Third International Conference on Credit and Operational Risks HEC Montréal - April 13, 2007...
-
Upload
edwin-elliott -
Category
Documents
-
view
214 -
download
0
Transcript of Third International Conference on Credit and Operational Risks HEC Montréal - April 13, 2007...
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: [email protected]
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
Defaultat Exposure
FlowCash Recovery 1 dPV
LGD
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) 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
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
d̂
d̂
d̂
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
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
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
15
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
16
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
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
SSEd 123.001205.0ˆ
20
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
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