1. Credit Risk Nicolas Beudin & Maxime Riche

2. Agenda 1. Overview 2. Valuation 3. Dealing with credit risk 4. Conclusion 5. Appendix 2

3. Overview

4. Definition BorrowerLender Credit Risk 4

5. Players Households Insurance companies, asset management firms, investments banks, depository institutions… Financial InstitutionsGovernmentsCorporatesNon-profit organizations 5

6. Corporate bonds Electricity, gas, water… Public utilities Roads, trucks, airlines… Transportations Banks, insurances, brokerages… Financial InstitutionsIndustrials 6

7. Corporate bonds Bond indentures MaturitySecurity Provisions for retirement 7

8. Valuation

9. Value Models Ratings Historical Stats Probability of default Recovery rate Probability of default Recovery rate Moody’s S&P Fitch Moody’s S&P Fitch Merton (Black & Scholes) 9

10. Bonds Safety Coverage ratios: EBIT/Interest Cash flow to debt: Free cash flow/Total debt Profitability ratio: Return on Capital Leverage ratio: Total Debt/Capital Financial key ratios 10

11. Rating Classes Rating Category Coverage Ratio Cash Flow to Debt % Return on Capital % LT Debt to Capital % AAA17.555.428.215.2 AA10.824.622.926.4 A6.815.619.932.5 BBB3.96.614.041.0 BB2.31.911.755.8 B1.0(4.6)7.270.7 Source: Bodies, Kane, Marcus 2002 Table 14.3 11

12. Credit Spreads Spread = Cost of borrowing – Risk-free rate 12

13. Dealing with credit risk

14. Try to mitigate it (at the source) Collateralisation with assets GuaranteesCovenants Price it Various models Hedge it / Share it SecuritizationInsurance Dealing with CR? 14

15. Types of Credit Derivatives Credit Default Swaps (CDS) Credit Spread Options & Forwards, TRS... Structured Credit Collateralized Debt Obligations (CDOs) ABS, MBS, CLOs, CMOs... Dealing with CR? 15

16. CDS Structure Default Protection Buyer, A Default Protection Buyer, A Default Protection Seller, B Default Protection Seller, B Spread = xx bps per year Payoff if there is default by reference entity Source : Fundamentals of Options and Futures, J. Hull 16

17. CDO Bond 1 Bond 2 Bond 3  Bond n Average Yield 8.5% Bond 1 Bond 2 Bond 3  Bond n Average Yield 8.5% Trust Tranche 1 1 st 5% of loss Yield = 35% Tranche 1 1 st 5% of loss Yield = 35% Tranche 2 2nd 10% of loss Yield = 15% Tranche 2 2nd 10% of loss Yield = 15% Tranche 3 3rd 10% of loss Yield = 7.5% Tranche 3 3rd 10% of loss Yield = 7.5% Tranche 4 Residual loss Yield = 6% Tranche 4 Residual loss Yield = 6% Source : Fundamentals of Options and Futures, J. Hull 17

18. Conclusion

19. Credit risk has become a key concern Financial engineeringReduce the risk or spread it ? 19

20. Thank you ! 20

21. Appendix

22. Merton model Idea to use OPM to price credit risk E Market value of equity F Face value of debt V Market value of company Bankruptcy D Market value of debt F Face value of debt V Market value of company F Loss given default 22

23. Toward Black Scholes formulas Increase the number to time steps for a fixed maturity The probability distribution of the firm value at maturity is lognormal Time Value Today Bankruptcy Maturity 23

24. Valuation 24 Value of a risky debt : Credit spread : Using Black & Scholes : Discount factor Face Value Probability of default Expected loss given default Loss if no recovery Expected Amount of recovery given default

25. Example 25 Data Market value unlevered company € 100,000 Debt = 2-year zero coupon Face value € 60,000 Risk-free interest rate5% Volatility unlevered company30% Using Black-Scholes formula Market value unlevered company € 100,000 Market value of equity € 46,626 Market value of debt € 53,374 Discount factor0.9070 N(d 1 )0.9501 N(d 2 )0.8891 Using Black-Scholes formula Value of risk-free debt € 60,000 x 0.9070 = 54,422 Probability of default N(-d 2 ) = 1-N(d 2 ) = 0.1109 Expected recovery given default V e rT N(-d 1 )/N(-d 2 ) = (100,000 / 0.9070) (0.05/0.11) = 49,585 Expected recovery rate | default = 49,585 / 60,000 = 82.64%

26. References 26 Fabozzi, F. J., & Modigliani, F. (2009). Capital Markets Institutions and Instruments. Pearson International Edition. Hull, J. C. (2008). Fundamentals of Futures and Options Markets. Pearson International Edition. Pirotte, H. (2010). Course of Advanced Finance. Risky Debt. Brussels: Solvay Brussels School of Economics and Management. Bodies, Kane, Marcus 2002 Table 14.3 http://www.bondchannel.bridge.com http://www.paulfellcartoons.com