Third International Conference on Credit and Operational Risks

Third International Conference on Credit and Operational Risks HEC Montréal - April 13, 2007 Discount Rate for Workout Recoveries: An Empirical Study* B. Brady, P. Chang, P. Miu**, B. Ozdemir & D. Schwartz * The paper can be downloaded at http: //ssrn. com/abstract=907073. Opinions expressed are those of the authors and are not necessarily endorsed by the authors’ employers. ** Correspondence should be addressed to Peter Miu, De. Groote School of Business, Mc. Master University, 1280 Main Street West, Hamilton, Ontario L 8 S 4 M 4, Canada, tel: 1 -905 -525 -9140 ext. 23981, fax: 1 -905521 -8995, email: miupete@mcmaster. ca

Background • To implement advanced IRB approach of Basel II, banks need to estimate economic value of LGD given historical recovery cash flows • Banks need to determine the rate to be used to discount recovery cash flows back to time of default 2

Background • Discount rate should be commensurate with opportunity costs of holding defaulted asset over workout period, including an appropriate risk premium required by asset holders • Guidance on Paragraph 468 of the Framework Document states that: “when recovery streams are uncertain and involve risks that cannot be diversified away, net present value calculations must reflect the time value of money and a risk premium appropriate to the undiversifiable risk. ” 3

Background • Without appropriate risk adjustment, over- (under -) estimate LGD and thus assign too much (little) regulatory capital to instruments with low (high) recovery risk • Should we use different discount rates? • • • for different instrument types for instruments default in recession for instruments issued by different industries for investment grade vs. speculative grade for instruments default during industry-specific stress period 4

Outline of Presentation • • Methodology Data Segmentation Estimation of discount rate – Segment level – Sub-segment level • Regression analysis • Conclusion 5

Methodology • Suppose we observe market price (Pi) of defaulted instrument i 30 days after default, it is related to expected future recoveries (E[Ri]) via discount rate (d) • Solve for most-likely estimate of d by minimizing sum of square of difference (SSE) between realized and expected recovery of large number of instruments 6

Methodology • By grouping defaulted instruments into different segments of uniform LGD risk, we can therefore solve for • point estimate • asymptotic standard deviation of • confidence interval of 7

LGD Data • S&P’s Loss. Stats Database • only consider formal bankruptcy events (i. e. exclude e. g. distressed exchanges and other reorganization events) • A total of 1, 128 defaulted instruments with matching ultimate recovery values and trading prices 30 days after default • From a total of 446 identical obligor default events from 1987 to 2005 • variety of industries and instrument types 8

LGD Data Security S&P’s Rating Type Secured Unsecured 317 811 Investment Nongrade investment grade 88 398 Bank debt Senior secured bond 222 102 Others 642 Senior unsecured sub. bond 395 237 Sub. bond Junior sub. bond 161 11 9

Segmentations • Secured vs. unsecured: recovery risk is higher for unsecured due to lack of collateral • Earliest S&P’s rating (investment grade (IG) vs. non-investment grade (NIG)): creditors pay more attention to monitor/mitigate LGD risk of lowly-rated obligors rather than highly-rated ones • Industry sector (technology vs. non-technology): • high recovery risk if collateralized by intangible assets • originally secured instrument becomes essentially “unsecured” when collateral loses its perceived value 10

Segmentations • Default during market-wide stress periods (when S&P’s speculative grade default rates higher than 25 -year average of 4. 7%) • uncertainty around values of collaterals and obligor’s assets increases during recession • investors demand higher risk premium • short-term effects in secondary market: excess supply of defaulted debts during recession • if required rate of return increases together with lower expected recovery → even higher PD/LGD correlation 11

Segmentations • Default during industry-specific stress periods (when industry’s speculative grade default rates higher than 4. 7%) • financial distress is more costly to borrowers if they default when their competitors in same industry are experiencing cash flow problems • uncertainty around collateral value increases (collaterals are mostly industry specific, e. g. fiberoptic cable for telecom sector) • if industry-specific stress is more important than market-wide stress → diversification of LGD risk across industries 12

Segmentations • Debt above (DA) and debt cushion (DC) (whethere is debt that is superior (subordinated) to each bond/bank loan) • can better control for variability of debt structure of defaulted obligor than classifying by instrument type • classification: (1) no DA and some DC; (2) no DA/DC (3) no DC and some DA; (4) some DA/DC • “no DA/DC” has low recovery risk: all creditors share equally in underlying assets resulting in predictable recovery • “some DA/DC” has high recovery risk: both senior and junior positions will be vying for a portion of obligors’ assets; large coordination effort 13

