Portfolio Optimization via Generalized Multivariate Shrinkage

The shrinkage method of Ledoit and Wolf (2003; 2004a; 2004b) has shown certain success in estimating a well-conditioned covariance matrix for high dimensional portfolios. This paper generalizes the shrinkage method of Ledoit and Wolf to a multivariate shrinkage setting, by which the well-conditioned covariance matrix is estimated using the weighted averaging of multiple priors, instead of single ones. In fact, it can be argued that the generalized multivariate shrinkage approach reduces estimation errors and uncertainty when projecting the true covariance matrix onto the line, spanned by priors joining to the sample covariance matrix. Hence, the generalized multivariate shrinkage is less subjected to sampling variation. Empirically, I use the U.S. firms to form portfolios for out-of-sample forecast. Using Ledoit and Wolf's approach as benchmark, out-of-sample portfolios constructed from the proposed method gain significant variance reductions and sizable improvement of information ratios. JEL Classifications: G11, G12