Hedge Funds Returns and Market Factors

Transcription

1 Master s Thesis Master of Arts in Economics Johns Hopkins University August 2003 Hedge Funds Returns and Market Factors Isariya Sinlapapreechar Thesis Advisor: Professor Carl Christ, Johns Hopkins University Abstract As a group, hedge funds are highly heterogeneous. Different strategies exhibit very different riskreturn tradeoffs. The goal of this paper is to examine the performance, risk and returns of various hedge funds strategies. Some hedge funds perform well in bear markets, while others do not. Part 1 introduces the characteristics of hedge funds, provide a description of various investment styles, discuss hedge funds return drivers and risk-return trade-off, and review existing literature on financial theories related to hedge funds. Part 2 involves an empirical study that observes return characteristics of different hedge fund strategies based on various market situations over the 110-month period between April 1994 and May The study is done with the awareness that there is a major lack of transparency in hedge fund data, which casts doubt on the accuracy with which the results represent the universe of hedge fund. For this reason, it involves exploring performance results before as well as after the estimated biases are corrected for.

2 Acknowledgements I would also like to thank my thesis advisor, Professor Carl Christ, for his guidance, his patience and for his support in helping me complete this work. I would like to thank Dr. Pierre-Yves Moix and RMF Investment Management for having provided the hedge fund data, for the time and energy spent in advising me while writing the thesis. 2

3 PART 1 I. INTRODUCTION While there is no standard definition of hedge funds, they are generally regarded as private investment vehicles for high net worth individuals and institutions. Hedge funds are typically structured as either private partnerships or offshore companies wherein the manager or general partner has a significant personal stake in the fund. Their objective is to generate above-average returns for their investors. Their freedom from much regulatory controls probably best distinguishes them from the more traditional investment styles such as mutual funds. The hedge fund industry had its birth in 1949 as an equity fund created by Alfred Winslow Jones as a general partnership to provide maximum flexibility in portfolio construction. In 1952 Jones took both long and short position in securities to increase returns, and while reducing net market exposure, used leverage to further enhance performance. The early 90 s marked a real boom in the development of hedge funds. The number of hedge funds has rapidly increased as a result of the new wealth that had been created by the unprecedented bull-run in the equity market, and was further heightened by the Internet bubble and valuation concerns in the global equity markets since More strategies became available for investors to invest in. The number of funds in the hedge funds industry today is estimated to range between 2,500 and 6,000, managing approximately US$1trillion. Within half a century after its birth the term hedge fund takes on a much broader context. It is applied to a wide range of alternative funds, including some that may use high-risk strategies without actually hedging against market risk. In addition to traditional hedge funds, a group of investment pools that are also regarded as part of hedge funds are commodity pools, where commodity trading advisors manage funds and provide advice for trading futures contracts or options on future contracts. Many funds that are called hedge fund do not actually hedge market risk but instead use high risk strategies. Different funds are exposed to different kinds of risks. This paper explores how hedge fund strategies differ from each other, and hence their return characteristics. 3

4 II. MUTUAL VERSUS HEDGE FUND CHARACTERISTICS Hedge funds differ from mutual funds in many ways. Hedge funds are often called alternative investments because they seek to generate returns by using many investment techniques not seen in mutual funds (traditional funds). These techniques include short selling, hedging, arbitrage, leveraging and derivatives or synthetic positions. While mutual funds are not able to protect portfolios other than by going into cash or shorting a limited amount of stock index futures, hedge funds are often more able to protect portfolios against declining markets. Hedge funds are much less regulated than mutual funds. They do not deal with public investors but instead serve as investment vehicles for wealthy or institutional investors, who are regarded to be more sophisticated than the general public. In the US, according to the Investment Company Act of 1940, a hedge fund is exempt from the SEC regulation by not making public offerings and having no more than 99 investors. The number was recently increased to 499 investors, given that each has over US$5 million in assets [Fung and Heish 1999]. This privilege comes at the cost of restrictions on public advertising and information dissemination about funds activities, even if they had interests to do so. 1 This is one reason the sector still remains relatively opaque to the general investing public. Mutual funds and hedge funds also differ in fee structure. Mutual funds generally collect management fees based on a percentage of assets under management. In contrast, in addition to a fixed fee, hedge funds always remunerate managers with performance related incentive fees, which is prohibited to mutual funds. Many investors believe hedge funds to provide better downside protection than mutual funds because of several reasons. Unlike traditional funds, hedge funds face few guidelines regarding their security and duration limits, and the capital market they can trade in. The freedom of operation is more limited to mutual fund managers than hedge fund managers because the latter can concentrate on their best bets rather than holding overly diversified positions. While mutual fund mangers have a relative return target, hedge fund managers seek an absolute return target. The latter cares not only about the long-term compounded returns of their investments but also how their wealth changes during the investment period. An absolute return manager tries to increase wealth by balancing opportunities with risk and run portfolios that are diversified and hedge against strong fluctuations. The goal is to generate pure alpha by hedging the primary risk (e.g., stock market and interest rate risk) that drive returns in the traditional asset classes. The strategies involve the exploitation of mispricings and inefficiencies in global capital markets by accepting idiosyncratic risk in return for generating high, risk-adjusted ratios of return with low correlation to traditional assets (Ineichen 2000). 1 It is believed that some funds such as major macro funds, through their large size and highly leveraged position can influence and manipulate the market. The funds themselves, however, may not be entirely guilty for their large impact, since every move a major player makes is copied by many smaller funds. This is one reason why hedge funds do not disclose their positions. 4

