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 in mean-risk optimization. However, there are several reasons for using CVaR instead of variance. Nonetheless, mean-variance can be a useful tool for illustrating fundamental investment concepts and principles. 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 industry 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, Monte Carlo simulation, synthetic market data generator, tail risks, convex optimization, Python Programming Language

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