An Empirical Study of the Returns on Defaulted Debt and the Discount Rate for Loss-Given-Default

An Empirical Study of the Returns on Defaulted Debt and

the Discount Rate for Loss-Given-Default

Michael Jacobs, Ph.D., CFASenior Financial EconomistCredit Risk Analysis Division

Office of the Comptroller of the Currency December, 2008

The views expressed herein are those of the author and do not necessarily represent the views of the Office of the Comptroller of the Currency or the Department of the Treasury.

Outline

• Preliminary Remarks & Additional Disclaimers• Background and Motivation• Introduction and Conclusions• Review of the Literature• Basel Requirements• Theoretical Model• Measurement Methodology• Empirical Results & Econometric Model• Analysis of the Impact on Regulatory Capital• Benchmark Analysis of LGD Discount Rates• Summary and Future Directions

Preliminary Remarks & Additional Disclaimers

• While this study is largely empirical in nature and reports estimation results, in no way are we recommending that banks use a particular discount rate, nor that they take a particular approach to deriving it

• The purpose here is to bring some clarity to the issue, to survey what has been thought and done about it, and help practitioners and supervisors organize their own approaches

• We do believe that we provide some useful benchmarks that can at least provide a point of reference to banks, but we do not mean these to be taken as prescriptions

• But we feel obligated to reference Basel requirements, and to the extent that it is know that there is so much uncertainty in LGD estimation, we believe that banks should at least consider recovery risk and discount rates for LGD

Background and Motivation• Financial institutions worldwide are implementing the Basel II

advanced internal ratings-based (IRB) approach to regulatory-capital, a challenge and a key activity for many

• A misunderstood & little studied aspect of this is the proper discount factor for recoveries on defaulted debt, an ingredient in the calculation of economic loss-given-default (LGD)

• This risk adjustment is necessitated by the sometimes lengthy durations of default resolution periods and complicated by the non-marketability of the bulk of banks’ loan portfolios

• While there may be theoretical arguments for risk adjustment (i.e., economic models), the application is complicated by the randomness of both recovery cash flows magnitudes and timing

• Note that the maintained hypothesis herein is that the proper objective for capital measurement is the estimation of loss distributions under physical measure

Background and Motivation (continued)

• 3 suggestions for the discount rate: risk-free term structure, opportunity cost of funds or comparable risky rate of return

• Risk-free term structure (Carey & Gordy, 2007) hinges on things like hedgibility of recovery risk & degree to which systematic

• Opportunity cost of funds (WACC, cost of debt) assume the defaulted loan is replaced with one of typical risk in the portfolio

• Comparable risky rate (punitive rate, contract rate at default) appropriate to defaulted exposures (most in line with workout practice and supervisory requirements?)

• Implication for IRB institutions: potential of not assigning enough regulatory capital to instruments with high recovery risk

• Few studies have investigated the influence of varying the discount rate by segment on economic LGD or capital

• Apart from Basel or credit risk, relevance to defaulted asset investors or finance academicians studying such markets

Introduction and Conclusions• Empirical study of returns on defaulted debt for the large

corporate defaulted (i.e., Chapter 11 & distress) universe (U.S., 1985-2007) using Moody’s Ultimate LGD Database (MULGD)

• Compare alternative discount rate measures: return on defaulted debt (RDD), most likely discount rate (MLDR), and derived from structural credit or regression based models

• Reference issues in credit risk management / measurement, supervisory requirements (Basel II Advanced IRB) and the finance of distressed debt investing

• Application of advanced / cutting edge statistical methods– Estimation of the beta-link generalized linear model (BLGLM) for RDD – Full-information maximum likelihood estimation of 2-factor extension of

asymptotic risk factor structural (“Basel”) credit model having both systematic & idiosyncratic recovery risk

• Find average RDD (MLE estimate of MLDR) 29.2% (21.3%), higher than previous benchmarks (e.g., JPMC 15%) or varied implications of model based approaches (ranging in 7-11%)

Introduction and Conclusions (continued)

• Empirical discount rates found to depend on facility structure factors: increase in superior collateral rank, higher seniority rank or better protected tranches (less/more debt above/below)

• Debt market information: greater market implied loss severity atdefault implies better performance (mispricing?)

• Obligor characteristics: increase for more highly rated obligorsat origination, firms more financially leveraged & higher market / book or having higher cumulative abnormal equity returns

• Evidence of procyclicality in discount rate measures: elevated in periods of economic downturn according to industry default rates (Moody’s 12 mos. trailing speculative grade default rate)

• Influence of macroeconomic factors: discount rate estimates increasing in short-term interest rates (need a dynamic model?)

• Discounting recoveries using a regression model RDD significantly increases economic LGD & regulatory capital: 73 (113) bps vs. a constant punitive 25% (contractual coupon) rate

Review of the Literature• “Implicit discounting” through reliance on near-default prices of

defaulted debt: Carty and Lieberman (1996), Gupton and Stein (2005), Frye (2000 a,b,c), Barco (2007)

• Ultimate recovery approach to LGD looks secondary market prices at emergence: Keisman et al (2000), Emery et al (2007)– But does not address the discounting question per se (both these use

contract rate at last cash-pay date)• Workout LGD approach supposedly sets a rate appropriate to

the risk of Banks’ recovery cash flows: Asarnow & Edwards (1995), Eales & Bosworth (1998), Araten et al (2003) – JPMC / Araten justifies 15% by return on Moody’s Defaulted Corporate

Bond index (Hamilton and Berthault, 2000) in 1982-2000• Defaulted debt as an asset class: introduced by Guha (2003)

and Schuerman (2003)– Machlachlan (2003): a CAPM motivated approach, finding 200 bps over

risk-free rate, and compares this to other approaches– Depends on correlation of “recovery process” to “the market”: Hamilton &

