Minimum Rényi entropy portfolios

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 re...

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Veröffentlicht in:Annals of operations research Jg. 299; H. 1-2; S. 23 - 46
Hauptverfasser: Lassance, Nathan, Vrins, Frédéric
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.04.2021
Springer Nature B.V
Schlagworte:
Business and Management
Combinatorics
Entropy
Entropy (Information theory)
Information theory
Kurtosis
Normality
Operations research
Operations Research/Decision Theory
Optimization
Parameter uncertainty
Risk
S.I.: Recent Developments in Financial Modeling and Risk Management
Theory of Computation
Uncertainty
Higher-order moments
Risk parity
Risk measure
Portfolio selection
Rényi entropy
Shannon entropy
Information theory
ISSN:0254-5330, 1572-9338
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Zusammenfassung: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.
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ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-019-03364-2