B. Brady, P. Chang, P. Miu**, B. Ozdemir & D. Schwartz

1. Third International Conference on Credit and Operational RisksHEC Montréal - April 13, 2007Discount 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, 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.ca

2. 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

3. 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.”

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

6. 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

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. 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. LGD Data

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. 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. 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. 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. 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

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

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. 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 IndSi = “1” if defaults during industry stress period DADC1,i= “1” if there is no DA and no DC DADC2,i = “1” if there is some DA and some DC Ty1,i= “1” if Senior Unsecured Bond Ty2,i = “1” if Senior Subordinated Bond TTRi = weighted average time-to-recovery (in years)

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