Berthault (2000), Altman and Jha (2003) find about 20%

Review of the Literature (continued)

• The risk-free rate (Carey and Gordy, 2007): pricing expected recoveries under risk neutral measure– Can we consider cash flows in reference data-set are already adjusted

for the investor’s risk aversion?• Empirically derived ex-post returns on defaulted debt without

risk adjustment (Brady et al, 2006)– The MLDR by various segments using S&P LossStats: similar to what

we do here but quite different results • Option adjusted spread (OAS) methodology: Kupiec (2007)

– Argues that the approach of Brady et al (2006) leads to bias due to timing & magnitude of recovery cash-flow uncertainty

• Cost of funds measures (debt/equity, WACC): proposed by several Banks internally for IRB purposes (no citation)

• Some banks using average contract rate in current non-defaulted portfolio?

Advanced IRB & Other Supervisory Requirements

• FSA (2003, page 68, Annex 3): "Firms should use the same rate as that used for an asset of similar risk. They should not use the risk-free rate or the firm’s hurdle rate (unless the firm only invests in risky assets such as defaulted debt instruments).”

• IAS 39 (2003): "Effective original loan rate (the rate that exactly discounts expected future cash payments or receipts through the expected life of the financial instrument)."

• Early U.S. guidance (BCBS, 2005): “When recovery streams are uncertain and involve risk 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.”

• The Basel II Final Rule in the U.S. (OCC et al, 2008, Page 450):“Where positive or negative cash flows on a wholesale exposure to a defaulted obligor or a defaulted retail exposure … occur after the date of default, the economic loss must reflect the net present value of cash flows as of the default date using a discount rate appropriate to the risk of the defaulted exposure.”

Theoretical Framework• A very general (not too useful) expression for expected LGD is:

[ ]( ), ,

1

Ds

Csr c

sc C s tP

t tt

c e dF c sE LGD ELGD

EAD

ττ

τ

−

= =≡ = −∫ ∫ %

• Where c(τ): uncertain recovery cash flows (times), Fc,τ(): their joint distribution, EAD: exposure-at-default, rs

D: risk-adjusted discount rate (maybe time dependent, a function of risk drivers & random), P: physical probability measure. But in practice:

( )11

1s

Ts

t sDs tt

cLGDEAD r=

= −+

∑

• Key distinction: quantifying an LGD parameter from observed cash flows in reference data vs. forecasting cash-flows & timings implies discounting at a risk-adjusted rate vs. a the risk-free term structure

Theoretical Framework (continued)

• Turning to the determination of rsD, start with the asymptotic

single risk factor framework of Gordy (2000) & Vasicek (2000), based upon the Merton (1974) structural modeling framework

• In an intertemporal version of this framework, we may write the stochastic process describing the instantaneous evolution of the ith representative firm’s (or PD segment) asset return at time t as: ,

,,

i ti i i t

i t

dVdt dW

Vμ σ= +

• Where Vi,t is the asset value, μi is the drift (which can be taken to be the risk-free rate rrf under risk-neutral measure), and Wi,tis a standard Weiner process that decomposes as:

2, , , ,1i t i X t i X i tdW dX dZρ ρ= + −

• The standard Weiners processes Xt & Zi,t are the systematic & idiosyncratic risk factors, respectively; and the factor loading ρi,Xis either firm-specific or obligors in segment i


• It follows that the instantaneous asset-value correlation (AVC) amongst firms (or segments) i and j is given by:

• As in the Basel framework, assuming the factor loading to be constant amongst firms within a specified segments implies an intra-segment AVC given by ρi,X

2=Ri• If we identify this with the correlation to a market portfolio -

arguably a reasonable interpretation in a ASRF world – then it follows from the standard CAPM that the beta relating the market’s to the representative firm’s asset return is:

,,, , ,

, ,

1 , j ti tVi j i x j x

i t j t

dVdVCor

dt V Vρ ρ

⎡ ⎤=⎢ ⎥

⎢ ⎥⎣ ⎦

, ,,

, ,,

,

,

,i t M ti M

i t M t i ii M

MM tM

M t

dV dVCov

V V RdV

VarV

σβ

σ

⎡ ⎤⎢ ⎥⎣ ⎦ = =⎡ ⎤⎢ ⎥⎣ ⎦


• In this setting the proper discount rate for LGD in the ith

segment, riD, is equal to the expected return on the defaulted

firm’s assets, which is given by the risk-free rate rrf and the firm-specific risk-premium δi :

• Where rM is return on a market index and σi (σM) is volatility of the firm’s asset (market) return

• We consider an extension of this framework that admits systematic and idiosyncratic variation in the recovery process:

( ) ,i iD

i rf M rf rf i M rf iM

Rr r r r r MRP r

σβ δ

σ= + − = + = +

2, ,, ,

1R RR R R

i t t i ti X i XdW dX dZρ ρ= + −

• The standard Weiners XtR and Zi,t

R are the systematic risk and the idiosyncratic risk factors particular to recovery, respectively; and the factor loading ρi,X is for loans in “recovery class” i

• Implement this 2 stages: make assumptions on rM, rRF ,σi and σM based upon external sources & from Moody’s annual default (drt,i) / loss rate (lrt,i) data estimate:

• Assume the systematic factors on the PD and LGD “sides” to be standard and bivariate normally distributed with correlation r:

( ) 0 1, ~ ,

0 1TR

t t

rdX dX N

r⎛ ⎞⎛ ⎞ ⎛ ⎞⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎝ ⎠

( ), ,, , , ,R

T

r s r X s XPD LGD rρ ρ

• Segments are now ratings-”r” & seniorities-”s” indexing an expected PD / LGD combination (“cell”) and the likelihood contribution for year t is derived from App.2 of the paper as:

