Hedge Funds*
3. Replication of Hedge Fund Returns
constituent strategy-based sub-indices relative to other investable indices and non-investable and strategy-based indices in terms of risk and return to determine whether the investable index created based on a larger sample size is a better representation of the performance of hedge funds.25Their results show that for many hedge fund strategies, the RBC indices perform either markedly superior or inferior to other comparable indices. In addition, the RBC indices generally have higher volatility at the sub-index level and higher equity betas. However, the index history is still too short for a definitive conclusion.
Although the proliferation of investable indices is one step closer to benchmarking the hedge fund performance precisely, Schneeweis et al. (2003) note that one should not expect any one single hedge fund index to track the performance of hedge fund managers even within the same strategy. However, as for traditional securities, for a strategy-pure index of hedge funds, a portfolio of similar funds should have performance similar to that of the representative hedge fund index. The lack of a clear hedge fund benchmark, however, is not indicative of an inability to determine a comparable return for a hedge fund strategy. Hedge fund strategies within a particular style often trade similar assets with similar methodologies and are sensitive to similar market factors. Thus, replication of hedge fund returns is feasible.
also suggest that a declining alpha is indicative of the declining quality of the average hedge fund manager. Due to low entry barriers to the hedge fund industry, it has attracted numerous managers with a lower level of skill. The new managers tend to dilute the average perform- ance and hence the average alpha of the entire industry. With a declin- ing alpha, Wall Street investment houses and investors are interested in finding ways of replicating hedge fund returns that are not subject to the capacity constraint and high performance fees.
Others suggest that different hedge fund strategies exhibit different exposures to various systematic risk factors and alpha is not simply a function of manager skill (Schneeweis and Spurgin, 1998;
Géhin and Vaissié, 2006). Put another way, hedge funds make bets on different market risk factors (or betas), traditional and alternative; the bet made on the manager skill is the alpha. Géhin and Vaissié (2006) show that alpha will be reduced if exposures to other risk factors (i.e., alternative betas) are accounted for. However, it does not mean that the opportunity for alpha has been reduced by the increasing number of hedge funds which are believed to have driven away the market inefficiencies and hence reducing the alpha for everybody. Géhin and Vaissié believe that alpha is generated more by successful bets on dif- ferent exposures rather than by exploiting market opportunities, and thus alpha is not threatened by a problem of industry capacity con- straint. In sum, previous research has shown that hedge fund returns can be replicated and so can alpha.
In subsequent sections, we discuss two principal means of estab- lishing comparable portfolios which replicate hedge fund returns. One is using a single or multi-factor based methodology and the other is using optimization to create tracking portfolios with similar risk and return characteristics.
3.1 Factor-Model Based Replication
Previous academic studies have used both the single-factor and multi- factor models in identifying the sources of hedge fund returns (e.g., Fung and Hsieh, 1997; Schneeweis and Spurgin, 1998). The single- factor model suggests that returns of a hedge fund are a function of
its exposure to the market risk. An example of a single-factor model is the market model in which the single factor is proxied by a market index (e.g., S&P 500) and measured by the “traditional beta.” The multi- factor model suggests that hedge fund returns are a function of the fund’s exposure to the market risk (traditional beta), other systematic risk factors (measured by the so called “alternative betas”) and manager’s skill (measured by the alpha). The systematic risk factors may include the volatility risk (specific to the hedge fund strategy), default risk, and liquidity risk (Fung and Hsieh, 1997, 2002; Schneeweis and Spurgin, 1998).26The multi-factor model can be linear or non-linear.
Based on these factor models, academic research has also focused on direct replication of the underlying strategies and uses location and volatility factors as well as trend-following momentum models to cap- ture explicitly the implicit option payoff. In the non-linear multifac- tor models, the option-like payoff in the hedge funds is caused by the use of derivatives, leverage, and dynamic trading strategy, as well as the asymmetric performance fee (Mitchell and Pulvino, 2001; Fung and Hsieh, 2001; Agarwal and Naik, 2004). However, Schneeweis and Spurgin (2001) find that in previous studies, after taking market factors, changes in volatility and momentum factors into considera- tion, option-like payoff variables generally have little to add as explana- tory variables. In other words, while the use of certain location and trading strategy factors is consistent with the return of the underlying strategy, such factors may not directly represent the underlying trading process.
Hasanhodzic and Lo (2007) provide some evidence that linear replication can be successful for certain strategies while offering cer- tain advantages to hedge fund investing, such as more transparency, increased liquidity and fewer capacity constraints. However, they warn that the heterogeneous risk profile of hedge funds and the non- linear risk exposures greatly reduce the ability of these models to consistently replicate hedge fund returns. Likewise, Schneeweis and
26Non-directional hedge funds (e.g., convertible arbitrage, and market neutral long-short) are generally considered to be nonexposed to the market risk, but they are exposed to the volatility risk, default risk and liquidity risk.
Kazemi (2001a) note that each hedge fund strategy is designed to directly trade certain financial instruments in a pre-designed manner.
For instance, a particular hedge fund strategy may be designed to capture returns in markets which are: 1) delta neutral/long gamma;
2) low volatility/high trend; 3) low volatility/high market conver- gence; 4) decreasing credit spreads; and 5) market-factor driven.
3.2 Tracking Portfolio Based Replication
Recently, research has also focused on developing passive indices (e.g., tracking portfolios) which are either based on active managers who trade similar to the strategy in question and/or on individual security holdings within a particular strategy designed to minimize the return differential between the hedge fund strategy and the pas- sive index. For example, Schneeweis and Kazemi (2001a, 2001b) have created passive indices both from factors that underlie the strategy and financial instruments that are used in the strategy to track the return of the hedge fund strategy. Their results indicate that active hedge fund management gives evidence of positive alpha relative to the cited tracking portfolios.
3.3 Other Approaches to Hedge Fund Replication
In addition to the two approaches mentioned above, there are other approaches to hedge fund replication. Instead of identifying the return- generating betas, Amin and Kat (2003), and Kat and Palaro (2005) have attempted to replicate the distribution of hedge fund returns. The underlying idea is based on the notion that much of the trading activ- ity undertaken by hedge funds is not creating value, but merely alter- ing the timing of the returns available from traditional assets. In other words, many hedge funds are simply distorting readily available asset distributions. The authors attempt to find a better way to distort these distributions without actually investing in hedge funds.
Recently, Papageorgiou et al. (2007) use a multi-variate extension of Dybvig’s (1988) payoff distribution model to replicate the mar- ginal distribution of most hedge fund returns and their dependence
on other asset classes. Their model attempts to improve the ineffi- ciency and inconsistency in the Kat and Palaro (2005) model of repli- cation. Papageorgiou, Rémillard, and Hocquard conclude that their model can replicate the hedge fund returns.27More importantly, they suggest that their results “reinforce the notion that on aggregate, hedge funds are simply repackaging beta returns.”