Conditional value-at-risk in portfolio optimization: Coherent but fragile

Authors:
Andrew E. B. Lim;J. George Shanthikumar;Gah-Yi Vahn
Affiliations:
Department of Industrial of Engineering & Operations Research, University of California, Berkeley, CA 94720, United States;Krannert School of Management, Purdue University, West Lafayette, IN 47907, United States;Department of Industrial of Engineering & Operations Research, University of California, Berkeley, CA 94720, United States
Venue:
Operations Research Letters
Year:
2011

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Abstract

We evaluate conditional value-at-risk (CVaR) as a risk measure in data-driven portfolio optimization. We show that portfolios obtained by solving mean-CVaR and global minimum CVaR problems are unreliable due to estimation errors of CVaR and/or the mean, which are magnified by optimization. This problem is exacerbated when the tail of the return distribution is made heavier. We conclude that CVaR, a coherent risk measure, is fragile in portfolio optimization due to estimation errors.