There are several advantages to the CoVaR measure First while CoVaR focuses on

# There are several advantages to the covar measure

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There are several advantages to the ° CoVaR measure. First, while ° CoVaR focuses on the contribution of each institution to overall system risk, traditional risk measures focus on the risk of individual institutions. Regulation based on the risk of institutions in isolation can lead to excessive risk-taking along systemic risk dimensions. To see this more explicitly, consider two institutions, A and B , which report the same VaR , but for institution A the ° CoVaR = 0 , while for institution B the ° CoVaR is large (in absolute value). Based on their VaR s, both institutions appear equally risky. However, the high ° CoVaR of institution B indicates that it contributes more to system risk. Since system risk might carry a higher risk premium, institution B might outshine institution A in terms of generating returns in the run up phase, so that competitive pressure might force institution A to follow suit. Regulatory requirements that are stricter for institution B than for institution A would break this tendency to generate systemic risk. One could argue that regulating institutions± VaR might be su¢ cient as long as each insti- tution±s ° CoVaR goes hand in hand with its VaR . However, this is not the case, as (i) it is not welfare maximizing that institution A should increase its contribution to systemic risk by fol- lowing a strategy similar to institution B institution and (ii) empirically, there is no one-to-one connection between an institution±s ° CoVaR (y-axis) and its VaR (x-axis), as Figure 1 shows. Another advantage of our co-risk measure is that it is general enough to study the risk spillovers from institution to institution across the whole °nancial network. For example, ° CoVaR j j i captures the increase in risk of individual institution j when institution i falls into 2 Just as VaR sounds like variance, CoVaR sounds like covariance. This analogy is no coincidence. In fact, under many distributional assumptions (such as the assumption that shocks are conditionally Gaussian), the VaR of an institution is indeed proportional to the variance of the institution, and the CoVaR of an institution is proportional to the covariance of the °nancial system and the individual institution. 2
WB WFC JPM BAC C MER BSC MS LEH GS AIG MET FNM FRE -6 -5 -4 -3 -2 -1 CoVaR -12 -11 -10 -9 -8 -7 Institution VaR Commercial Banks Investment Banks Insurance Companies GSEs CoVaR vs. VaR Figure 1: The scatter plot shows the weak link between institutions±risk in isolation, measured by VaR i (x-axis), and institutions±contribution to system risk, measured by ° CoVaR i (y-axis). The VaR i and ° CoVaR i are unconditional 1% measures estimated as of 2006Q4 and are reported in weekly percent returns for merger adjusted entities. VaR i is the 1% quantile of °rm returns, and ° CoVaR i gives the percentage point change in the °nancial system±s 1% VaR when a particular institution realizes its own 1% VaR . The institutions used in the °gure are listed in Appendix D.

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