  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.
