fdic/jfsr 6th annual bank research conference september 13, 2006 discount rate for workout...
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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. ** 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: [email protected]
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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