OPTIMAL HEDGE FUND STYLE ALLOCATION UNDER HIGHER MOMENTS JeanFrançois Bacmann and Sébastien Pache
INTRODUCTION
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 strategyspecific 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 skewnessandkurtosisadjusted parametric VaR model that replaces the standard deviation in the mean/standard deviation framework.
Bacmann and Pache find meanvariance 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 insample and outofsample 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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BIBLIOGRAPHY
 Agarwal, V., Daniel, N. and N. Naik, 2002, "Determinants of MoneyFlow and RiskTaking Behaviour in the Hedge Fund Industry," Working paper (Georgia State University).
http://www.GloriaMundi.org/picsresources/rbadn.pdf
 Amenc, N., Martellini, L., 2002b, "Portfolio Optimization and Hedge Fund Style Allocation Decisions", Journal of Alternative Investments, 5(2), 7?20.
 Athayde, G. and R. Flôres Jr., 2004, "Finding a Maximum Skewness Portfolio – a General Solution to ThreeMoments Portfolio Choice," Journal of Economic Dynamics and Control, 28(7), 13351352.
http://www.GloriaMundi.org/picsresources/rbgf.pdf
 Athayde, G. and R. Flôres Jr., 2002, "On Certain Geometric Aspects of Portfolio Optimisation with Higher Moments," Working paper (EPGE).
http://www.GloriaMundi.org/picsresources/rbgaf.pdf
 Bacmann, J.F and S. Scholz, 2003, "Alternative Performance Measures for Hedge Funds," AIMA Journal.
http://www.GloriaMundi.org/picsresources/rbbs.pdf
 Berenyi, Z., 2002, "Measuring Hedge Fund Risk with MultiMoment Risk Measures," Working paper University of Munich.
 Bernardo, A. and O. Ledoit, 2000, "Gain, Loss and Asset Pricing," Journal of Political Economy, 108(1).
 Brooks, C. and H. Kat, 2002, "The Statistical Properties of Hedge Fund Index Returns and Their Implications for Investors," Journal of Alternative Investments, Fall, pp. 2644.
http://www.GloriaMundi.org/picsresources/rbcbhk.pdf
 Cascon, A., Keating, C. and F. Shadwick, 2002, "The Mathematics of the Omega Measure," working paper, The Finance Development Centre.
 Favre, Laurent and J. Galeano, 2002, "MeanModified ValueatRisk Optimization with Hedge Funds," Journal of Alternative Investments 5(2).
http://www.GloriaMundi.org/picsresources/rbfg.pdf
 Jondeau, E. and M. Rockinger, 2002, "The Allocation of Assets Under Higher Moments," Fame Research Paper 71.
http://www.GloriaMundi.org/picsresources/rbejmr.pdf
 Keating, C. and F. Shadwick, 2002, "A Universal Performance Measure," The Journal of Performance Measurement 6 (3).
http://www.GloriaMundi.org/picsresources/rbks.pdf
 Li, D., 1999, "Value at Risk Based on the Volatility, Skewness and Kurtosis," Working paper (Riskmetrics Group).
http://www.GloriaMundi.org/picsresources/rbdxl.pdf
 Michaud, R., 1998, Efficient Asset Management (Cambridge, MA: Harvard Business School Press).
 Pratt, J. and R. Zeckhauser, 1987, "Proper Risk Aversion," Eoconmetrica 55(1).
 Ranaldo, A. and L. Favre, 2003, "How to Price Hedge Funds: From Two to FourMoment CAPM," Working paper (UBS Global Asset Management).
http://www.GloriaMundi.org/picsresources/rbarlf.pdf
 Roy, A., 1952, SafetyFirst and the Holding of Assets, Econometrica 20.
 Schmidhuber, C. and P.Y. Moix, 2001, "Fat Tail Risk: The Case for Hedge Funds," AIMA Newsletter (SeptDec).
 Scott, R. and P. Horvath, 1980, On the direction of preference for moments of higher order than the variance, Journal of Finance 35(4).
 Siegmann, A. and A. Lucas, 2002, "Explaining Hedge Fund Investment Styles by Loss Aversion: A Rational Alternative," Working paper (Vrije University).
http://www.GloriaMundi.org/picsresources/rbasal.pdf
 Signer, A. and L. Favre, 2002, "The Difficulties of Measuring the Benefit of Hedge Funds," Journal of Alternative Investments 5(1).
 Sortino, F. and L. Price, 1994, "Performance Measurement in a Downside Risk Framework," Journal of Investing, 5965.
 Stutzer, M., 2000, "A Portfolio Performance Index," Financial Analysts Journal 56(3).
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ERRATA AND OTHER MATERIAL
 Other research by JeanFrançois Bacmann:
Bacmann, JF, and S. Scholz, 2004, "Adding Hedge Funds to Traditional Investments," AIMA Journal (June).
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 More research by JeanFrançois Bacmann:
SSRN website
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