( ), , , ,, | , , , ,Rt r t s r r X s s X

l dr lr PD LGD rρ ρ =

( )( ) ( )

( )( ) ( )

( )2 1 2 12 1 2 11 1

, , , ,2

, ,0 0 , ,

1 11 1, |

R R

R R

si X r i X i X i X

i X i X i X i X

LGD vLGD uu v r dudv

u v

ρ ρρ ρφ φ

ρ φ ρ ρ φ ρ

− −− − ⎛ ⎞⎛ ⎞ − Φ − − Φ− Φ − − Φ ⎜ ⎟⎜ ⎟ Φ⎜ ⎟⎜ ⎟

⎝ ⎠ ⎝ ⎠∫ ∫


Empirical Methodology: The Return on Defaulted Debt (RDD)

• Here we describe empirically based approaches to measuring the performance of defaulted debt, which may be compared to the model-based approached previously discussed, and potentially could be taken for LGD discount rate estimates

• RDD is simply the annualized net rate of return on defaulted debt from the time of default to the time of resolution:

• ith(sth) denotes loan (segment), PE (PD) price at emergence (default), tE (tD) respective times and ri,s

D is the RDD

, ,

1

, ,,

, ,

1E Di s i sE

i

Di

E t ti s tD

i s Di s t

Pr

P

−⎛ ⎞⎜ ⎟= −⎜ ⎟⎝ ⎠

, ,

1

, ,

1 , ,

1 1E DDi s i ss E

i

Di

E t tNi s tD

s D Dis i s t

Pr

N P

−

=

⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟= −⎢ ⎥⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

∑

• An estimate for the discount rate for the sth “LGD segment” is an arithmetic averages across Ns

D defaulted loans:

Empirical Methodology: The Most Likely Discount Rate (MLDR)

• We pursue an alternative to RDD (Brady et al, 2006) in which the price of defaulted debt is considered as the expected, discounted recovery over the resolution period:

• To account for that we cannot observe expected recovery prices ex ante, invoke market rationality that in homogenous segments normalized average pricing errors should be “small”:

:

( ) , ,

, ,

, ,

,1

Ei

D E Di i s i s

P Et i s tD

i s t t tDi s

E PP

r−

⎡ ⎤⎣ ⎦=

+

( ) , ,

,, , , ,,

, ,, ,

1E Di s i s

E Di i

Di

t tE D Di si s t i s t

i s D E Di s i si s t

P P r

P t tε

−− × +

≡× −

%

• Assume: pricing errors are standard normal & LGD uncertainty proportional to sqrt(tE-tD), then solve by maximum likelihood:

( ) ( ) , ,

, , ,

,, , , ,, ,

1 1 , ,, ,

1ˆ arg max arg max log arg max log

E Di s i sD D

s s E Di i

D D Di s i s i s D

i

t tE D DN Ni si s t i s tD

i s i s D E Dr r ri i i s i si s t

P P rr LL

P t tφ ε φ

−

= =

⎡ ⎤⎛ ⎞− × +⎢ ⎥⎜ ⎟⎡ ⎤= = =⎣ ⎦ ⎢ ⎥⎜ ⎟× −⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

∑ ∑%

Empirical Results: Data Description• Starting point: Moody’s Ultimate LGD Database™ (“MULGD”)

• February 2008 release (3886 defaulted instruments 1985-2007 for 683 defaulted borrowers)

• Comprehensive database of defaults (bankruptcies and out-of-court settlements)• Broad definition of default (“quasi-Basel” according to Moody’s)

• Largely representative of the U.S. large corporate loss experience

• Most obligors have rated debt (S&P or Moody’s) & traded equity at some point prior to default

• Merged with various public sources of information • www.bankruptcydata.com, Edgar SEC filing, LEXIS/NEXIS, Bloomberg,

Compustat and CRSP; LPC DealScan in (covenants) progress• Note all covariates measured at approx. 1 year to default from

these sources (even if available MULGD – went to SEC filings, etc.)

Empirical Results: Data Description (continued)

• MULGD has information on all classes of debt in the capital structure at the time of default– Exceptions: trade payables & other off-balance sheet obligations

• Observations detailed by:– Instrument characteristics: debt type, seniority ranking, debt above /

below, collateral type – Obligor / Capital Structure: industry, proportion bank / secured debt,

number of creditor classes / number instruments– Defaults: amounts (EAD, AI), default type, coupon, dates / durations– Resolution types : emergence from bankruptcy, Chapter 7 liquidation,

acquisition or out-of-court settlement

• Recovery / LGD measures: prices of pre-petition (or received in settlement) instruments at emergence or restructuring – Sub-set: prices of traded debt at around default (30-45 day avg.)

Empirical Results: RDD by Instrument & Default Event Type

• We decide to exclude the 76 out-of-court settlements: very short resolution times -> bias results & distribution seems very different from bankruptcies

• Mean RDD (MLE of MLDR) 29.2% (21.3%), both above prior benchmarks, with much variability (std dev of RDD / MLE std error 114.2% / 116.5%)

• Maximum 893.8% even after eliminating 37 clear outliers (all > 30K% RDD!)• Loans have seemingly much higher (lower) RDD (MLDR) 43.3% (14.5%)• Revolvers appear close to other loans & less risky by MLDR (15.2%) but

more like the broader sample by average RDD (32%)

MLE Est.

MLE Std Err Avg Std Dev Min Max MLE Est.

MLE Std Err Avg Std Dev Min Max MLE Est.

