Modern portfolio theory, while foundational, struggles with extreme sensitivity to input parameters and a tendency to select highly concentrated portfolios, often leading to out-of-sample underperformance. This research addresses these critical gaps by introducing the Generalized Robust Mean-Variance-Entropy (GRMVE) framework, a novel Mixed-Integer Quadratic Programming (MIQP) model designed for adaptive, multi-period investment settings. The GRMVE framework integrates budgeted uncertainty to mitigate the risk of estimation errors in expected returns, while simultaneously incorporating Yager’s entropy to mathematically enforce structural diversification and prevent over-concentration. The framework is empirically validated using a dynamic, expanding-window re-optimization approach over a 72-month horizon on a pre-selected universe of 60 assets spanning all 11 sectors of the S&P 500. Out-of-sample results demonstrate that the GRMVE framework achieves highly competitive risk-adjusted returns compared to the famously resilient Naive (1/n) strategy and the state-of-the-art Mean-CVaR model. Crucially, it overcomes the severe portfolio concentration and prohibitive trading turnover associated with scenario-based tail-risk models (CVaR) and the extreme instability of non-robust mean-variance models. By successfully navigating severe market downturns and volatile recoveries with significantly lower drawdowns, the findings highlight the GRMVE framework as a highly practical, computationally tractable, and structurally resilient solution for institutional portfolio management.
Khosravi et al. (Thu,) studied this question.