5 III. CLASSIFICATION A standard classification of hedge funds does not currently exist. Nevertheless, strategies are generally segregated into two broad categories based on the degree of market exposure. Nondirectional strategies, which can be decomposed into relative-value and event-driven strategies, have relatively low correlation to the overall market. Managers within these groups take long and short positions in securities exposed to comparable risks in order to generate excess returns while eliminating systematic risk. Directional strategies, also called market timing strategies, are more exposed to the market than their non-directional counterpart. Rather than seeking return from arbitrage opportunities by identifying mispricings and inefficiencies in financial markets, fund managers take bets on market movements. The rest of this section describes the main characteristics of the sub-styles in more detail. 1. RELATIVE VALUE STRATEGIES Relative value strategies involve capitalizing on the mispricings of related securities or financial instruments. Managers goal is to hedge exposure to risks such as price movement of underlying securities, market interest rates, foreign currencies and the movement of broad market indices. They base their strategies on a formula or some analysis, and profit when instruments approach their theoretical value. Convertible Arbitrage. Arbitrageurs attempt to buy undervalued instruments that are convertible into equity and then hedge out the market risks. These instruments are often either convertible bonds or convertible preferred shares. Managers may view the discounted price of a convertible in terms of underpriced volatility, optionality, or other input variables. A typical opportunity exists when convertibles of a company are believed to be too cheap and/or equity too expensive. Here a manager would long convertible bond and short the underlying stock. The risk is that volatility will turn out lower than predicted. In another situation, the manager buys distressed convertible bonds and hedges by selling short the underlying equity. Fixed income Arbitrage. Arbitrageurs take offsetting long and short positions in similar fixed income securities that are fundamentally interrelated. Opportunities exist with the occurrence of temporary credit anomalies. A basic strategy is to purchase a government bond and simultaneously sell future contracts on that bond. Bond futures have delivery options that allow different bonds to satisfy the contract. Opportunities exist as investors bet on which bond would become cheap to deliver at maturity, and the shifts in supply and demand for the underlying bond. Other strategies include yield curve arbitrage and yield curve spread trading, and arbitrage between liquid mutual funds containing illiquid municipal bonds with treasury bonds. Equity Market Neutral: Fundamental Arbitrage. Equity market fundamental arbitrage managers seek to profit by exploiting pricing inefficiencies between related equity securities, neutralizing exposure to market risk by combining long and short 5

6 positions. A typical example of this strategy is to build portfolios made up of long position in strong companies and taking short positions in weak companies that are in the same industry. A pair trade, where one share category of the same economic entity is bought and the other is sold is often involved. For example, a manager can create two stocks that are based on the same economic entity, but deviate in price. Such a pair trade does not involve market or sector risk. Other pair trades involve trading voting rights, or buying savings shares and selling ordinary shares. One could define Equity Market Neutral as Long/Short Equity style with zero market exposure. Equity Market Neutral: Statistical Arbitrage. The idea of the strategy is similar to equity market fundamental arbitrage strategy. It is sometimes called statistical arbitrage as its main concept is to apply statistical analysis to historical data to identify profitable trading opportunities. It involves hypothesizing a systematic opportunity for unusual returns, and then using historical data to back-test the hypothesis. Once an empirical pattern is found, analysts try to find an intuitive explanation. If successful, a strategy is identified and implemented. Often managers come from academic background. They balance long and shorts carefully to eliminate sources of risk that are not expected to create returns. Portfolios are typically structured to be market, industry and sector neutral. 2. EVENT DRIVEN STRATEGIES Event-driven strategies involve identifying securities that can benefit from any extraordinary transactions. Because event-driven strategies concentrate on taking advantage of the valuation disparities produced by corporate events, such as takeovers, restructures, mergers, liquidations and bankruptcies, their performance rely less on overall stock market gains than traditional equity investment approaches. Merger Arbitrage / Risk Arbitrage. Specialists in this category invest simultaneously in long and short positions in companies involved in a merger or acquisition. In the case of a cash tender offer, the risk arbitrager tries to capture the difference between the tender price and the price at which the target company s stock is trading. In stock swap mergers, risk arbitrageurs are typically long the stock of the acquired company, and short the stock of the acquiring company. Distressed Securities. Funds in this category invest in debt or equity of companies experiencing financial or operational difficulties. Most private and institutional investors are not willing to keep below investment grade securities on their books, allowing the strategy to take the advantage of the largely discounted price of distressed securities. While a company is restructuring, the prices of its various financial instruments can be mispriced. To extract profits, managers purchase the undervalued security and take short trading positions in the overpriced security. Active managers sometimes participate in creditor committees and be directly involved in the restructuring and refinancing process. 6

