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

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Table 3: Summary Statistics for the unfiltered return series DowJones Index Depository Insurance Broker-Dealer Others Mean 0.0116 0.0396 0.0557 0.0472 0.0572 Std.dev 2.1113 2.8772 2.9194 4.4298 3.4317 Skewness 0.3022 0.7225 0.4246 1.3455 0.7839 Kurtosis 14.107 23.0947 27.9047 31.3129 25.5438 5%-VaR(left) -2.7719 -3.9201 -4.0153 -4.8486 -3.8385 5%-VaR(right) 2.7517 4.6253 4.5193 5.5541 4.0362 5%-ES(left) -0.2496 -0.3258 -0.3275 -0.3693 -0.3864 5%-ES(right) 0.2655 0.3616 0.3591 0.4283 0.4352 P-Value Jarque-Bera 0.0000 0.0000 0.0000 0.0000 0.0000 Ljung-Box 0.0001 0.0137 0.2187 0.0225 0.1909 This table provides summary statistics on the daily holding period return of some major US financial institutions and DowJones U.S. Financial Index for the period from 2000/01/03 until 2011/12/30. For each category, we report the average value across all institutions about the mean,the standard deviation, the skewness, the kurtosis, the 5% VaR and ES for the left and right tail of distribution. The second last row gives the median over all institutions of p-value of Jarque-Bera test for normality. and the last row reports the median of p-value for the Ljung-Box test with m = log(T ) lags. Table 4: Summary Statistics on Parameter Estimates(medians) DowJones Index Depository Insurance Broker-Dealer Others Panel A: GARCH Model σt 2 = ω + αe 2 t−1 + γe 2 t−1I (ei,t−1
Table 5: AIC for the Different Copula Models The metric for Goodness of Fit(GoF) test of Copula model will be Akaike’s Information Criterion(AIC) AIC := 2k − 2log(ĉ(u, v; ˆθ)) Comparing Dependence Structures Using Information Criteria(AIC) Sample (2000/01/03 ∼ 2011/12/31) Q5 Q25 MEAN Median Q75 Q95 Static Model Gaussian -3159.956 -2555.641 -1862.686 -1830.318 -1189.603 -479.192 Clayton -2501.409 -2118.555 -1534.261 -1539.268 -989.298 -406.144 Frank -3042.834 -2528.719 -1838.441 -1822.108 -1176.598 -513.067 Gumbel -3077.362 -2507.419 -1777.572 -1722.641 -1120.790 -428.260 RotGumbel -3070.431 -2590.530 -1849.739 -1837.672 -1181.537 -473.883 Student -3287.925 -2769.306 -1966.828 -1941.210 -1244.634 -517.695 SJC -3120.191 -2594.273 -1859.488 -1830.459 -1201.617 -485.712 G+RG+N -3300.940 -2773.381 -1976.469 -1955.856 -1253.859 -511.862 G+RG+F -3291.014 -2785.613 -1977.939 -1938.122 -1259.680 -528.553 C+G+F -3273.078 -2755.918 -1954.758 -1917.125 -1255.380 -516.206 C+G+N -3310.359 -2783.591 -1981.901 -1965.040 -1260.544 -515.251 Dynamic Model Gaussian -3349.462 -2700.856 -1992.150 -2028.358 -1295.944 -515.971 Gumbel -3219.850 -2590.012 -1895.849 -1886.464 -1226.038 -478.020 RoGumbel -3182.384 -2677.920 -1953.231 -1979.007 -1260.206 -517.688 Student -3424.752 -2859.831 -2084.023 -2098.774 -1348.755 -563.794 SJC -3246.307 -2676.910 -1953.047 -1941.163 -1268.510 -519.535 The acronyms ”SJC” refers to symmetrized Joe-Clayton Copula, which was proposed by Andrew Patton (2006). Dynamic Copula model was estimated following the ”Generalized Autoregressive Score”(GAS) model suggested by Creal,et al(2011), which was discussed in section 3.2. The acronyms ”G+RG+N” refers to mixture copula model of Gumbel+Rotated Gumbel+Normal. ”G+RG+F”: Gumbel+Rotated Gumbel+Frank. ”C+G+F”: Clayton+Gumbel+Frank. and ”C+G+N” : Clayton+Gumbel+Normal Table 6: Summary Statistics of P-Value For Unconditional Coverage and Independence Test for CoV aR Estimates r i,t V aRt(τ) i CoV aR (τ) τ = 0.05 Margin-Copula Margin-Copula Margin-Copula Margin-Copula Margin-Copula Norm - Norm Skewt - Norm Skewt - T Skewt - RotGumbel Skewt - Gumbel Q5 LR ucp 0.000 0.072 0.114 0.044 0.000 LR indp 0.130 0.179 0.194 0.185 0.135 Q10 LR ucp 0.000 0.167 0.184 0.048 0.001 LR indp 0.138 0.216 0.235 0.215 0.142 Q25 LR ucp 0.000 0.349 0.418 0.090 0.004 LR indp 0.273 0.296 0.340 0.341 0.201 Q50 LR ucp 0.002 0.680 0.705 0.514 0.050 LR indp 0.537 0.390 0.411 0.473 0.633 Q75 LR ucp 0.015 0.842 0.856 0.808 0.157 LR indp 0.747 0.479 0.544 0.617 0.830 Q95 LR ucp 0.189 0.942 0.973 0.956 0.275 LR indp 0.928 0.681 0.663 0.721 0.935 LR ucp refers to Kupiec’s (1995) test statistics for unconditional coverage testing. LR indp is Christofersen’s (1998) test statistics for Independence testing. The acronyms Q5 denotes the 5% quantile of the summary statistics of P-Value. 43
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: Table 2: Bivariate Copula Functions
Page 45: Table 8: Systemic Risk Rankings:

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