MLE Std Err Avg Std Dev Min Max

Bonds and Term Loans 1121 21.74% 128.51% 28.86% 121.85% -100.00% 893.76% 73 52.54% 104.03% 38.86% 135.78% -91.87% 846.73% 1194 21.86% 120.83% 29.48% 122.71% -100.00% 893.76%

Bonds 888 23.88% 162.22% 23.27% 119.93% -100.00% 893.76% 71 52.54% 104.03% 38.86% 135.78% -91.87% 846.73% 959 24.02% 150.44% 24.50% 121.32% -100.00% 893.76%

Revolvers 141 15.24% 3.57% 31.95% 58.58% -100.00% 340.51% 3 N/A N/A 0.01% 4.04% 0.00% -0.03% 144 15.24% 3.57% 31.28% 58.14% -100.00% 340.51%

Loans 374 14.45% 32.83% 43.31% 106.72% -100.00% 853.84% 5 N/A N/A 0.01% 0.01% 0.00% 0.03% 379 14.45% 32.83% 42.74% 106.13% -100.00% 853.84%

Total 1262 21.31% 114.15% 29.21% 116.49% -100.00% 893.76% 76 52.54% 104.03% 37.33% 133.25% -91.87% 846.73% 1338 22.38% 107.83% 29.67% 117.46% -100.00% 893.76%

Cnt

RDDRDDBankruptcy Out-of-Court

Table 1.1 - RDD1 and MLDR2 Observations by Default and Instrument Type (Moody's Ultimate LGD Database 1987-2007)

MLDRMLDRMLDR

CntCnt

RDDTotal

Empirical Results: Distributions of RDD by Instrument & Default Event

• RDD is “naturally” floored at -100% but has an extremely long right tail

• There were a few credible cases where debt selling for pennies at default went for close to par at emergence!

• As we have a prior that this is probably the best case, we expect a limited domain, so something “like” a beta distribution might be best to model the distribution of RDD

0 2 4 6 8 10

0.0

0.1

0.2

0.3

0.4

0.5

Figure 1: Dis tribution of Return on Defaulted Debt (All Ins trum en

Moody's Ultimate LGD Database 1987-2007RDD.Ann.0

Distributions of RDD by Instrument &Default Event (continued)

• While out-of-court settlements have a long tail, the distribution is less peaked & possibly multi-modal vs. bankruptcies

• Bankruptcies clearly have more mass near zero as compared to out-of-court

• Studying various features of the distributions, and prior considerations (amount of uncertainty present at default), lead us to believe that these are fundamentally different

0 2 4 6 8 10

0.0

0.1

0.2

0.3

0.4

0.5

F igure 2.1: Distribution of Return on Def aulted Debt (Bankruptcies)

Moody's Ultimate LGD Database 1987-2007RDD.Data.Bnkrpt[, 1]

0 2 4 6 8 10

0.0

0.10

0.20

0.30

F igure 2.2: Distribution of Return on Def aulted Debt (Out-of -Court Settlements

Moody's Ultimate LGD Database 1987-2007RDD.Data.Outcrt[, 1]

• KS test for difference in distributions significant (p-value = 0.0024)

Distributions of RDD by Instrument &Default Event (continued)

• Bonds share the long tail, but the distribution is slightly more peaked as compared with loans

• Bonds have some more mass near zero as compared to loans

• Studying various features of the distributions, and prior considerations, lead us to believe that these are not so fundamentally different as to necessitate separating them in further analysis

0 2 4 6 8 10

0.0

0.1

0.2

0.3

0.4

F igure 3.1: Distribution of Return on Def aulted Debt (Bonds)

Moody's Ultimate LGD Database 1987-2007RDD.Data.Bond[, 1]

0 2 4 6 8 10

0.0

0.10

0.20

0.30

F igure 3.2: Distribution of Return on Def aulted Debt (Loans)

Moody's Ultimate LGD Database 1987-2007RDD.Data.Outcrt[, 1]

• KS test for difference in distributions insignificant (p-value = 0.2792)

Empirical Results: RDD and MLDR by Collateral & Seniority

• Central tendencies generallydecrease for lower seniorities ranks (but peak at sen. sec.)

• Mean RDD & MLE of MLDR higher for secured vs. unsecured, but not clear ranks (RDD peaks @ CA/CS but MLDR little difference)

• Similar pattern for dispersion measures – higher for secured but across groups non-monotonic

Revolving Credit / Term Loan

Senior Secured Bonds

Senior Unsecured Bonds

Senior Subordinated Bonds

Subordinated Bonds

Total Instrument

Count 374 142 437 179 130 1262Mean of RDD 43.3% 50.7% 22.5% 23.9% -5.0% 29.2%MLE of MLDR 14.5% 38.4% 20.9% 21.9% 16.5% 21.3%Std Dev of RDD 106.7% 116.4% 104.5% 158.6% 104.1% 116.5%MLE Std Err of MLRD 32.8% 101.3% 17.4% 13.7% 15.1% 114.2%

Table 2.1 - Central Tendency and Dispersion Measures of RDD and MLDR by Seniority Rank (Moody's Ultimate LGD Database 1987-2007)

Cash, Accounts Receivables & Guarantees

Inventory, Most Assets & Equipment

All Assets & Real Estate

Current Assets & Capital Stock

PPE & Second Lien

Total Secured

Total Unsecured

Total Collateral

Count 7 19 323 84 54 500 762 1262Mean of RDD 27.8% 31.1% 43.4% 59.6% 54.8% 46.4% 17.9% 29.2%MLE of MLDR 33.3% 20.6% 30.4% 34.0% 33.7% 31.7% 18.3% 21.3%Std Dev of RDD 36.9% 31.5% 118.6% 104.5% 104.3% 118.0% 112.0% 116.5%MLE Std Err of MLRD 13.4% 7.8% 44.5% 9.2% 10.4% 28.8% 10.8% 114.2%

Table 2.2 - Central Tendency and Dispersion Measures of RDD and MLDR by Major Collateral Category (Moody's Ultimate LGD Database 1987-2007)

• Dispersions pattern not as clear: overall seems to decline for MLDR (not so much RDD) but peaks at senior sen. sec. (sen. sub.)

