Hedge Fund Market Risk Exposures: A Survey (2024)

1Hedge Funds pool investors’ money and invest those funds with the objective of offering extra returns. Unlike traditional investment funds however, Hedge Funds benefit from a broad flexibility with respect to the type of investment positions they take and the type of assets they invest in. They combine long and short positions in traditional investments but also in illiquid securities and derivatives. Contrary to other investment funds, Hedge Funds do not fall under strict regulations, enjoying thus a larger freedom in investment.

2Hedge Fund (hereafter HF) investment behaviours have consequences on their return structure. Unlike classical investment funds, they do not intend to follow market movements. Therefore, while the returns on classical funds like Mutual Funds are mainly driven by movements in the markets they invest in, Hedge Funds develop non-linear relationships with various market indexes. Besides, because of their complex investment strategies, financial risks related to Hedge Funds are particularly multiform and various, ranging from liquidity, credit, volatility risks to more complex non-gaussian risks – Fung and Hsieh (1997), Fung and Hsieh (1999), Amenc et al. (2003), Schneeweis and Spurgin (2003), Agarwal and Naik (2004) –.

3HF returns are therefore hardly captured by traditional models. The Capital Asset Pricing Model (hereafter referred to as CAPM) as well as the empirical CAPM of Fama and French (1993) and Carhart (1997) have been shown to model HF returns very poorly (see Fung and Hsieh (1997, 1999), Amin and Kat (2003)). The problem lies in the fact that these models only linearly reward one source of risk, while HF returns can neither be linearly explained, nor modelled with one single factor. On the one hand, the dynamic use of leverage and rapid changes in their asset exposures cause low linear correlations between Hedge Funds and other classes of asset. On the other hand, Hedge Funds invest in more than one market segment at a time.

4Numerous attempts have been made in the literature to capture their particular return variability. For instance, a generalized stylistic classification (hereafter GSC) groups Hedge Funds according to “where” (location) and “how” (strategy) manager trades. This GSC is widely used in the literature. Funds with similar location and strategy have correlated returns, so this classification can extract returns related to common risk exposures in Hedge Funds. Qualitative and quantitative classifications of HF investment strategies could be performed. Qualitative methodologies put together funds based on their self-disclosed trading strategies to commercial databases such as TASS, Hedge Fund Research Inc., Barclay [1] (see Lhabitant (2001)). Depending on the data provider, equally-weighted or value-weighted averages of returns (of funds entering each group) constitute the peer-group style factors. Quantitative methodologies essentially perform various statistical clustering technics. Fung and Hsieh (1997) and Amenc et al. (2003) exploit correlations individual Hedge Funds have with the HF common return structures extracted by Principal Component Analysis or PCA. Brown and Goetzmann (2003) and Gibson and Gyger (2007) exploit cross-correlations between Hedge Funds [2] (Brown and Goetzmann (2003), Gibson and Gyger (2007)). Each cluster time-series of average returns then form the return-based style factor [3].

5Some caveats have however been pointed out for style analysis. Although these models deliver conclusive results in explaining HF returns, they are only informative about how funds behave relative to one another, and/or about the underlying common return structure. The methodology does not highlight the way returns are driven.

6The objective of this paper is precisely to understand HF risk exposures and to reformulate these style factors in order to shed light on the underlying risk drivers. The idea is to decompose the HF return generating process and to map the reported HF returns onto reliable factors that are transparent, rule-based and with sufficient long return histories. This review of the literature is devoted to the analysis of HF market risk exposures and risk pricing. It takes a risk-based approach of HF returns and examines numerous studies that try to model their specific payoff structure. Therefore, it does not focus on other aspects such as operational risk, HF diversification benefits, or the biases in HF databases.

7The rest of the paper is organized as follows. Section 2 presents a factor model approach of HF returns. Section 3 shows preliminary evidence about the HF particular non-linear return structure. It explains why linear factor models do not work for Hedge Funds and why a higher-moment CAPM should be preferred. We consider two ways of dealing with the strong non-linear return structure of Hedge Funds. Section 4 presents distribution-based factors, while Section 5 introduces a set of regressors with option-like features. Section 6 explores the use of predefined systematic trading strategies as risk factors and reports the risk factors that appear the most statistically significant by HF strategy. Section 7 focuses on HF non-market risks like liquidity or credit risks. Section 8 concludes.

