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

27 Pages Posted: 15 Feb 2008  

Andre Lucas

VU Amsterdam - School of Business and Economics; Tinbergen Institute

Arjen Siegmann

VU University Amsterdam

Multiple version iconThere are 2 versions of this paper

Date Written: 2007-05


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 semi-variance 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.

Suggested Citation

Lucas, Andre and Siegmann, Arjen, The Effect of Shortfall as a Risk Measure for Portfolios with Hedge Funds (2007-05). Journal of Business Finance & Accounting, Vol. 35, Issue 1-2, pp. 200-226, January/March 2008. Available at SSRN: https://ssrn.com/abstract=1091590 or http://dx.doi.org/10.1111/j.1468-5957.2007.02054.x

Andre Lucas (Contact Author)

VU Amsterdam - School of Business and Economics ( email )

De Boelelaan 1105
Amsterdam, 1081 HV
+31 20 598 6039 (Phone)
+31 20 598 6020 (Fax)

HOME PAGE: http://personal.vu.nl/a.lucas

Tinbergen Institute

Roetersstraat 31
Amsterdam, 1018 WB

HOME PAGE: http://www.tinbergen.nl

Arjen Siegmann

VU University Amsterdam ( email )

De Boelelaan 1105
Dept. of Finance
Amsterdam, NOT IN US OR CANADA 1081 HV
+31205986581 (Phone)

HOME PAGE: http://personal.vu.nl/a.h.siegmann

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