7 3. OPPORTUNISTIC STRATEGIES Macro (or Global Macro) Global macro funds use opportunistic strategies that take advantage of shifts in macroeconomic trends. They do not make money by exploiting market inefficiency, but by anticipating a price change early. Managers base their decisions on expected rates of change in interest rates, inflation, economic cycles, foreign exchange and physical commodities. Their investment strategies are highly flexible. They trade all instruments in all markets and all asset classes. Big macro players using high leverage can influence the market, and the effect is further amplified by observant smaller players. Macro funds have the highest profile in the industry and include the world s top trading talents, and are ones usually blamed for causing past economic catastrophes. 2 Equity Hedge (Long/Short Equity) Equity hedge funds comprise of the largest style segment in the hedge fund industry, representing around 30.6% of all funds and 29.8% of all assets under management, and are active globally in all equity markets. These strategies aim to profit from divergences in the performances of different stocks and sectors. Unlike the traditional long-only traditional managers, long/short managers have the freedom to use leverage, take short positions, and hedge long positions. Portfolios are often more concentrated than traditional funds, with the focus that can be regional, sector specific or style specific. Superior stock selection skill can result in doubling the alpha. Short positions can serve the purpose of hedging against market risk, and manager can add value by buying winners as well as selling losers. In addition, managers earn interest on the short position. Short Selling Short sellers seek to profit from a decline in the value of stocks. They borrow a stock and sell it on the market with the intention of purchasing it back later at a lower price. This short-selling creates a restricted cash asset, held as proceeds by the brokerage firm that holds the account, and liability that the short seller must return the borrowed shares at some future date. The discipline also has a fixed income component, since the short seller earns interest, or short interest rebate on the proceeds. The aim of a hedge fund is to avoid loss, that is, to avoid declines in wealth at any time. This means that one would expect returns to have smaller standard deviation than traditional asset classes such as equities and bonds. While there are many styles and sub-styles of hedge fund, and different data vendors have their own method of classification, the paper discusses the main styles believed to be efficient in characterizing the industry. While the HFR database groups its hedge fund data into over thirty categories/indices, the paper chooses to discuss the nine categories whose descriptions are provided above. See Appendix A for a more detailed description of the data used in this analysis. 2 Macro hedge funds had a significant short position in the pound sterling in 1992, and many believe them to have caused the resulting sterling devaluation and withdrawal from the European Monetary System. They were also largely involved in the build-up of the Asian crisis in 1997 by heavily shorting the baht and buying dollars in the spot market. 7

8 IV. HEDGE FUNDS PERFORMANCE IV.1 ISSUES IN HEDGE FUND PERFORMANCE ANALYSIS Part 2 of this study will discuss how various hedge fund strategies can provide unique return as well as risk-reduction opportunities. In this section, we examine the various issues involved in hedge fund performance analysis. Biases A major concern for investors and in hedge fund research is the presence of biases in the databases. Because hedge fund managers are not obligated to report their transactions or earnings to any official agency, no database contains a complete record of all existing hedge funds. Fung and Hsieh (2000) show that constructions of hedge fund indices face four potential sources of bias, which are listed and defined below. Survivorship bias. Survivorship bias results when managers with poor track records exit the business, while managers with good records remain. Data vendors provide only information on hedge funds that are still in operation and that choose to report. Omission of funds that went bankrupt contributes to upward biases in performance measure. Fung and Hsieh estimate the survivorship bias for hedge funds performance in the TASS database to be around 3 percentage points per year. They do this by obtaining the sample of hedge funds that reported during a time period. Then they computed the average return of all funds in the sample and compared that with the funds that did not become defunct (no longer present in the database) at the end of the period. They noted, however, that their finding is only a sample estimate; though all dead funds are defunct funds, not all defunct funds (funds that exited the database) are dead funds. This problem seems inevitable, as there simply does not exist a complete hedge fund database. Therefore, their estimation of survivorship bias include some selection bias as well. Selection bias. The voluntary nature of hedge fund database data collection process leads to several sources of bias. Funds that perform well might have more incentive to be listed in the database, resulting in an upward bias. On the other hand, having performed well in the past and reaching their critical size, these funds might have no incentive to attract new investors. This effect would result in a downward bias. Fung and Hsieh estimate these two opposite biases to cancel and selection bias become negligible. Fund managers also select data vendors to whom they report or not report their performance. In 2000, Liang found only 465 common funds out of the 1,162 funds in HFR and 1,627 funds in the TASS database. Therefore, the databases provide information that is not representative of the whole population. In addition to biases arising from the freedom of funds to decide to participate in a database, the database vendors may have inclusion criteria that also result in selection bias. For example, the Hedge Fund Research (HFR) database excludes managed futures while the TASS asset management database includes them. Overall, it has been difficult for researchers to estimate the level of selection that exists, since one cannot observe the unobservable hedge funds in the population. 8