8This sub-section presents a series of investable benchmarks corresponding to long-only exposures in domestic or international equity or fixed-income risks, commodity and currency risks that have been used to replicate the payoffs of Hedge Funds. They characterize HF returns as follows

9

10where R_t is the return on Hedge Fund F at time t (in excess of the risk-free rate), ?_it is the return on factor i at time t, and ?_i the fund exposure to the risk factor i, corresponds to how much of the fund return can be replicated by investing in the set of i indexes, ?_t is the return related to extra risk not taken into account by the i indexes, and finally ? is the extra return you can get by investing in the fund i.e. the fund abnormal performance. An example of such a buy-and-hold multifactor model can be found in Liang (1999) who reproduces the Sharpe (1992) 8-asset-class-factor model on Hedge Funds [4]. His model explains between 23% and 77% of the cross-sectional variation of the HF styles.

11Agarwal and Naik (2000a, 2000b, 2001) provide some extensions over the Sharpe style analysis of HF returns. Their papers perform a similar Sharpe style analysis with equity-style factors [5], 3 bond-like factors [6], the Federal Reserve Trade-Weighted Dollar Index, and the Goldman Sachs Commodity Index. They moreover introduce a Lehman High Yield Composite Index in the original Sharpe model, and integrate the possibility of leverage and short sale in the analysis. Their model provides adjusted R-squares slightly superior to the ones displayed in Liang (1999).

12Such a generalized Sharpe style analysis has rapidly been mimicked in the literature [7]. These extended works have however detected a considerable degree of variability in the factor exposures over time.

13Hedge Funds are shifting very rapidly asset classes. Therefore, non-linear estimation techniques could be carried out on the covariance factors to make these regressors dynamic, replacing (1) by

14

15where betas have now their own dynamics.

16A detailed analysis of dynamic models used in the HF literature is out of the scope of the paper. Nevertheless, the following examples provide some illustrations of what could be done. For instance, market timing models – see, e.g. Treynor and Mazuy (1966) or Henriksson and Merton (1981) – have been performed to model the use of superior information about the expected level of the market index for adjusting the HF risk exposures. Amenc et al. (2003), Fung and Hsieh (2004a), Kat and Miffre (2006), and Chen and Liang (2007) introduce various financial indicators to adjust the HF exposures to risks. All these studies illustrate that the return of a Hedge Fund at time t can be partly forecasted by public information among which returns of the market R_m,t and/or a broader set of economic variables z to define. In all cases, time-varying betas take essentially the following form:

17

18where I_t = R_mt in case of market timing models or I_t = z_t-1 in case of conditioning factor models.

19Moving-window regressions, state-space models and regime-switching models also tried to relate changes in HF risk exposures to market regimes [8]. In state-space models, alphas and betas are modelled as autoregressive processes, while in regime-switching models, the exposures to risk factors are dependent on the regime states. Bollen and Whaley (2009) compare the relevance of using a regime-switching model over a state-space model of beta loadings. They show that the regime-switching model must be preferred for modelling sharp transitions in risk exposures over a short period of time, while state-space models must be preferred for translating smooth transitions over a long time period. Besides, Bacmann et al. (2008) show that the rolling-window methodology delivers good results as long as the market conditions are stable over time. When conditions are sharply changing, such a procedure fails to translate the dynamism in risk exposures.

20To disentangle the particular non-linear return structure of Hedge Funds, one could either use a classical asset-based factor model while performing a time-varying estimation technique as discussed above or introduce the non-linearities within the regressors while performing a linear estimation of the model. In this paper, we explore how non-linear regressors like multimoment factors (capturing the non-gaussian risks in Hedge Funds) could capture the non-linear comovements of Hedge Funds with market indexes.

21Hedge Funds take positions on stock, fixed-income, commodity, currency markets in the US and worldwide. As a result, HF returns are related to the evolution of these underlying markets. Comovements of HF returns with market portfolios of these underlying markets should thus be priced. Hereafter, these corresponding risk premiums are referred to covariance factors. They capture the part of HF returns stemming from exposures to buy-and-hold traditional risk factors.