• “Counterintuitive story” – greater recovery risk in better ranked / secured loans?

RDD and MLDR by Collateral & Seniority (continued)

• Graphically, the “hump shape” in average RDD or MLE estimate of MLDR within seniority classes or major collateral categories is somewhat more evident than decline

Figure 5.1: Central Tendency Measures of RDD and MLDR Observations by Seniority Rank (MULGD Database 1987‐2007)

‐10.0%

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

Revolving Credit /Term Loan

Senior SecuredBonds

Senior UnsecuredBonds

SeniorSubordinated

Bonds

SubordinatedBonds

Total Instrument

Mean of RDD MLE of MLDR

Figure 6.1: Central Tendency Measures of RDD and MLDR Observations by Collateral Category

(MULGD Database 1987‐2007)

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

Cash, AccountsReceivables &Guarantees

Inventory, MostAssets &Equipment

All Assets &Real Estate

Non‐CurrentAssets &

Capital Stock

PPE & SecondLien

Total Secured Total Unsecured Total Collateral

Mean of RDD MLE of MLDR

Empirical Results: RDD and MLDR Measures by Year of Default

• Identify “downturn periods” as 1990-91 and 2000-02 when Moody’s default rate is elevated

• RDD & MLDR somewhat elevated in bad periods (but lagging a little in recent one)

• Similar pattern for dispersions (but now lagging more / less prominent for RDD / MLDR)

• The story for cyclicality be? –the market over-reacts and overly beats this debt down at around contraction periods?

• Beware: censoring problem (low counts in beginning & end of sample)

YearCount of RDD

Average of RDD

Std Dev of RDD

MLE Est of MLDR

MLE Std Err of MLDR

Average LGD at Default2

Average of Moody's Speculative Grade Default Rate

Average of Total Defaulted Amount ($MM)4

Average of Time-to-Resolution (Yrs.)5

1987 5 -5.03% 10.81% -2.90% 202.18% 70.08% 4.71% 3,803 2.03791988 11 -1.34% 50.08% 9.07% 12.37% 63.80% 3.32% 3,697 2.01231989 14 29.07% 108.33% 35.47% 29.34% 74.55% 4.80% 7,915 2.26381990 64 46.40% 143.41% 17.58% 91.36% 75.63% 10.36% 26,148 1.69911991 92 43.75% 117.69% 39.44% 35.02% 57.15% 9.85% 25,252 1.60741992 27 32.54% 172.26% 5.33% 15.73% 58.89% 6.13% 6,340 1.73091993 10 1.32% 91.31% 13.38% 31.14% 51.10% 3.02% 3,912 1.17401994 6 -27.64% 40.67% 12.11% 20.54% 70.57% 2.42% 3,926 0.95741995 35 27.45% 107.80% 11.27% 26.85% 41.96% 3.19% 8,966 2.07641996 25 27.43% 73.00% 20.42% 19.46% 44.32% 2.18% 5,223 1.35721997 17 9.14% 61.15% -1.27% 12.81% 46.65% 2.27% 4,386 1.31591998 33 -37.79% 49.62% -25.43% 9.69% 57.05% 3.77% 8,837 1.34711999 92 6.83% 53.26% 10.74% 6.53% 65.01% 6.12% 28,296 1.34682000 105 ‐3.95% 67.96% 7.59% 60.25% 62.63% 7.93% 34,383 1.73942001 257 16.15% 101.98% 24.59% 10.97% 58.25% 11.39% 96,929 1.73142002 207 50.77% 147.80% 32.83% 17.41% 61.61% 7.89% 183,801 1.30212003 106 64.24% 161.24% 46.20% 15.92% 49.34% 5.83% 43,151 0.98262004 75 46.60% 88.50% 15.73% 8.63% 33.12% 3.31% 22,863 0.78112005 63 42.59% 118.00% 50.84% 53.22% 35.58% 2.33% 43,461 1.11602006 9 29.65% 88.81% -6.25% 20.82% 32.50% 1.73% 2,355 0.56522007 9 9.98% 46.68% -31.19% 8.24% 18.97% 1.26% 3,388 0.2189Total 1,262 29.21% 116.49% 22.38% 107.83% 55.78% 7.14% 567,520 1.4594

Table 3 - RDD1, MLDR2, LGD3, Default Rate4, Dollar Loss5 and Duration6 of Defaulted Instruments by Cohort Year

(Moody's Ultimate LGD Database 1987-2007)

RDD and MLDR Measures by Year of Default (continued)

Figure 7.1: Central Tendency Measures of RDD and MLDR Observations by Year of Default (MULGD Database 1987‐2007)

‐60.00%

‐40.00%

‐20.00%

0.00%

20.00%

40.00%

60.00%

80.00%

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

Total

Average of RDD MLE Est of MLDR

Figure 7.2: Dispersion Measures of RDD and MLDR Observations by Year of Default


0.00%

50.00%

100.00%

150.00%

200.00%

250.00%

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

Total

Std Dev of RDD MLE Std Err of MLDR

• Graphically, you “sort of” get a sense of the cyclicality in average RDD or MLE estimate of MLDR (or their dispersions), but there is s a lot more going on (e.g., the local peak in RDD / MLDR in the mid-90’s)

