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

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Table 7: Comparison of ∆CoV aR and MES Measures (2000/01/03 ∼ 2011/12/30) Distress Definition r i,t = V aRt(τ) i ∆CoV aR = (τ) τ = 0.05 Margin-Copula Margin-Copula Margin-Copula Panel A AB(quantile) Norm - Norm Skewt - Norm Skewt - T Overall 1.73 1.68 2.28 2.23 Depository 1.95 1.92 2.52 2.40 Insurance 1.55 1.46 2.06 2.06 Broker-Dealer 1.68 1.70 2.33 2.26 Others 1.67 1.61 2.22 2.18 AB(quantile) refer to the estimation of ∆CoV aR by quantile regression following Adrian and Brunnermeier (2011). Norm-Norm represents bivariate normal joint distribution. As proposition 1 shows, the close form solution in this case is ∆CoV aR = ρσ m Fɛ −1 (τ) Distress Definition r i,t V aRt(τ) i ∆CoV aR (τ) τ = 0.05 Margin-Copula Margin-Copula Margin-Copula Panel B Norm - Norm Skewt - Norm Skewt - T Overall 1.16 1.81 1.93 Depository 1.27 2.00 2.02 Insurance 1.05 1.64 1.84 Broker-Dealer 1.17 1.85 1.95 Others 1.13 1.76 1.92 MES = E(r it |r mt q 0.05 ) Margin-Copula Margin-Copula Margin-Copula Panel C Norm - Norm Skewt - Norm Skewt - T Overall 3.38 3.75 4.23 Depository 3.52 3.90 4.27 Insurance 2.80 3.13 3.63 Broker-Dealer 4.26 4.78 5.37 Others 3.57 3.91 4.48 Norm-Norm represents bivariate normal joint distribution. The close form solution in this case is MES = E(r it |r mt q 0.05 ) = ρ σi σ m E(r mt |r mt q 0.05 ). 44
Table 8: Systemic Risk Rankings: ∆CoV aR , Tail Dependence, MES, β and SRISK Rank ∆CoV aR Tail-DeP MES β SRISK LEV MV 1 NYX JPM AIG AIG C FRE BAC 2 BAC C LEH LEH JPM FNM JPM 3 JPM BAC WB WB BAC NCC WFC 4 C TROW FNM FNM AIG MS C 5 GNW BEN FRE FRE FNM WB GS 6 AIZ LM BAC BAC MS AIG MET 7 TROW AXP C C FRE ETFC PRU 8 AXP PFG ABK ABK GS SLM MER 9 TMK PRU MS MS MER MER STT 10 FNF UNM MBI SLM WB C AIG Pairs ∆CoV aR Tail-DeP MES β SRISK LEV MV ∆CoV aR - 5 2 2 3 1 3 Tail-DeP 5 - 2 2 3 1 4 MES 2 2 - 9 7 6 3 β 2 2 9 - 7 7 3 SRISK 3 3 7 7 - 7 6 LEV 1 1 6 7 7 - 3 MV 3 4 3 3 6 3 - Notes: The upper panel displays the ranking of the top 10 financial institutions based on the estimation of ∆CoV aR , Tail Dependence (Tail-DeP), MES, conditional CAPM β and SRISK which are all estimated by the student t copula with marginal distribution being skewed student t distribution. The last two columns display the firms’ characteristics: Leverage (LEV) and Market Capitalization (MV). In the lower panel, we report the number of concordant pair between every two systemic risk measure. The ranking is implemented on September 17, 2008 when Lehman Brothers filed for bankruptcy. Table 9: Rank similarity ratio for the top 10 most risky Institutions 2007/06/29 2007/12/31 2008/02/29 2008/06/30 2008/09/17 2009/01/30 2010/06/30 ∆CoV aR vs Tail-DeP 0.60 0.60 0.70 0.50 0.50 0.70 0.60 MES vs Tail-DeP 0.30 0 0.30 0.30 0.30 0.30 0.30 SRISK vs Tail-DeP 0.40 0.30 0.40 0.40 0.30 0.30 0.30 ∆CoV aR vs β 0 0 0.40 0 0.30 0.30 0.30 MES vs β 0.90 0.90 1.00 1.00 0.90 0.90 0.90 SRISK vs β 0.30 0.30 0.40 0.30 0.70 0.30 0.30 ∆CoV aR vs LEV 0 0 0 0.10 0.10 0 0 MES vs LEV 0.30 0.40 0.50 0.40 0.50 0.30 0.40 SRISK vs LEV 0.80 0.60 0.60 0.50 0.70 0.30 0.50 ∆CoV aR vs MES 0 0 0.10 0 0.20 0.20 0.10 ∆CoV aR vs SRISK 0.20 0.30 0.20 0.40 0.30 0.30 0.20 MES vs SRISK 0.30 0.30 0.40 0.30 0.70 0.30 0.20 Notes: The table presents the rank similarity measure between each pair of systemic risk measure displayed in the first column. The similarity ratio measure is simply defined as the proportions of top 10 risky firms that are simultaneously identified as SIFIs by the two rankings at a given date. The acronyms “Tail-Dep” and “LEV” represent tail dependence and Leverage, respectively. 45
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 and 32: isk measure (last panel of Table 9)
Page 33 and 34: References Acharya, V. V., Pedersen
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: Table 5: AIC for the Different Copu

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