On the (Mis)Use of Conditional Value-at-Risk and Spectral Risk Measures for Portfolio Selection - A Comparison with Mean-Variance Analysis

We study portfolio selection using Conditional Value-at-Risk and, as its natural extension, spectral risk measures instead of the variance. We do not focus only on the derivation of the efficient frontiers, but also consider the choice of optimal portfolios within an integrated framework. We find that spectral risk measures tend towards corner solutions. If a risk free asset exists, diversification is never optimal. Similarly, for risky assets we obtain only limited diversification. The reason is that spectral risk measures are based on a regulatory concept of diversification that differs fundamentally from the reward-risk tradeoff underlying the traditional mean-variance framework