Empirical Results: Term Structures of RDD and MLDR

• TTR (TID): time from default (last cash pay) date to resolution (default)

• Both mean RDD & MLE of MLDR show a bumpy overall decline in TID

• But dispersion of RDD (MLDR) U-shaped (humped) in TID

• RDD generally falls in TTR while MLDR peaks at 4th quintile

• Both show non-monotone decline in dispersion

1st Quintile TTR

2nd Quintile TTR

3rd Quintile TTR

4th Quintile TTR

5th Quintile TTR Total

Mean of RDD 70.8% 41.4% 17.8% 26.4% 7.5% 29.2%MLE of MLDR 23.6% 16.8% 21.4% 42.9% 18.5% 21.3%Std Dev of RDD 178.5% 156.6% 91.3% 84.7% 45.0% 116.5%MLE Std Err of MLRD 96.6% 5.7% 7.6% 18.3% 6.7% 114.2%

Table 3.1 - Central Tendency Measures of RDD and MLDR Observations by Quintiles of Time-to-Resolution


1st Quintile TID

2nd Quintile TID

3rd Quintile TID

4th Quintile TID

5th Quintile TID Total

Mean of RDD 41.3% 27.6% 31.0% 29.8% 21.3% 29.2%MLE of MLDR 27.6% 16.7% 25.9% 24.2% 13.3% 21.3%Std Dev of RDD 145.6% 94.5% 93.1% 120.1% 133.0% 116.5%MLE Std Err of MLRD 24.7% 6.6% 53.5% 5.5% 26.9% 114.2%

Table 3.2 - Central Tendency Measures of RDD and MLDR Observations by Quintiles of Time-in-Distress (Moody's Ultimate LGD Database 1987-2007)

• Story for what are kind of seeing –uncertainty gets more “settled”longer under “watch” prior to default or as bankruptcy proceeds?

• TID shows no univariate correlation & neither in regressions (OK for TTR)

Term Structures of RDD and MLDR (continued)

• We get some sense of the bumpy downward path in discount rate measures and their volatilities in these duration buckets

Figure 8.1: Central Tendency and Dispersion Measures of RDD and MLDR Observations by

Quintiles of Time‐to‐Resolution (MULGD Database 1987‐2007)

0.0%

20.0%

40.0%

60.0%

80.0%

100.0%

120.0%

140.0%

160.0%

180.0%

200.0%

1st Quintile TTR 2nd Quintile TTR 3rd Quintile TTR 4th Quintile TTR 5th Quintile TTR Total

Mean of RDD MLE of MLDR Std Dev of RDD MLE Std Err of MLRD

Figure 8.2: Central Tendency and Dispersion Measures of RDD and MLDR Observations by

Quintiles of Time‐in‐Distress(MULGD Database 1987‐2007)

0.0%

20.0%

40.0%

60.0%

80.0%

100.0%

120.0%

140.0%

160.0%

1st Quintile TID 2nd Quinti le TID 3rd Quinti le TID 4th Quintile TID 5th Quinti le TID Total

Mean of RDD MLE of MLDR Std Dev of RDD MLE Std Err of MLRD

Empirical Results: RDD and MLDR by Original Credit Rating

• Discount rate measures generally higher for better rated: RDD (MLDR) 33.3%-26.1% (23.7%-18.5%) inv. gr.-junk

• Pattern non-monotonic by finer categories: RDD / MLDR peak at BBB

• “Fighting spirit” vs. more recovery risk for ”fallen angels”?

CountAverage of RDD

Standard Deviation RDD

MLE Estimate of MLDR

MLE Standard Error of MLDR

AA-A 130 26.43% 63.36% 20.67% 28.16%BBB 58 48.62% 110.94% 111.61% 51.45%BB 299 18.10% 91.67% 22.13% 7.18%B 497 32.06% 140.92% 13.24% 13.68%

CC-CCC 89 19.58% 78.55% 18.30% 7.93%Investment Grade (BBB-A) 188 33.28% 80.75% 23.70% 25.89%

Junk Grade (CC-BB) 885 26.09% 212.83% 18.48% 8.10%Total 1262 29.21% 116.49% 21.31% 114.15%

Rating G

roups

Table 5 - RDD1 and MLDR2 of Defaulted Instruments by Credit Rating at Origination


Figure 9.1: Central Tendency Measures of RDD and MLDR Observations by Credit Rating at Origination


0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

120.00%

AA‐A BBB BB B CC‐CCC InvestmentGrade (BBB‐A)

Junk Grade (CC‐BB)

Total

Rating Groups

Average of RDD MLE Estimate of MLDR

Figure 9.2: Dispersion Measures of RDD and MLDR Observations by Credit Rating at Origination


0.00%

50.00%

100.00%

150.00%

200.00%

250.00%

AA‐A BBB BB B CC‐CCC InvestmentGrade (BBB‐A)

Junk Grade (CC‐BB)

Total

Rating Groups

Standard Deviation RDD MLE Standard Error of MLDR

• Disagreement in dispersion pattern: MLDR(RDD) higher inv. gr. (junk)

Empirical Results: RDD and MLDR by Tranche Safety & Position

• Both measures are U-shaped in quintiles of TSI, but RDD shows overall increase

CountAverage RDD

Standard Deviation RDD MLDR

MLE Std Err MLDR

1st Quintile TSI 154 33.03% 162.52% 33.84% 28.96%2nd Quintile TSI 324 9.55% 97.95% 21.29% 20.71%3rd Quintile TSI 372 26.55% 109.95% 14.38% 38.66%4th Quintile TSI 326 43.63% 116.28% 25.05% 3.22%5th Quintile TSI 86 53.23% 99.63% 29.62% 32.06%

