The Effect of Shortfall as a Risk Measure for Portfolios with Hedge Funds

Authors

  • André Lucas,

    1. The authors are respectively from VU University Amsterdam and Tinbergen Institute; and VU University Amsterdam and Netherlands Central Bank (DNB). A previous version of this paper has circulated under the title ‘Explaining Hedge Fund Strategies by Loss Aversion’. The authors thank Emmanuel Acar, Cees Dert, Chris Gilbert, Frank van den Berg, Marno Verbeek, Jenke ter Horst, an anonymous referee, and participants of the European Investment Review 2nd annual conference, EFMA meeting 2003 and EFA 2003, for helpful comments and suggestions.
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  • Arjen Siegmann

    Corresponding author
    1. The authors are respectively from VU University Amsterdam and Tinbergen Institute; and VU University Amsterdam and Netherlands Central Bank (DNB). A previous version of this paper has circulated under the title ‘Explaining Hedge Fund Strategies by Loss Aversion’. The authors thank Emmanuel Acar, Cees Dert, Chris Gilbert, Frank van den Berg, Marno Verbeek, Jenke ter Horst, an anonymous referee, and participants of the European Investment Review 2nd annual conference, EFMA meeting 2003 and EFA 2003, for helpful comments and suggestions.
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  • They thank Ting Wang for computational assistance. Siegmann acknowledges financial support from the Dutch National Science Foundation (NWO).

* Address for correspondence: Arjen Siegmann, VU University Amsterdam, The Netherlands.
e-mail: asiegmann@feweb.vu.nl

Abstract

Abstract:  Current research suggests that the large downside risk in hedge fund returns disqualifies the variance as an appropriate risk measure. For example, one can easily construct portfolios with nonlinear pay-offs that have both a high Sharpe ratio and a high downside risk. This paper examines the consequences of shortfall-based risk measures in the context of portfolio optimization. In contrast to popular belief, we show that negative skewness for optimal mean-shortfall portfolios can be much greater than for mean-variance portfolios. Using empirical hedge fund return data we show that the optimal mean-shortfall portfolio substantially reduces the probability of small shortfalls at the expense of an increased extreme crash probability. We explain this by proving analytically under what conditions short-put payoffs are optimal for a mean-shortfall investor. Finally, we show that quadratic shortfall or semivariance is less prone to these problems. This suggests that the precise choice of the downside risk measure is highly relevant for optimal portfolio construction under loss averse preferences.

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