Multi-Period Portfolio Optimization Under Uncertainty using Diversification Measure

Abstract

Modern Portfolio Theory, with the introduction of the mean-variance model, established the first theoretical framework for portfolio selection. While the mean-variance model is widely used as the foundation for a broad range of problems in this field, it is criticized by researchers for its high sensitivity to input parameters and its tendency to select concentrated portfolios. To address these shortcomings, this research introduces the Robust Mean-Variance Entropy model. The Robust Mean-Variance Entropy model seeks to control the risk arising from estimation error by employing robust optimization. Furthermore, by incorporating Yager's entropy as a diversification measure, it aims to increase the diversification of the optimal portfolio by preventing concentrated allocations. The proposed model, which has a multi-period structure, was studied over an 18-month period, and its performance was evaluated and validated using historical data from the top 20 stocks of the S&P 500 index. When compared to an equally weighted portfolio, the results of the Robust Mean-Variance Entropy model show that while achieving high returns that were very close to its counterpart, the model demonstrated impressive performance in terms of risk management, effectively protecting its underlying capital during market downturns.