MFIN 7011: Credit Risk Management Summer, 2007 Dragon Tang

1. Lecture 8 Recovery Rate Thursday, July 19, 2007 Readings: Altman (2006) and Schuermann (2004) MFIN 7011: Credit Risk ManagementSummer, 2007Dragon Tang Recovery Rate

2. Recovery Rate • Objectives: • Importance and stylized facts about recovery rates • Determinants and practical consideration of recovery risk Recovery Rate

3. Recovery Rates (RR) • LGD is the ratio of losses to exposure at default • RR=1-Loss Given Default (LGD) • Defaultable bond value =risk-free bond value – $EL • For example, a one-year corporate bond has expected loss of $5 compared to risk-free bond value $100, then the bond value is $95 and yield is $100/$95 -1 =5.26% • %Exptected Loss (EL) = Probability of Default (PD) * LGD; $EL=PD*LGD*Exposure At Default (EAD) • Focus was on PD, for simplicity Recovery Rate

4. Recovery Rates (RR) in Credit Risk Models • Early structural models: • PD and RR are functional characteristics of the firm. Therefore RR is endogenous. • PD and RR are inversely related. • Recent structural models: • RR is exogeneously specified and independent from firm value • PD and RR are independent • Reduced-form models: • RR is exogeneous (constant or stochastic but independent from PD) • PD and RR are assumed to be independent for tractability Recovery Rate

5. Loss Given Default (LGD) • LGD is traditionally assumed to be independent of PD • LGD is often assumed to be idiosyncratic for individual firms and constant on average • However, this is often not the case • LGD(RR) is positively(negatively) correlated with PD • LGD is time-varying, higher in economic downturns Recovery Rate

6. Historical Recovery Rates (Acharya, Bharath, and Srinivasan (2007)) Recovery Rate

7. Why Care About Recovery Rates? • Important for portfolio credit risk management • Especially for the calculation of Value-at-Risk (VaR), which is similar to LGD • Basel II capital adequacy calculation allows banks to calculate their own, so-called internal based rating (IRB), LGD • Accurate calculation reduces likelihood of bank failure • Important for pricing corporate bonds and loans and better investment management • Important for credit derivatives market where recovery is the traded product Recovery Rate

8. Stylized Facts about Recovery Rates • Average recovery rate is about 37.7% for loans and bonds across different seniority levels. However, recovery rates are bimodal: either high (~80%) or low (~20%). RR is not related to the size of the loan/bond. • Bakshi, Madan, and Zhang (2006): when default probability increases by 4%, recovery rate declines by 1% • LGD/RR is 10% higher/lower in economic downturns • Acharya, Bharath, and Srinivasan (2007):Recovery rate is 10% lower in distressed industry (“fire sale effect”). Tangible asset-intensive industries have higher RR  Recovery risk can be systematic! • Recovery to face value is most practical (compared to recovery to market value and recovery to Treasury) • More attention from industry: LGD rating by Moody’s LossCalc in 2002; Recovery ratings: S&P 2003, Fitch 2005 Recovery Rate

9. Historical Recovery Rate 0.50 0.35 0.25 1982 2000 1990 Issuer weighted recovery for corporate loans. 1982-2003 by Moody’s KMV. Recovery Rate

10. Historical Data (Altman et al (2004) Recovery at Defaulta on Public Corporate Bonds (1974–2003) and Bank Loans (1989-Q3–2003). Based on prices just after default on bonds and 30 days after default on loans. Recovery Rate

11. Measurement and Estimation of LGD LGD includes three types of losses: • The loss of principal • The carrying costs of non-performing loans, e.g. interest income foregone • Workout expenses (collections, legal, etc.) Recovery Rate

