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 a quadratic loss function measuring the distance between the estimated allocation and the optimal one. The cross-validation type criterion takes a similar form for the four regularization methods. Preliminary simulations show that regularizing yields a higher out-of-sample performance than the sample based Markowitz portfolio and often outperforms the 1 over N equal weights portfolio. We thank Marc Henry for his helpful comments.