Optimal Portfolio Selection using Regularization

The mean-variance principle of Markowitz (1952) for portfolio selection gives disappointing results once the mean and variance are replaced by their sample counterparts. The problem is ampli…ed when the number of assets is large and the sample covariance is singular or nearly singular. In this paper, we investigate four regularization techniques to stabilize the inverse of the covariance matrix: the ridge, spectral cut-o¤, Landweber-Fridman and LARS Lasso. These four methods involve a tuning parameter that needs to be selected. The main contribution is to derive a data-driven method for selecting the tuning parameter in an optimal way, i.e. in order to minimize the expected loss in utility of a mean-variance investor. The cross-validation type criterion takes a similar form for the four regularization methods. The resulting regularized rules are compared to the sample-based meanvariance portfolio and the naive 1/N strategy in terms of in-sample and out-ofsample Sharpe ratio and expected loss in utility. The main …nding is that a regularization to covariance matrix drastically improves the performance of meanvariance problem and outperforms the naive portfolio especially in ill-posed cases, as demonstrated through extensive simulations and empirical study.