that 82% of multi-managers adopted the Sharpe ratio as an important indicator [Amenc et al. (2004)]. 93

110 The objective of this chapter is to examine whether the available data on HFs and FOHFs can reveal the risk-return trade-off and, if so, to find an appropriate risk measure that captures the cross-sectional variation in HF and FOHF returns. The current research extends that of Liang and Park (2007) by focusing on the comparison of the risk-return trade-off in HFs and FOHFs and including recent hedge fund data which covered a period of Global Financial Crisis (GFC). Understanding the risk-return relationship in HFs and FOHFs will greatly help investors build more profitable investment strategies. With the dramatic growth of HFs and FOHFs, it is essential to find the most appropriate risk measures that capture the cross-sectional variation in these types of funds. Traditional risk management such as mean-variance analysis, the Sharpe ratio and Jensen's alpha assume a normal distribution measure of returns. As a consequence, the traditional measures of returns incorporate the standard deviation. This would appear to be inappropriate for risk measures of HFs and FOHFs. In order to overcome this problem, the focus in this chapter is on alternative risk measures such as semi-deviation, Value-at-Risk (VaR), expected shortfall and tail risk. They were compared with standard deviation in terms of their ability to describe the crosssectional variation in expected returns of HFs and FOHFs. Firstly, the various estimated risk measures were analysed at the portfolio level of HFs and FOHFs by adopting the Fama and French (1992) approach. Secondly, the estimated risk measures were compared at the individual HF and FOHF levels by using univariate 37 and multivariate cross-sectional regressions. Additional independent variables were incorporated into the analysis in order to distinguish age, size and liquidity effects from the relationship between risk and expected return. These regressions were run with and without investment 37 The univariate regression model is a simple regression model where one variable is regressed on another variable. 94

111 strategy dummy variables. The results from both HF and FOHF data were then analysed to show if there existed any difference between them. Liang and Park (2007) analysed the risk-return trade-off with the same risk measures adopted in this chapter but using only HF data. They found that the expected shortfall using the Cornish-Fisher expansion captured the cross-sectional variation in expected returns of HFs better than did other risk measures studied. In the present study, the risk and return characteristics of FOHFs turned out to be different from those of HFs. However, the crosssectional regression results using HFs were similar with those of Liang and Park (2007) except for the regression involving VaR. There is invariably a clear trade-off between risk and expected return. One cannot be viewed without consideration of the other. A risk-return target employed by hedge funds is not the same as that of traditional investments such as stocks, bonds and mutual funds. Most hedge fund investors expect high returns to compensate them for the corresponding risks that they are exposed to. Risk measures for HF and FOHF investments are particularly important due to the illiquid character of the investments, the long lock-up periods on capital and the infrequent redemption notice periods enforced on investors. The remainder of this chapter is arranged as follows: Section 4.2 contains the empirical results and section 4.3 concludes the chapter. 95

112 4.2 Empirical Results Results at the Portfolio Level of HFs and FOHFs Table 4.1 shows the cross-sectional relation at the portfolio level between the Cornish-Fisher expected shortfall (ES_cf) at the 95% confidence level and expected returns for all HFs and FOHFs based on the sample of Live, Dead and Combined Funds. The time-series (180 months) average returns and ES_cf of the ten portfolios formed by ranking the ES_cf are presented in the Table 4.1. Table 4.1 Average Returns of HF and FOHF Portfolios Formed According to a 95% Cornish-Fisher Expected Shortfall: January, 1995 to December, 2009 Portfolios were formed on a monthly basis. For each month, 10 equally weighted portfolios were formed on the basis of ranked values according to a 95% Cornish-Fisher expected shortfall estimated from the previous 36 to 60 monthly returns (as available) for each HF and FOHF. The table shows the 95% Cornish-Fisher expected shortfall and returns of each portfolio calculated from HFs and FOHFs. The reported 95% Cornish-Fisher expected shortfall is the time-series (180 months) average of the average 95% Cornish-Fisher expected shortfall of all HFs and FOHFs in each portfolio. The reported return is the time-series (180 months) average of the monthly equal-weighted portfolio returns (in percent). HF FOHF Live Dead Combined Live Dead Combined Low ES_cf 2 ES_cf 3 ES_cf 4 ES_cf 5 ES_cf 6 ES_cf 7 ES_cf 8 ES_cf 9 ES_cf High ES_cf ES_cf Return ES_cf Return ES_cf Return ES_cf Return ES_cf Return ES_cf Return All 96

113 The results from the alternative eight risk measures are similar 38. As an example of monotonicity of average returns, we focused on a particular risk measure, Cornish-Fisher expected shortfall, given in Table 4.1. The results in Table 4.1 indicate that, for ES_cf, when moving from a low risk portfolio to a high risk portfolio, there was almost a monotonic increase in the average return of HFs in the Live and the Combined Fund. The monotonically increasing risk-return relation did not appear for the case of Dead HFs. This might be caused by the fact that some funds with very high risk and negative return eventually joined the Dead Fund database. By contrast, all the samples of Live, Dead and Combined FOHFs rarely showed this monotonically increasing risk-return relationship. It can be observed in Table 4.1 that when they were compared within the same portfolio, the average value of the ES_cf risk measures for all HFs were always greater than that corresponding to the FOHFs except for the low ES_cf portfolio. Table 4.2 shows the average return differential between the low risk portfolio and high risk portfolio. The p-value in brackets was obtained from the nonparametric Wilcoxon test 39 for the average return differential for Live Funds, Dead Funds, and Combined Funds. 38 The results from the other risk measures are presented in Appendix 4.A. 39 It is well established in the literature that the reported returns of HFs and FOHFs are not normally distributed and, therefore, a parameter t-test is not appropriate. 97

114 Table 4.2: Test for Average Return Differential between the Most Risky Portfolio and the Least Risky Portfolio Return Differential HF FOHF Live Dead Combined Live Dead Combined High SD - Low SD % (0.0099) % (0.2234) % (0.0108) % (0.1229) % (0.8474) % (0.6290) High SEMD - Low SEMD % (0.0104) % (0.2499) % (0.0114) % (0.0931) % (0.7466) % (0.5129) High VaR_np - Low VaR_np % (0.0540) % (0.2622) % (0.0287) % (0.3706) % (0.5651) % (0.9427) High VaR_cf - Low VaR_cf % (0.0554) % (0.5367) % (0.1254) % (0.3509) % (0.4097) % (0.9411) High ES_np - Low ES_np % (0.0143) % (0.4260) % (0.0399) % (0.3006) % (0.6398) % (0.5970) High ES_cf - Low ES_cf % (0.0169) % (0.3239) % (0.0614) % (0.2834) % (0.5234) % (0.7245) High TR_np - Low TR_np % (0.0130) % (0.1799) % (0.0127) % (0.1799) % (0.7713) % (0.5012) High TR_cf - Low TR_cf % (0.0087) % (0.2461) % (0.0245) % (0.2566) % (0.9394) % (0.4493) Although the return differentials between the high risk portfolio and the low risk portfolio were not the same across the eight risk measures, the test results were, nevertheless, similar. From Table 4.2, the Live HF samples showed that the average return of the low risk portfolio differed significantly from the average return of high risk portfolio at the conventional significant levels. This was true for all risk measures. In the case of the Dead HFs, there were no significant differences between the average returns of the low risk portfolio and the high risk portfolios. Funds in the Combined HFs presented similar results across all the risk measures except for the portfolio formed by VaR_cf, which showed an insignificant result. The differences in the average returns of the low risk and the high risk portfolios for risk measures including the SD, SEMD, VaR_np, ES_np, TR_np and TR_cf were all significant at the 5% level, whereas, for ES_cf they were significant at the 10% level. 98

115 The results for the FOHFs contrasted with those of HFs. All portfolios in the Live, Dead, and Combined FOHFs did not indicate a significant average return differential between the low risk portfolio and the high risk portfolio in all eight risk measures. These results can be expected from the fact that the FOHFs did not show any monotonically increasing relationship between risk and return as shown in Table 4.1. It should be noted that in almost all FOHF portfolios, the average differential calculated by subtracting the average return of the low risk portfolio from the average return of the high risk portfolio was a negative value 40. Also, it can be observed that the value of return differential for all HFs was always higher than that corresponding to the FOHFs. This was true for all eight risk measures. As a consequence, the cross-sectional relationship between risk and return of FOHFs was observed to be not the same as that of HFs. Figure 4.1 presents returns of the Combined HF and Combined FOHF portfolios formed by ranking the ES_cf in order to compare the crosssectional relationship between the risk and return of HFs and FOHFs. The figures for the alternative eight risk measures were very similar 41. Figure 4.1 Returns of Portfolios Sorted by 95% ES_cf: January, 1995 to December, 2009 Returns (%) Portfolio Sorted by ES_cf Combined HF Combined FOHF 40 For the Live FOHF portfolios formed by SD, SEMD and VaR_np, the average return differential between the low risk portfolio and high risk portfolio was a positive value. 41 The figures for the other risk measures are presented in Appendix 4.B. 99

