Shrinkage estimation of higher-order comoment matrices: Is complexity always better than simplicity?

Our paper systematically investigates whether simple equal-weighted portfolios of estimators outperform complex shrinkage methods in estimating higher-order comoments for portfolio optimization. Empirical results demonstrate that simple equal-weighted portfolios of estimators provide superior out-of-sample performance, achieving higher Sharpe ratios (with improvements of up to 5%) and lower maximum drawdowns (with a decrease of up to 6%) compared to shrinkage methods. Robustness tests confirm the consistency of these results across varying levels of risk aversion coefficients and alternative objective functions. Additionally, portfolios based on higher-order moments consistently outperform global minimum variance portfolios in terms of risk-adjusted returns and tail risk management. Our findings extend the “simplicity is effective” principle to higher-order comoment estimation, providing practical tools for investors navigating asymmetric and fat-tailed markets.