We're Chained: an analysis of systemic risk in finance

Abstract

This dissertation presents two papers on how to deal with simple systemic risk measures to assess portfolio risk characteristics. The first paper deals with the Granger-causation of systemic risk indicators based in correlation matrices in stock returns. Special focus is devoted to the Eigenvalue Entropy as some previous literature indicated strong re- sults, but not considering different macroeconomic scenarios; the Index Cohesion Force and the Absorption Ratio are also considered. Considering the S&P500, there is not ev- idence of Granger-causation from Eigenvalue Entropies and the Index Cohesion Force. The Absorption Ratio Granger-caused both the S&P500 and the VIX index, being the only simple measure that passed this test. The second paper develops this measure to capture the regimes underlying the American stock market. New indicators are built using filtering and random matrix theory. The returns of the S&P500 is modelled as a mixture of normal distributions. The activation of each normal distribution is governed by a Markov chain with the transition probabilities being a function of the indicators. The model shows that using a Herfindahl-Hirschman Index of the normalized eigenval- ues exhibits best fit to the returns from 1998-2013.