9 Multi-period sampling bias. Most hedge fund return series are very short. Multi-period sampling bias refers to the situation whereby some hedge funds might have shorter return history than the historical return period investors require before they decide to invest. The short return histories might yield misleading results. However, Fung and Hsieh (2000) estimate multi-period sampling bias to be very small, if it exists at all. Back-filling (or instant history) bias. Before reporting to a data vendor, fund managers undergo an incubation period during which they trade with small amount money, usually their own capital or that from friends and relatives. After satisfactory performance (if any), these managers decide to market themselves to data vendors. The vendors back-fill database with historical returns of the incubation period. The fact that the fund manager can choose when to reveal the fund s record, or whether to reveal it at all, makes it reasonable to assume that the record of returns from the incubation period is higher than in reality. The estimation of instant history bias would involve computing the difference of returns between the incubation period and the total average performance. Fung and Hsieh estimate the bias in the TASS database to be around 1.4 percentage points per year. They do this by averaging the difference between the observable portfolio and the adjusted portfolio. The adjusted portfolio is simply constructed as the observable portfolio after dropping the first 12 monthly return of every fund. Strategic self-misclassification There are several caveats to the classification and performance analysis of hedge fund strategies. Hedge fund databases such as TASS and Managed Account Reports (MAR) collect their information from survey responses and disclosure documents, and classifies hedge funds into different categories according to the reported investment strategies. These categories are sometimes vaguely defined. Brown and Goetzmann (1997) observes that in almost all mutual fund cases that they study, changes in self-classification leads to increasing returns relative to the benchmark. They suggest that we should expect a more severe problem in the far less regulated world of hedge funds. 9

10 IV.2. RETURN DRIVERS The major reason for the dramatic increase in hedge fund investment in the last decade is that within a particular asset class (e.g. stocks), securities tend to move together especially in periods of extreme market movements and that mutual funds fail to outperform comparative indices. As mentioned in the previous section, many investors and researchers believe hedge funds to provide better downside protection than mutual funds. Research has shown that many hedge fund strategies provide diversification benefits relative to traditional stock and bond investments. Based on funds that chose to reveal their performance statistics to data vendors, hedge funds have shown to outperform passive indices. Both macro and micro factors play important roles in hedge fund performance. The returns of some hedge fund strategies are driven by the same market forces that drive traditional stock and bond investments, such as market return, credit spreads, yield curve and market volatility. These strategies are often regarded as return enhancers. Some hedge fund strategies, on the other hand, are little affected by the above variables, and are regarded as return diversifiers. In addition, fund-specific characteristics such as fund size and fund age have also been reported to affect fund performance. Schneeweiss and Kazemi (2001) observe that larger funds tend to underperform smaller funds on a return basis, but have lower risk. This is consistent with the belief that smaller funds may take riskier positions. In addition, research has shown that successful hedge funds appear to pay much higher incentive fees. The incentive-based performance fees is believed to attract the most talented investment managers to the industry, and also because hedge fund managers usually have a substantial portion of their personal wealth at risk in their funds, there is a higher incentive to preserve wealth. Edwards and Caglayan (2001) runs a regression analysis of excess returns on size, the reciprocal of size (to capture non-linearity in the relationship), age, and management and incentive fees. Size variables are statistically significant for all funds except for global macro and global funds. They find the level of incentive fee to be statistically significant and positively related to excess returns of every hedge fund investment style 3. They find the management fee to be negatively correlated with excess returns but statistically insignificant. Lastly, age is only statistically significant at 1% for global macro funds and market neutral funds, and 5% significant for global funds. Performance Persistence An investor is likely to ask whether it is possible to identify funds that will perform well in the future. The usefulness of past hedge fund data is often a topic of controversy. Many findings support that performance is positively associated with the level of incentive fees. A more obvious indication for 3 Their estimates were risk-adjusted, as one might suspect that higher incentive fee managers may be prone to take more risks. They also did not find a relationship between the level of incentive fee and the volatility of a hedge fund s returns. While this may support the notion that the use of asymmetrical incentive fee structure can improve the performance of funds by attracting more skilled managers, one wonders if the reason behind this finding is merely because the high return funds earned incentive fees and others do not. 10

11 the existence of superior managerial skill is to look at the persistence of hedge funds returns. If topperforming hedge funds continue to keep up their performance over a long time period, it might seem convincing that their success is due to skill rather than luck. However, we must also note that luck could be responsible for some funds having outstanding performance over a long period of time. There is no guarantee how well past returns reflect future performance. Studies that have been conducted on hedge fund performance persistence yield mixed results. Edwards and Caglayan (2001) find evidence of performance persistence among top-performing hedge funds as well as among losers, though the evidence differs significantly by investment style. On the other hand, Agarwal and Naik (2000) find evidence of performance persistence that is due primarily to repeated-losers rather than repeated-winners. Lastly, Brown, Goetzmann, and Ibbotson (1999), using annual returns of offshore hedge funds, do not find evidence of persistence. To summarize, the view that superior manager skill exists is still a subject of controversy. It is, however, a widely accepted notion that hedge funds with similar investment styles generate similar returns. One might think of hedge fund returns as a combination of manager skill in processing information and the underlying return in the strategy itself. However, an investor choosing in which funds to invest should always keep in mind that the measures of return persistence, such as the comparison of past months return to this month s return may not provide a consistent determination of expected relative future performance. Many methodological issues such as survivorship bias and backfill bias arise when using historical data. Patterns of repeated above-average returns may occur merely by chance. [Schneeweiss(2001) studied that the longer the investment period, the lower the relative return difference between top and bottom portfolios.] In addition, the ability of historical data to classify managers into similar trading strategies is still an open question. Lastly, due to less stringent disclosure requirements, it is difficult to obtain exact data on holdings of hedge funds. 11

