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

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  • André Lucas
  • Arjen Siegmann

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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  • André Lucas & Arjen Siegmann, 2008. "The Effect of Shortfall as a Risk Measure for Portfolios with Hedge Funds," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 35(1‐2), pages 200-226, January.
    • Handle: RePEc:bla:jbfnac:v:35:y:2008:i:1-2:p:200-226
    DOI: 10.1111/j.1468-5957.2007.02054.x
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    2. Ines Fortin & Jaroslava Hlouskova, 2015. "Downside loss aversion: Winner or loser?," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(2), pages 181-233, April.
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    5. Madalina Gabriela ANGHEL & Gyorgy BODO & Okwiet BARTEK, 2016. "Model of Static Portfolio Choices," Romanian Statistical Review Supplement, Romanian Statistical Review, vol. 64(1), pages 49-53, January.

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