116 As can be seen from the Figure 4.1, the ES_cf risk measure presented different risk-return trade-off between HFs and FOHFs. The generally accepted risk-return relationship was found in the case of the HFs. However, FOHFs did not show the monotonically increasing riskreturn relationship. These results suggested that, even though HFs were more volatile than FOHFs, investing in FOHFs could be riskier than investing in HFs if the investment decision was only based on this interpretation of the risk-return relationship. Overall, while the risk-return trade-off for HFs can be found from the available data, the FOHFs barely disclose a clear relationship between risk and return. As indicated above, the results from the analysis across the eight alternative risk measures at the portfolio level were similar. This made it difficult to conclude that there was an appropriate risk measure capturing cross-sectional relationship between risk and return for both HFs and FOHFs. One lesson from this analysis is that investors should bear in mind the different risk-return relationships between FOHFs and HFs and be more cautious about investment in the FOHFs than in HFs due to the unanticipated risk-return relationship of FOHFs Results at the Individual Level of HFs and FOHFs: A Cross-sectional Regression According to the empirical results from the analysis at the portfolio level, the available data on HFs seemed to reveal the risk-return trade-off. However, all risk measures presented a similar significance level for testing the difference of average returns between the low risk portfolio and the high risk portfolio. This result made it difficult to determine an appropriate risk measure to capture the cross-sectional variation. Furthermore, it should be noted that fund specific information could be lost when we tested at the portfolio level, although aggregating may produce more reliability in the statistical testing process. 100

117 Before conducting cross-sectional regressions for risk measures, univariate cross-sectional regressions of HF and FOHF returns on age, size and liquidity were performed to test the significance of these fund characteristics. Table 4.3 shows the results of these regressions. Table 4.3 Univariate Cross-Sectional Regressions of HF and FOHF returns on Age, Size and Liquidity: January, 1995 to December, 2009 The average slope is the time-series (180 months) average of the monthly cross-sectional regression slopes for January, 1995 to December, The p-value in brackets was obtained from a standard t- test. Age was calculated on a daily basis. Fund size was measured by ln(a) where A is funds assets under management. Fund liquidity was measured by lockup period on a yearly basis. Panel A shows the results from univariate cross-sectional regression for HFs without HF strategy dummy variables as defined in equation (3.9) to (3.11) and with HF strategy dummy variables as defined in equation (3.14) to (3.16). Panel B shows the results from univariate cross-sectional regressions for FOHFs without FOHF strategy dummy variables as defined in equation (3.9) to (3.11) and with FOHF strategy dummy variables as defined in equation (3.14) to (3.16). Panel A : Cross-Sectional Regressions for HFs Model Without Fund Strategy Dummy Variables With Fund Strategy Dummy Variables Live Dead Combined Live Dead Combined Age ln(a) Lockup Beta R^2 Beta R^2 Beta R^ % 0.57% 0.83% (0.0002) (0.0000) (0.0316) % 0.61% (0.0000) (0.0000) (0.0094) % 0.40% (0.0000) (0.0000) (0.0044) % 7.32% (0.0000) (0.0000) (0.0608) % 6.04% (0.0000) (0.0000) (0.0011) % 5.74% (0.0000) (0.0000) (0.0000) 1.89% 0.70% 6.93% 5.86% 5.51% 101

118 Table 4.3 (Continued) Panel B : Cross-Sectional Regressions for FOHFs Model Without Fund Strategy Dummy Variables With Fund Strategy Dummy Variables Live Dead Combined Live Dead Combined Age ln(a) Lockup Beta R^2 Beta R^2 Beta R^ % 1.57% 0.92% (0.9171) (0.1971) (0.0283) % 2.20% (0.1074) (0.0180) (0.2648) % 1.09% (0.4256) (0.0978) (0.2495) % 11.56% (0.9590) (0.7179) (0.0309) % 9.60% (0.3981) (0.0668) (0.6371) % 9.54% (0.4949) (0.0591) (0.1850) 1.98% 0.73% 10.66% 9.80% 8.99% For HFs, all three variables were significant at the 1% level in all regression models except for the lockup period variable for Live HFs. The younger HFs provided significantly higher returns than the older HFs. The smaller the HFs, the higher the returns. The HFs with longer lockup period had significantly higher returns than the HFs with shorter lockup period. This was the case for the Live, Dead and Combined HFs. The results for FOHFs were different from those for the HFs. It is interesting to note that the age appeared not important to all FOHF returns. Fund size seemed to be a significant factor for Dead and Combined FOHF returns, while it seemed not to be for Live FOHF returns. In contrast, lockup variable showed significance at the 5% level only for the Live FOHF returns. Results from the cross-sectional regression model for the Dead and the Combined FOHFs showed that the direction of the time-series average of the regression slope for size was different from that for the Dead and the Combined HFs. The larger FOHFs in the Dead and the Combined sample provided higher returns than the smaller FOHFs. 102

119 Table 4.4 shows the results of univariate and multivariate cross-sectional regressions of HF and FOHF returns on the ES_cf with a set of fund characteristics that include fund age, size and liquidity The results from univariate and multivariate cross-sectional regression of HF and FOHF returns on the other risk measures are presented in Appendix 4.C. 103

120 Table 4.4 Average Values of the 180 Regression Slopes from the Month-by-Month Regressions of HF and FOHF Returns on 95% Cornish-Fisher Expected Shortfall, Age, Size and Liquidity: January, 1995 to December, 2009 The average coefficients are the time-series (180 months) average of the monthly cross-sectional regression slopes for January, 1995 to December, The p-value in brackets was obtained from a standard t-test. Age was calculated on a daily basis. Fund size was measured by ln(a) where A is funds assets under management. Fund liquidity was measured by lockup period on a yearly basis. Panel A shows results from univariate and multivariate cross-sectional regressions for HFs without HF strategy dummy variables as defined in equation (3.8) and (3.12) and with HF strategy dummy variables as defined in equation (3.13) and (3.17). Panel B shows results from univariate and multivariate cross-sectional regressions for FOHFs without FOHF strategy dummy variables as defined in equation (3.8) and (3.12) and with FOHF strategy dummy variables as defined in equation (3.13) and (3.17). Panel A : Cross-Sectional Regressions for HFs Univariate Regression Multivariate Regression Model Without Strategy Dummy Variables With Strategy Dummy Variables Without Strategy Dummy Variables With Strategy Dummy Variables Live Dead Combined Live Dead Combined Live Dead Combined Live Dead Combined ES_cf Age ln(a) Lockup R^ (0.0058) 7.34% (0.3511) (0.0043) (0.0060) (0.2567) (0.0127) (0.0034) (0.6203) (0.0009) (0.6813) (0.6110) (0.2764) (0.5962) (0.1475) (0.0902) (0.4232) (0.1368) (0.1211) (0.0412) (0.4726) (0.0008) (0.6715) (0.3323) (0.2299) (0.5436) (0.0262) (0.0349) (0.1920) (0.1454) (0.0146) 6.26% 5.24% 13.89% 10.17% 10.31% 9.84% 7.04% 6.57% 15.82% 11.46% 11.25% 104

121 Table 4.4 (Continued) Panel B : Cross-Sectional Regressions for FOHFs Univariate Regression Multivariate Regression Model Without Strategy Dummy Variables With Strategy Dummy Variables Without Strategy Dummy Variables With Strategy Dummy Variables Live Dead Combined Live Dead Combined Live Dead Combined Live Dead Combined ES_cf Age ln(a) Lockup R^ (0.8076) 11.43% (0.7112) (0.9665) (0.7709) (0.9710) (0.8393) (0.9779) (0.5202) (0.6187) (0.1287) (0.6349) (0.1801) (0.0883) (0.1300) (0.7883) (0.2290) (0.0762) (0.1873) (0.5917) (0.3735) (0.8328) (0.0641) (0.9140) (0.1040) (0.1243) (0.4564) (0.9579) (0.1265) (0.0850) (0.1471) 8.48% 8.33% 17.79% 15.74% 14.65% 15.11% 13.78% 11.69% 21.71% 20.66% 17.74% The time-series average of the coefficients from the cross-sectional regressions of the onemonth ahead returns on the risk measure were used to determine which explanatory variables on average had non-zero expected premiums. Panel A presents the results from crosssectional regressions for the HFs, while Panel B shows the results from cross-sectional regressions for the FOHFs. In each regression model in Table 4.4, the first row indicates the average of the time-series coefficients, β t, for one or more covariates over the 180 months from the January, 1995 to the December, The p-values from a standard t-test appear in 105

