1. Models for Risk Aggregation and Sensitivity Analysis: An Application to Bank Economic Capital Hulusi Inanoglu and Michael Jacobs, Jr. Enterprise and Credit Risk Analysis Divisions June 2009 The views expressed herein are those of the authors and do not necessarily represent the views of the Office of the Comptroller of the Currency or the Department of the Treasury.

18. Empirical Results: Summary Statistics (Call Report Data)

19. Empirical Results: Summary Statistics (Call Reports & CRSP)

20. Empirical Results: Summary Statistics (Call Report Variables)

21. Empirical Results: Summary Statistics (Call Report & CRSP)

22. Empirical Results: Summary Statistics (Risk Proxies)

23. Historical Quarterly Risk Proxies: Loss Distributions (1984-2008)

24. Historical Quarterly Risk Proxies: Loss Distributions (Top 200 Banks 1984-2008)

25. Historical Quarterly Risk Proxies: Time Series (1984-2008)

26. Historical Quarterly Risk Proxies: Time Series (Top 200 Banks 1984-2008)

27. Pairwise Correlations: Pearson vs. Spearman (5 Risk Types 1984-2008)

28. Pairwise Correlations, Scatters & Histograms (5 Risk Types 1984-2008)

29. Pairwise Correlations, Scatters & Histograms: 5 Risk Types (Top 200 Banks 1984-2008)

30. Spearman Correlations: 5 Risk Types Transformed Data

31. Spearman Correlations: 5 Risk Types Transformed Data (Top 200 Banks)

32. Dependograms of Multivariate Groupwise Independence Tests

33. Dependogram of Multivariate Groupwise Independence Tests – Top 200 Banks

34. Multivariate Groupwise Independence Tests: P-Values

35. Alternative Risk Measures: 99.97 th Percentile VaR

36. 99.97 th Percentile Dollar VaR Across Banks and Methodologies

37. 99.97 th Percentile VaR/BVA Across Banks and Methodologies

38. 99.97 th Percentile VaR Diversification Benefit Across Banks and Methodologies