22The way HF managers are compensated strongly modify the fund payoffs. Beyond the fixed management fee, HF managers participate in the profits generated by the funds. In case of an extra profit (defined as a profit in excess of the hurdle rate), managers are paid an extra fee which is proportional to the generated profit. As HF managers earn incentive fees for gains but do not rebate fees to investors for losses, the net-of-fee return distribution of a Hedge Fund is a non-linear function of the original gross return distribution. Especially, it can be viewed as a call option on the value of the fund (Panageas and Westerfield (2009)). This is further compounded by the high-water mark feature that implies HF managers to recover the losses from previous periods before receiving any performance bonus. Such feature adds further convexity to the net-of-fee payoffs by creating not a single option but a sequence of options (at each point in time) with changing strike prices: when the fund value increases, the high-water mark also increases but when the fund value decreases, the water-mark is not adapted. (Please refer to the work of Ruckes and Sevostiyanova (2011) for further details). Because most studies on Hedge Funds are looking at net-of-fee returns, one should pay attention to the asymmetry it creates in the return distribution. [9]

23Hedge Funds pursue leveraging and other speculative investment practices in markets they invest in. Hedge Funds do not intend to track broad-based indices: they actively search for risk exposures that differ from the market beta, i.e. they look for “alternative” betas. Their management combines multiple and complex positions in derivatives, in illiquid assets (causing positive serial correlation in HF returns) as well as in many other type of assets. Dynamic trading, short selling and borrowing are also integrative features of their management strategy (Fung and Hsieh (1997), Ackermann et al. (1999), Liang (1999), Agarwal and Naik (2000a), Stulz (2007), Bollen and Whaley (2009)). As a result, HF returns are dynamically driven by their underlying market risk factors. In addition to traditional risk factors, some alternative risk factors should thus be introduced in benchmark models in order to capture the strategy-specific portion of HF returns.

24The following subsections analyze in depth the consequences of HF investment strategies on their return distribution.

33The literature records many attempts to include higher-moment effects in Hedge Fund pricing. Empirical work has been limited to the second, the third, and the fourth comoments as there are no a priori behaviourist arguments for explaining investors’ attitudes towards moments of order higher than four.

34A first stream relies on the hypothesis that a selection of higher-order powers of the market index comprises a simple polynomial approximation to a non-linear functional relation between the returns of Hedge Funds and the market index. Spurgin et al. (2001) and Chen and Passow (2003) for example model the square and the cube of the S&P 500 as a proxy for skewness and kurtosis dependence respectively. Kat and Miffre (2006) question however the relevance of such factors to proxy for higher-order comoment premiums as they can be mixed up with the market timing measure of Treynor and Mazuy (1966). Besides, Ranaldo and Favre (2005) and Ding and Shawky (2007) also perform a four-moment model by regressing HF returns on the levels of variance, skewness, and kurtosis attained in the market. The regression coefficients in both models correspond to the statistical measures of covariance, coskewness and co*kurtosis.

35A second stream of research computes elaborated distribution-based factors. They intend to capture the prices of volatility, skewness, and kurtosis that are implicit in the market. This approach relies on the four-moment asset pricing model as defined in Jurczenko and Maillet (2006) which linearly relates the expected return on a specific security to the return of the riskless asset, to the return of a portfolio that spans variance, to the return of a portfolio that spans skewness, and finally to the return of a portfolio that spans kurtosis. So far the literature has proposed two ways for benchmarking these returns.

44In Section 3, I show that HF return payoffs may present option-like features. Their payoffs are often compared to short positions in put options on the S&P 500. Any appropriate combination of options could thus mechanically replicate their complicated payoff [13] (Breeden and Litzenberger (1978)).

45Some authors try to deal with the low specification levels of traditional factor models by including option-based factors. Working on Mutual Funds, Glosten and Jagannathan (1994) first propose to value option-like payoffs. Their work consists in approximating some non-linear payoffs by a collection of options on a selected number of benchmark index returns. It has rapidly been replicated on Hedge Funds.

46The literature on the use of option-based factors for explaining the HF return generating process has been growing over time. The most important contributions are listed below.

