Minimum Rényi entropy portfolios

  • Nathan LassanceEmail author
  • Frédéric Vrins
S.I.: Recent Developments in Financial Modeling and Risk Management


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 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.


Portfolio selection Shannon entropy Rényi entropy Risk measure Information theory Higher-order moments Risk parity 


Supplementary material

10479_2019_3364_MOESM1_ESM.pdf (274 kb)
Supplementary material 1 (pdf 273 KB)


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Authors and Affiliations

  1. 1.Louvain FinanceUCLouvain (BE)Louvain-la-NeuveBelgium
  2. 2.Louvain Finance, Center for Operations Research and EconometricsUCLouvain (BE)Louvain-la-NeuveBelgium

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