Class 5 Credit risk models

1. Class 5Credit riskmodels

2. Up to now • Why credit risk is harder to model than market risk • What affects credit losses • Probability of default • Loss given default (LGD) / Recovery rate (RR=1–LGD) • Credit exposure • How to measure credit risk • Internal approach: analyzing company’s characteristics • External approach: using market data on bonds and stocks

3. What if there is no external rating?

4. Internal rating systems • Criteriа • Probability of default • Recovery rate • Horizon • Usually, 1 year • Scale • According to S&P/Moody’s or its own • Factors: what are the 5C?

5. What can we learn (and cannot learn) from financial reports? • Different financial ratios • Liquidity, leverage, profitability, turnover,… • Backward-looking • Extrapolation of the past into the future gives imprecise forecast • Often reports are corrupted • To misguide tax authorities, minority shareholders, banks, etc. • In Russia: little trust to reports • RAS is clearly inferior to IAS • IAS has become compulsory for the exchange-listed companies • Role of human factor • Expert’s opinion: visit to the company, talks with top managers • But: possibility of corruption and subjectivity

6. Credit scoring models: a statistical approach to predicting default • Statistical model: PD = function of the borrower’s characteristics • How to evaluate the model? • Type-1 error: default by the borrower who received a loan • Type-2 error: predicting default for the good borrower • Typical strategies: • RusskiStandart vs. Sberbank in 2000s Bad borrowers Good borrowers Income Credit history

7. Which factors can be used in retail lending scoring models? • Gender, age, family • Registration • Car, apartment, dacha • Income • Debt • Credit history • Conviction • …

8. Altman (1968): scoring model for firms Z = 1.2X1 + 1.4X2 + 3.3X3 + 0.6X4+ 0.999X5 • Dependent variable: Z-score • Sample: 66 companies, half of which defaulted • Determinants of PD • X1: Working Capital to Assets • X2: Retained Earnings to Assets • X3: EBIT to Assets • X4: Market Value of Equity to Book Value of Liabilities • X5: Sales to Assets • Interpretation • Z > 3: default is unlikely • 2.7 < Z ≤ 3: closer to “dangerous zone” • 1.8 < Z ≤ 2.7: likely default • Z ≤ 1.8: very high PD • Results: • More than 90% firms correctly classified

9. What are pros and cons of scoring models? • ‘Optimal’ treatment of factors • …without subjectivity • Automated decisions • Quick • Economy of scale • Flexibility: calibrate models • …for behavior, collectors, fraud • …with non-linear or step-wise functional forms • Required by regulators (Basel II) • Need large and clean data base • Ideally, including rejected applicants • Some data are hard to verify (quickly and cheaply) • Model risk • How “average” results fit each specific segment • How often the model should be reevaluated

10. What can we learn from bond spread? • Bond spread: • Difference in yields of risky bond and risk-free bond • For a one-period zero-coupon bond: BS ≡ R-Rf≈ PD*LGD • LGD: relative to face value • PD: risk-neutralprobability • Which factors influence bond spread besides credit risk? • Macro factors (market liquidity) • Bond-specific factors • Is bond spread a better measure of credit risk than credit rating? • Ratings often react with a lag to the change in bond spread • Bond spreads may change due to other factors or noise

11. Are spreads of high-yield bonds in the US too low? • The average yield ≈ 5.5% • Cf. long-term average 10% over the past 20 years • Close to long-term average yield of investment-grade corporate bonds • Low defaults: 2.6% in 2012, 2.3% in 2013 • Below the long-term historical average of 4.8% • Due to low leverage, lots of cash, little need in refinancing • How will the Fed’s tapering affect the bond market?

12. European sovereign bond spreads

14. What can we learn from CDS spread? • Credit default swap (CDS): agreement between two parties to exchange the credit risk of a reference entity • Similar to buying insurance against default • What is the difference? • Why did it become so popular? • CDS started in early 1990’s, was standardized in 1999 • CDS spread = Premium paid by the protection buyer to the protection seller • Quoted in basis points p.a. of the contract’s notional amount • Paid quarterly • In case of default, the protection seller covers occurred losses • Usually, buyer delivers the asset (bonds, loans) to seller and receives 100% of notional • For a one-year bond: CDS spread ≈ PD*LGD • Just like bond spread, CDS spread depends on other factors: • Liquidity, counterparty risk, equity risk premia, market sentiment (speculation),… • The basket (first-to-default) swap is harder to value

15. Пример: Tyco

17. European sovereign CDS spreads

18. What is a better measure of credit risk: CDS spread or bond spread? • No arbitrage conditions should ensure that CDS spread ≈ bond spread • Indeed, credit risk prices for bonds and CDS are equal over the long term • What could be the reason for short-term price differentials? • Factors unrelated to the credit risk (especially liquidity) • Contractual arrangements in CDS contract • Restructuring clauses • Delivery options • Quotation differences