12 V. FINANCIAL MODELS Capital Asset Pricing Model (CAPM) The capital market pricing model is probably the oldest and most widely known theory linking risk and return, and serves as an important tool for estimating expected returns. The core concept of CAPM is that investors can eliminate non-systematic risks, by holding a diversified portfolio of assets. These risks, also called diversifiable, non-market, or idiosyncratic risks, are specific to an individual asset, for example, the risk attached to managers skill. Some risks, such as that of a global recession, cannot be eliminated through diversification. Therefore, even a basket of all of the shares in a stock market will still be risky. Investors must be rewarded for investing in such a risky basket by earning above a risk-free rate. Assuming investors diversify away idiosyncratic risks, how an investor values any particular asset should depend crucially on how much the asset s price is affected by the risk of the market as a whole. The CAPM is written as E[R i ] = R f + ß i (E[R m ]- R f ) where, E[R i ] is the expected return rate on security i R f is the rate of a risk-free investment ( i.e. T-Bill) E[R m ] is expected rate of return on market portfolio (e.g. S&P 500) The equation describes a linear relationship between risk and return. In the context of the CAPM, the alpha is the difference between the expected excess return on the security and the actual return. The market s risk contribution is captured by a measure of relative volatility, beta, which indicates how much an asset s price is expected to change when the overall market changes. The equation implies that investors require higher levels of expected returns to compensate them for higher expected systematic risk. More specifically, the CAPM framework suggests that the asset expected return is proportionally related to the beta of the asset with respect to market portfolio. For example, an asset with the beta of 3 is expected to have a risk premium that is three times as high as the market portfolio s risk premium. The CAPM was highly revolutionary. The CAPM defines systematic risk as the exposure of a security to market fluctuations, and not the volatility of a security. Using the fact the realization is simply the expectation plus random error, the model provides an evaluation method for assets and performance of portfolio managers. One writes the market model that follows as: where, R it - R ft = α i + + ß i [R mt - R ft ] + e it R it is the return on asset i R ft is the rate of a "risk-free" investment, i.e. T-Bill R mt is the return rate of the appropriate asset class e it is the stochastic error term α i is the intercept for asset i Here the alpha of a stock is its expected return in excess of the fair expected return predicted by the CAPM. The beta of a stock is a measure of its systematic risk. 12

13 Asset Class Factor Model (ACFM) Much research has been done in seeking asset-based style factors to model hedge fund returns. Sharpe (1992) proposed an asset-class model that reduces mutual fund styles to a model involving a limited number of major asset classes 4. Many studies apply the analysis of this form to analyzing hedge-fund risk. The model is written as: R t = α + w k F kt + e t where, R t is the return on hedge fund for a particular strategy at period t F kt is the return on asset class k realised at period t w k is the style weights e t is the error component at period t α is the intercept of the regression The model determines a portfolio s exposure to different asset classes. Although the Sharpe's return based style analysis cannot be applied to hedge funds in its conventional form, most return drivers research in hedge fund industry departs from this model. There are several restrictions imposed on the estimation of the model. The style weights are constrained to be positive and to sum to one. These restrictions imply that the relationship between fund return and factor return is linear, and that fund exposure to an asset class remains unchanged over a regression period. Departures from the ACFM generally involve relaxing the two constraints. Since hedge funds often involve shorting techniques, such a model needs to allow for negative style weights. In addition, the model must also account for the fact that hedge funds can hold a significant proportion of their portfolio in cash, and that style weights do not necessarily have to add up to one. The nature of the ACFM makes them more suitable for analyzing mutual funds than hedge funds in many ways. Mutual fund managers generally hold long positions in predefined types of asset classes and are constrained to very little or no leverage. In contrast, hedge funds often reallocate their positions, use leverage, short-selling and invest in derivative instruments to profit from financial forecasts. This causes non-linear relationships between hedge fund returns and traditional asset classes. Many researchers are involved in finding a solution to this problem. All the studies found however, that individual hedge-fund returns have lower correlations with standard asset class returns than do mutual fund returns. In addition, hedge funds with market neutrality, arbitrage, or commodity trading styles have substantially low to nil exposure to the major asset classes. Hedge fund investment risks are often multi-dimensional and asymmetrical, thus making risk-return relationship almost impossible to model (Kao 2002). 4 Twelve asset classes are defined in the original paper. They include T-bill, intermediate-term government bonds, long-term government bonds, corporate bonds, mortgage-related securities, large-capitalization value stocks, large capitalization growth stocks, medium-capitalization stocks, small-capitalization stocks, non-us bonds, European stocks and Japanese stocks. 13

