Fragility of CVaR in portfolio optimization

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 aggravated by optimization. This prob- lem 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.