19. Greece: CDS spread vs. bond spread

20. CreditMetrics (1997) • Credit risk is modeled as a change in credit rating • Using migration probabilities • Compute a probability distribution of the future value of the instrument using • Forward rates for each rating • Thus, account for duration and spread effects • Recovery rate in case of default (depending on seniority) • Estimate VaR as a difference between given quantileand expected value • Bottom up approach: • First estimate VaR for each instrument • Then aggregate to portfolio VaR accounting for correlations • See computations in the Excel file

21. Migration of credit ratings

22. CreditMetrics: critique and potential for improvement • Relying on credit ratings • Assuming homogeneity within the same rating class • Using discrete migration matrix based on average historical frequencies • Credit Portfolio View: adjust transition probabilities according to the current stage of the business cycle • Downgrade probabilities are higher during the recession • Ignoring market risk • It is better to use stochastic interest rates • Easy to account for this via Monte Carlo

23. Merton (1974) • The company’s capital structure includes • Equity, with value E • Debt (zero-coupon), with face value F and maturity T • Default occurs at maturity if VT<F • Stockholders receive at T: max(VT-F,0) • Creditors receive at T: min(VT, F) • Stockholders: call option on the value of the company V • Exercise date: T • Price of the underlying asset: V • Volatility: σV

24. Merton model: illustration

25. Derivation of the parameters • V and σV are unobservable, derived from two equations: • The value of equity by Black-Scholes: E=V*N(d1)-Fe-rTN(d2) • r: risk-free rate • d1=[ln(V/F) + T(r+σ2/2)] / [σV√T], d2=d1-σV√T • The equation for stock volatility: σEE = N(d1) σVV • Risk-neutral probability of default: PD = 1-N(d2) = N(-d2)

26. Merton’s model: Implicit assumptions • Stockholders’ behavior – as given • Though they are interested in raising risk • Lognormal distribution • Underestimate PD at short horizon • Bankruptcy when V is below the face value of debt • Default may be different from bankruptcy

27. KMV Portfolio Manager (1998) • Estimate V and σV based on equity prices • Compute distance to default • Empirically estimated default point: DPT = short-term liabilities + ½ long-term liabilities • Distance to default: DD = ln[E(V)-DPT]/σV • in %, in σ

28. Estimating EDF (cont.)

29. Estimating EDF • The historical frequency of defaults with given distance to default: EDF = # defaults / # firms (with given DD) • EDFis a continuous company-specific risk measure • Credit rating is an ordinal measure

30. Example: EDF for FedEx • Why did EDF change? • Increase in asset volatility • Increase in financial leverage

31. EDF vs. credit ratings

32. EDF vs. credit ratings • EDFgoes up 1-2 years before the default • Ratings agencies react with a lag

33. EDF vs. credit ratings • The probability of keeping (changing) the rating seems overstated (understated) by the rating agencies

34. What are pros and cons of EDF? • Company-specific • Continuous • Not biased by periods of high or low defaults • Quick reaction • EDF rises sharply 1-2 years before the default • Best applied to publicly traded firms • Relies on market liquidity and efficiency • Ignores more complicated features of the debt • Seniority, collateral, etc.

35. Credit derivatives as risk management tool • May be linked to different types of credit risk: • Credit event, value of the underlying asset, recovery rate, maturity • Completing the market • Risk managers hedge credit risk • Investors find interesting instruments to speculate • Arbitrageurs can short-sell credit risk • Separating credit riskmgt from the underlying asset • Banks can clean the balance without selling loans • Tax considerations / underpricing / client • Hedge funds can invest in credit risk, with leverage • Avoid transfer of property rights and administrative costs • Rapid growth since the end of 1990s until the crisis

36. Risks of credit derivatives • Correlation • Simultaneous default of the underlying asset and protection seller • Basis • Legal • 1999, 2003: ISDA adopted standard terms and documentation • Liquidity • Credit derivatives are usually traded OTC • Protection: • Bilateral netting • Option for premature abortion of the contract in the case of the counterparty’s financial distress

37. Do credit derivatives reduce or raise systemic risk? • It is argued that CDS contributed to the global financial crisis of 2008 • Many traders speculated on CDS linked to the mortgage market • …and investment banks exposed to mortgages: Bear Stearns, Lehman Brothers • …contributing to their decline • What were the problems? • How it was resolved: • ISDA: standardization of contracts and settlement • CCP: centralized clearing party • More transparency (central repository) • More than 90% contracts are covered by collateral • (Banning naked CDS)