Premium
The Effect of Shortfall as a Risk Measure for Portfolios with Hedge Funds
Author(s) -
Lucas André,
Siegmann Arjen
Publication year - 2007
Publication title -
journal of business finance and accounting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.282
H-Index - 77
eISSN - 1468-5957
pISSN - 0306-686X
DOI - 10.1111/j.1468-5957.2007.02054.x
Subject(s) - expected shortfall , downside risk , hedge fund , portfolio , semivariance , econometrics , economics , portfolio optimization , sharpe ratio , spectral risk measure , risk measure , tail risk , hedge , skewness , context (archaeology) , actuarial science , financial economics , mathematics , statistics , finance , ecology , paleontology , biology , spatial variability
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.