Segmentations • Instrument type • similar to DA/DC, provides information about seniority of creditor within list of claimants • classification: (1) bank debt (2) senior secured bond, (3) senior unsecured bond, (4) senior subordinated bond, (5) subordinated bond, and (6) junior subordinated bond 14

Point estimate Overall Standard deviation Confidence Interval 5% 95% 14. 0 1. 8 11. 1 16. 9 Secured 11. 8 4. 8 3. 9 19. 7 Unsecured 14. 3 1. 9 11. 2 17. 4 22. 8 5. 0 14. 6 31. 0 6. 4 3. 8 0. 2 12. 7 Technology 24. 4 5. 8 14. 8 34. 0 Non-Technology 13. 0 1. 9 9. 8 16. 2 In recession 15. 7 4. 2 8. 8 22. 6 Not in recession 13. 6 2. 0 10. 3 16. 9 21. 5 2. 7 17. 1 25. 8 8. 1 3. 0 3. 1 13. 1 Secured vs. Unsecured Investment vs. Non-investment Grade Investment grade Non-investment grade Technology vs. nontechnology Market-wide recession Industry-specific stress period Industry in stress period Industry not in stress period 15

Point estimate Standard deviation Confidence Interval 5% 95% Debt Above (DA) & Debt Cushion (DC) No DA and some DC 21. 2 3. 7 15. 1 27. 3 No DA/DC 0. 9 7. 9 -12. 1 13. 8 No DC and some DA 8. 6 3. 0 3. 7 13. 6 29. 3 4. 0 22. 7 35. 8 Bank Debt 13. 3 6. 7 2. 3 24. 3 Senior Secured Notes 11. 0 6. 9 -0. 3 22. 2 Senior Unsecured Notes 27. 5 3. 1 22. 4 32. 7 Senior Subordinated Notes 3. 8 5. 7 -5. 6 13. 2 Subordinated Notes 8. 9 3. 8 2. 7 15. 1 Some DA/DC Instrument type 16

Sub-Segment Results • Examine robustness of differences in discount rates across segments by controlling for other ways to segment data • Repeat analysis at sub-segment level crossing all segments considered previously • Look for statistically significant (at 95% confidence level) difference from segment-level discount rate • Only consider those sub-segments with more than or equal to 50 valid LGD observations 17

18

Risk-Return Trade-off • Regress point estimates of discount rates (expected return) against an intercept and SSE (proxy of recovery risk) across all segments • R-square is found to be 11% and slope coefficient of 0. 123 is highly statistically significant with a tstatistic of 12. 4 19

Regression Analysis of Internal Rate of Return where Pi = trading price (in $ per $1 nominal value) Seci = “ 1” if secured IGi = “ 1” if earliest rating is IG Ind. Si = “ 1” if defaults during industry stress period DADC 1, i = “ 1” if there is no DA and no DC DADC 2, i = “ 1” if there is some DA and some DC Ty 1, i = “ 1” if Senior Unsecured Bond Ty 2, i = “ 1” if Senior Subordinated Bond TTRi = weighted average time-to-recovery (in years) 20

Constant (1) (2) (3) (4) (5) (6) (7) 0. 428*** 9. 264 0. 417*** 10. 386 0. 335*** 6. 290 0. 462*** 10. 899 0. 426*** 9. 083 0. 591*** 6. 641 0. 412*** 5. 020 Trading price (per $1) Secured -0. 484*** -4. 890 -0. 015 -0. 293 IG (earliest S&P rating) 0. 104 1. 274 -0. 062 -0. 819 0. 264*** 2. 956 0. 182** 2. 052 0. 085* 1. 684 0. 144*** 2. 902 -0. 249*** -3. 534 -0. 231*** -3. 251 -0. 265*** -3. 708 -0. 056 -0. 837 -0. 033 -0. 475 -0. 022 -0. 312 0. 187** 2. 210 Industry-specific stress period 0. 120** 2. 454 DA and DC No DA, No DC Some DA, some DC Instrument type Senior unsecured bond 0. 033 0. 620 0. 033 0. 437 -0. 020 -0. 261 Senior subordinated bond -0. 088 -1. 353 -0. 135 -1. 608 -0. 144* -1. 695 Time to recovery (year) R-square (adjusted) -0. 103*** -4. 902 -0. 110*** -5. 241 -0. 093*** -4. 414 -0. 102*** -4. 956 -0. 103*** -4. 958 -0. 116*** -5. 407 -0. 103*** -4. 753 0. 025 0. 030 0. 031 0. 036 0. 027 0. 071 0. 048 21

Conclusion • Both instrument type and DA/DC are important determinants of LGD discount rate • Industry-specific stress condition is a more important determinant than market-wide recession • IG has a significantly higher discount rate than NIG • Other industry effects are however weak 22