Volatility, Correlation and Tails for Systemic Risk Measurement

by Christian T. Brownlees of the New York University, and
Robert Engle of the New York University

June 2011

Abstract: In this paper we propose an empirical methodology to measure systemic risk. Building upon Acharya et al. (2010), we think of the systemic risk of a financial institution as its contribution to the total capital shortfall of the financial system that can be expected in a future crisis. We propose a systemic risk measure (SRISK) that captures the expected capital shortage of a firm given its degree of leverage and Marginal Expected Shortfall (MES). MES is the expected loss an equity investor in a financial firm would experience if the overall market declined substantially. To estimate MES, we introduce a dynamic model for the market and firm returns. The specification is characterized by time varying volatility and correlation, which are modelled with the familiar TARCH and DCC. We do not make specific distributional assumptions on the model innovations and rely on flexible methods for inference that allow for tail dependence. The model is extrapolated to estimate the equity loss of a firm in a future crisis and consequently the capital shortage that would be experienced depending on the initial leverage. The empirical application on a set of top U.S. financial firms finds that the methodology provides useful rankings of systemically risky firms at various stages of the financial crisis. One year and a half before the Lehman bankruptcy, eight companies out of the SRISK top ten turned out to be troubled institutions. Results also highlight the deterioration of the capitalization of the financial system starting from January 2007 and that as of July 2010 the system does not appear fully recovered.

JEL Classification: C22, C23, C53.

Keywords: Systemic Risk, Volatility, Correlations, Tails, Forecasting

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