Variance for Intuition, Cvar for Optimization

Abstract

This article presents some of the pros and cons of variance and CVaR as portfolio risk measures in mean-risk optimization. While variance is the original risk measure, thoroughly studied for the past 70 years, this article argues that there are practically no reasons for continuing to use variance instead of CVaR. Although mean-CVaR is computationally more complex, the analytical benefits strongly outweigh mean-variance. Mean-variance can still be a useful tool for illustrating fundamental investment concepts, but it should not be used for investment management in practice. The case study illustrates that mean-variance and mean-CVaR optimization converge to the same results when demeaned Gaussian P&L is used in CVaR optimization. Hence, contrary to what seems to be the current standard, it is recommended to use demeaned P&L for CVaR optimization.

Documented Python code that replicates the results of the case study is available in the open-source package fortitudo.tech. More information about the package can be found on https://os.fortitudo.tech.

Keywords: Portfolio optimization, mean-variance, mean-CVaR, tail risks, convex optimization, risk budgeting, Monte Carlo simulation, synthetic market data generator, Python Programming Language

JEL Classification: B26, C02, C15, C61, G11