Assessing systematic risk in the S&P500 index between 2000 and 2011: A Bayesian nonparametric approach

Abstract

We develop a Bayesian nonparametric model to assess the effect of systematic risks on multiple financial markets, and apply it to understand the behavior of the S&P500 sector indexes between January 1, 2000 and December 31, 2011. More than prediction, our main goal is to understand the evolution of systematic and idiosyncratic risks in the U.S. economy over this particular time period, leading to novel sector-specific risk indexes. To accomplish this goal, we model the appearance of extreme losses in each market using a superposition of two Poisson processes, one that corresponds to systematic risks that are shared by all sectors, and one that corresponds to the idiosyncratic risk associated with a specific sector. In order to capture changes in the risk structure over time, the intensity functions associated with each of the underlying components are modeled using a Dirichlet process mixture model. Among other interesting results, our analysis of the S&P500 index suggests that there are few idiosyncratic risks associated with the consumer staples sector, whose extreme negative log returns appear to be driven mostly by systematic risks.