14 PART II There are various measures to describe hedge fund risk and performance, such as fund s standard deviation of returns, percentage of negative months. Risk-adjustment ratio including Sharpe ratio (excess returns divided by volatility of excess returns) and appraisal ratio (significance of the intercept of a CAPM type of regression) are also popular. However, these measures do not completely address the concerns that in certain market conditions, extreme and unexpected investment results may occur. Perhaps the most important aspect in hedge fund risk analysis is to understand the nature of trading strategies and the underlying risk elements of each strategy. This way, one can develop clear, reasonable expectations for a fund. While there is no guarantee that past hedge fund performance will determine future performance, a main goal of this paper is to observe the sustainability of hedge fund return characteristics. The last section introduces the concept behind various hedge fund strategies. This section explores the correlation characteristics of nine hedge fund strategies with respect to various macro economic factors, namely the equity market, the bond market, market volatility and credit risk spread. Exhibit 1 shows the monthly statistics of the nine hedge fund strategies compared to the returns of the S&P 500 and JPM Global Government Bond. It also considers three portfolios: one that consists of only non-directional strategies, another that consists of only directional categories, and one that consists of all strategies combined together. Exhibit 2 explores hedge fund performance during the most extreme months of the equity market in the past nine years. Exhibit 3 studies the performance during various movements of the equity and bond markets. Exhibit 4 shows regressions that compare each strategy's returns with the returns of equity and bond indices. Exhibit 5 is a summary of single factor performance characteristics; it shows the averages of returns of hedge funds during different levels of equity and bond returns, and of market volatility and credit risk spread. See Appendix A for data description. Exhibit 1B focuses on the performance during the months between September 2000 and October, when equity market performed poorly. It also serves to study the persistence of return volatility and correlation statistics of each hedge fund strategy. Exhibit 1C is constructed with the awareness that there exists significant biases in the hedge fund database. It calculates the average-month return and risk-adjusted return taking into account an estimated amount of upward bias that might make hedge funds seem more attractive relative to the traditional asset classes than in actuality. The reader should be aware of the issues that make hedge fund data imperfect. Hedge fund investing is highly heterogeneous by nature; therefore style attributes capture only partly the characteristics of a particular hedge fund strategy. The freedom involved in performance disclosure that hedge funds managers have, combined with the complexity of their investment strategies make identification and analysis of hedge fund styles difficult. 14

15 1. RELATIVE VALUE STRATEGIES Convertible Arbitrage The Convertible Arbitrage out-performs the S&P 500 index in the sample period. Monthly returns are around.95%, which is.14% higher than the S&P 500 index returns. In addition, the.99% volatility is much lower than the 4.69% achieved by the S&P 500 index. Convertible arbitrage has the second lowest volatility of all strategies analyzed. It is also lower than bond volatility. The strategy is in the top three strategies, with equity market neutral statistical arbitrage and equity market neutral fundamental arbitrage strategies, based on the worst 1-month loss. It is ranked number one in terms of Sharpe ratio, which is calculated to be See Exhibit 1. Exhibit 2 shows that negative returns are not significantly concentrated during equity market declines. Overall, there appears little relation between the two sets of return. Exhibit 4.A.1 shows that the alpha of the Convertible Arbitrage to the S&P 500 is.009, while the beta measuring exposure to the equity market is very low (0.064). This indicates that the returns of convertible arbitrage are not achieved through taking on equity market risk. The R- square value to the S&P 500 is also small (0.0907). The R-square value to JPM Global Government Bond is , while the alpha and beta values are and , respectively. One might expect a positive beta to bond, i.e., negative correlation to changes in interest rates. However, the offsetting effect exists in that in case of high interest rate, short sale of stock generates return. The worst case scenario for the strategy would then be when interest rates rise as well as equity markets. In summary, convertible arbitrage is a very attractive strategy, ideal for positive expected return and low correlation to equities. It is a relatively safe strategy even in equity market declines. Exhibit 1B reveals that the strategy achieves the highest ratio even in the period when equity market performs poorly. Exhibit 5.2 shows that the strategy performs below average when bonds perform well. One can see from Exhibit 5.3 that the strategy performs well when market volatility is at a moderate level. Exhibit 5.4 shows that increasing stock volatility is associated with increasing gains, but only until this reaches an extreme level, after which returns drop. Above-average returns are also found when credit risk premium is low and decreasing. This is expected since narrowing credit spread means gains on bonds. Fixed Income Arbitrage The Fixed Income Arbitrage generally under-performs the S&P 500 index, yielding the average monthly return of.45%, which is lower only to that of short-selling strategy. The fixed income arbitrage strategy has 1.25% volatility, yielding the Sharpe ratio of Out of the nine strategies analyzed, fixed income arbitrage strategy is ranked number eight in terms of Sharpe ratio. The volatility is lower than that of S&P 500 and JPM Bond indices. The return distribution has long, thick left tail characteristics. See Exhibit 1. 15

