Shannon Entropy as a Measure of Risk Based on Modern Portfolio Theory

Abstract

The proxy for risk is variance based on modern portfolio theory. The stock returns typically follow asymmetric distribution leading to implausible estimation of risk. This study replaces variance with Shannon Entropy as a measure of risk and applies it to modern portfolio theory. It accommodates asymmetric distributions, and it is fully nonparametric. The study employs portfolio optimization based on variance and Shannon Entropy for MINT, Visegrád group, and CIVETS markets. The results are compared using tracking error. The study reports that the mean-variance portfolio optimization tracking errors are higher than those of the Shannon Entropy portfolio optimization. This implies that the portfolio estimated, using the latter, closely follows its benchmark. The study benefits investors in better understanding the risk assessment and making plausible decisions based on return-entropy portfolio optimization adjusted for the desirable benchmark index.