The last decade has seen an increase in the number of hedge funds and availability of hedge fund data both on individual hedge funds and on hedge fund indexes. Unlike mutual funds, hedge funds engage in dynamic strategies, use leverage, take concentrated bets and have non-linear payoffs. Colossal losses for hedge funds in Fixed Income strategy in 1998, Long/Short Equity and Global Macro strategies in 2002 and recent losses in Convertible Bond Arbitrage strategy are all attributed to different reasons and risk exposures. Therefore, it is important to understand and model time-varying risk exposures for various strategies and obtain reliable estimates for predicted exposures of hedge fund returns to various market risk factors in different market environments.
Hedge fund strategies greatly differ from each other and have different risk exposures. Fung and Hsieh (2001) analyzed a trend following" strategy and Mitchell and Pulvino (2001) studied a risk arbitrage" strategy. Both studies find the risk return characteristics of the hedge fund strategies to be nonlinear and stress the importance of taking into account option-like features while analyzing hedge funds. Moreover, Agarwal and Naik (2004) show that the non-linear option-like payoffs called also Asset-Based Style Factors (ABS-Factors introduced by Fung and Hsieh (2002a))are not restricted just to these two strategies, but are an integral part of payoffs of various hedge fund strategies.
Hedge funds may exhibit non-normal payoffs for various reasons such as their use of options, or more generally dynamic trading strategies. Unlike most mutual funds (Koski and Pontiff (1999) and Almazan et al.(2001)), hedge funds frequently trade in derivatives. Further, hedge funds are known for their opportunistic" nature of trading and a significant part of their returns arise from taking state-contingent bets.
Nevertheless, there is still a limited understanding of the real non-linear exposure to risk factors of the different hedge funds strategies. Up to this point, most of the studies on hedge funds performance have been based either on (i) the classical linear factor model applied to mutual funds, (ii) non-parametric models or (iii) linear factor models with option-like factors. We are unaware of any published evaluation of the profitability or risk of hedge funds based on parametric non-linear models. In this paper, in line with the asset pricing perspective proposed by Bekaert and Harvey (1995), we suggest to analyze the exposure of hedge fund indexes with a factor model based on regime switching, where non-linearity in the exposure is captured by factor loadings that are state dependent. The regime switching approach is able to identify when the market risk factor is characterized by normal conditions, down-market or up-market and the state dependent factor loading is able to capture the exposure of the hedge fund to the market risk factor in these different states. Our empirical results show that our switching regime beta model can explain a large proportion of the variation in returns of hedge funds.
The reason of this greater ability is that the link between a hedge fund and market risk factors, due to dynamic strategies employed by hedge funds, is characterized by a phase locking model. For example, we might have that most of the time, market betas are very low, but suddenly market betas become very high. If we use simple linear models with linear factors, then betas will be close to zero, so we are not capturing a small-probability down-market event that would lead to the phase-locking behavior.
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