A Bayesian asymmetric approach to modelling volatility on portfolios with many assets

Abstract

A Bayesian approach for estimating and forecasting asymmetric GARCH models with Student’s t-distributed errors is proposed for modelling dynamic principal components of a hedge fund portfolio. The case study used is a hedge fund portfolio with 106 assets from various European exchanges. MCMC methods simulate the posterior distribution of the model parameters and, depending on the number of dynamic principal components used on the reconstruction, the resulting predictive distributions allow us to obtain a measure for the predictive ability of the models and forecast risk. The current study follows a similar published study by the same authors where a Bayesian GARCH(1,1) approach with t-distributed errors is used instead, and thus potential asymmetry in the volatility was not accounted for. Asymmetry in GARCH models can be an important inclusion in modelling financial volatility due to its capability of capturing leverage effect scenarios where negative shocks have a stronger impact on volatility than positive shocks. A Student’s t GJR(1,1) approach is used to cater for asymmetry, and the predictive performance of the proposed method is evaluated using an extended time horizon of the case study as a test period. We compare the predictive performance of multiple models with the formerly proposed Bayesian GARCH(1,1) approach using the same number of dynamic principal components and show that, models that cater for asymmetry tend to have better predictive ability, with a lower number of principal components. Risk measures are also evaluated for the different models.