122 parentheses and the average R 2 for each regression model is presented in the last column of the table. It is interesting to note that the R 2 of the univariate regression model with an independent risk measure variable in Table 4.4 was much higher than that of the corresponding univariate regression model using fund characteristics as explanatory variables in Table 4.3. This result means that risk measures had much higher ability to explain hedge fund returns than fund characteristics such as fund age, size and liquidity. In order to compare alternative risk measures the univariate and multivariate cross-sectional regression results are summarised in Table 4.5. In each regression model in Table 4.5, the first row indicates the average of the time-series coefficients, β t, for risk measure covariate over the 180 months from the January, 1995 to the December, The symbols ***, ** and * indicate whether the risk measure coefficient for each regression model is significantly different from zero at the 1%, 5% and 10% level of significance, respectively. The average R 2 for each regression model appears in parentheses. 106

123 Table 4.5: Average Values of the 180 Regression Slopes from the Month-by-Month Regressions of HF and FOHF Returns on Eight Risk Measures: January, 1995 to December, 2009 The symbols ***, ** and * indicate whether the risk measure coefficient for each regression model is significantly different from zero at the 1%, 5% and 10% level of significance, respectively. The average R 2 for each regression model appears in parentheses. Panel A : Regressions for HFs Without Strategy Dummy Variables With Strategy Dummy Variables Risk Mesure Univariate Regression Multivariate Regression Univariate Regression Multivariate Regression Live Dead Combined Live Dead Combined Live Dead Combined Live Dead Combined SD SEMD VaR_np VaR_cf ES_np ES_cf TR_np TR_cf ** * ** * * * (8.93%) (5.83%) (6.31%) (11.36%) (7.65%) (7.64%) (15.25%) (10.88%) (11.24%) (17.09%) (12.20%) (12.21%) ** * ** * ** * * * (9.57%) (6.46%) (6.90%) (12.03%) (8.26%) (8.24%) (15.84%) (11.36%) (11.75%) (17.71%) (12.64%) (12.72%) * * * (8.77%) (6.15%) (6.24%) (11.28%) (7.85%) (7.62%) (15.03%) (11.08%) (11.16%) (16.95%) (12.38%) (12.14%) * * (8.92%) (7.33%) (6.45%) (11.36%) (8.09%) (7.82%) (15.13%) (11.16%) (11.30%) (17.00%) (12.46%) (12.29%) ** * ** * ** * * * (8.46%) (5.71%) (5.93%) (11.06%) (7.50%) (7.29%) (14.78%) (10.63%) (10.88%) (16.80%) (11.91%) (11.85%) 0.038*** ** *** * *** ** ** ** (7.34%) (6.26%) (5.24%) (9.84%) (7.04%) (6.57%) (13.89%) (10.17%) (10.31%) (15.82%) (11.46%) (11.25%) ** * ** * ** * * * (8.74%) (5.78%) (6.16%) (11.31%) (7.58%) (7.51%) (15.10%) (10.69%) (11.10%) (17.08%) (11.97%) (12.06%) *** ** ** * *** ** ** * (7.76%) (6.19%) (5.53%) (10.27%) (7.17%) (6.86%) (14.32%) (10.29%) (10.58%) (16.25%) (11.58%) (11.51%) 107

124 Table 4.5 (Continued) Panel B : Regressions for FOHFs Without Strategy Dummy Variables With Strategy Dummy Variables Risk Mesure Univariate Regression Multivariate Regression Univariate Regression Multivariate Regression Live Dead Combined Live Dead Combined Live Dead Combined Live Dead Combined SD SEMD VaR_np VaR_cf ES_np ES_cf TR_np TR_cf (14.73%) (10.53%) (11.16%) (18.13%) (16.18%) (14.61%) (19.60%) (17.32%) (16.22%) (23.34%) (22.34%) (19.47%) (15.63%) (10.77%) (11.56%) (18.96%) (16.27%) (14.93%) (20.47%) (17.37%) (16.57%) (24.18%) (22.30%) (19.72%) (14.02%) (8.83%) (9.82%) (17.35%) (14.47%) (13.01%) (19.24%) (15.99%) (15.11%) (22.96%) (20.94%) (18.20%) (14.64%) (8.72%) (9.67%) (18.07%) (14.22%) (13.03%) (19.96%) (15.78%) (15.18%) (23.73%) (20.76%) (18.34%) (13.57%) (9.54%) (9.94%) (17.06%) (15.05%) (13.42%) (18.99%) (16.22%) (15.34%) (22.86%) (21.29%) (18.58%) (11.43%) (8.48%) (8.33%) (15.11%) (13.78%) (11.69%) (17.79%) (15.74%) (14.65%) (21.71%) (20.66%) (17.74%) (14.10%) (10.39%) (10.68%) (17.56%) (15.81%) (14.09%) (19.29%) (16.88%) (15.96%) (23.12%) (21.89%) (19.11%) (12.16%) (9.49%) (9.40%) (15.80%) (14.81%) (12.67%) (18.20%) (16.55%) (15.41%) (22.10%) (21.35%) (18.38%) 108

125 Compared to the results from the test at the portfolio level in Table 4.1 and Table 4.2, the cross-sectional regression results made it possible to distinguish risk measures in terms of their ability to describe the cross-sectional variation in expected returns of HFs. As can be seen in the Panel A of Table 4.5, the semi-deviation, expected shortfall and tail risk measures in most cases represented greater levels of significance than the standard deviation in both the univariate and multivariate regressions for HFs. Particularly, the Cornish-Fisher expansion was marginally better than the nonparametric measures for both expected shortfall and tail risk. The results were consistent with those of Liang and Park (2007). The multiple regression coefficients (average R 2 ) of ES_cf and TR_cf with fund strategy dummy variables for Combined HFs were (11.25%) and (11.51%), respectively. They were positive and significantly different from zero at the 5% and 10% level, respectively. By contrast, the coefficient on standard deviation from the same model was not significant. Contrary to the results showing that semi-deviation, expected shortfall and tail risk were superior to the standard deviation, VaR failed to reveal as much explanatory power as standard deviation. Interestingly, the VaR_cf explained less cross-sectional variation than the VaR_np 43 in the multivariate model without strategy dummy variables. This was consistent with the results of VaR at the portfolio level in Table In addition, the inclusion of the strategy dummy variables in the regression models made it possible to compare the results for the standard deviation measure with the other risk measures, except for VaR. ES_cf and TR_cf retained their significance levels after the adjustment of strategy effects, while the other risk measures lost explanatory power due to inclusion of investment strategy dummy variables. The average R 2 increased after the inclusion of strategy dummy variables in all 43 This was different from the results of Liang and Park (2007) where VaR_cf showed more significance than VaR_np. 44 For Combined HFs, the p-value of testing average return differential between low VaR_np and high VaR_np portfolio (0.0287) is lower than that between low VaR_cf and high VaR_cf portfolios (0.1254). 109

126 regression models of HFs. This showed that each investment strategy tended to provide explanatory power for expected returns. When the FOHFs were examined separately, the results were found to be different from those of HFs. Unfortunately, none of the risk measures exhibited predictive ability for FOHF returns as shown in Panel B of Table 4.5. This was consistent with the results of FOHFs at the portfolio level in Table 4.2. Therefore, the risk and return characteristics of FOHFs were also found to be different from those of HFs when the eight risk measures were analysed at the individual level. 4.3 Conclusion The collapse of some high profile hedge funds such as the Long Term Capital Management (LTCM) in 1998, the Soros Fund in 2000 and two Bear Stearns Hedge Funds in 2007 has emphasized the importance of downside risk management in the hedge fund industry. Due to dynamic trading strategies, traditional risk management measures were not appropriate risk measures to be applied to HFs and FOHFs. In this chapter, the risk-return trade-off in HFs and FOHFs were investigated and compared by alternative risk measures such as semideviation, Value at Risk, expected shortfall and tail risk. Also these risk measures were compared with the standard deviation in terms of their ability to explain the cross-sectional variation in the HF and FOHF returns. As presented in the empirical results at the portfolio and individual levels, the FOHFs did not show the generally accepted risk-return trade-off. These results could be explained by the following facts. Firstly, as FOHFs were diversified portfolio of HFs, the variations of risk among FOHF portfolios formed by ranking a risk measure would be much less than risk 110

