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, 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

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• 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

Defaultat Exposure

FlowCash Recovery 1 dPV

LGD

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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.”

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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

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Outline of Presentation

• Methodology

• Data

• Segmentation

• Estimation of discount rate– Segment level– Sub-segment level

• Regression analysis

• Conclusion

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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) 301

Di

Ri tt

ii

d

REP

• 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

i

ttii

i P

dPRDi

Ri 301

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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

d̂

d̂

d̂

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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

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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

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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

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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

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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

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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

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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

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Pointestimate

Standard deviation

Confidence Interval5% 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

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Pointestimate

Standard deviation

Confidence Interval5% 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

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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

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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

SSEd 123.001205.0ˆ

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iiii

iiiiiii

TTRaTyaTya

DADCaDADCaIndSaIGaSecaPacr

9,28,17

,26,154321

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)

Regression Analysis of Internal Rate of Return

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(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

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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