A regularization approach to optimizing large portfolios under asymmetries in returns and risk attitudes

This article introduces a methodology for selecting large portfolios in the presence of asymmetries in asset returns and risk attitudes. Within this framework, the optimal portfolio depends on inverting the covariance matrix of returns. However, traditional estimators of this matrix become nearly singular when the number of assets is significantly larger than the sample size. This results in a selected portfolio that deviates substantially from the optimal one. To address this challenge, we propose four regularization techniques aimed at stabilizing the inverse of the covariance matrix: Ridge, Spectral Cut-Off, Landweber-Fridman, and Lasso for Nodewise Regression. These regularization techniques involve a tuning parameter that requires careful selection. To tackle this, we introduce a data-driven approach for choosing the optimal tuning parameter. Through extensive simulation exercise, we demonstrate the superior performance of the regularized optimal portfolio over several benchmark portfolios. Finally, we provide two empirical applications to illustrate the practical relevance of the proposed methods. In these applications, the results consistently show that incorporating asymmetries in returns and regularizing the inverse of the covariance matrix significantly improves the performance of the optimal portfolio. Specifically, our approach achieves higher Sharpe and Generalized Sharpe ratios, lower turnover, and greater stability compared to benchmark strategies.