CreditRisk: EstimatingDefaultProbabilitiesChapter 16RiskManagementandFinanciallnstitutions3e,Chapter16,CopyrightJohnC.Hull2012
Risk Management and Financial Institutions 3e, Chapter 16, Copyright © John C. Hull 2012 Credit Risk: Estimating Default Probabilities Chapter 16 1
Altman's Z-score (Manufacturingcompanies)page348X,=Working Capital/Total AssetsX,=Retained Earnings/Total AssetsX3=EBIT/Total AssetsX4=Market Value of Equity/Book Value of LiabilitiesXs=Sales/Total AssetsZ = 1.2X,+1.4X2+3.3X3+0.6X4+0.99X5If the Z > 3.0 default is unlikely; if 2.7 < Z < 3.0 we shouldbe on alert. If 1.8 < Z < 2.7 there is a moderate chance ofdefault; if Z < 1.8 there is a high chance of default2RiskManagementandFinancialInstitutions3e,Chapter16,CopyrightJohnC.Hull2012
Risk Management and Financial Institutions 3e, Chapter 16, Copyright © John C. Hull 2012 Altman’s Z-score (Manufacturing companies) page 348 ⚫ X1=Working Capital/Total Assets ⚫ X2=Retained Earnings/Total Assets ⚫ X3=EBIT/Total Assets ⚫ X4=Market Value of Equity/Book Value of Liabilities ⚫ X5=Sales/Total Assets Z = 1.2X1+1.4X2+3.3X3+0.6X4+0.99X5 If the Z > 3.0 default is unlikely; if 2.7 < Z < 3.0 we should be on alert. If 1.8 < Z < 2.7 there is a moderate chance of default; if Z < 1.8 there is a high chance of default 2
EstimatingDefault ProbabilitiesAlternatives: Use historical dataUse bond prices or asset swapsUseCDSspreads Use Merton's model3RiskManagementandFinancialInstitutions3e,Chapter16,CopyrightJohnC.Hull2012
Risk Management and Financial Institutions 3e, Chapter 16, Copyright © John C. Hull 2012 Estimating Default Probabilities ⚫ Alternatives: ⚫ Use historical data ⚫ Use bond prices or asset swaps ⚫ Use CDS spreads ⚫ Use Merton’s model 3
HistoricalDataHistorical data provided by rating agenciescan be used to estimate the probability ofdefaultRiskManagementandFinancialInstitutions3e,Chapter16,CopyrightJohnC.Hull20124
Risk Management and Financial Institutions 3e, Chapter 16, Copyright © John C. Hull 2012 Historical Data Historical data provided by rating agencies can be used to estimate the probability of default 4
CumulativeAverageDefaultRates%(1970-2010, Mo0dy's) Table 16.1, page 350Time (years)324571100.0000.0130.0130.0370.1040.2440.494Aaa0.0210.0590.1030.1840.2730.4430.619AaA0.0550.1770.3620.5490.7561.2392.136Baa0.1810.5100.9331.4271.9533.0314.9041.1573.1915.5968.14610.45314.44020.101Ba44.573B4.46510.43216.34421.51026.17334.72172.384Caa18.16330.20439.70947.31753.76861.1815RiskManagementandFinancialInstitutions3e,Chapter16,CopyrightJohnC.Hull2012
Risk Management and Financial Institutions 3e, Chapter 16, Copyright © John C. Hull 2012 Cumulative Average Default Rates % (1970-2010, Moody’s) Table 16.1, page 350 Time (years) 1 2 3 4 5 7 10 Aaa 0.000 0.013 0.013 0.037 0.104 0.244 0.494 Aa 0.021 0.059 0.103 0.184 0.273 0.443 0.619 A 0.055 0.177 0.362 0.549 0.756 1.239 2.136 Baa 0.181 0.510 0.933 1.427 1.953 3.031 4.904 Ba 1.157 3.191 5.596 8.146 10.453 14.440 20.101 B 4.465 10.432 16.344 21.510 26.173 34.721 44.573 Caa 18.163 30.204 39.709 47.317 53.768 61.181 72.384 5