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The Journal of Alternative Investments

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Article

Optimal Hedge Fund Allocation with Improved Estimates for Coskewness and Cokurtosis Parameters

Asmerilda Hitaj, Lionel Martellini and Giovanni Zambruno
The Journal of Alternative Investments Winter 2012, 14 (3) 6-16; DOI: https://doi.org/10.3905/jai.2012.14.3.006
Asmerilda Hitaj
is a research fellow at the University of Milano-Bicocca in Milan, Italy.
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  • For correspondence: asmerilda.hitaj1@unimib.it
Lionel Martellini
is a professor of finance at EDHEC Business School and scientific director at the EDHEC-Risk Institute in Nice, France.
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  • For correspondence: lionel.martellini@edhec.edu
Giovanni Zambruno
is a professor of quantitative finance at the University of Milano-Bicocca in Milan, Italy.
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  • For correspondence: giovanni.zambruno@unimib.it
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Abstract

Since hedge fund returns are not normally distributed, mean–variance optimization techniques are not appropriate and should be replaced by optimization procedures incorporating higher-order moments of portfolio returns. In this context, optimal portfolio decisions involving hedge funds require not only estimates for covariance parameters but also estimates for coskewness and cokurtosis parameters. This is a formidable challenge that severely exacerbates the dimensionality problem already present with mean–variance analysis. This article presents an application of the improved estimators for higher-order co-moment parameters, in the context of hedge fund portfolio optimization. The authors find that the use of these enhanced estimates generates a significant improvement for investors in hedge funds. The authors also find that it is only when improved estimators are used and the sample size is sufficiently large that portfolio selection with higher-order moments consistently dominates mean–variance analysis from an out-of-sample perspective. Their results have important potential implications for hedge fund investors and hedge fund of funds managers who routinely use portfolio optimization procedures incorporating higher moments.

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The Journal of Alternative Investments: 14 (3)
The Journal of Alternative Investments
Vol. 14, Issue 3
Winter 2012
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Optimal Hedge Fund Allocation with Improved Estimates for Coskewness and Cokurtosis Parameters
Asmerilda Hitaj, Lionel Martellini, Giovanni Zambruno
The Journal of Alternative Investments Dec 2011, 14 (3) 6-16; DOI: 10.3905/jai.2012.14.3.006

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Optimal Hedge Fund Allocation with Improved Estimates for Coskewness and Cokurtosis Parameters
Asmerilda Hitaj, Lionel Martellini, Giovanni Zambruno
The Journal of Alternative Investments Dec 2011, 14 (3) 6-16; DOI: 10.3905/jai.2012.14.3.006
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  • Article
    • Abstract
    • IMPROVED ESTIMATORS FOR HEDGE FUND RETURN COVARIANCE, COSKEWNESS, AND COKURTOSIS PARAMETERS
    • EMPIRICAL ANALYSIS
    • CONCLUSIONS
    • APPENDIX
    • ENDNOTES
    • REFERENCES
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