An Adaptive Regularization Approach to Portfolio Optimization

Abstract

We address the portfolio optimization problem using the global minimum variance portfolio (GMVP). The GMVP gives the weights as a function of the inverse of the covariance matrix (CM) of the stock net returns in a closed-form. The matrix inversion operation usually intensifies the impact of noise when the matrix is ill-conditioned, which often happens when the sample covariance matrix (SCM) is used. A regularized sample covariance matrix (RSCM) is usually used to alleviate the problem. In this work, we address the regularization issue from a different perspective. We manipulate the expression of the GMVP weights to convert it to an inner product of two vectors; then, we focus on obtaining accurate estimations of these vectors. We show that this approach results in a formula similar to those of the RSCM based methods, yet with a different interpretation of the regularization parameter’s role. In the proposed approach, the regularization parameter is adjusted adaptively based on the current stock returns, which results in improved performance and enhanced robustness to noise. Our results demonstrate that, with proper regularization parameter tuning, the proposed adaptively regularized GMVP outperforms state-of-the-art RSCM methods in different test scenarios.