CreditValueatRiskChapter 18RiskManagementandFinanciallnstitutions3e,Chapter18,CopyrightJohnC.Hull2012
Risk Management and Financial Institutions 3e, Chapter 18, Copyright © John C. Hull 2012 Credit Value at Risk Chapter 18 1
Rating Transitions One year rating transition probabilities arepublished by rating agenciesIf we assume that the rating transition in oneperiod is independent of that in other periods wecan calculate the rating transition for any period(see Appendix J and software)The “ratings momentum" phenomenon meansthat the independence assumption is notperfectly correct2RiskManagementandFinancialInstitutions3e,Chapter18,CopyrightJohnC.Hull2012
Rating Transitions ⚫ One year rating transition probabilities are published by rating agencies. ⚫ If we assume that the rating transition in one period is independent of that in other periods we can calculate the rating transition for any period (see Appendix J and software) ⚫ The “ratings momentum” phenomenon means that the independence assumption is not perfectly correct Risk Management and Financial Institutions 3e, Chapter 18, Copyright © John C. Hull 2012 2
One-Year Rating TransitionMatrix (% probability, Moody's 1970-2010)Table18.1page401InitialRatingatyearendAAaBAaaBaCaaCa-CDefaultRatingBaaAaa90.428.920.620.010.030.000.000.000.00Aa1.0290.128.380.380.050.020.010.000.02A5.520.510.030.010.062.8290.880.110.060.19Baa0.050.194.7989.414.350.820.180.02Ba0.010.060.410.590.091.226.2283.437.97B5.320.010.040.140.3882.196.450.744.739.41Caa0.000.020.020.160.534.6716.7668.43Ca-C0.000.000.000.000.392.8510.6642.5643.54Default0.000.000.000.000.000.000.000.00100.003RiskManagementandFinancialInstitutions3e,Chapter18,CopyrightJohnC.Hull2012
One-Year Rating Transition Matrix (% probability, Moody’s 1970-2010) Table 18.1 page 401 Risk Management and Financial Institutions 3e, Chapter 18, Copyright © John C. Hull 2012 3 Initial Rating Aaa Aa A Baa Ba B Caa Ca-C Default Aaa 90.42 8.92 0.62 0.01 0.03 0.00 0.00 0.00 0.00 Aa 1.02 90.12 8.38 0.38 0.05 0.02 0.01 0.00 0.02 A 0.06 2.82 90.88 5.52 0.51 0.11 0.03 0.01 0.06 Baa 0.05 0.19 4.79 89.41 4.35 0.82 0.18 0.02 0.19 Ba 0.01 0.06 0.41 6.22 83.43 7.97 0.59 0.09 1.22 B 0.01 0.04 0.14 0.38 5.32 82.19 6.45 0.74 4.73 Caa 0.00 0.02 0.02 0.16 0.53 9.41 68.43 4.67 16.76 Ca-C 0.00 0.00 0.00 0.00 0.39 2.85 10.66 43.54 42.56 Default 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 100.00 Rating at year end
Five-YearRatingTransitionMatrix (calculatedfromone-yeartransitions)Table18.2page401InitialRatingatendAAaBAaaBaCaaCa-CDefaultRatingBaaAaa61.1229.997.700.890.210.050.010.000.03Aa28.700.250.193.4561.894.710.730.070.01A0.449.720.040.603.241.060.2465.7818.884.640.972.06Baa0.221.6960.9812.930.1316.38Ba0.070.4420.073.700.523.4018.2044.698.92B1.640.040.200.833.2713.2843.0511.4926.21Caa0.010.080.230.933.5216.8018.672.9356.84Ca-C0.000.020.060.311.395.896.782.4083.15Default0.000.000.000.000.000.000.000.00100.00RiskManagementandFinancialInstitutions3e,Chapter18,CopyrightJohnC.Hull20124
Five-Year Rating Transition Matrix (calculated from one-year transitions) Table 18.2 page 401 Risk Management and Financial Institutions 3e, Chapter 18, Copyright © John C. Hull 2012 4 Initial Rating Aaa Aa A Baa Ba B Caa Ca-C Default Aaa 61.12 29.99 7.70 0.89 0.21 0.05 0.01 0.00 0.03 Aa 3.45 61.89 28.70 4.71 0.73 0.25 0.07 0.01 0.19 A 0.44 9.72 65.78 18.88 3.24 1.06 0.24 0.04 0.60 Baa 0.22 1.69 16.38 60.98 12.93 4.64 0.97 0.13 2.06 Ba 0.07 0.44 3.40 18.20 44.69 20.07 3.70 0.52 8.92 B 0.04 0.20 0.83 3.27 13.28 43.05 11.49 1.64 26.21 Caa 0.01 0.08 0.23 0.93 3.52 16.80 18.67 2.93 56.84 Ca-C 0.00 0.02 0.06 0.31 1.39 5.89 6.78 2.40 83.15 Default 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 100.00 Rating at end
One-Month Rating TransitionMatrix(calculatedfromone-yeartransitions)Table18.3page401InitialRatingatmonthendAAaBAaaBaCaaCa-CDefaultRatingBaaAaa99.160.820.020.000.000.000.000.000.00Aa0.0999.120.770.010.000.000.000.000.00A0.510.040.010.000.000.000.000.2699.180.010.020.01Baa0.000.4499.050.410.060.00Ba0.000.000.020.590.030.010.0998.460.79B0.000.000.010.020.5398.320.700.070.36Caa0.000.000.000.010.021.0196.790.671.48Ca-C0.000.000.000.000.040.281.534.9293.23Default0.000.000.000.000.000.000.000.00100.005RiskManagementandFinancialInstitutions3e,Chapter18,CopyrightJohnC.Hull2012
One-Month Rating Transition Matrix (calculated from one-year transitions) Table 18.3 page 401 Risk Management and Financial Institutions 3e, Chapter 18, Copyright © John C. Hull 2012 5 Initial Rating Aaa Aa A Baa Ba B Caa Ca-C Default Aaa 99.16 0.82 0.02 0.00 0.00 0.00 0.00 0.00 0.00 Aa 0.09 99.12 0.77 0.01 0.00 0.00 0.00 0.00 0.00 A 0.00 0.26 99.18 0.51 0.04 0.01 0.00 0.00 0.00 Baa 0.00 0.01 0.44 99.05 0.41 0.06 0.02 0.00 0.01 Ba 0.00 0.00 0.02 0.59 98.46 0.79 0.03 0.01 0.09 B 0.00 0.00 0.01 0.02 0.53 98.32 0.70 0.07 0.36 Caa 0.00 0.00 0.00 0.01 0.02 1.01 96.79 0.67 1.48 Ca-C 0.00 0.00 0.00 0.00 0.04 0.28 1.53 93.23 4.92 Default 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 100.00 Rating at month end