16 Exhibit 2 shows that the negative convertible arbitrage returns were not significantly concentrated during equity market declines. Overall, there appears little relation between the two sets of return. These results are supported by Exhibit 4.A.2 and 4.B.2, which show that the betas measuring the exposure to the equity to be insignificant (-0.035) and to bond markets (-.12) are quite low. The alpha to the S&P 500 is , and the alpha to the JPM Global Bonds is The positive alphas and low betas show that the return fixed income arbitrage achieves is not through taking interest rate of risk or equity market risk. The R-square value to U.S. equities is , and to global bonds. The small negative relationship(beta) to bond suggests that the fact that returns is positively related to interest rate. The fact that correlation is not so high is explained by the nature of the strategy, in which mispricings of related interest rate instruments are exploited, while arbitragers hedge away interest rate risk. Exhibit 5.2 shows that when bonds perform poorly, fixed income arbitrage yields relatively attractive returns. Likewise, negative returns in fixed income arbitrage are concentrated when bond market rises. One may interpret that fixed income arbitrage is an attractive investment when there exists interest rate and inflation uncertainty. Exhibit 5.1 shows that the strategy performs above average when equity market performs moderately. In addition, the strategy performs well when equity market volatility is low and increasing. Lastly, negative returns are often found when credit risk premium is low or increasing [Exhibit ], which can be explain by fixed income arbitrageurs often shorting disaster put options, and longing low credit, liquid fixed income instruments. Equity Market Fundamental Arbitrage The Equity Market Neutral yields the monthly average return of.66%. The equity market fundamental arbitrage strategy has the lowest volatility (.97%) and the lowest worst 1-month loss (- 1.67%) relative to other strategies discussed. The strategy is ranked number three in terms of Sharpe ratio (0.4066). It has produce negative returns only in the 21 months out of the 110 months analyzed. Exhibit 2, reveals that there is little relationship between the market and the performance of equity market fundamental arbitrage strategy. Both during the nine best and worst performing months, the strategy yields three months of negative returns. Exhibit 4.A.3 also shows that the Equity Market Neutral has relatively little relationship to the S&P 500. The strategy exhibits high alpha (0.007) and low beta (0.0287) to the S&P 500. Exposure to the market is negligible. The R- square value is This indicates that the returns on equity market fundamental arbitrage are not achieved through taking equity market risk. The strategy has a correlation to JPM Global Bond. Despite the little explanatory power the S&P 500 has on the strategy, Exhibit 3.A.3 shows that equity market fundamental arbitrage tends to perform better when in stronger equity markets; however, down markets are not associated with low returns. In Exhibit 5.2, there seems to be little relationship between the bond market and the performance of the strategy, but it is observable that the strategy tends to perform poorly when bond returns are high. Above-average returns are generally found when market volatility is low and increases moderately. Exhibit 5.5 reveals that high returns are 16

17 also found when credit risk premium is moderate to low. This makes sense since in these situation risk premium on equity declines as well. Equity Market Statistical Arbitrage The Equity Market Neutral: Statistical Arbitrage yields the monthly average return of.66%, which is lower than the average return of.81% of S&P index. Nevertheless, volatility is much lower (1.17% compared to 4.68%). The strategy has Sharpe ratio, which is relatively low. Equity market statistical arbitrage strategy has the worst 1-month loss lower to only equity market fundamental arbitrage strategy. It might also be worth noting that the strategy yields the smallest difference between the worst and best one month return. The return distribution is relatively normal. See Exhibit 1. From Exhibit 4.A.4, the alpha of the strategy (0.0053) is positive and the exposure to the equity market (0.1508) is not negligible. The R-square value of to equities is surprisingly high. It can be seen in Exhibit1 that apart from equity hedge, equity market neutral has the highest correlation to the equity market. Correlation to global bonds is positive but very low as expected. Despite the description that equity market statistical arbitrage portfolio are constructed to be market neutral, it is doubtful that the strategy takes little market risk. Exhibit 3.A.4 and 5.1 show that the strategy is highly exposed to equities and performs well when equity markets perform well. Exhibit suggests that he strategy performs well when credit risk premium is low and declining. This makes sense since in these situations risk premium on equity declines as well. Exhibit 5.3 suggests that the strategy performs above average when the implied volatility index is moderate or low. Declining volatility was associated with low return and, likewise, increasing volatility resulted in high return for equity market neutral funds. This is shown in Exhibit EVENT DRIVEN STRATEGIES Merger Arbitrage The Merger Arbitrage index slightly out-performs the S&P 500 during the sample period, yielding the average monthly return of.87%, which is.06% higher than that of the S&P 500. The strategy has the volatility of 1.10%, yielding the second highest Sharpe ratio (.4956) after Convertible Arbitrage. The strategy has the lowest volatility after convertible arbitrage and equity market fundamental arbitrage strategies. It also has lower volatility than bond and equity markets. It is interesting to note long thick tail on the downside of distribution. This is inherent in the nature of the strategy since a merger either goes through or it does not. In the case that the deal goes through, arbitragers profits from the merging stocks. If the deal fails, arbitrageur is left with long falling stock position, and a short position that rises. From Exhibit 4.A.5, the alpha and beta to the S&P 500 are and The exposure to equity market(beta) is slightly high relative to some relative-value strategies discussed above. The R- squared value is The relationship between the two sets of return is probably explainable by 17

