Does Tail Dependence Make A Difference In the ... - Boston College

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that ∆CoV aR is more in line with the “too interconnected to fail” paradigm, and SRISK is more related to the “too big to fail” paradigm. In contrast, MES offers a compromise between these two paradigms. 6 Concluding Remarks The global financial crisis initiated in 2008 has altered the regulators’ awareness of fragility of financial system. This paper develop a common framework based on copula model to estimate several widely used return-based systemic risk measures: Delta Conditional Value at Risk (∆CoV aR) and its Modified (∆CoV aR ), Marginal Expected Shortfall(MES) and its extension, systemic risk measure (SRISK). The nonlinear dependence of tail risk is straightforward to be accommodated in the copula model. By eliminating the discrepancy of the marginal distribution, the copula specification provide a flexibility to concentrate on the effect of the dependence structure in the estimation of systemic risk. Our empirical studies shows that the nonlinear dependence of tail risk does make a difference in the estimation of ∆CoV aR and MES. Simulation exercises reveal that ∆CoV aR originally proposed by AB(2011) is in conflict with dependence measures. The modified version of ∆CoV aR and MES is more consistent with dependence measures, which is line with economic intuition that stronger dependence strength results in higher systemic risk measures. Furthermore, we found that the linear quantile regression estimation of ∆CoV aR proposed by Adrian and Brunnermeier (2011) is inadequate to completely capture the non-linear contagion tail effect, which tends to underestimate systemic risk in the presence of lower tail dependence. We estimate the systemic risk contributions of four financial industry sample consisting of a large number of institutions for the sample period from January 2000 to December 2010, and we found that ∆CoV aR is observed to have a strong correlation with tail dependence. In contrast, MES is found to have a strong empirical relationship with firms’ conditional CAPM β. SRISK, however, provides further connection with firms level characteristics by accounting for information on market capitalization and liability. This stylized fact seems to imply that ∆CoV aR is more in line with the “too interconnected to fail” paradigm, and SRISK is more related to the “too big to fail” paradigm. In contrast, MES offers a compromise between these two paradigms. 32
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Page 1 and 2: Does Tail Dependence Make A Differe
Page 3 and 4: Figure 1: The upper panel graphs di
Page 5 and 6: more related to the “too big to f
Page 7 and 8: CoV aR (hereafter called CoV aR )
Page 9 and 10: Theorem 1 (Sklar)(1959) Let G be a
Page 11 and 12: Therefore the systemic risk measure
Page 13 and 14: Figure 3: This figure displays 8000
Page 15 and 16: (lower dependence with the market).
Page 17 and 18: higher value of systemic risk. Figu
Page 19 and 20: oth estimated based on the joint di
Page 21 and 22: Figure 8: This figure displays the
Page 23 and 24: the Goodness of Fit (GoF) of copula
Page 25 and 26: Depositories and Broker-Dealer comp
Page 27 and 28: 5.2 Empirical Results 5.2.1 Estimat
Page 29 and 30: [ Insert Table 6 Here ] Table 6 pre
Page 31: isk measure (last panel of Table 9)
Page 35 and 36: Appendix Proof on the relationship
Page 37 and 38: Therefore v = F Y (y) = Φ( y −
Page 39 and 40: In the case of continuous random va
Page 41 and 42: Table 2: Bivariate Copula Functions
Page 43 and 44: Table 5: AIC for the Different Copu
Page 45: Table 8: Systemic Risk Rankings:

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