Asset-based factor models

In the literature, there is little agreement over the number of relevant factors required to accurately describe hedge fund performance. Goodworth and Jones (2007), for example, stated that a satisfactory level of representativeness for broad-based FoHFs may be achieved considering up to 100 factors descriptive of various equity, bond, commodity and foreign exchange markets. The dimensionality of the model may be reduced by removing co-linear factors in a stepwise process. However, for the regression model, the intercept can be overstated when the model is not correctly specified with respect to systematic risk exposure. For all underspecified models there is the risk of beta being disguised as managerial skill or a hedge fund’s alpha (e.g. Jaeger & Wagner, 2005: 11; Kat & Miffre, 2008).

Fung and Hsieh (1997a) pioneered the development of factor models for hedge funds. As in a standard Arbitrage Pricing Theory (APT) framework according to Ross (1976), they assumed that a limited number of observable factors explain a significant proportion of the variation in hedge fund returns, where the error term of the regression function denotes idiosyncratic risk. The asset classes used in explaining hedge fund performance include three broad stock indices, two bond-market proxies, a trade- weighted dollar index and the gold price. Goodness-of-fit for regression ( ) is found to be below 25 percent for nearly half the hedge funds and managed futures in the sample.

Schneeweis and Spurgin (1998) increased the number of factors by including a commodity index as well as intra-month volatility indices to account for hedge funds and managed futures taking up long and short positions. They establshed that hedge funds and managed futures derive different sources of return and systemic risk compared to mutual funds: the explanatory power of models including intra-month volatility confirmed the exposure of managed futures to intramonth movements (replacing the passive equity index with the intra-month volatility produced comparable model goodness-of-fit).

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The results are similar for the inclusion of a futures-based commodity proxy in the estimation of hedge fund returns.

In a similar vein, Agarwal and Naik (1999) applied an asset class factor model to hedge funds in the spirit of the Sharpe (1992) 12-factor model and its application to mutual funds. They imposed the sum-of-coefficients constraint to ease the interpretation of factor loadings as portfolio weights. Imposing no constraints may be referred to as ‘weak style analysis’ and imposing the sum-of-coefficient constraint as ‘semi-strong style analysis’. Imposing both the sum-of-coefficients constraint as well as non- negativity constraint constitutes ‘strong style analysis’ (Horst, Nijmen & Roon, 2004). Since hedge funds use shorting techniques to limit their exposure, the non-negativity constraint is often relaxed when generalised style models are applied to hedge funds. To limit multicollinearity between the regressors, they employed a stepwise regression algorithm.

Similarly, Liang (1999) employed stepwise regression to identify factor loadings on equity, fixed income, commodity and cash proxies. Edwards and Caglayan (2001) employed a six-factor model including the Fama and French (1992) High-minus-Low (HML) and Small-Minus-Big (SMB) portfolios, the Carhart (1997) Winners-minus-Losers (WML) portfolio, as well as a yield curve proxy to determine hedge fund alphas.

Analogous approaches to estimate hedge fund risk factors include: Boyson (2003) on multifactor models using standard asset indices, HML and SMB portfolios and a momentum factor; Teo, Koh and Koh (2003) explaining returns in Asian hedge funds replacing US Equity and Bond proxies with regional indices; Harri and Brorsen (2004) and Hasanhodzic and Lo (2007) on linear 6-factor models based on broad asset indices; Capocci, Corhay and Hübner (2005) combining the factors from previous research including Agarwal and Naik (2004); Ammann and Moerth (2008b) working on asset class factor models for FoHFs; Eling (2009) comparing several factor models including CAPM and the Fama-French / Momentum extension; Eling and Faust (2010) constructing asset-class factor models for emerging markets hedge funds using various equity and bond proxies.

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Using look-back straddles on a number of standard asset indices, Fung and Hsieh (2002a) showed that primitive trend-following strategies (PTFS) can explain the returns in trend-following hedge funds. The PTFS subsumed the non-linear relationship between the hedge fund style factors and the markets in which hedge funds trade. In a similar approach, to account for the nonlinearities in the relationship between hedge funds and risk factors, Agarwal and Naik (2004) extended their original model by incorporating option-based risk factors. Other risk factors included the Fama-French SML and HML factors, the Carhart momentum factor, as well as a commodity proxy. The varied between 44 percent for the HFR Event Arbitrage index and 92 percent for the Equity Non-Hedge index. However, some market neutral strategies like Fixed Income Arbitrage or Equity Market Neutral were not represented. Related research indicated that the inclusion of option-based risk factors did not significantly improve upon the results for market neutral strategies (e.g., Fung & Hsieh, 2001: on the risk in fixed-income based hedge fund styles).

An extension of asset-class factor modelling is observed in models including asset- based style (ABS) factors as described in Fung and Hsieh (2003, 2011). The four equity ABS factors included the S&P 500, and emerging market index as well as Small Cap – Large Cap stock and Value- Growth stock proxies. The proxies for fixed income hedge funds included various yield curve spreads.2 The risk factors for hedge funds depended on the prevailing underlying strategy: Directional, event driven, market neutral / relative value. ABS factors aid investors in identifying (portable) alphas adjusted for systematic style risks (see also Fung & Hsieh, 2004a).

Extensive research has been conducted with respect to factor models considering the option-like payoff of hedge fund investments. Mitchell and Pulvino (2001) found that the return profile of risk arbitrage funds correlates with that of selling uncovered index put options. Kouwenberg (2003) accounted for nonlinearities by considering the exposure of

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hedge funds to two option strategy portfolios, the first one selling one-month put options and the second portfolio selling one-month call options on the S&P 500. A similar approach was used by Jaeger and Wagner (2005) employing the Chicago Board of Trade’s BuyWrite Monthly Index (BXM), which mimics a covered-call-writing strategy using the S&P 500. An updated application of the PTFSs described in Fung and Hsieh (2001) can be found in Kosowski, Naik and Teo (2005). The hypothetic hedge funds used in Levchenkov, Coleman and Li (2009) to compare various approaches to hedge fund return modelling are option based market timing dynamic strategies. Some researchers suggested using non-linear asset pricing models to account for hedge funds’ exposure to higher moments of market indices (e.g. Ranaldo & Favre, 2005; Ding & Shawky, 2007).

Aragon (2007) argued that an ex ante estimation of an appropriate model to describe the systematic risk of hedge funds may be difficult to achieve. Four models were considered for hedge funds of the HFN database: A lagged market model including contemporaneous as well as lagged terms for the value-weighted market index to account for illiquidity; a broad market model including passive equity, fixed income and commodity benchmarks; an option model accounting for the dynamic market risk exposure as presented in Fung and Hsieh (2001) and Agarwal and Naik (2004); a Fama-French four factor model including a momentum factor and a market index. The quality of the regression models was found to be comparable across all four models.