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

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.