Bayesian Value at Risk Metrics for Equity Portfolios

Abstract

We develop a Bayesian framework for estimating high quantiles of the relative return loss distribution of equity portfolios. This framework allows for the incorporation of both quantitative data via a parametric model for the loss distribution as well as qualitative information, specified independent of the data, by the choice of a prior distribution over the model parameters. We apply these methods in the case of one and two dimensional models to estimate distribution parameters and associated error bounds from which 99% VaR values are estimated. Finally, we systematically apply our framework to four test portfolios, compute summary statistics related to model performance, and report the results.

Keywords: Bayesian Inference, Value at Risk, Burr Distribution

JEL Classification: C11