1. FDIC/JFSR 6th Annual Bank Research Conference September 13, 2006 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.http://ssrn.com/abstract=907073 ** Correspondence should be addressed to Peter Miu, DeGroote School of Business, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4M4, Canada, tel: 1-905-525-9140 ext. 23981, fax: 1-905- 521-8995, email: miupete@mcmaster.camiupete@mcmaster.ca

2. 2 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 Background

3. 3 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.”

4. 4 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

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

6. 6 Methodology Suppose we observe market price (P i ) of defaulted instrument i 30 days after default, it is related to expected future recoveries (E[R i ]) 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

7. 7 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

8. 8 LGD Data S&P’s LossStats 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

9. 9 LGD Data SecuritySecuredUnsecured 317811 S&P’s Rating Investment grade Non- investment grade Others 88398642 TypeBank debtSenior secured bond Senior unsecured bond Senior sub. bond Sub. bond Junior sub. bond 22210239523716111

10. 10 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

11. 11 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

12. 12 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. fiber- optic cable for telecom sector) if industry-specific stress is more important than market-wide stress → diversification of LGD risk across industries

13. 13 Segmentations Debt above (DA) and debt cushion (DC) (whether there 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

14. 14 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

15. 15 Point estimate Standard deviation Confidence Interval 5% 95% Overall14.01.811.116.9 Secured vs. Unsecured Secured11.84.83.919.7 Unsecured14.31.911.217.4 Investment vs. Non-investment Grade Investment grade22.85.014.631.0 Non-investment grade6.43.80.212.7 Technology vs. non- technology Technology24.45.814.834.0 Non-Technology13.01.99.816.2 Market-wide recession In recession15.74.28.822.6 Not in recession13.62.010.316.9 Industry-specific stress period Industry in stress period21.52.717.125.8 Industry not in stress period8.13.03.113.1

16. 16 Point estimate Standard deviation Confidence Interval 5% 95% Debt Above (DA) & Debt Cushion (DC) No DA and some DC21.23.715.127.3 No DA/DC0.97.9-12.113.8 No DC and some DA8.63.03.713.6 Some DA/DC29.34.022.735.8 Instrument type Bank Debt13.36.72.324.3 Senior Secured Notes11.06.9-0.322.2 Senior Unsecured Notes27.53.122.432.7 Senior Subordinated Notes3.85.7-5.613.2 Subordinated Notes8.93.82.715.1

17. 17 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

18. 18

19. 19 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 t-statistic of 12.4

20. 20 where P i = trading price (in $ per $1 nominal value) Sec i = “1” if secured IG i = “1” if earliest rating is IG IndS i = “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 TTR i = weighted average time-to-recovery (in years) Regression Analysis of Internal Rate of Return

21. 21 (1)(2)(3)(4)(5)(6)(7) Constant0.428*** 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)-0.484*** -4.890 Secured-0.015 -0.293 0.104 1.274 -0.062 -0.819 IG (earliest S&P rating)0.187** 2.210 0.264*** 2.956 0.182** 2.052 Industry-specific stress period 0.120** 2.454 0.085* 1.684 0.144*** 2.902 DA and DC No DA, No DC-0.249*** -3.534 -0.231*** -3.251 -0.265*** -3.708 Some DA, some DC-0.056 -0.837 -0.033 -0.475 -0.022 -0.312 Instrument type Senior unsecured bond0.033 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)-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 R-square (adjusted)0.0250.0300.0310.0360.0270.0710.048

22. 22 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