Minimum Rényi Entropy Portfolios

Annals of Operations Research, Forthcoming

37 Pages Posted: 16 May 2017 Last revised: 25 Aug 2019

See all articles by Nathan Lassance

Nathan Lassance

UCLouvain - UCLouvain, Louvain School of Management - Louvain Finance

Frédéric D. Vrins

Louvain Finance Center (LFIN), UC Louvain; Center for Operations Research and Econometrics (CORE), UC Louvain

Date Written: August 23, 2019

Abstract

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 through the "amount of randomness" conveyed by its returns. We achieve this by using an objective function that relies on the exponential of Rényi entropy, an information-theoretic criterion that precisely quantifies the uncertainty embedded in a distribution, accounting for higher-order moments. Compared to Shannon entropy, Rényi 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 Rényi entropy that extends a robust sample-spacings estimator initially designed for Shannon entropy. A portfolio selection application illustrates that minimizing Rényi entropy yields portfolios that outperform state-of-the-art minimum variance portfolios in terms of risk-return-turnover trade-off. We also show how Rényi entropy can be used in risk-parity strategies.

Keywords: Portfolio selection, Shannon entropy, Rényi entropy, Risk measure, Information theory, Risk parity

JEL Classification: G11

Suggested Citation

Lassance, Nathan and Vrins, Frederic Daniel, Minimum Rényi Entropy Portfolios (August 23, 2019). Annals of Operations Research, Forthcoming . Available at SSRN: https://ssrn.com/abstract=2968660 or http://dx.doi.org/10.2139/ssrn.2968660

Nathan Lassance (Contact Author)

UCLouvain - UCLouvain, Louvain School of Management - Louvain Finance ( email )

voie du roman, 34
Louvain-la-neuve, 1348
Belgium

Frederic Daniel Vrins

Louvain Finance Center (LFIN), UC Louvain ( email )

Voie du Roman Pays 34
Louvain-la-Neuve, 1348
Belgium

HOME PAGE: http://www.uclouvain.be/frederic.vrins

Center for Operations Research and Econometrics (CORE), UC Louvain ( email )

Voie du Roman Pays 34
Louvain-la-Neuve,, B-1348
Belgium

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