127 variations among HF portfolios. Secondly, FOHF investors were observed to achieve less return than HF investors due to the different fee structure between HFs and FOHFs. While a HF charges a management and incentive fee, a FOHF charges extra fees at the underlying HF level as well as management and incentive fees at the FOHF level. Lastly, the negative relationship between risk and return in Dead FOHFs would considerably affect the risk-return trade-off in overall FOHFs. Therefore, it can be expected that FOHFs did not display the statistically significant positive relationship between risk and return under the circumstances discussed above. When the HFs were examined separately, the Live and the Combined HFs presented monotonically increasing risk-return relationships across the portfolios based on the estimated risk measures. The results at the individual level for the Live and the Combined HFs showed that semi-deviation, expected shortfall and tail risk were superior to the standard deviation in terms of their ability to explain the cross-sectional variation in expected returns, while VaR did not reveal as much explanatory power as did standard deviation. The Cornish- Fisher expansion was slightly better than nonparametric measures for both expected shortfall and tail risk. Furthermore, ES_cf and TR_cf kept their significance level when the investment strategy effects were included in the models, while the other risk measures decreased their explanatory power after controlling strategy effects. The fund characteristics such as size, age and liquidity displayed explanatory power in crosssectional variation for both the Combined HF and FOHF returns. However, the directions of age and size effects on expected returns were found to be different between the Combined HFs and FOHFs. The risk measures explained HF and FOHF returns better than the fund characteristics such as age, size and liquidity. Also the inclusion of the investment strategy 111

128 dummy variables in all regression models of HFs increased average R 2. This meant that each investment strategy tended to provide explanatory power for expected returns. It can be concluded from the empirical results that the available data on HFs and FOHFs exhibited different risk-return trade-offs. The ES_cf or TR_cf could be an appropriate risk measure for HF return. While appropriate alternative risk measures for the HFs could be found, it was difficult to determine the risk measures that best captured the cross-sectional variation in FOHF returns. Therefore, FOHF investors should apply different investment strategies from those adopted when investing in HFs. Also they should be more cautious about investment in FOHFs than that in HFs in terms of the risk-return relationship. 112

129 Chapter 5 - Modelling and Evaluating Predictive Accuracy of Financial Distress in Hedge Funds and Funds-of-Hedge Funds: A Cross-Sectional Approach 5.1 Introduction The role of hedge funds in financial markets has become a controversial issue due to large losses by high profile hedge funds prior and subsequent to the Global Financial Crisis (GFC). The collapse of Long-Term Capital Management in 1998, the Soros Fund in 2000 and Amaranth in 2006 resulted in losses of 3,600 million, 5,000 million and 6,400 million US dollars, respectively. These losses were primarily due to excess leverage during the Russian default crisis, the internet and technology bubble and energy price shocks. While most of the academic literature recognized that the hedge funds industry provided risk sharing and liquidity to the financial market, there was also an opposite view that increased systemic risk of the financial system and associated financial instability can result from the nature of funds exposure to risk. The demise of the Bear Sterns funds in 2008 occurred at the onset of the GFC and heralded the start of further collapses of investment banks and other hedge funds. While hedge funds can leverage limited investments so as to make very large bets that were perceived to have the ability to move markets 45, the extensive use of leverage in these funds also appeared to suggest a high level of risk [Brown and Goetzmann (2003)]. Additionally, the use of leveraged strategies by hedge funds raised concerns about their liquidity effects in times of market stress [Adrian (2007)]. Given the extreme effects on the investment environment caused by the onset of the GFC in 2008, the issues surrounding the risk of 45 Sun, Wang and Zhang (2010) and Titman and Tiu (2009) argued that the better hedge funds do not make such bets. 113

130 investing in hedge funds and their potential illiquidity, along with the associated but reduced risk of funds-of-hedge funds, have been of prime concern to the international investment community. In this chapter, the failure probability of individual hedge funds (HFs) and funds-of-hedge funds (FOHFs) was investigated separately by using two unique datasets, namely, the Live Funds and the Dead Funds provided by Hedge Fund Research Inc. (HFR). Using a survival analysis technique known as the Cox Proportional Hazards model, the current study established a survival/hazard models that determined the factors which contributed most to survival and failure probabilities, and provided forecasts of survival probability until a specific failure time for HFs and FOHFs. The current research extended Chapman et al. (2008) and Ng (2008) by focusing on the comparison of the financial distress forecasting models of HFs and FOHFs under three alternative risk measures of fund failure. By applying a filter criteria based on returns and assets under management of funds, groups of failed funds were distinguished from Dead Funds. The Cox Proportional Hazards (CPH) model based on cross-sectional analysis was estimated for HFs and FOHFs by incorporating covariates suggested from previous literature [Gregoriou (2002), Chapman et al. (2008), Ng (2008), Baba and Goko (2009)]. Additionally, the effects of the three alternative return risk measures including standard deviation, Cornish-Fisher Value-at-Risk (VaR) and Cornish-Fisher expected shortfall on a fund s survival were compared by estimating the corresponding three models for HFs and FOHFs. Following estimation of the models, we conducted an out-ofsample forecast and evaluated the predictive accuracy of the models for both the HFs and the FOHFs. The results showed that the size, historical performances, strategies, fees, lock-up period as well as the minimum investment requirements were significant covariates in explaining HF 114

131 failure. As for the FOHFs, fees and the lockup period were less important. In addition, downside risk measures were found to have more explanatory power to explain HF and FOHF failure than did standard deviation. When examining the predictive accuracy of the models in an out-of-sample context, both the signal detection model and ROC curves showed that the CPH models were able to distinguish between failed and non-failed funds. Hedge fund investors are challenged with large information asymmetries and high search costs. Furthermore, entry into and exit from active management involves non-trivial costs [Liang (1999) and Ng (2008)]. The results of this study will allow investors to better estimate the expected lifetime of a HF or a FOHF, before any funds are allocated to it, as well as providing better warning signals about possible fund liquidation to investors already committed. This chapter is structured as follows: In Section 5.2 covariates incorporated into the model are discussed. The method used to estimate survival probabilities of funds, along with the preliminary examination is discussed in Section 5.3. Empirical results are presented in Section 5.4 with the conclusion in Section Covariates A wide range of covariates which were anticipated to impact on HF and FOHF failure were considered and incorporated in the estimation of the cross-sectional model. They can be classified as follows: i) performance measures ii) return risk measures iii) fund size measures iv) liquidity v) leverage vi) fee structure vii) strategy, and viii) domicile. Table 5.1 below shows the list of all covariates examined in this study. 115

132 Table 5.1 The List of Covariates Classification 1. Performance Measures 2. Return Risk Meaasures 3. Fund Size Measures 4. Liquidity 5. Leverage 6. Fee Structure 7. Strategy 8. Domicile Covariates Mean Return Winning Ratio Standard Deviation Cornish-Fisher Value at Risk Cornish-Fisher Expected Shortfall Asset Under Management Minimum Investment Lockup Period Redemption Frequency Notice Period Management fee Incentive Fee High Water Mark Hurdle Rate These variables constituted the covariates within the CPH models from which the survivor functions were estimated Performance Measures There is invariably a clear relationship between a fund s performance and its survival. It is obvious that funds with a better performance are less likely to fail. Hence, negative coefficients on the performance measures are expected. The performance measures adopted in this study included mean return and winning ratio. The vast majority of funds in the Live and the Dead Fund databases reported each fund s return net of all fees on a monthly basis. The minority of funds which reported returns according to another definition, or with 116

133 different time period basis, were removed to minimize error. That is, monthly returns net of all fees were utilized to calculate the performance related measures. Previous studies incorporated skewness and kurtosis of return as explanatory variables in the CPH model [Chapman et al.(2008), Ng (2008) and Baba and Goko (2009)]. Alternatively, the current study incorporated downside return risk measures which captured the information about higher moments of a fund s return in the CPH models Mean Return Mean return was calculated as sample mean of monthly returns over a fund s lifetime. A number of extant studies showed that the funds with low mean returns had higher risk of failure than the funds with high mean returns [ Liang (2000), Brown, et al. (2001), Gregoriou (2002), Malkiel and Saha (2005), Baquero et al. (2005), Chapman et al. ( 2008), Ng (2008) and Baba and Goko (2009)] Winning Ratio The winning ratio is defined as the ratio of the number of positive monthly returns to the total number of monthly returns over a fund s life. Hence, the winning ratio was calculated by dividing the number of positive monthly returns by the number of total months. The previous studies including Chapman et al. (2008), Ng (2008) and Baba and Goko (2009) presented negative relationship between the winning ratio and a fund s failure. 117

