Dynamic return scenario generation approach for large-scale portfolio optimisation framework

Abstract

In this paper, we propose a complex return scenario generation process that can be incorporated into portfolio selection problems. In particular, we assume that returns follow the ARMA–GARCH model with stable-distributed and skewed t-copula dependent residuals. Since the portfolio selection problem is large-scale, we apply the multifactor model with a parametric regression and a nonparametric regression approaches to reduce the complexity of the problem. To do this, the recently pro posed trend-dependent correlation matrix is used to obtain the main factors of the asset dependency structure by applying principal component analysis (PCA). How ever, when a few main factors are assumed, the obtained residuals of the returns still explain a non-negligible part of the portfolio variability. Therefore, we propose the application of a novel approach involving a second PCA to the Pearson correlation to obtain additional factors of residual components leading to the refinement of the f inal prediction. Future return scenarios are predicted using Monte Carlo simula tions. Finally, the impact of the proposed approaches on the portfolio selection prob lem is evaluated in an empirical analysis of the application of a classical mean–vari ance model to a dynamic dataset of stock returns from the US market. The results show that the proposed scenario generation approach with nonparametric regression outperforms the traditional approach for out-of-sample portfolios.