Systematic Risk Under Extremely Adverse Market Conditions

Abstract

Extreme losses are the major concern in risk management. However, the dependence between financial assets and the market portfolio is known to change under extremely adverse market conditions. This is why we develop a measure of systematic tail risk, the tail regression beta, defined by an asset’s sensitivity to large negative market shocks, and establish the estimation methodology. In our estimation methodology we exploit the heavy tail feature of financial returns instead of applying a linear regression based on tail observations. We find that the estimator of the tail regression beta has a similar structure as the estimator of the regular beta from regression analysis. Simulations show that our estimation methodology yields an estimator that has a lower mean squared error than just performing regressions in the tail. In an empirical exercise we compare the tail regression beta of industry portfolios to regular systematic risk measures: the market beta and the downside beta. The results demonstrate that the portfolio sensitivity to regular systematic risk is in general different from the sensitivity to systematic risk in severe market downturns. Hence, for risk management purposes, estimating the tail regression beta is an informative addition to the regular beta analysis. Furthermore, the tail regression beta is a useful instrument in both portfolio risk management and systemic risk management. We demonstrate its applications in analyzing Value-at-Risk (VaR) and Conditional Value-at-Risk (CoVaR).