Optimal Shrinkage-Based Portfolio Selection in High Dimensions

In this article, we estimate the mean-variance portfolio in high-dimensional case using recent results from theory of random matrices. We construct a linear shrinkage estimator which is distribution-free and optimal sense maximizing with probability 1 asymptotic out-of-sample expected utility, that is, objective function for different values risk aversion coefficient particular leads to maximization utility minimization variance. One main features our inclusion estimation related sample mean vector into optimization. The properties new are investigated when number assets p size n tend simultaneously infinity such p/n→c∈(0,+∞). obtained under weak assumptions imposed on distribution asset returns, namely existence 4+ε moments only required. Thereafter perform numerical empirical studies where small- large-sample behavior derived investigated. suggested shows significant improvements over existent approaches including nonlinear three-fund rule, especially dimension larger than size. Moreover, it robust deviations normality.