39. Genest et al (2009) Copula Goodness-of-Fit Test P-values Across Banks and Methodologies

41. Alternative Risk Measures: 99 th Percentile Expected Shortfall

42. Normal Approximation Loss Distributions

43. Normal Approximation Loss Distribution: Top 200 Banks

44. Empirical Copula Simulated Loss Distributions

45. Empirical Copula Simulated Loss Distribution: Top 200

46. Gaussian Copula Simulated Loss Distributions

47. Gaussian Copula Simulated Loss Distribution: Top 200 Banks

48. Gaussian Copula vs. Normal Approximation & Empirical Copula Loss Distributions

49. Gaussian Copula vs. Normal Approximation & Empirical Copula Loss Distribution: Top 200 Banks

50. T-Copula Simulated Loss Distributions

51. T-Copula Simulated Loss Distribution: Top 200 Banks

52. Student-T Copula vs. Normal Approximation & Empirical Copula Loss Distributions

53. Student-T Copula vs. Normal Approx. & Empirical Copula Loss Distributions: Top 200 Banks

54. Archimadean (Gumbel) Simulated Loss Distributions

55. Archimadean (Gumbel) Simulated Loss Distribution: Top 200 Banks

56. Gumbel Copula vs. Normal Approximation & Empirical Copula Loss Distributions

57. Gumbel Copula vs. Normal Approx. & Empirical Copula Loss Distributions: Top 200 Banks

58. Archimadean (Clayton) Simulated Loss Distributions

59. Archimadean (Clayton) Simulated Loss Distribution: Top 200 Banks

60. Clayton Copula vs. Normal Approximation & Empirical Copula Loss Distributions

61. Clayton Copula vs. Normal Approx. & Empirical Copula Loss Distributions for Top 200

62. Archimadean (Frank) Simulated Loss Distributions

63. Archimadean (Frank) Simulated Loss Distribution: Top 200 Banks

64. Frank Copula vs. Normal Approximation & Empirical Copula Loss Distributions

65. Frank Copula vs. Normal Approx. & Empirical Copula Loss Distributions for Top 200

66. Bootstrap Analysis of Risk Measures: 99.97 th Percentile VaR

67. Bootstrap of Correlations: 99.97 th Percentile Dollar VaR Across Banks and Methodologies

68. Bootstrap of Margins: 99.97 th Percentile Dollar VaR Across Banks and Methodologies

69. Bootstrap Analysis of Risk Measures: VaR Diversification%

70. Bootstrap of Correlations: 99.97 th Perc. VaR % Diversification Benefit Across Banks and Methodologies

71. Bootstrap of Margins: 99.97 th Perc. VaR % Diversification Benefit Across Banks and Methodologies

73. Bootstrapping of Value-at-Risk: Normal Approximation

74. Bootstrapping of Value-at-Risk: Normal Approximation (Top 200 Banks)

75. Bootstrapping of Diversification Percentage: Normal Approximation

76. Bootstrapping of Diversification Percentage: Normal Approximation (Top 200 Banks)

77. Bootstrapping of Value-at-Risk: Empirical Copula

78. Bootstrapping of Value-at-Risk: Empirical Copula (Top 200 Banks)

79. Bootstrapping of Diversification Percentage: Empirical Copula

80. Bootstrapping of Diversification Percentage: Empirical Copula (Top 200 Banks)

81. Bootstrapping of Value-at-Risk: Gaussian Copula (Correlations)

82. Bootstrapping of Value-at-Risk (Correlations): Gaussian Copula (Top 200 Banks)

83. Bootstrapping of Diversification %: Gaussian Copula (Correlations)

84. Bootstrapping of Diversification % (Correlations): Gaussian Copula (Top 200 Banks)

85. Bootstrapping of Value-at-Risk: Gaussian Copula (Margins)

86. Bootstrapping of Value-at-Risk (Margins): Gaussian Copula (Top 200 Banks)

87. Bootstrapping of Diversification %: Gaussian Copula (Margins)

88. Bootstrapping of Diversification % (Margins): Gaussian Copula (Top 200 Banks)

89. Bootstrapping of Value-at-Risk: T- Copula (Correlations)

90. Bootstrapping of Value-at-Risk (Correlations): Student-T Copula (Top 200 Banks)

91. Bootstrapping of Diversification %: T-Copula (Correlations)

92. Bootstrapping of Diversification % (Correlations): Student-T Copula (Top 200 Banks)

93. Bootstrapping of Value-at-Risk: T-Copula (Margins)

94. Bootstrapping of Value-at-Risk (Margins) : Student-T Copula (Top 200 Banks)

95. Bootstrapping of Diversification %: T-Copula (Margins)

96. Bootstrapping of Diversification % (Margins): Student-T Copula (Top 200 Banks)

97. Bootstrapping of Value-at-Risk: Archimadean Gumbel (Correl’s)

98. Bootstrapping of Value-at-Risk (Correlations) : Archimadean Gumbel (Top 200 Banks)

99. Bootstrapping of Diversification %: Archimadean Gumbel (Correl’s)

100. Bootstrapping of Diversification % (Correlations) : Archimadean Gumbel (Top 200 Banks)

101. Bootstrapping of Value-at-Risk: Archimadean Gumbel (Margins)

102. Bootstrapping of Value-at-Risk (Margins): Archimadean Gumbel (Top 200 Banks)

103. Bootstrapping of Diversification %: Archimadean Gumbel (Margins)

104. Bootstrapping of Diversification % (Margins): Archimadean Gumbel (Top 200 Banks)

105. Bootstrapping of Value-at-Risk: Archimadean Clayton (Correl.’s)

106. Bootstrapping of Value-at-Risk (Correlations): Archimadean Clayton (Top 200 Banks)

107. Bootstrapping of Diversification %: Archimadean Clayton (Correl.’s)

108. Bootstrapping of Diversification % (Correlations): Archimadean Clayton (Top 200 Banks)

109. Bootstrapping of Value-at-Risk: Archimadean Clayton (Margins)

110. Bootstrapping of Value-at-Risk (Margins): Archimadean Clayton (Top 200 Banks)

111. Bootstrapping of Diversification %: Archimadean Clayton (Margins)

112. Bootstrapping of Diversification (Margins): Archimadean Clayton (Top 200 Banks)