18 the fact that more companies undergo mergers and acquisitions in high equity market. Correlation to bond market is negative but low (-0.081). Exhibit 5.1 shows most negative returns occur in down markets, but positive returns are not dependent on the direction of the market. This can be rationalized since deals usually fail in bear markets. In calm markets, however, the risk of the strategy is also often attached to the legal (e.g. antitrust) outcomes. According to Exhibit the strategy seems uninfluenced by market volatility and credit risk premium. This is not surprising since the spreads should converge despite market volatility. To a large extent, risk is expected to depend heavily on regulatory environment and less so on capital markets. Distressed Securities Arbitrage Exhibit 1 shows that the Distressed Securities Arbitrage slightly outperforms the S&P 500 index in the sample period, yielding the average monthly return of.88%. The volatility of 1.64% is also lower than the return volatility in equity or bond markets, but high relative to other strategies in the non-directional category. This yields the Sharpe ratio of The best and worst one month returns are also most extreme in the non-directional category. Exhibit 4.A.6 calculates the alpha of the Distressed Securities Arbitrage to the S&P 500 to be The beta was.1633, which is higher than any strategy discussed so far. Here one can also see that the dispersion of returns is higher than any other event-driven or relative-value strategies. The R-square value to equity market is , and to bond market. The alpha and beta to JPM Global Government Bonds are and , respectively. Exhibit 5.1 shows that the strategy performs well when equity market performs well, but the best months are not found not during the S&P 500 best-performing months. This might make sense intuitively if those months are considered months following a recession, during which distressed securities arbitrageurs should consider happy times. Exhibit 5.2 shows that distressed securities arbitrage perform above average when bond market performs well. According to Exhibit , the strategy performs well when equity market volatility is low or moderate and not increasing. In addition, the strategy performs poorly when credit risk premium widens. This is expected since, as in fixed income arbitrage, investors often short a disaster put option. 3. OPPORTUNISTIC STRATEGIES Macro The Macro suggests that the strategy yields better average monthly return (.96%) than S&P 500 returns and is less volatile. The volatility of 2.16% yields Sharpe ratio. The strategy is the third most volatile strategy. There are 37 months out of the 110 months analyzed during which the strategy yields negative returns. Macro returns have.030 correlation to the JPM Global Bond. Exhibit 2 and 5.1 show that negative macro returns occur in down markets where as extreme 18

19 positive returns occur in strong equity markets. Exhibit 4.A.7 and 4.B.7 shows that the alpha of the Macro index to the S&P 500 is.0073 while the beta measuring exposure to the equity market is Dispersion of returns is higher than those of any strategy described so far. The R-squared value is According to Exhibit 5, the strategy exhibits high returns when equity market performs well and when market volatility is low and not changing. There is little relationship between macro returns and bond returns. The strategy performs well when credit risk premium is low or declining. In general macro strategy is hard to analyze because of its heterogeneity. Equity Hedge The strategy yields the highest average return of all strategies, at 1.24% per month. However, based on risk-adjusted returns, equity hedge is still ranked below most arbitrage strategies. The volatility of 2.82% is lower than S&P 500 volatility, but makes the strategy the third most volatile of all strategies analyzed. The Sharpe ratio is Exhibit 1B shows that equity hedge strategy provides little downside protection. During the period of down market analyzed, the Sharpe ratio was , which is the lower than that of any other strategy. Equity hedge funds are attractive for equity investors trying to reduce risk without sacrificing expected returns. The ability to sell short allows managers to capitalize on opportunities unavailable to most traditional managers. From Exhibit 4.A.8, the alpha to the S&P 500 is 0.009, and the beta is The strategy has the highest correlation to equities (0.674) from the range of all strategies analyzed here. The correlation became even higher in the recent down market (0.838 during Sep00-Oct02). Exhibit 5.1 also shows that equity hedge performs well during months of high returns on S&P 500, and performs terribly when S&P 500 performs poorly. This strong relation lies in the strategy s long bias nature. As for traditional long bias stock investment, the long bias equity-based hedge fund strategy is impacted primarily by the changes of the risk and return of the stock market. In addition to the high correlation to equities, this pattern is shown again in Exhibit 5.1. From Exhibit 5.5 and 5.6 he strategy tends to perform well when credit risk premium is low or declining. This is expected since when credit risk premium declines, risk premium on equity declines as well. Furthermore, Exhibit 5.4 shows that declining volatility is associated with high return on this strategy. This is easily understood since declining volatility is associated with smaller equity risk premium. Short Selling The Short Selling is the least attractive strategy based on average monthly returns. The monthly return of.40% is lower than S&P 500 return as well as JP Morgan Global Government return. The strategy has 6.84% volatility, yielding.0110 Sharpe ratio. So far the strategy is the most volatile, has the lowest Sharpe ratio and the worst one-month loss (-21.21%) over the period analyzed. See Exhibit 1. 19