134 5.2.2 Return Risk Measures Although the performance measures seemed to be the most significant factor in determining a fund s survival, the risk measures should also be considered as a most important determinant of failure. The majority of previous studies that used survival analysis adopted the variance of the return as a covariate representing return risk 46. Alternatively, Liang and Park (2010) investigated the effects of downside risk measures that reflected higher moments of returns for hedge fund failures. They showed that funds with high expected shortfall were more likely to fail, while standard deviation lost the explanatory power when other explanatory variables were added [Liang and Park (2010)]. In this study, two downside risk measures were examined and compared with standard deviation. They were Cornish- Fisher VaR and Cornish- Fisher Expected Shortfall. All risk measures were estimated on a monthly basis over a fund s lifetime and the average values of the monthly risk measures for each fund were incorporated as a fixed covariate. The return risk measures adopted in this chapter are well defined in Section Fund Size Measures The fund size measures were based on the asset under management (AUM) in the database. As with the return data, the majority of the AUM were reported on a monthly basis in United States dollars. The AUM denominated in other currencies was converted to US dollar by the end of the month exchange rate. Additionally, the minimum investment variable was included in this category. 46 These studies include: Brown et al. (2001), Grecu, Malkiel and Saha (2007), Chapman et al. (2008), Ng (2008) and Baba and Goko (2009) among others 118

135 Assets under Management (AUM) The AUM in a fund s last reporting month was used as a fixed fund size covariate. Consistent with the previous studies, the AUM was converted to the natural logarithm of AUM in US dollars and incorporated in the models. It was expected that funds with large AUM were more flexible to market flows affecting their status, hence were less likely to be liquidated. This expectation was supported by extant studies about hedge fund survival 47. They showed that the fund size was negatively related to the fund failure. However, there were some studies which found the overall effect of fund size on the fund s survival was unclear. The fund size represented by AUM was reported to be related to hedge fund returns by crosssection. The empirical evidence in those studies found that the funds with small AUM outperformed the funds with large AUM [Ammann and Moerth (2005), Herzberg and Mozes (2003) and Hedges (2003) Bali et al. (2007) and Liang and Park (2010)]. While the funds with the large AUM indicated the more stability, the funds with the small AUM provided better returns, which were in turn expected to have less probability of failure. It follows that the overall effect of AUM on a fund s survival should be determined empirically Minimum Investment The minimum investment covariate indicates the minimum initial investment which is required for a new investor. The vast majority of funds report it in US dollars. The minimum investment denominated in other currencies was converted to US dollar by month-end exchange rates. The funds with a lower minimum investment were likely to have small-scale and more risk-averse investors who tended to favour more stable funds with longer survival 47 See Liang (2000), Gregoriou (2002), Amin and Kat (2003), Malkiel and Saha (2005), Baquero, Horst and Verbeek (2005), Chapman et al. (2008), Ng (2008) and Baba and Goko (2009). 119

136 time. In contrast, the funds with a higher minimum investment were likely to have larger institutional investors and high net-worth investors who had a tendency to place high demand on fund managers for larger returns. This probably led to a lower survival time [Chapman et al. (2008)]. Therefore, a negative relationship between minimum investment and survival time was expected Liquidity In this study, the role of fund liquidity on HF and FOHF survival was examined. Three variables related to the cancellation policy of the hedge funds were used as liquidity covariates. They were the lockup period, redemption frequency and notice period Lockup Period The lockup period implies the minimum holding period before investors can redeem their assets. The effect of a lockup period on a fund s survival was expected to be positive. Funds with a longer lockup period tended to survive longer. This was due to the fact that fund managers were more likely to create stable performances if they could decrease the possibility of abrupt asset outflow by investors. This hypothesis can be supported by previous studies. Fund liquidity, as represented by the lockup period, was reported to be related to hedge fund returns by cross-section. Liang (1999), Liang and Park (2007) and Aragon (2004) found a liquidity premium in hedge fund returns using the lockup provision of the fund. They showed that the HFs with longer lockup period had significantly higher returns than HFs with shorter lockup period. In this study, the lockup period was converted to the common unit of days. 120

137 Redemption Frequency All observations in the Live and the Dead Fund databases reported the redemption frequency ranging from monthly, quarterly, semi-annually to yearly. The redemption frequency indicates the frequency at which investors can redeem their assets. For consistency with the other liquidity variables, this variable was converted to days, so that a higher value indicated a lower redemption frequency. As with the lockup period, funds having a low redemption frequency were expected to have lower probability of failure Notice Period The notice period variable indicates the time period in days required for processing of redemptions. The funds with a longer notice period give fund managers a chance to prepare for redemptions and prevent them from closing out unrealised profit opportunities by force. Thus, it was expected that higher notice periods ensure longer survival time Leverage It is well known that hedge funds have very flexible investment options and one of the important options is the use of leverage. Leverage enables a fund to increase its return on investment. On the other hand, funds with large leverage are more likely to have greater return volatility, leading to be at higher risk of failure. The impact of leverage on hedge fund survival is one of the interesting issues unresolved in the literature. A number of previous studies showed the negative effect of leverage on hedge fund performance and survival [Fung and Hsieh (1997), Liang (2000) and Chan, Getmansky and Lo (2006)]. Contrary to this 121

138 finding, Rouah (2005), Chapman et al. (2008), Ng (2008) and Baba and Goko (2009) did not find a significant relationship between leverage and hedge fund survival. This result was possibly due to the fact that an important factor contributing to HF failure was undoubtedly overall investment risk, not just that attributable to leverage. Accordingly, it was posited that the leverage variable might become redundant upon inclusion of the return and risk measures [Ng (2008)]. One of the important objectives of this study is to determine the role of leverage on HFs and FOHFs survival. Unfortunately, the HFR database provided only one single field for leverage information as to whether the fund was allowed to use leverage and if so, in some cases, whether this leverage was limited with a maximum ratio. In this study, leverage variable was represented by three categorical dummy variables. That is, the covariate was given a value of 0 if the fund had no leverage, 1 if the fund had leverage capped at a maximum rate and 2 if the fund had open-ended leverage Fee Structure The unique characteristic of hedge funds is their fee structure. Each fund imposes a performance-based incentive fee as well as a management fee. This is an important distinguishing factor between hedge funds and mutual funds. As such, the role of this fee structure on hedge funds performance and survival is an interesting issue still discussed in the literature. It was generally expected that hedge fund managers tended to be more risk taking to achieve a high absolute return due to the incentive fee. In this study, four covariates representing the fee structure were employed to examine the impact of the fee structure on 122

139 survival of HFs and FOHFs. They were management fee, incentive fee, hurdle rate and high water mark Management Fee Most HFs and FOHFs charge a management fee of between one and two percentage of fund assets to cover administrative expenses. A number of previous studies showed the impact of management fee on hedge funds performance and survival. Baba and Goko (2009) found the positive impact of management fee on funds survival, while any significant relations were not found in Chapman et al. (2008) and Ng (2008). In addition, Ackermann et al. (1999), despite recognising the difficulty of assessing the management fee impact on fund s survival, showed funds with higher management fee tended to provide higher returns. In recognition of the flaw in using percentage fee, as described by Agarwal et al. (2007), the management fee was examined as a US dollar value in this study rather than as a percentage. The management fee covariate was calculated by multiplying the percentage by the average asset under management of the fund s entire life Incentive Fee In contrast to the management fee, incentive fees are only imposed on the funds with good performance and are highly variable across the funds. A vast range of funds apply the incentive fee with high water mark or hurdle rate provision. The incentive fee is intended to encourage higher returns to investors by relating managerial compensation to the fund performance. Accordingly, fund managers may be enticed to increase their portfolio variance 123