NDA / SDB4 427 44.16% 103.17% 25.29% 6.87%SDA / SDB5 232 25.08% 124.31% 35.39% 8.46%NDA / NDB6 154 26.30% 122.01% 12.03% 93.37%NDB / SDA7 449 18.12% 121.14% 19.72% 17.73%

Total 1262 29.21% 116.49% 21.31% 114.15%

Table 6 - RDD1 and MLDR2 of Defaulted Instruments by Tranche Safety Index3 (TSI) Quintiles and Categories


Debt Tranche G

roups

Figure 10.1: Central Tendency Measures of RDD & MLDR by Tranche Safety Index & Debt Position Categories


0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

1stQuinti le

TSI

2ndQuinti le

TSI

3rdQuinti le

TSI

4thQuintile

TSI

5thQuintile

TSI

NDA / SDB4 SDA / SDB5 NDA /NDB6

NDB / SDA7 Total

Debt Tranche Groups

Average RDD MLDR

Figure 10.2: Dispersion Measures of RDD & MLDR by Tranche Safety Index & Debt Position Categories


0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

120.00%

140.00%

160.00%

180.00%

1stQuintile

TSI

2ndQuinti le

TSI

3rdQuintile

TSI

4thQuintile

TSI

5thQuintile

TSI

NDA / SDB4 SDA / SDB5 NDA /NDB6

NDB / SDA7 Total

Debt Tranche Groups

Standard Deviation RDD MLE Std Err MLDR

[ ]1 % % 12

TSI Debt Below Debt Above≡ − +

• RDD higher for NDA/SDB (best) vs. NDB /SDA (worst) group, but not so MLDR

• St dev RDD increasing in worst tranches, but not as clear for MLDR

Empirical Results: RDD and MLDR Measures by Obligor Industry

• Difficult to discern a “story” & lack of agreement between RDD / MLDR

• High RDD: Aerospace/…,High Tech/…,Leisure/… but high MLDR Consumer/…,Leisure/…

• Low in both: Healthcare/… & Transportation

Figure 11.1: Central Tendency Measures of RDD & MLDR by Industry (MULGD Database 1987‐2007)

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

35.00%

40.00%

45.00%

Aerospace / Auto /Capital Goods /Equipment

Consumer / ServiceSector

Energy / NaturalResources

Healthcare /Chemicals

High Technology /Telecommunications

Leisure Time / Media Transportation Forest / BuildingProducts /

Homebuilders

Grand Total

RDD Average MLDR MLE Estimate

AverageStandard Deviation

MLE Estimate

MLE Standard Error

Aerospace / Auto / Capital Goods / Equipment 156 41.30% 122.21% 22.29% 22.80%Consumer / Service Sector 235 34.27% 121.28% 28.84% 61.19%Energy / Natural Resources 183 26.56% 55.42% 20.35% 34.96%Healthcare / Chemicals 93 24.03% 90.98% 17.99% 10.77%High Technology / Telecommunications 225 40.98% 159.31% 17.92% 6.94%Leisure Time / Media 114 36.58% 114.81% 26.42% 13.25%Transportation 236 6.02% 99.95% 5.76% 16.04%Forest / Building Products / Homebuilders 20 23.01% 128.62% 34.94% 21.06%Grand Total 1,262 29.21% 116.49% 22.38% 107.83%

MLDR

Table 7 - RDD1 and MLDR2 of Defaulted Instruments by Industry (Moody's Ultimate LGD Database 1987-2007)

Industry Group

RDD

Count

Figure 11.2: Dispersion Measures of RDD & MLDR by Industry(MULGD Database 1987‐2007)

0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

120.00%

140.00%

160.00%

180.00%

Aerospace / Auto /Capital Goods /Equipment

Consumer / ServiceSector

Energy / NaturalResources

Healthcare /Chemicals

High Technology /Telecommunications

Leisure Time / Media Transportation Forest / BuildingProducts /

Homebuilders

Grand Total

RDD Standard Deviation MLDR MLE Standard Error

Correlation Analysis of RDD: Financial / Valuation Covariates

• Book leverage & market / book strong positive drivers (appear in regressions)

• Cash-flow measures inversely correlated (FAR makes one of the regressions)

• Liquidity dimension: only ICR has a significantly inverse relationship

• Some profitability measures negatively related to RDD (NI/TA, ROA & ROE)

Variable Cnt Median Mean Std DevCorr with RDD

BVTL / BVTA 1111 117.00% 138.89% 73.94% 17.18%BVTL / MVTA 1111 97.00% 91.23% 12.02% -1.23%MVTA 790 2.0913 2.0691 0.9462 -8.15%Net Sales 980 2.8596 2.8035 0.6744 -2.69%BVA 983 3.0659 3.0362 0.5958 -1.83%Tobin's Q 735 84.01% 100.69% 61.21% -0.12%MVTA / BVTA 1111 127.00% 153.82% 83.03% 18.50%BVI / BVTA 773 18.34% 21.02% 20.98% 2.00%PE Ratio 791 -0.3084 -2.2438 14.8584 4.02%CR 911 113.41% 133.57% 84.43% 2.33%ICR 982 0.01 (1.43) 4.56 -6.57%WC / BVTA 914 2.86% -5.88% 38.10% 2.87%CF / CL 902 -0.06% -31.79% 122.08% -2.98%FAR 881 13.30% 9.27% 35.02% -12.56%FCF / BVTA 946 0.06% -8.02% 20.07% -4.03%CFO / BVTA 954 0.47 102.76 988.72 1.26%NI / BVTA 1111 -8.00% -20.71% 38.64% -2.85%NI / MVTA 1111 -4.00% -11.67% 17.93% 0.21%RE / BVTA 971 -22.57% -55.95% 97.26% -6.69%ROA 971 -7.08% -19.29% 27.95% -8.13%ROE 971 -1.85% 17.41% 568.41% -2.78%

