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


Operations Research Letters


Management Science and Operations

Publication Year



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.


Portfolio optimization; Conditional value-at-risk; Expected shortfall; Coherent measures of risk; Mean-CVaR optimization; Mean-variance optimization

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