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An Entropy-Based Approach to Portfolio Optimization.

Peter Joseph Mercurio1, Yuehua Wu1, Hong Xie2

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Summary
This summary is machine-generated.

This study introduces Return-Entropy Portfolio Optimization (REPO), a novel method using entropy for risk in portfolio management. REPO significantly outperforms traditional Mean-Variance Portfolio Optimization (MVPO) in historical data analysis.

Keywords:
Markowitz mean variancecapital asset pricing modeldiversificationentropy portfolio optimizationinvestment riskmodern portfolio theoryportfolio optimizationportfolio selectionreturn entropy

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Area of Science:

  • Quantitative Finance
  • Financial Risk Management
  • Computational Finance

Background:

  • Mean-Variance Portfolio Optimization (MVPO), pioneered by Harry Markowitz, is a foundational approach to risk-averse investing.
  • Traditional MVPO faces practical limitations in portfolio risk assessment and computation.
  • Entropy offers a robust alternative measure for quantifying risk in financial portfolios.

Purpose of the Study:

  • Introduce a new framework, Return-Entropy Portfolio Optimization (REPO), for portfolio optimization.
  • Address key practical limitations of MVPO by incorporating entropy as a primary risk measure.
  • Simplify the computational complexity of portfolio entropy calculations.

Main Methods:

  • Developed a novel combinatorial approach to compute portfolio entropy within the REPO framework.
  • Formulated REPO using a mean-entropy objective function, contrasting with MVPO's mean-variance objective.
  • Utilized combinatorial generating functions to streamline entropy calculations in the optimization objective.

Main Results:

  • REPO successfully addresses five practical concerns associated with MVPO.
  • Empirical comparison via emulation on historical data demonstrated REPO's superior performance.
  • REPO significantly outperformed MVPO in a substantial majority of simulated portfolio scenarios.

Conclusions:

  • The Return-Entropy Portfolio Optimization (REPO) framework offers a significant improvement over traditional MVPO.
  • REPO provides a more computationally tractable and effective method for portfolio risk management.
  • The findings suggest REPO as a promising alternative for modern portfolio construction and optimization.