140 in order to maximise this compensation. This hypothesis was supported by previous studies. Baquero et al. (2005), Chapman et al. (2008) and Baba and Goko (2009) found a positive relationship between the incentive fee and hazard rate. On the other hand, no evidence of a significant effect of the incentive fee on funds survival was found in Ackermann et al. (1999) and Ng (2008). Agarwal et al. (2007) examined the managerial incentives against hedge fund performance. They showed that managerial incentives were linked to better performance. Also, they found that two different fund managers who imposed the same percentage incentive fee received very different dollar value of incentives. Accordingly, using percentage incentive fee as a variable did not capture the complete effect of managerial incentives [Agarwal et al. (2007)]. As with the management fee covariate, the incentive fee covariate was used as a US dollar value in this study. This was firstly calculated by multiplying the fund s average monthly return by the average monthly asset under management to evaluate the profit per month over the fund s lifetime. This figure was then multiplied by the incentive fee to calculate the dollar value of the incentive fee obtained by the fund manager High Water Mark Most hedge funds incentive fees are paid out according to a high water mark provision. Funds with high water marks allow managers to earn the incentive fee only after they recoup all past losses. It was anticipated that the high water mark of a hedge fund can increase the probability of a fund s liquidation because the fund manager tended to be more risk taking in order to earn an incentive fee when the fund return was negative. This hypothesis was supported by the results in the literature [Brown et al. (1999), Liang (2000), Brown et al. 124

141 (2001)]. On the contrary, the negative relationship between the high water mark and a fund s liquidation was found in Chapman et al. (2008) and Baba and Goko (2009). This result can be explained by the fact that the high water mark provision may have imposed additional pressure on fund manager to achieve high returns and maintain a stable portfolio. Necessarily, the aggregate effect of high water mark provision should be evaluated empirically. In this study, a dummy variable was used to indicate a fund with high water mark provision Hurdle Rate The hurdle rate represents the minimum return, such as the Treasury Bill rate or LIBOR, which should be achieved for a fund manager to be able to earn an incentive fee. For funds with a hurdle rate provision, the incentive fees can be charged on the basis of the profit from investment above the hurdle rate. A fund bounded by a hurdle rate provision was indicated by a binary variable where the value of 1 was ascribed to funds with a hurdle rate and 0 otherwise. As with the high water mark provision, the aggregate effect of the hurdle rate provision on a fund s survival did not seem to be clear and, accordingly, should be judged empirically Strategy Each fund in the database reports the strategy it employs. The strategy has been considered as an important element of a fund s performance because each strategy has its own return drivers and risk levels. A number of studies examined the strength of one strategy over another on the basis of a funds performance in the literature [Fung and Hsieh (1997), Brown, Goetzmann and Ibbotson (1999), Agarwal and Naik (2000), Brown and Goetzmann (2003) 125

142 and Ding and Shawky (2005)]. Others, namely, Chapman et al. (2008), Ng (2008) and Liang and Park (2010) used the strategy employed by each fund as covariates in the CPH regression model to investigate the effect of strategy on a fund s survival. The strategy of HFs and FOHFs is classified into 4 categories. In this study, a number of dummy variables indicating funds strategies were created to examine the impact of strategies on a fund s survival. The HF strategy dummy variables are categorised into Equity Hedge, Event Driven, Macro, and Relative Value, while the FOHF strategy dummy variables are categorised into Conservative, Diversified, Market Defensive, and Strategic Domicile Each fund in the HFR databases reports whether it is an offshore vehicle or not. Offshore funds which are based outside the United States are not exposed to the same regulations placed on hedge funds based in the United States. Ng (2008) showed that offshore funds had higher hazard rates than those of the US-based funds, while a significant effect for domicile on a fund s survival was not found in Chapman et al. (2008). In this study, an indicator variable was used whereby 1 was coded if a fund was an offshore vehicle and 0 otherwise. 5.3 Description of Approach The financially failed HFs and FOHFs were selected from the Dead Fund database as the first step. As a preliminary analysis, the difference in the survivor functions between HFs and FOHFs was tested with the survivor functions of HFs and FOHFs estimated from the Life- Table Method. Prior to constructing the survival forecasting models for HFs and FOHFs, three risk measures, namely, standard deviation, Cornish-Fisher VaR and Cornish-Fisher 126

143 expected shortfall, were compared in terms of their ability to explain failure of HFs and FOHFs. Lastly, predictive accuracy of the estimated CPH models for HFs and FOHFs was tested and compared through the Signal Detection Model, ROC curves and the AUROC Classifying Funds Failures The CPH model can be used to examine the risk of failure of funds that have undergone the event of interest (financial distress), as well as those that have not. However, it is necessary to determine which funds are truly failures in order to accurately define failure times. A failed fund is defined as one that has discontinued reporting to the Hedge Fund Research (HFR) database for reasons of financial distress. The remainder of the funds in the databases are included in the risk set at each failure time. Estimating the model by using genuinely failed HFs and FOHFs is of critical importance for the accurate predictive use of the model. The approach taken to select failure times in Brown et al. (2001) and Gregoriou (2002) simply used the complete observable portfolio of Dead Funds as failure times in their estimation. The problem with this approach was that not all funds in the Dead Fund database had necessarily suffered from financial distress. HFR classified each fund in the Dead Fund database on the basis of their reason for removal from the service. These categories were (i) Closed to New Investments, (ii) Liquidated, or (iii) No Longer Reporting (No Reason). In recent papers, Baquero, Host and Verbeek (2005) and Baba and Goko (2009) used as failure times for their study only those funds for which the exit reason was nominated as liquidated. Despite the reason for removal from the database being stated as liquidation, some funds did not genuinely experience some degree of financial distress. The fund could quite possibly had closed, merged, failed, or been reorganised. It was also possible that funds classified by 127

144 HFR as Closed to New Investment may have been underperforming to the point of financial distress and closed to further investment in order to preserve the reputation of managers. The approach taken for the selection of failure times in this study, as distinct from the aforementioned studies, sought to appropriately distinguish between funds that had dropped out of the reporting mechanism due to financial distress, rather than for any other reason. Various filters were applied to ensure that the funds selected had experienced financial distress. One filter was to examine the return distributions of the sample portfolio of liquidated funds. If the liquidated funds, according to the HFR classification, showed significant negative tails in their return distributions, while those whose classification was listed as No Reason or Closed funds did not, then this would have provided evidence that liquidated funds were the funds closed due to financial difficulties. If no distinction was found, then further filters were needed. These included the examination of the average returns and assets under management (AUM) for the life of each fund, as well as for the last 12 and 24 months. By calibrating the returns in these filters, a clearer picture was formed as to the financial status of each fund and, importantly, this enabled the formation of a sample of genuine failures. After consideration of methods adopted in the previous studies to define failure [Chapman et al. (2008) and Ng (2008)], the following four criteria were applied to distinguish failed funds from the Dead Fund database. They were: i) Funds must be represented in the Dead Fund database, and must have ii) decreasing AUM in the last 24 months 48, iii) average monthly returns which are less than 0.25% in the last 12 months, and 48 This is defined as the percentage change in fund s asset under management within the last 24 months. That is, (AUM at the last report / AUM at 24 months prior to the last report)

145 iv) average monthly returns which are less than 0.25% in the last 24 months. After distinguishing failed funds from other closed funds in the Dead Fund database, the funds were classified into three categories: i) all funds included in the Live Fund database were assumed to be Survivors, ii) funds that passed the failure filter, but were included in the Dead Fund database were classified as Likely Survivors, and iii) failed funds selected by all the failure criteria were classified as Failures. In an effort to examine whether the criteria of selecting failure were appropriate or not, the summary statistics of the above three classes of the funds were compared and reported in the Section The average lifetime monthly return differentials between the survivor fund group and the likely survivor fund group, as well as the failed fund group and likely survivor fund group, were tested by using the nonparametric Wilcoxon test. 49 In addition, failure rates of the HFs and FOHFs were calculated and compared Preliminary Examination of the HFs and FOHFs The majority of recent studies of hedge fund survival used the Cox s regression method. This chapter also employed the semi-parametric Cox Proportional Hazards (CPH) model as the main approach to analyse the survival of the HFs and FOHFs. Nonetheless, estimating nonparametric survivor functions was still valuable for preliminary examination of the data. Once all HFs and FOHFs in the Dead Fund database were classified into failed and likely survival funds, 50 the difference in the survivor functions between HFs and FOHFs were 49 It is well established in the literature that the reported returns of HFs and FOHFs are not normally distributed and, therefore, a parametric t-test is not appropriate. 50 The likely survivor funds from the Dead Fund database were treated as the survivor funds. 129

