Double-Edged Sword of Diversification: Commodities and African Equity Indices in Robust vs. Optimal Portfolio Strategies

This study empirically investigates a central tension in quantitative finance: the divergence between theoretically optimal and robust portfolio construction under real-world estimation uncertainty. Using a dynamic, time-varying optimization framework, we compare the performance of three distinct strategies: the Maximum Sharpe ratio (P1), Minimum Variance (P2), and Maximum Entropy (P3) portfolios, with and without commodity proxy inclusion (gold and oil) in a multi-asset universe featuring prominent African equity indices. Our key finding challenges classical theory: the robust Maximum Entropy portfolio (P3) achieved superior realized risk-adjusted returns (Sharpe ratio: 1.164) compared to the theoretically optimal Maximum Sharpe portfolio (P1, Sharpe: 0.788). This result validates the “estimation-error maximization” critique, as P1’s performance was undermined by its sensitivity to noisy inputs. Conversely, the Minimum Variance portfolio (P2) successfully fulfilled its objective, achieving the lowest volatility (~5%) at the cost of modest returns (3.01–3.64%), illustrating the classic risk–return trade-off. Euler decomposition revealed that even this low-volatility portfolio exhibited significant concentration risk, with over 40% of its risk attributable to just three assets. The role of commodities is proven to be strategy contingent. They significantly enhanced returns and the Sharpe ratio for the aggressive P1 but were marginally detrimental to the robust P3. African market indices played specialized roles: Egypt and Nigeria acted as return drivers in P1, Morocco became a major risk contributor within the concentrated P2 strategy, and South Africa provided key diversification in the well-balanced P3. Ultimately, the study demonstrates that portfolio risk is determined more by asset concentration and diversification quality than by geographic labels, and that robust diversification methodologies outperform fragile theoretical optima in practice. We conclude that portfolio construction must prioritize robustness to estimation error and explicit risk-balancing to ensure stable, real-world performance.