Minimum Rényi entropy portfolios

Abstract

Accounting for the non-normality of asset returns remains one of the main challenges in portfolio optimization. In this paper, we tackle this problem by assessing the risk of the portfolio through the “amount of randomness” conveyed by its returns. We achieve this using an objective function that relies on the exponential of Renyi entropy, an information-theoretic criterion that precisely quantifies the uncertainty embedded in a distribution, accounting for higher-order moments. Compared to Shannon entropy, Renyi entropy features a parameter that can be tuned to play around the notion of uncertainty. A Gram–Charlier expansion shows that it controls the relative contributions of the central (variance) and tail (kurtosis) parts of the distribution in the measure. We further rely on a non-parametric estimator of the exponential Renyi entropy that extends a robust sample-spacings estimator initially designed for Shannon entropy. A portfolio-selection application illustrates that minimizing Renyi entropy yields portfolios that outperform state-of-the-art minimum-variance portfolios in terms of risk-return-turnover trade-off. We also show how Renyi entropy can be used in risk-parity strategies.