Capturing time variation within systemic risk estimation

Abstract: Systemic risk can be defined as the risk to the whole financial system. Financial institutions may contribute more or less to this risk, and measuring the systemic risk contributions of institutions is of central importance for regulators. This is important since it makes it possible to determine to what extent different institutions contribute to the overall systemic risk of the financial system and hence which ones are more or less systemically important. Adrian & Brunnermeier (2011) proposes the systemic risk measure CoVaR, which builds on the framework of Value-at-Risk (VaR). The definition of CoVaR is the qth% VaR of institution j (or in the case of this essay, the European financial system) given that another institution i is at its qth% VaR. ∆CoVaR measures the change in the VaR for institution j given that institution i is in distress (compared to its normal state), and estimates the marginal risk contribution for a given institution. To obtain time variation in the estimates, the authors suggests using state variables that condition the mean and volatility of the risk measure. This essay tries to answer the question whether the systemic risk estimates obtained by using the CoVaR methodology, and the systemic risk contribution rankings between banks, are sensitive to the selection of these state variables. Using equity price data for 141 European banks, and data for 20 state variables during the time period from 31st of December 2002 to 30th of September 2022, this essay estimates VaR, CoVaR, ∆CoVaR and ∆$CoVaR using quantile regressions, following the methodology of Adrian & Brunnermeier (2011). Using four different state variable selection methods including the one suggested by Adrian & Brunnermeier, the supervised and unsupervised machine learning methods of Lasso regression and PCA, and a randomized method, systemic risk contributions over time are estimated and the banks are ranked according to these estimates. The results of this essay suggests that the CoVaR risk measure indeed is sensitive to the choice of state variables selection method, where both the estimates as well as rankings differs between the methods.