High-dimensional expected utility portfolios under the spiked covariance model

This paper tackles the key challenge of estimating high-dimensional covariance matrices for portfolio optimization by proposing a new framework that combines the Spiked Covariance Model with expected-utility maximization. We develop spectrally corrected estimators for the Optimal Expected Utility and Global Minimum Variance portfolios via a parameterized inverse-covariance formulation, with parameters chosen to maximize asymptotic out-of-sample expected utility—directly linking statistical estimation to financial performance. Extensive Monte Carlo simulations and an empirical study on S&P 500 constituents (2010–2024) show that our approach consistently outperforms standard benchmarks, including the sample covariance and linear/nonlinear shrinkage methods, delivering superior and more stable out-of-sample results in high-dimensional settings.