A Fuzzy Entropy Approach for Portfolio Selection

Abstract

Portfolio management typically aims to achieve better returns per unit of risk by building efficient portfolios. The Markowitz framework is the classic approach used when decision-makers know the expected returns and covariance matrix of assets. However, the theory does not always apply when the time horizon of investments is short; the realized return and covariance of different assets are usually far from the expected values, and considering additional factors, such as diversification and information ambiguity, can lead to better portfolios. This study proposes models for constructing efficient portfolios using fuzzy parameters like entropy, return, variance, and entropy membership functions in multi-criteria optimization models. Our approach leverages aspects related to multi-criteria optimization and Shannon entropy to deal with diversification, and fuzzy and fuzzy entropy variants provide a better representation of the ambiguity of the information according to the investors’ deadline. We compare 418 optimal portfolios for different objectives (return, variance, and entropy), using data from 2003 to 2023 of indexes from the USA, EU, China, and Japan. We use the Sharpe index as a decision variable, in addition to the multi-criteria decision analysis method TOPSIS. Our models provided high-efficiency portfolios, particularly those considering fuzzy entropy membership functions for return and variance.

Keywords

• portfolio selection
• fuzzy entropy
• Shannon’s entropy
• multi-criteria optimization
• TOPSIS