Given the importance of the loss function choice [Christoffersen, P. and K. Jacobs (2004) The importance of the loss function in option valuation. J. Financial Economics 72: 291-318], this paper proposes the nonparametric technique of cross validation, to tuning the shrinkage intensity estimation of Ledoit and Wolf [Ledoit, O. and W. Michael (2003) Improved estimation of the covariance matrix of stock returns with an application to portfolio selection. J. Empirical Finance 10: 603-621; Ledoit, O. and W. Michael (2004) Honey, I Shrunk the Sample Covariance Matrix. J. Portfolio Management 30: 110-119; Ledoit, O. and W. Michael (2004) A well-conditioned estimator for large-dimensional covariance matrices. J. Multivariate Analysis 88: 365-411]. By aligning the loss function of out-of-sample forecast identical to the one used for the shrinkage intensity estimation, the proposed cross validation approach shows the significant gains in terms of both the variance reduction and information ratio improvement to various portfolios of the U.S. firms.

cross validation, shrinkage targeting, portfolio choice, shrinkage intensity, loss function