56Unlike other asset pricing models, primitive trading strategies offer investable performance benchmarks which are able to replicate the passive part of HF returns (Fung and Hsieh (2007b)).

57Primitive trading strategies are made of a static linear combination of investable risk factors; they range from a static selection of buy-and-hold risk factors to more complicated strategies such as trend-following, market timing or insurance-like strategies. Lookback straddles for instance have been used to mimic the returns of trend-following strategies. Fung and Hsieh (2001, 2002b, 2004b) and Spurgin (2001) consider the returns on lookback straddles on major asset markets (stocks, bond futures, currency futures, interest rate futures and commodity futures) for capturing the non-linear return structure of HF payoffs. Market timing strategies have also been modelled as a dynamic linear combination of the underlying asset and an investment in the risk-free rate, creating an option-like strategy (Henriksson and Merton (1981), Merton (1981), Leland (1999)). More generally, the HF concave payoffs have been captured by short positions in exchange-traded put options (Mitchell and Pulvino (2001), Agarwal and Naik (2004), Fung and Hsieh (2011)). This rule-based trading factor captures the fact that Hedge Funds may be selling insurance policies. By their insurance-like strategies, fund managers accept a series of steady returns (independent of the stock prices) for a small risk of experiencing extreme negative returns.

58A typical replication procedure is carried out in two steps. First, stepwise regression is used to select a suitable set of primitive trading strategies that are able to describe HF returns. The beta loadings are then estimated over the period the Hedge Fund needs to be replicated. Second, a portfolio with the same risk exposures is constructed. Considering a set of risk factors and a set of time-varying beta exposures ?_it, the replicating portfolio is identified as follows:

59

60The difference between the original HF return and its constructed benchmark return gives the performance of the fund.

61Simpler primitive trading strategies reproduce the HF risk/return profile through investments in liquid instruments on standard asset classes. For instance, Schneeweis et al. (2003) use a linear factor approach to create clones of European Hedge Funds. They perform a rolling-window regression of Hedge Funds to estimate the fund beta exposures to equity risk, interest rate risk, credit risk, and volatility risk. Similarly, Hasanhodzic and Lo (2007) use a set of liquid instruments on standard asset classes (US dollars, US corporate bonds, credit spread, US stock markets, commodities, as well as the equity implied volatility) to replicate the returns on Hedge Funds. Contrary to Schneeweis et al. (2003), they demonstrate the superiority of static estimates of the fund risk exposures for defining their HF clones over dynamic estimates inferred from rolling-window regressions.

62Depending on the type of HF strategies, different types of factor should be considered within the replication models. Therefore, the rest of the section proceeds with an analysis of the most significant risk exposures embedded in the main HF styles: Equity Hedge Funds, Event Driven Funds, Global/Macro Funds, and Relative Value Funds.

63Equity Hedge strategy takes long and/or short positions primarily in equity and equity-derivative securities. As a consequence, most funds display significant exposures to proxies for the US stock market as well as to the relative performance between small and large cap stocks, between value and growth stocks and between persistent “winner” and “loser” stocks (Agarwal and Naik (2000a), Agarwal and Naik (2004), Jaeger and Wagner (2005), Gatev et al. (2006), Fung and Hsieh (2011)). Dupleich et al. (2010) even show that three factors – namely the market, the momentum and the value factors – could explain a large part of the Equity HF return variation. According to Chan et al. (2007), these funds also take large bets in the worldwide stock market. Long/short Equity Hedge strategies present significant positive exposures to these factors while the Short Selling strategy displays negative exposures. HF equity strategies moreover exhibit extreme positive or negative higher-moment exposures (see Agarwal et al. (2009)). For instance, Equity Hedge or Short Selling strategies are exposed to slightly positive skewness, whereas equity non-hedge strategies exploit tail risk in equity markets (Agarwal and Naik (2000b), Agarwal and Naik (2004), Liang (2004)). The changes in the equity implied volatility also constitute an important pricing factor (Agarwal and Naik (2004), Giannikis and Vrontos (2011)).

