A Bayesian Non-Parametric Approach to Asymmetric Dynamic Conditional Correlation Model With Application to Portfolio Selection

Abstract: We propose a Bayesian non-parametric approach for modeling the distribution of multiple returns. In particular, we use an asymmetric dynamic conditional correlation (ADCC) model to estimate the time-varying correlations of financial returns where the individual volatilities are driven by GJR-GARCH models. The ADCC-GJR-GARCH model takes into consideration the asymmetries in individual assets' volatilities, as well as in the correlations. The errors are modeled using a Dirichlet location-scale mixture of multivariate Gaussian distributions allowing for a great flexibility in the return distribution in terms of skewness and kurtosis. Model estimation and prediction are developed using MCMC methods based on slice sampling techniques. We carry out a simulation study to illustrate the flexibility of the proposed approach. We find that the proposed DPM model is able to adapt to several frequently used distribution models and also accurately estimates the posterior distribution of the volatilities of the returns, without assuming any underlying distribution. Finally, we present a financial application using Apple and NASDAQ Industrial index data to solve a portfolio allocation problem. We find that imposing a restrictive parametric distribution can result into underestimation of the portfolio variance, whereas DPM model is able to overcome this problem.