# Presentation: 729347

## 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://](http://ssrn.com/abstract=907073)__[ssrn.com](http://ssrn.com/abstract=907073)__[/abstract=907073](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](mailto:miupete@mcmaster.ca)_

## 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

- 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

## 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.”

## 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

## Outline of Presentation

- Methodology
- Data
- Segmentation
- Estimation of discount rate
- Segment level
- Sub-segment level
- Regression analysis
- Conclusion

## 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

## 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

## 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

## LGD Data

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

## 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

## 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

## 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

## 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

## 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

## Slide 15

|  | Point
estimate | Standard deviation | Confidence Interval
5%              95% |  |
| --- | --- | --- | --- | --- |
| Overall | 14.0 | 1.8 | 11.1 | 16.9 |
| Secured vs. Unsecured |  |  |  |  |
|   Secured | 11.8 | 4.8 | 3.9 | 19.7 |
|   Unsecured | 14.3 | 1.9 | 11.2 | 17.4 |
| Investment vs. Non-investment Grade |  |  |  |  |
|   Investment grade | 22.8 | 5.0 | 14.6 | 31.0 |
|   Non-investment grade | 6.4 | 3.8 | 0.2 | 12.7 |
| Technology vs. non-technology |  |  |  |  |
|   Technology | 24.4 | 5.8 | 14.8 | 34.0 |
|   Non-Technology | 13.0 | 1.9 | 9.8 | 16.2 |
| Market-wide recession |  |  |  |  |
|   In recession | 15.7 | 4.2 | 8.8 | 22.6 |
|   Not in recession | 13.6 | 2.0 | 10.3 | 16.9 |
| Industry-specific stress period |  |  |  |  |
|   Industry in stress period | 21.5 | 2.7 | 17.1 | 25.8 |
|   Industry not in stress period | 8.1 | 3.0 | 3.1 | 13.1 |

## Slide 16

|  | 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 |
|   Some DA/DC | 29.3 | 4.0 | 22.7 | 35.8 |
|  |  |  |  |  |
| Instrument type |  |  |  |  |
|   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 |

## 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

## Slide 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 t-statistic of 12.4

## Regression Analysis of Internal Rate of Return

- 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)

## Slide 21

|  | (1) | (2) | (3) | (4) | (5) | (6) | (7) |
| --- | --- | --- | --- | --- | --- | --- | --- |
| Constant | 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) |  |  |  |  |  | -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 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) | -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) | 0.025 | 0.030 | 0.031 | 0.036 | 0.027 | 0.071 | 0.048 |

## 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