64Event Driven Funds invest in securities of companies involved in corporate-related events like mergers, restructurings or financial distress. In particular, Agarwal and Naik (2000b), Mitchell and Pulvino (2001), Agarwal and Naik (2004), and Jaeger and Wagner (2005) observe significant exposures of Event Driven Funds to the relative performance of small over large cap stocks, of value over growth stocks, and of persistent “winner” over persistent “loser” stocks. Fung and Hsieh (2001) moreover point out that most Event Driven Funds present significant negative skewness and kurtosis exposures, meaning that the fund payoffs present an asymmetric tail towards negative returns with regard to the distribution of the market portfolio. Returns on Merger Arbitrage strategies but also on risk arbitrage strategies in general can be approximated using a short position in exchange-traded put options (Mitchell and Pulvino (2001), Huber and Kaiser (2004)). Returns on high yield bonds are also expected to be significant for this particular HF strategy as this factor represents the returns on distressed firms (Fung and Hsieh (2007b), Lucas et al. (2009)). The VIX (Volatility Implied Index) should also be considered when pricing Event Driven Funds (Giannikis and Vrontos (2011)).

65Global Macro Funds take advantage of price movements on major markets (currencies, stocks, commodities,…). Their investment strategies (making use of leverage and derivatives) are based on a set of macroeconomic analyses that form HF managers’ market views. As a consequence, this category is particularly exposed to the Emerging Market (bond or stock) Index, to the Federal Reserve Bank Weighted Dollar Index, to the Goldman Sachs Commodity Index, to the World Government and Corporate Bond Index (Agarwal and Naik (2000a), Huber and Kaiser (2004)) but also to US equities (Fung and Hsieh (1999)). Teo (2009) also finds out significant long exposures of the Macro Fund returns to high-yield currencies and significant short positions in low-yield (more liquid) currencies. According to Fung and Hsieh (1999), Global Macro Funds behave either as a long position in short calls or in long puts.

66We finally consider returns of Relative Value Funds. The fund strategy benefits from the realization of a valuation discrepancy in the relationship between multiple securities. As argued by Mitchell and Pulvino (2001) and Agarwal and Naik (2004), the fund returns are related to equity markets returns but in a non-linear way. Therefore, these funds present significant exposures to the US and the worldwide stock markets, as well as to the relative performance of small over large cap stocks, and of persistent “winner” over “loser” stocks (Agarwal and Naik (2004), Jaeger and Wagner (2005), Gatev et al. (2006)). More specifically, asymmetric exposure in the US equity factor has been found from the significance of the option-like factors defined by Agarwal and Naik (2004) [16] and Fung and Hsieh (2004b). Indeed, the convergence-based strategies performed by Fixed-Income Funds (buying the cheapest and selling the most expensive asset) constitute the reverse of a trend-following strategy and therefore can be modelled as a short position in lookback straddles. Government and corporate bond returns as well as returns on high yield bonds, emerging market bonds and stocks are also important factors to be considered when pricing Relative Value Funds (Giannikis and Vrontos (2011)). Besides, among Relative Value strategies, Fixed-Income Convertible Arbitrage Funds have been mimicked using the return spread between Moody’s Baa corporate bonds and the 10-year constant maturity interest rate or using the yield curve interest spread (such as in Fung and Hsieh (2002a) and Duarte et al. (2007)). Besides, according to Agarwal et al. (2011), a large proportion of the return variation in convertible arbitrage strategies could be captured from a long position in convertible bonds and a short position in the shares of the convertible bond issuers (in order to hedge the equity risk). Finally, Ranaldo and Favre (2005) show that extreme return variations are embedded in risk arbitrage strategies. Therefore, they relate the returns on these funds to co*kurtosis risks since the insertion of such fund into a diversified portfolio will strengthen the likelihood of extreme returns.

67As non-linear payoffs are not restricted to particular HF strategies but are common characteristics across all HF styles, Agarwal and Naik (2004) and Fung and Hsieh (2004b) propose to summarize these results into two simplified asset-based factor models. The model of Agarwal and Naik (2004) is composed of a set of buy-and-hold factors and exchange-traded at-the-money and out-of-the money put and call options. On the contrary, Fung and Hsieh (2004b) perform a seven-asset-based factor model composed of two equity-like factors, two bond-like factors and the returns on lookback straddles on bonds, currencies, and commodities. Both models have been shown to capture a large part of the variability in HF returns and have been largely used in the literature as benchmark factor model.