146 tested. Also, the survivor functions of HFs and FOHFs were estimated through nonparametric methods Testing for Difference in the Survivor Functions between HFs and FOHFs As previously mentioned, a FOHF is a portfolio of HFs. As a consequence, the survivor function of FOHFs is expected to differ from that of HFs as FOHFs are less risky instruments than HFs. A question to be examined is whether the survival probabilities of the two groups at specified future failure times differ significantly. An obvious approach in answering this question is to test the null hypothesis that the future survivor probabilities are the same in the two groups. That is, H 0 : S HF (i t ) = S FOHF (j t ) for all t, where i and j represent a particular HF and FOHF, respectively, and t is a specified future failure time. Three alternative statistics were calculated to test this null hypothesis: the log-rank statistic 51, the Wilcoxon statistic, and the likelihood-ratio statistic. The log-rank statistic was calculated as a sum of the deviations of observed numbers of failures from expected numbers of failures, while the Wilcoxon statistic was a weighted sum. Accordingly, even though both statistics tested the same null hypothesis, they differed in their sensitivity to variations from that hypothesis 52 [Allison(1995)].The likelihood-ratio test was generally inferior to the other two tests because it was calculated under the additional assumption that the hazard function was constant in each group, indicating an exponential distribution for event times [Allison(1995)]. In addition, the two survival curves were presented on the same axes for visual comparison. 51 It is also known as the Mantel-Haenszel statistic. 52 The log-rank test is more powerful for detecting difference between two groups within the framework of Cox Proportional Hazard model. In contrast, the Wilcoxon test is more powerful than the log-rank test in situations where event times have log-normal distributions with a common variance, but with different means in the two groups. 130

147 Estimating the Survivor Functions of HFs and FOHFs: The Life-Table Method The Kaplan-Meier method and the Life-Table method usually have been employed to estimate the nonparametric survivor functions [Gregoriou (2002), Gregoriou, Kooli and Rouah (2008) and Baba and Goko (2009)]. The Kaplan-Meier method is most appropriate for smaller data sets with precisely measured event times. In contrast, the Life-Table method is suitable for large data sets with a more crudely measured event time. Accordingly, due to the large data sets involved in this study, the Life-Table method was used for estimating the survivor functions of HFs and FOHFs. Furthermore, the Life-Table method can provide estimates and plots of the hazard function. The Life-Table method provides a number of statistics for event times that are grouped into intervals, rather than for each specific event time. The drawback of the Life-Table method is the fact that the interval of the event time is usually chosen randomly, leading to arbitrariness in the results and probable confusion about how to choose the intervals. As a result, some information is unavoidably lost within the Life-Table method [Allison (1995)]. Some of the statistics the Life-Table method produce are not of major interest in themselves, but are necessary for calculating the other statistics. Only two statistics of interest are reported in this study: the survival and the hazard statistics. The survival statistic represents the Life-Table estimate of the survivor function, that is, the probability that the event occurs at a time greater than or equal to the start time of each interval. The survival probability of interval i with starting time t i, S(t i ), is calculated from the conditional probabilities of failure as detailed in equation (5.1): i 1 S(t i ) = j=1 (1 q j ) (5.1) where q i is the conditional probability of failure for interval i. 131

148 The hazard column in the life-table is of greater interest. It is the estimate of the hazard rate at the midpoint of each interval. This statistic is calculated by equation (5.2): h(t im ) = d i b i (n i w i 2 d i 2 ) (5.2) where, for the i th interval, t im is the midpoint, d i is the number of events, b i is the width of the interval, n i is the number still at risk at the beginning of the interval, and w i is the number of cases censored within the interval. The denominator of the equation is an approximation to total exposure times which is the sum of all the individual exposure time within the interval i. For each individual, exposure time is the amount of time actually observed within the interval. As shown in the equation, all events and all censoring are assumed to occur at the midpoint of the interval. [Allison(1995)]. Additionally, two graphs of hazard function for HFs and FOHFs are displayed to diagrammatically compare the hazard rate of the two groups Risk Measures Explaining Survival of HFs and FOHFs One of the most significant determinants of a fund failure is its risk. A number of previous studies showed HF and the FOHF returns were not normally distributed and displayed excess kurtosis and negative skewness [Fung and Hsieh (1997), Agarwal and Naik (2001), Amin and Kat (2003), Huston, Lynch and Stevenson (2006) among others]. Due to the nature of negative skewness and excess kurtosis in the HF and the FOHF returns, any risk estimation which assumed a normal distribution of these returns would severely underestimate the actual risk exposures. Most prior research on hedge fund survival used return variance as a covariate in the regression models [Brown et al. (2001), Grecu et al. (2007), Chapman et al. (2008), Ng (2008) and Baba and Goko (2009) among others]. Liang and Park (2010) compared downside 132

149 risk measures that reflected higher moments with standard deviation. They found that the funds with high expected shortfall had a high hazard rate, while the standard deviation lost the explanatory power when other explanatory variables were added. In this study, two alternative risk measures were estimated and compared with standard deviation in order to be incorporated in the failure prediction models for HFs and FOHFs Estimating the Risk Measures Three risk measures including standard deviation, Cornish-Fisher VaR and Cornish-Fisher expected shortfall were estimated to be compared in terms of their ability to explain HF and FOHF survival. They were calculated by the same procedure. Monthly returns over the previous 36 to 60 months (as available) were used to estimate risk measures for each month within the test period. The estimation window started from each fund s initial date of joining the HFR, while the test period of each fund started from 60 months after the initial date of joining the HFR. This calculation was repeated by rolling the sample forward by one month ahead until the risk measure of December 2009 was calculated. Funds having a return history of less than 36 months at particular month were excluded from the sample for that month. Then the average values of the monthly risk measures for each fund were incorporated as a fixed covariate in the proportional hazards models Comparison of the Risk Measures The univariate Cox Proportional Hazard models were estimated to compare the alternative downside risk measures with the standard deviation in terms of their ability to explain HF and 133

150 FOHF failures. Each risk measure was incorporated as a fixed covariate in a separate model on the basis of its average value during test periods for each fund Model Construction for HFs and FOHFs Survival The cross-sectional Cox (1972) Proportional Hazard Model was used to construct both HF and FOHF survival models. A wide range of covariates 53 were incorporated in the models to determine the factors impacting on failures of HFs and FOHFs Multicollinearity Examination Before estimating regression models, the presence of multicollinearity among covariates was examined. Given the wide range of covariates used in the estimation models, it was suspected that some of the information included in factors may overlap across the covariates. It should be noted that the existence of high degree multicollinearity does not provide efficient estimates in the proportional hazard model. In order to evaluate the presence and magnitude of multicollinearity, rank correlations for each covariate were calculated Estimating Cox (1972) Proportional Hazard Model for HFs and FOHFs Given the purpose of this study is forecasting failures of HFs and FOHFs, the Cox (1972) Proportional Hazard Model is based on a cross-sectional analysis with fixed covariates due to the forecasting limitations of the time-varying CPH model 54. To begin with, three global null 53 The covariates are described in Section The forecasting limitations of time-varying CPH model are explained in Section

151 hypothesis tests were performed to evaluate the explanatory power of the model as a whole: a likelihood-ratio test, a score test, and a Wald test. 55 The null hypothesis was that all the coefficients in the model are zero. That is, the model incorporating the covariates as a whole did not demonstrate significant explanatory power. If this hypothesis was rejected, then it was considered worthwhile to examine individual coefficients of each covariate for statistical significance. Additionally, the hazard ratios of each covariate and their statistical significance were examined. Additional to the wide range of covariates explained in Section 5.2, three return risk measures including standard deviation, Cornish-Fisher VaR and Cornish-fisher expected shortfall were included as a covariate in each of three different models. As a consequence, each fund group, namely, HFs and FOHFs had its own three model specifications. 5.4 Empirical Results Failed Funds Identification The HFs and FOHFs included in the Dead Fund database after applying the criteria of selecting failed funds detailed in Section were divided into two groups. One group of funds was classified as likely survivors, while the other group was considered as failed due to poor performance. The method of selecting failed funds was found to be very effective in distinguishing those funds among the Dead Funds which had discontinued reporting for reasons of poor performance from those funds which had exited for any other reason. 55 General properties of these tests are presented in Allison (1995). 135

152 As a consequence, the samples of the Dead HFs (1329) and FOHFs (535) were successfully classified into two groups with 528 HFs and 801 HFs classified as failures and likely survivors, respectively. As well, 250 FOHFs (failures) and 285 FOHFs (likely survivors) were categorised in a similar fashion. The failure rate 56 of the HFs was 18.77% (528/2813), while 21.51% (250/1162) of the FOHFs failed. From the Dead Funds that ceased reporting, 39.73% (528/1329) of the HFs were classified as the failures, while 46.73% (250/535) of FOHFs were categorised similarly. These values indicated that, compared with the HFs, a higher percentage of FOHFs had discontinued reporting due to poor performance rather than for any other reason. Table 5.2 and Table 5.3 provide summary statistics for the classified fund groups of HFs and FOHFs, respectively. These summary statistics revealed primary results relating to the performance drivers. 56 The failure rate was calculated as follow: Number of the failed funds/total number of the funds. Further, recall from Section that the total of first-filtered Live and Dead HFs and FOHFs is 2813 and 1162, respectively. 136

