Application of Kernel Smoothing Methods with Cross-Validation Criterion Bandwidth Choice to Two-Stage Portfolio Selection

Well-known portfolio selection processes often employ either a mean-variance or expected utility framework. This paper deals with a portfolio selection process based on shortfall chance. Onerecent portfolio selection study based on shortfall chance used the nonparametric kernel method with Silverman’s bandwidth choice. This bandwidth choice assumes that the data distribution of interest is Gaussian. However, this bandwidth choice may be ineffective, as numerous empirical studies refer that financial asset returns are not Gaussian. Accordingly, an alternative method is proposed in this paper, based on the bandwidth choice with cross-validation criterion. In order to show the effectiveness of the proposed method, it is applied to simulated data from three non-Gaussian distributions and empirical data from three stock markets. The results of these experiments illustrate that the proposed method performs similarly or better than three conventional portfolio selection methods that respectively rely on Silverman’s bandwidth choice, Sharpe Ratio, and Stutzer’s PPI.