68Such models could therefore be used to clone HF returns. For instance, Darolles and Mero (2011) use a set of buy-and-hold factors and the option-based factors of Agarwal and Naik (2004) to replicate the returns of a set of individual Hedge Funds. Their methodology allows to dynamically select the set of asset-based factors to be used to mimic HF passive returns. The authors even demonstrate the importance of taking into account time-varying risk profile in the replication procedure as their dynamic approach outperforms the static replication performed by Hasanhodzic and Lo (2007).

69Note however that a distinction should be made between HF replication for investment purpose and replication with an academic objective. Indeed, the improvement of the replicated models will inevitably come at the price of illiquid investments (such as investment in illiquid options), which does not match the investment objectives (Roncalli and Weisang (2011)).

70Hedge Fund trading strategies are particularly exposed to credit and liquidity risks. Therefore, term spreads – defined as the spread between thirty- (or ten-) year and one-year treasury bills – and credit spreads – defined as the spread between BBB and AAA ten-year corporate bond yields – have often been introduced into a multifactor approach of HF returns. See for instance the work of Edwards and Caglayan (2001), Amenc et al. (2003), Agarwal and Naik (2004), Fung and Hsieh (2004b) and Amenc et al. (2010).

71But investing in illiquid securities has also often been related to a stale pricing problem (Getmansky et al. (2004), Jagannathan et al. (2010)). Market prices are not always available for securities that are not actively traded. Therefore, a problem occurs when, for monthly reporting purpose, fund managers have to price these illiquid securities and use either the last available traded price or a smoothing evolving model to estimate the actual price. Some part of asset returns is reported contemporaneously, while another part shows up in future returns. Besides, return smoothing due to managed pricing is another cause of spuriousness in time-series modelling. Such practice is used to manipulate the performance of the fund and to spread volatility over time (Asness et al. (2001), Bollen and Pool (2008)). In case of fraudulent return smoothing, managerial manipulations are more likely in some market conditions (see Bollen and Pool (2008)); a model of conditional smoothing could thus determine the timing of the revelation of some information into asset returns.

72Stale and managed pricing produce significant levels of positive serial correlation in reported HF returns (Asness et al. (2001), Getmansky et al. (2004)). As both make data non-synchronous with the contemporaneous factors, it may also bias downward the estimates of the HF return exposure.

73Following Fama (1965), Ibbotson (1975), Schwert (1977), and Geltner (1993), the fund returns at time t can be expressed as a weighted average of the true value at time t and t – 1. As a consequence, some authors have applied the following formula for “de-lagging” the serially correlated HF returns (see Conner (2003), Okunev and White (2003)):

74

75where R_t is the unsmoothed returns, R^*_t smoothed returns, and ? the first-order autocorrelation of the fund. Introducing lagged factors in the regression-based analysis is another way to deal with this issue (e.g. Asness et al. (2001), Brooks and Kat (2002), Kat and Lu (2002), Getmansky et al. (2004), Ibbotson and Chen (2006), Ding and Shawky (2007)).

76Recently, Khandani and Lo (2009) have tried to use correlation-sorted portfolios of Hedge Funds to construct a liquidity premium. They make the hypothesis that, by investing in illiquid assets or assets difficult to price, Hedge Funds tend to smooth their returns over several periods and, as a result, display high levels of positive autocorrelation. Therefore, they sort Hedge Funds into five portfolios according to their autocorrelation level, and form their liquidity premium as the spread between the highest and the lowest autocorrelation-sorted portfolios.

77Similarly, Sadka (2010) and Teo (2011) demonstrate that liquidity risk is priced in HF returns. Sorting individual Hedge Funds into portfolios according to their liquidity beta (i.e., the covariation of the fund returns with changes in a proxy for liquidity risk), both papers show that funds that significantly load on the liquidity proxy outperform low-loading funds except in times of financial distress. Using a set of individual Hedge Funds, Sadka (2010) displays a significant monthly average premium of 1.43% for liquidity risk. The author even shows that the liquidity return spread cannot be explained by the redemption or lockup period or by the seven asset-based factors of the Fung and Hsieh (2004b) model. Teo (2011) goes one step further by analyzing liquidity risk in liquid funds (with monthly redemption). Even in liquid Hedge Funds, Teo (2011) observes a significant spread of about 5.8% per year. His measure is robust to the proxy used for liquidity. Aragon (2007) also documents a significant risk premium related to the liquidity risk in HF returns. Contrary to Sadka (2010), he demonstrates a relationship between illiquidity and share restriction (measured by the lockup period).

