Minimum Rényi entropy portfolios

Accounting for the non-normality of asset returns remains challenging in robust portfolio optimization. In this article, we tackle this problem by assessing the risk of the portfolio via the "amount of randomness" conveyed by its returns. We achieve this using an objective function that relies on the exponential of Rényi entropy, an information-theoretic criterion that precisely quanties the uncertainty embedded in a distribution, accounting for higher-order moments. Compared to Shannon entropy, Renyi entropy features a parameter that controls the way uncertainty is measured. A Gram-Charlier expansion shows that the parameter controls for the relative contributions of the central (variance) and tail (kurtosis) parts of the distribution. We further rely on a non-parametric estimator of the exponential Renyi entropy, which extends a robust sample-spacings estimator initially designed for Shannon entropy. A portfolio selection application illustrates that minimizing Renyi entropy yields portfolios that outperform robust minimum variance portfolios in terms of risk-return-turnover trade-off.