OPTIMAL HEDGE FUND STYLE ALLOCATION UNDER HIGHER MOMENTS
Jean-François Bacmann and Sébastien Pache
Bacmann and Pache, tackle the problem of optimization of asset allocation to hedge funds, taking into account nonnormality in hedge fund returns. They implement an approach that is robust to the empirically observed negative skewness and excess kurtosis of hedge fund index returns, two characteristics of return distributions, which are generally agreed to be disliked by risk averse investors.
Bacmann and Pache accomplish this by making somewhat different behavioral assumptions about investors.
In the first case they assume that investors choose a portfolio to minimize the chance that returns will fall below a threshold level at some future date. The optimum portfolio is characterized by a statistic called the Stutzer index, a higher index value being more desirable.
In the second case they assume that investors choose a portfolio to maximize the ratio of the expected gains above a threshold level to the expected losses below that threshold level. The optimum portfolio is characterized by the Omega ratio, a higher value corresponding to a more desirable portfolio.
To evaluate the effects of nonnormality on portfolio selection, they construct an empirical portfolio optimization exercise. They assume an investor is allocating among 10 strategy-specific hedge fund indexes and an index intended to proxy for a commodity futures fund. Bacmann and Pache then compare optimal portfolios using the Stutzer index and the Omega ratio, and use as benchmarks the mean/standard deviation portfolio allocation framework and a skewness-and-kurtosis-adjusted parametric VaR model that replaces the standard deviation in the mean/standard deviation framework.
Bacmann and Pache find mean-variance portfolios usually overweight indices with negative skewness and high kurtosis relative to the new measures, a point in the favor of the new measures.
As a corollary they find the new measures tend to produce optimal portfolios with less negative skewness and less excess kurtosis. These results are broadly the same for both in-sample and out-of-sample experiments. Their findings suggest that their proposed measures may have something useful to say to investors, when returns exhibit departures from normality.
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ERRATA AND OTHER MATERIAL
- Other research by Jean-François Bacmann:
Bacmann, J-F, and S. Scholz, 2004, "Adding Hedge Funds to Traditional Investments," AIMA Journal (June).
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- More research by Jean-François Bacmann:
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