12. Measurement and Estimation of LGD • There are broadly three ways of measuring LGD for an instrument: • Market LGD: observed from market prices of defaulted bonds or marketable loans soon after the actual default event • Workout LGD: The set of estimated cash flows resulting from the workout and/or collections process, properly discounted, and the estimated exposure • Implied Market LGD: LGDs derived from risky (but not defaulted) bond prices using a theoretical asset pricing model • similar to recovery to market value (RMV), recovery to face value (RFV) and recovery to Treasury value (RT) Recovery Rate

13. Timing of the cash flows from the distressed asset Cash flows should be discounted The correct rate would be for an asset of similar risk Average LGD for a portfolio: price-weighting, default weighting, time-weighting Workout LGD Recovery Rate

14. LGD is to look at credit spreads on the non-defaulted risky bonds The spread above risk-free bonds is an indicator of the risk premium This spread reflects expected loss and then LGD Implied Market LGD Recovery Rate

15. Recovery Analytical Recovery Rating Scale Description Expectation _________________________________________________________ 1+ Highest 100% of Principal 1 High 100% of Principal 2 Substantial 80-100% of Principal 3 Meaningful 50-80% of Principal 4 Marginal 25-50% of Principal 5 Negligible 0-25% of Principal Similarly for Moody’s LGD and Fitch’s Recovery Rating (RR) What should the relationship between recovery rating and credit rating be? S&P Recovery Ratings Recovery Rate

16. Moody’s LossCalc LossCalc: Moody’s tool/methodology for calculating LGD • Time horizon: immediate or one-year LossCalc uses predictive information on five different levels to predict debt specific LGD: • Collateral • Seniority • Firm: leverage, distance to default etc. • Industry • Macroeconomy Recovery Rate

17. Downturn LGD To capture the impact of macroeconomic condition on LGD, the Fed proposes LGD in downturn = 0.08 + 0.92 * long-term LGD However, it is still uncertain how material the effect of correlation between macroeconomic variables and LGD on bond price and yields can be. Recovery Rate

18. LGD Modeling Approaches In the order of technicality: • Contingency or look-up table: construct historical recovery database • Basic regression: observed recovery on different seniority, industry etc. • Advanced regression: observed recovery on macroeconomic conditions, industry condition, firm characteristics, and issue features • Machine learning: run simulation with artificial intelligence! Recovery Rate

19. Recovery distributions are bimodal Makes parametric modeling of recoveries difficult, using rather non-parametric Seniority and collateral matter Monitoring and structuring matter Senior secured - flat distribution Senior unsecured – bimodal distribution Practical Considerations Recovery Rate

20. A very convenient distribution for the RR is the beta distribution. The distribution is bounded between 0 and 1. There are only two parameters (alpha and beta) and they allow for various shapes of the distribution. RR Distribution Recovery Rate

21. Recovery Rate

22. Basel II requires banks to use more risk sensitive methods for calculating credit risk capital requirements Move from the Foundation to the Advanced IRB approach What does LGD mean and what is its role in IRB How is LGD defined and measured What drives differences in LGD What approaches can be taken to model or estimate LGD Basel II and LGD Recovery Rate

23. LGD Modeling at Banks • Using the aforementioned approaches • Each borrower will have one probability of default, but LGD may be different for different loans to the same borrower • Different ways to obtain average LGD for the bank making many loans: • Dollar-weighting: total $ loss/total $ exposure • Default-weighting: simple average of individual LGD (sum of LGDs divided by number of defaults) • Time-weighting: the average of the average over time • LGD=0% cases should be treated differently Recovery Rate

24. Economic loss versus Accounting loss Extra costs Realizing collateral value Internal costs of workout department External costs Time delays in what is recovered Extra benefits Penalties for delays Interest Related Issues Recovery Rate

25. Open Questions LGD is on-going research and much remains unknown: • Are investors afraid of recovery risk? • How systematic is recovery risk? • How much premium do investors require for bearing recovery risk? • How much does recovery risk contribute to total credit risk or credit spread? • Do shareholders care about recovery risk? • … Recovery Rate

26. Summary • Stylized facts about LGD/RR • Factors affecting LGD • Next: Credit Derivatives Recovery Rate