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
Interpretation The table shows the probability ofdefault for companies starting with aparticular credit ratingA company with an initial credit rating ofBaa has a probability of 0.181% ofdefaulting by the end of the first year,0.510% by the end of the second year,and so onRiskManagementandFinancialInstitutions3e,Chapter16,CopyrightJohnC.Hull20126
Risk Management and Financial Institutions 3e, Chapter 16, Copyright © John C. Hull 2012 Interpretation ⚫ The table shows the probability of default for companies starting with a particular credit rating ⚫ A company with an initial credit rating of Baa has a probability of 0.181% of defaulting by the end of the first year, 0.510% by the end of the second year, and so on 6
Do DefaultProbabilities Increasewith Time? For a company that starts with a goodcredit rating default probabilities tend toincrease with time For a company that starts with a poorcredit rating default probabilities tend todecrease with time7RiskManagementandFinancialInstitutions3e,Chapter16,CopyrightJohnC.Hull2012
Risk Management and Financial Institutions 3e, Chapter 16, Copyright © John C. Hull 2012 Do Default Probabilities Increase with Time? ⚫ For a company that starts with a good credit rating default probabilities tend to increase with time ⚫ For a company that starts with a poor credit rating default probabilities tend to decrease with time 7
Hazard Rate ys. UnconditionalDefaultProbabilityThe hazard rate or default intensity is theprobability of default over a short period oftime conditional on no earlier default The unconditional default probability is theprobability of default as seen at time zeroRiskManagementandFinancialInstitutions3e,Chapter16,CopyrightJohnC.Hull20128
Risk Management and Financial Institutions 3e, Chapter 16, Copyright © John C. Hull 2012 Hazard Rate vs. Unconditional Default Probability ⚫ The hazard rate or default intensity is the probability of default over a short period of time conditional on no earlier default ⚫ The unconditional default probability is the probability of default as seen at time zero 8
Properties ofHazard ratesSuppose that 2(t) is the hazard rate at time tThe probability of default between times t andt+△t conditional on no earlier default is 2(t)△tThe probability of default by time t is1 - e-() where ^(t) is the average hazard rate betweentime zero and time t9RiskManagementandFinancialInstitutions3e,Chapter16,CopyrightJohnC.Hull2012
Properties of Hazard rates ⚫ Suppose that l(t) is the hazard rate at time t ⚫ The probability of default between times t and t+Dt conditional on no earlier default is l(t)Dt ⚫ The probability of default by time t is where is the average hazard rate between time zero and time t Risk Management and Financial Institutions 3e, Chapter 16, Copyright © John C. Hull 2012 9 t t e ( ) 1 −l − l(t)
RecoveryRateThe recovery rate for a bond is usuallydefined as the price of the bond 30 daysafter default as a percent of its face value10RiskManagementandFinancialInstitutions3e,Chapter16,CopyrightJohnC.Hull2012
Risk Management and Financial Institutions 3e, Chapter 16, Copyright © John C. Hull 2012 Recovery Rate The recovery rate for a bond is usually defined as the price of the bond 30 days after default as a percent of its face value 10