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Does Mean-CVaR Outperform Mean-Variance? Theoretical and Practical Perspectives

This paper provides a systematic investigation of the relative performance between the two mainstream portfolio optimisation methods: mean-variance and mean-Conditional Value-at-Risk (CVaR) from both theoretical and practical perspectives. Using portfolios representing the entire US stock market, we confirm the theoretical outperformance of mean-CVaR in the frictionless market. We explain the popularity of mean-variance in a practical investment context by showing that the superiority of mean-CVaR disappears when simple historical sample inputs and transaction costs are incorporated. We further reveal that the relative performance between the two optimisation methods is significantly influenced by the characteristics of the constituent stocks in the portfolio as well as the stock market condition. Our findings have important implications in shaping investment decisions.