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Time-Varying Coefficient Model for Hedge Funds

Nowadays, it is well known that investing in Mutual Funds, on average, underperform passive investment strategies. One class commonly called Hedge Funds are defined as pooled investment vehicles that are privately organized, and not widely available to the general investing public. Hedge Funds are private partnerships that use advanced investment strategies and can use derivatives, leverage and short selling. Over the last few years, Hedge Funds have become the favorites of many private as well as institutional investors. Hedge Funds follow investment strategies that are substantially different from the non-leveraged, long-only strategies conventionally followed by investors. During alternative investment seminars and conferences, Hedge Fund managers boast about their ability to produce something they refer to as “alpha”or “absolute return”in the sense that performance is not due to primary asset classes performance. They do not aim to track and try to beat a certain benchmark, but instead are focused on pure return generation. Hence Hedge Funds generate alpha, as opposed to depending on beta and performance should normally result from active management decisions combined with the skills of their advisors. However statistical analysis shows that many of them retain significant exposure to different types of market risk factors.

Consequently, it is essential for qualified investors to determine whether or not these strategies are sensitive to the market and whether they can find alpha through the manager’s skill. For these reasons, an increasing focus has been directed to the performance of Hedge Funds and their factor exposures.

Mostly, owing to the theory of CAPM or APT, fund performances are assessed by a parametric model with the hypothesis of normality and linearity of coefficients, as well as, the non-dynamic behavior of beta. Some researchers expanded the parametric model to the world of Hedge Funds. Fung and Hsieh (2001, 2004a) developed factors used to replicate trend-following strategies. Agarwal and Naik (2000) suggested an approach using option-based returns in order to capture the non-linearity in beta. Recently, Bollen and Whaley (2008) tested for structural change and used two econometric models in order to capture the dynamic in beta.

In this paper, we attempt to go a step further than the previous research. First, by developing the result from Bollen and Whaley (2008) by testing up to five multiple structural changes. We showed that the relative number of breaks by fund has increased over the last few years, resulting in the increase of the use of leverage.

Secondly, by developing a new model for Hedge Funds which can take into consideration their distinctly non-normal characteristics, the dynamic in manager skill, as well as, the dynamic trading represented respectively by alpha and beta. This model allows us to relax traditional parametric models and to exploit possible hidden structure. For example, what manager skill is the most important? Is it the skill to pick and choose the right stocks, bonds, any other financial products, or is it the skill to anticipate market events? If we consider that alpha estimated from a linear model contains the two skills, how can we separate and study them? Can we find a different proportion of positive-alpha funds? This model specifically allows us to look into how managers behave in relation to strong events and whether or not they succeed to generate alpha. Moreover, Hedge Fund managers are likely to change trading strategies in order to obtain “absolute return”. Therefore, the exposure to a risk factor can change during special events and can have some deep implications for a Fund of Funds or a portfolio. Often it has been merely stated that during an event, risk to a specific factor can increase or decrease. Our study also portrays how the beta exposure or risk behaves in relation to market reaction, as well as, alpha during two agitated periods; the equity bubble crisis (the Equity Bubble hereafter) and LTCM crisis (LTCM hereafter).

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Time-Varying Coefficient Model for Hedge Funds