Optimal Shrinkage-Based Portfolio Selection in High-Dimensions

Abstract
In this talk we provide an overview of our recent findings in the high-dimensional mean- and minimum variance portfolio optimization using the theory of random matrices. We construct the regularized and non-regularized linear shrinkage estimators for the portfolio weights which are distribution-free and optimal in the sense of maximizing with probability one the asymptotic out-of-sample expected utility or minimization of the out-of-sample variance. The asymptotic properties of the new estimators are investigated when the number of assets $p$ and the sample size $n$ tend simultaneously to infinity such that $p/n \rightarrow c\in (0,+\infty)$. The results are obtained under weak assumptions imposed on the distribution of the asset returns, namely the existence of the $4+\varepsilon$ moments is only required. The suggested estimators show significant improvements over the existent approaches including the nonlinear shrinkage estimator and the three-fund portfolio rule, especially when the portfolio dimension is larger than the sample size. Moreover, they are robust to the deviations from normality.

If you are interested to join thisseminar online, please send an email to seminar@tinbergen.nl before Friday morning March 4.