153 Table 5.2 HFs Classification The Duration indicates the average lifetime of the fund. The Lifetime Return, Return Last 24 Months and Return Last 12 Months denote the average monthly return of the funds in each class during entire lifetime, last 24 months and last 12 months, respectively. The AUM Last Month represents average asset under management of the funds in the last month, while AUM Depletion is the average percentage change in fund s asset under management within the last 24 months. The Winning Ratio and the Return Standard Deviation indicate the average values for each class Survivor HFs Likely Survivor HFs Failed HFs Number of Funds Duration (months) Lifetime Return (%) Return Last 24 Months (%) Return Last 12 Months (%) AUM Last Month ($) 250,747,014 83,913,044 43,639,050 AUM Depletion (%) Winning Ratio Return Standard Deviation (%) Table 5.3 FOHFs Classification The Duration indicates the average lifetime of the fund. The Lifetime Return, Return Last 24 Months and Return Last 12 Months denote the average monthly return of the funds in each class during entire lifetime, last 24 months and last 12 months, respectively. The AUM Last Month represents average asset under management of the funds in last month, while AUM Depletion is the average percentage change in fund s asset under management within the last 24 months. The Winning Ratio and the Return Standard Deviation indicate the average values for each class. Survivor FOHFs Likely Survivor FOHFs Failed FOHFs Number of Funds Duration (months) Lifetime Return (%) Return Last 24 Months (%) Return Last 12 Months (%) AUM Last Month ($) 207,162, ,884, ,388,804 AUM Depletion (%) Winning Ratio Return Standard Deviation (%)

154 The performance variables including Lifetime Return, Return Last 12 Months, and Return Last 24 Months showed marginal different values between the survivor and the likely survivor groups in each table. However, there was a big gap in the failed group for both HFs and FOHFs. In contrast, the statistics of AUM Last Month and AUM Depletion were markedly different among three groups for both HFs and FOHFs. The statistics of AUM Last Month showed the highest value in the survivor group and the lowest value in the failed group, while the values of AUM Depletion were highest in the likely survivor group and lowest in the failed group for both HFs and FOHFs. Interestingly, the Return Standard Deviation variable had different results between HFs and FOHFs. The failed HFs showed the highest return volatility among the HFs, which was expected. For the FOHFs, the return standard deviation of the likely survivor group of the FOHFs was greater than that of the failed FOHFs. This was probably due to more of them having outliers that distort the group means. This result suggested that the standard deviation may not be an appropriate risk measure for FOHFs. As expected, the statistics of Winning Ratio showed the lowest values in both HF and FOHF failed groups. In an effort to examine whether the criteria of selecting failures was appropriate or not, the average lifetime monthly return differentials between the survivor fund group and the likely survivor fund group, as well as the failed fund group and likely survivor fund group, were tested using the nonparametric Wilcoxon test. 57 Table 5.4 presents the p-values obtained from the Wilcoxon test. 57 As previously discussed, it is well established in the literature that the reported returns of HFs and FOHFs are not normally distributed and, therefore, a parameter t-test is not appropriate. 138

155 Table 5.4 Testing Homogeneity of Lifetime Monthly Returns for Fund Classification The p-value was obtained from a Wilcoxon test of the average lifetime monthly return differential between fund classification groups. The test was performed for the survivor group and the likely survivor group, as well as for the likely survivor group and the failed group. Survivors vs Likely Survivors ( p value) Likely Survivors vs Failures ( p value) HF < FOHF < For HFs, the average lifetime monthly return between the survivor group and likely survivor group was not significantly different, while the average lifetime monthly return of the likely survivor group was significantly different from that of the failed group at the 1% level. Similar, but not as definite results were found for the different groups of FOHFs. The lifetime monthly return of the likely survival FOHFs was significantly different from that of the failed FOHFs at the 1% level, whereas the lifetime monthly return between survival FOHFs and likely survival FOHFs was not significantly different, albeit, marginally so at the 6% level. The results showed that the method of selecting failed funds was effective at distinguishing between funds which had exited the database due to the poor performance and those that had dropped out for other reasons. It was obvious that this filtering process was more informative than simply treating all funds which were classified liquidated as failed funds. 139

156 5.4.2 Preliminary Analysis for HFs and FOHFs Test of Difference in the Survival Functions between HFs and FOHFs The FOHFs are investment vehicles which make it possible to diversify the risks of investing in HFs given they are portfolios of HFs. As a result, the lifetime of a FOHF was expected to differ from that of a HF due to FOHFs being less risky instruments than HFs. Prior to developing different survival forecasting models for HFs and FOHFs, it was regarded as useful to test for differences in the corresponding survival curves for the two fund groups in order to justify the construction of different forecasting models. Three test methods including the log-rank test, the Wilcoxon test and the likelihood-ratio test were used for this purpose. The total number of HFs and FOHFs included in the sample were 2813 and 1162, respectively. Of all the funds, 2285 HFs and 912 FOHFs were censored because they were still alive, making the censored rates of 81.23% and 78.49%, respectively, while 528 HFs and 250 FOHFs failed. Interestingly, the failure rate of the FOHFs (21.51%) was higher than that of the HFs (18.77%). The test results are presented in Table 5.5. In each test, the null hypothesis is that the future survivor probabilities are the same in the two groups of HFs and FOHFs. That is, H 0 : S HF (i t ) = S FOHF (j t ) for all t, where i and j represent a particular HF and FOHF, respectively, and t is a specified future failure time. Table 5.5 Testing Homogeneity of Survival Curves for HFs and FOHFs Test Chi-Square DF Pr>Chi-Square Log-Rank Wilcoxon Likelihood Ratio

157 The results of the log-rank test, the Wilcoxon test and the likelihood-ratio test all rejected the null hypothesis. This provided evidence to support the hypothesis that the survival curves of the HFs and FOHFs were different from each other. These results provided justification to build separate failure forecasting models for the HFs and FOHFs. Figure 5.1 shows the Kaplan-Meier survival curves 58 for the two groups of HFs and FOHFs. Before 50 months, the two survival curves were essentially the same showing that the survival probability was almost one. The gap that developed after 50 months reflected the fact that the survival probabilities of the HFs were higher than those of the FOHFs across their lifetimes. Figure 5.1 Survival Curves of HFs and FOHFs 58 The Kaplan-Meier survival curve, also known as the Product-Limit survival curve, is a series of horizontal steps of declining magnitude which, when a large enough sample is taken, approaches the true survival function for that population. 141

158 Nonparametric Survival Functions of HFs and FOHFs: The Life-Table Method The estimated survival probability and hazard rate based on the Life-Table method are reported in the Table 5.6. Table 5.6 Survival and Hazard Estimates of HFs and FOHFs: Life-Table Method Interval of Duration HF FOHF [Lower, Upper) Survival Hazard Survival Hazard As can be seen from Table 5.6, the survival probabilities of the HFs were higher than those of the FOHFs after the duration interval of 60 to 80 months. For example, the estimated probability that a HF will not fail until 100 months or later was , while the corresponding probability for a FOHF was The FOHFs showed higher hazard rates than the HFs at the midpoint in almost duration interval. The hazard rate of the FOHFs was at 90 months, while the HFs had a hazard rate of for the same duration. The hazard functions of the HFs and FOHFs are shown diagrammatically in the Figure

159 Figure 5.2 Hazard Function of HFs and FOHF HF FOHF The hazard rate of failure of both HFs and FOHFs increased until a specific duration interval and then dropped. After dropping until the 100 to 140 month interval, the hazard rate of failure increased again until 150 months and then decreased. Even though the general shapes of the hazard functions of the two fund groups were similar, the magnitude and timing of the hazards were different. The hazard rate of a HF s failure rose until the 40 to 60 month interval to , while the FOHF represented the highest hazard rate of failure at for the 60 to 80 month interval. That is, the HFs provided the greater hazard rate earlier than did the FOHFs, with the degree of the hazard rate of failure of the HFs much less than that of the FOHFs. In addition, the hazard rate of failure of both HFs and FOHFs showed the highest value at 150 months, but the hazard rate of failure of the HFs (0.0068) was less than that of the FOHFs (0.0085). 143