78While Sadka (2010) and Teo (2011) directly price liquidity from HF returns, Patton and Ramadorai (2010) demonstrate that daily and monthly US liquidity is able to capture a large part of changes in HF risk exposures. Cao et al. (2011) moreover show that fund managers reduce the absolute magnitude of their risk factor exposures when liquidity in the market is poor and vice versa. They conclude to significant timing skills in Hedge Funds as they observe a significant spread in adjusted return between the top and low liquidity timing funds.

79Hedge Funds display a strong non-linear return structure, resulting in significant higher-order moments in their return distribution. Without being exhaustive, the following reasons have been advanced in the literature for explaining this evidence. First, Hedge Funds are dynamic in their investment strategies and their risk allocation, replicating option-like payoffs. Second, they have fewer restrictions on the use of leverage, short selling, and derivatives. Finally, they massively invest in not-frequently traded securities.

80An investment in Hedge Funds thus constitutes a whole package made, on the one hand, of low volatility and attractive diversification properties for the traditional asset classes, but, on the other hand, of serial correlation and non-normality in their return distribution. Ignoring these particular features will inevitably show up in alpha returns. This paper identifies Hedge Funds (hereafter HF) risk drivers that depart from the linearity assumption of the market model and introduces non-linear effects into the factors of the return generating process. Non-linearities in HF return payoffs are usually analyzed through a set of option-contract time-series. Previous empirical research on HF performance however fails to model all HF non-normality risks. We discuss the marginal significance of a new set of regressors corresponding to the higher-moments of the joint return density of Hedge Funds with the market. As there are no a priori grounding for using moments of order higher than four, we limit our valuation to coskewness and co*kurtosis risks in Hedge Funds and promote a four-moment asset pricing framework.

81The survey emphasizes that Hedge Funds are not exempted from systematic risks. Although they mix dynamic, leveraged and opportunistic trading, Hedge Funds transact in asset markets similar to those used by traditional managers, while being exposed to alternative sources of risk. Especially, this literature review decomposes the return generating process of Hedge Funds into the HF first, second, and third comoments with some market indexes.

82The multifactor analysis of HF returns defended in this paper provides a metric to judge the systematic risks embedded in HF investments. Its practical applications are numerous. First, the model constitutes a benchmark against which investors can evaluate HF risk exposures and can measure the quality of their HF investment by separating HF manager’s skills from systematic risk exposures. Passive returns on Hedge Funds can indeed be replicated by an appropriate set of transparent and liquid risk factors: the value-added of the fund on the risk exposures can therefore be evaluated by difference. On this basis, investors can gauge whether the performance fees are appropriate or whether their capital is exposed to desired risks. Most investors are indeed interested in the HF diversification/hedging potential for their more traditional portfolio. Second, by quantifying HF risk exposures, the model allows to form clusters of Hedge Funds according to their real investment style and to compare them to the classification recorded in HF databases. Finally, decomposing HF returns into their asset allocation allows the regulators to evaluate potential convergence of systematic risk exposures among Hedge Funds. It also allows HF counterparties (that hold Hedge Funds in their portfolio) to aggregate HF risk into their capital-at-risk requirement in a risk management objective.

83The paper raises some issues about the modelling of the return generating process in Hedge Funds. First issue to be addressed is how to compute distribution-based variables in such a comprehensive way that they could compete with the other sets of variables. Second issue to be addressed is how to discriminate between all these different sets of premiums. Multicollinearity in variables could indeed mask the statistical significance of some valuable variables. Besides, the heterogeneity among and between HF main strategies, seems to be another challenge to deal with when selecting a relevant set of variables for analyzing Hedge Funds. Future research should address these issues.