Regularized Robust Strategic Asset Allocation under Stochastic Variance-Covariance of Asset Returns

Abstract

This study considers a finite-time robust consumption-investment problem under a quadratic security market model with stochastic variances and covariances of asset returns, as well as stochastic interest rates, market price of risk, and inflation rates. Because the optimal portfolio is proportional to the inverse of the stochastic variance-covariance matrix of asset returns, it becomes unstable when near-singularity of the variance-covariance matrix occurs. We propose a regularized consumption-investment problem in which the near-singularity risk is introduced into the budget constraint equation as a regularization term. We show that the optimal regularized portfolio can be stable and decomposed into the product of the ''standard deviation,'' ''correlation,'' and ''investment control'' factors. As the optimal regularized robust portfolio contains an unknown function that is a solution to a nonlinear PDE, we derive an approximate optimal regularized portfolio. Our numerical analysis shows that the market timing effects in the approximate optimal regularized asset allocation are significant and nonlinear, and all factors contribute to these market timing effects. JEL classification: C61, G11