Ebook Value at Risk and the Cross-Section of Hedge Fund Returns
Due to flexible trading strategies, advantageous fee structure, low correlations with traditional asset classes, and light regulatory oversight, hedge funds have gained tremendous popularity lately. It is estimated that there are over 7,000 hedge funds worldwide with at least $870 billion under management. The NYSE market makers estimate that during 2004 about half of the daily trading volume comes from hedge funds. Although hedge funds are initially created for accredited investors, institutional investors such as investment banks, public and private pension funds, university endowments and foundations are heavily involved in investing in this alternative investment vehicle. This increasing involvement by institutional investors has raised public concerns on the risk profile of hedge funds and the fiduciary duties of the financial institutions.
Academic literature on hedge funds has been largely focused on performance measures. For example, Fung and Hsieh (1997) extend Sharpe’s (1992) style analysis framework by including dynamic hedge fund investment strategies and argue that the extended model can provide an integrated framework for style analysis. Brown, Goetzmann, and Ibbotson (1999) examine the performance of offshore hedge funds and attribute their performance to style effects rather than managerial skills. Ackermann, McEnally, and Ravenscraft (1999) conclude that hedge funds outperform mutual funds but find mixed results when comparing them with various benchmarks. Liang (1999) finds that hedge fund investment strategies are different from those of mutual funds. Recently, Agarwal and Naik (2004) propose a general asset class factor model comprising of option-based and buy-and-hold strategies to benchmark hedge fund performance.
All of the aforementioned studies analyze hedge fund performance relative to certain benchmarks. An equally important question, largely unanswered, is about the risk profile of hedge funds and how to relate risk to fund returns. The debacle of Long-Term Capital Management LP (LTCM) highlighted the need for more academic studies on hedge fund risk exposure. In this paper, we address the following primary questions: How to measure hedge fund risk? Can fund characteristics such as Value at Risk explain the cross-sectional variation in hedge fund returns? Do defunct funds have different risk profile from that of the live ones? Are other fund characteristics such as size, age, and liquidity factor proxies for fund risk?
Due to speculative bet and dynamic trading strategies, hedge fund returns often exhibit fat tails that are affected by event risk. For example, hedge funds suffered from huge losses during the 1997 Asian Currency Crisis and the 1998 Russian Debt Crisis. Hence, the traditional risk measures such as standard deviation may not fully capture the risk characteristics of hedge funds. In fact, Jorion (2000) adopts a VaR approach to analyze LTCM’s failure and concludes that LCTM underestimates its risk profile due to its reliance on short-term history. Gupta and Liang (2005) compare VaR and traditional risk measures in evaluating hedge fund risk and conclude that VaR is a better measure for hedge fund risk than standard deviation due to negative skewness and substantial kurtosis in hedge fund returns. Meanwhile, assuming normality can underestimate the true risk and is inappropriate in determining capital adequacy for the hedge fund industry. Furthermore, Bali and Gokcan (2004) estimate VaR for hedge fund portfolios using the thin-tailed normal distribution, the fat-tailed generalized error distribution, the Cornish Fisher (CF, 1937) expansion, and the extreme value theory (EVT) based approach of Bali (2003) that considers higher-order moments like skewness and kurtosis. They find the EVT approach and the CF expansion capture the tail risk better than the other approaches. Finally, using a mean-conditional VaR framework, Agarwal and Naik (2004) demonstrate that the standard mean-variance framework can underestimate the tail risk of hedge funds.
The above papers indicate that VaR provides a better characterization of hedge fund risk than the traditional measures such as standard deviation. In addition to VaR, hedge fund returns can be affected by other risk factors such as liquidity risk. In fact, Liang (1999) indicates that the lockup feature is related to hedge fund returns. Recently, Aragon (2004) argues that the abnormal performance of hedge funds can be largely explained by liquidity risk premium that is measured by the lockup period. Many hedge funds have the lockup feature. Money invested in such funds is not allowed to withdraw immediately and fund managers have the flexibility to invest in illiquid securities. Aragon (2004) finds that the funds with lockup features outperform those without by 4% on an annual basis. In addition, Getmansky, Lo, and Makarov (2004) find that serial correlation in hedge fund returns is stronger compared to the traditional assets like mutual funds. They argue the autocorrelation pattern can be explained by return smoothing or illiquidity in asset returns.
One of the most important relations in the asset pricing literature is the link between expect return and risk of an asset. It is well documented that the expected asset returns are related to systematic risk or market risk (the CAPM model), factor risk such as macroeconomic variables (the APT framework), and Fama-French (1992, 1993) factors such as size and book-to-market. Following the asset pricing literature, we examine the cross-sectional relation between expected return, risk, and other explanatory variables of hedge funds in this paper.
Our main focus is to test the presence and significance of a relationship between VaR and expected returns on hedge funds. We estimate VaR using the empirical distribution as well as the Cornish-Fisher (CF) expansion to incorporate the higher-order moments in fund returns. The empirical results indicate that the average return difference between the high VaR and low VaR portfolios is both statistically and economically significant: Buying the higher VaR portfolio while short selling the low VaR portfolio generates an average annual return of 9% for the sample period of January 1995-December 2003. These results hold not only for univariate sorting based on historical VaRs but also for the bivariate sorting (first by age, asset size, or liquidity and then VaR). The cross-sectional regression results indicate that VaR indeed has significant power in predicting hedge fund returns, even after controlling for fund characteristics such as age, size, and liquidity risk.
Based on the observed risk changing patterns, we develop a trading rule to identify the expected to live funds and the expected to disappear funds. We expect that the future live funds will not have much change in their VaRs while the future defunct funds will most likely to face with a significant increase in their VaRs. The trading rule is to buy the expected to live funds and sell the expected to disappear funds. With this simple trading rule, we can generate an annual profit of 8-10% depending on the investment horizon.
To mitigate the survivorship bias issue, we analyze not only the live funds but also the defunct funds. We document that the risk profile of the defunct funds is different from that of the live funds. For the live funds, the risk-return relation is positive: the higher the tail risk, the higher the hedge fund return. However, this relation is reversed for the defunct funds: the higher the tail risk, the lower the realized return simply because high risk wipes out fund assets and makes them defunct. This makes intuitive sense. When a fund takes high risk, it may generate very high return so that the fund will survive. This is the exact relation for live funds. However, high risk may also wipe out fund asset; hence it causes the fund to disappear. Therefore, for the defunct funds, the inverse relationship is consistent with the market’s experience: high risk funds will lose capital and hence become defunct. Interestingly, some large and low risk funds choose to voluntarily stop reporting. Their performance is even better than the corresponding live funds. This risk-return relation for defunct funds is more complicated than what is implied by survivor conditioning.
To the best of our knowledge, this paper is the first that explores the cross sectional relation between hedge fund risk and return at both the individual fund level and the portfolio level in an asset pricing framework. The paper also contributes to the literature by showing how to measure hedge fund risk and how to explain the cross-sectional variability in hedge fund returns.
The paper is organized as follows. Section 2 describes the data and methodology. Section 3 presents the empirical results. Section 4 provides some robustness checks. Section 5 concludes the paper.
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