An Entropy-Based Approach to Portfolio Optimization.

Peter Joseph Mercurio,Yuehua Wu,Hong Xie

doi:10.3390/e22030332

Peter Joseph Mercurio, Yuehua Wu + Show 1 more

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https://doi.org/10.3390/e22030332

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Journal: Entropy	Publication Date: Mar 14, 2020
Citations: 26	License type: CC BY 4.0

Affiliation: York University, Royal Bank of Canada

Abstract

This paper presents an improved method of applying entropy as a risk in portfolio optimization. A new family of portfolio optimization problems called the return-entropy portfolio optimization (REPO) is introduced that simplifies the computation of portfolio entropy using a combinatorial approach. REPO addresses five main practical concerns with the mean-variance portfolio optimization (MVPO). Pioneered by Harry Markowitz, MVPO revolutionized the financial industry as the first formal mathematical approach to risk-averse investing. REPO uses a mean-entropy objective function instead of the mean-variance objective function used in MVPO. REPO also simplifies the portfolio entropy calculation by utilizing combinatorial generating functions in the optimization objective function. REPO and MVPO were compared by emulating competing portfolios over historical data and REPO significantly outperformed MVPO in a strong majority of cases.

Highlights

Markowitz [1] introduced the world’s first fundamentally sound quantitative approach to portfolio selection in 1952
return-entropy portfolio optimization (REPO) and mean-variance portfolio optimization (MVPO) were compared by emulating competing portfolios over historical data and REPO significantly outperformed MVPO in a strong majority of cases
The aim of this paper is to introduce a single optimization problem that solves all five issues with the MVPO method

Summary

Introduction

Markowitz [1] introduced the world’s first fundamentally sound quantitative approach to portfolio selection in 1952. He proposed an algorithm that finds the optimal capital allocation across a set of assets based on user-controlled risk parameters. Based on the volatility of random returns, Markowitz’s mean-variance portfolio optimization (MVPO). Markowitz’s variance-based approach to risk mitigation formed the foundation for modern portfolio theory and investment analysis, and inspired the basis for the capital asset pricing model (CAPM) introduced independently by Sharpe (1964) [3], Lintner (1965) [4,5], and Mossin (1966) [6]

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