Table 8.1 - Summary Statistics on Financial Statement and Market Valuation Variables and Correlations with RDD (Moody's Ultimate LGD

Database 1987-2007) • Size by market value of total assets inversely correlated (somewhat less extent by net sales & book value assets)

y = 0.258x ‐ 0.107R² = 0.034

‐200.00%

0.00%

200.00%

400.00%

600.00%

800.00%

1000.00%

0 1 2 3 4 5 6

RDD

MV / BV

Figure 12.1: Annualized Return on Defaulted Debt vs. Market‐to‐Book Value (MULGD Database 1987‐2007)

Correlation Analysis of RDD: Firm Level Equity Price Covariates

• 1-year expected return (just avg. to 1 yr. prior to default) is mildly negatively correlated

• Relative larger defaulted firms, in terms or either market cap or stock price, have poorer debt performance

• Firms trading nearer to the high point of their 3-year trading range also tend to have lower RDDs, but it is a weak correlation

• 1 month equity volatility has a weak positive relationship

y = 0.430x + 0.313R² = 0.011

‐200%

0%

200%

400%

600%

800%

1000%

‐150% ‐100% ‐50% 0% 50% 100% 150% 200%

RDD

CAR

Figure 12.4: Annualized Return on Defaulted Debt vs. Cumulative Abnormal Equity Returns (MULGD Database

1987‐2007)

• CARs (only variable here in the regressions) in the 90 days to the 1-year horizon to default has strongpositive correlationVariable Cnt Median Mean Std Dev

Corr with RDD

1-Yr Expected Equity Return 1111 -81.00% -73.93% 41.35% -6.36%1-Month Equity Return Volatility 1111 206.00% 262.88% 410.89% 2.31%Market Cap to Relative to Market 1111 -12.7400 -13.1512 1.9645 -8.61%Stock Price to Relative to Market 1111 9.00% 13.04% 14.16% -5.40%Stock Price Trading Range 1111 0.54% 3.01% 8.56% -2.78%Cumulative Abnormal Returns 1111 0.00% -5.13% 29.42% 10.90%

Table 8.2 - Summary Statistics on Equity Price Performance Variables and Correlations with RDD


Correlation Analysis of RDD: Firm Level Capital Structure Covariates

• Strongest relationship is a positive one for proportion of secured debt

• Measures of “capital structure complexity”, number of instruments or of major creditor classes, have small negative correlations with RDD

• Percent bank and sub debt also a mild direct association with RDD

Variable Cnt Median Mean Std Dev

Corr with RDD

Number of Instruments 3886 6.0000 10.5252 12.8458 -4.01%Number of Creditor Classes 3886 2.0000 2.5980 1.1071 -3.17%Percent Secured Debt 3886 42.22% 43.43% 32.63% 9.21%Percent Bank Debt 3886 39.92% 40.78% 30.84% 7.32%Percent Subordinated Debt 3886 38.81% 40.34% 31.23% 5.60%

Table 8.3 - Summary Statistics on Capital Structure Variables and Correlations with RDD


y = 0.349x + 0.146R² = 0.008

‐200%

0%

200%

400%

600%

800%

1000%

0% 20% 40% 60% 80% 100% 120%

RDD

PBD

Figure 12.5: Annualized Return on Defaulted Debt vs. Percent Secured Debt (MULGD Database 1987‐2007)

• Work-in-progress: analysis of bank lender concentration by Herfindahlindex: expected relationship?(evidencethat lower → ↑ firmwide recoveries)

• No variables from this group are in the final regression models

• Note generally very little change in these from 1 yr. prior to default

Correlation Analysis of RDD: Firm Level Credit Quality Covariates

• Although the univariate correlation is modest in size, a result from this group result that carries over to the regressions is that higher LGD at default is indicative of higher RDD

• The investment grade dummy has only a small positive correlation here but appears significantly in regressions

• A higher spread over risk-free rate or contractual coupon is inversely correlated at similar magnitude but not appearing in the regressions

y = 0.399x + 0.066R² = 0.012

‐200%

0%

200%

400%

600%

800%

1000%

‐20% 0% 20% 40% 60% 80% 100% 120%

RDD

LGD

Figure 12.6: Annualized Return on Defaulted Debt vs. Loss‐Given‐Default (MULGD Database 1987‐

2007)

• Altman Z: relatively sizable negative correlation but not in any regressions (issues: limited availability & over-lap)


Corr with RDD

Altman Z-Score 733 0.5266 -0.1010 2.2087 -11.23%Credit Spread 1262 8.70% 8.11% 3.95% -5.66%Contractual Coupon Rate 3886 9.00% 8.64% 3.89% -5.76%LGD at Default 1375 60.00% 55.78% 31.28% 6.88%Moody's Original Credit Rating Investment Grade 3178 0.0000 0.1954 0.3966 2.35%Moody's Original Credit Rating (Major Code) 3178 4.0000 3.3106 1.0784 -0.03%Moody's Original Credit Rating (Minor Code) 3178 14.0000 12.5296 3.4435 1.92%Moody's Long Run Default Rate (Minor Code) 3178 0.0249 0.0337 0.0461 0.29%

Table 8.4 - Summary Statistics on Credit Quality / Credit Market Variables and Correlations with RDD


• Caveat on LGD at default in RDD model: 1-year horizon issue

Correlation Analysis of RDD: Instrument / Contractual Covariates

• The TSI has a decently sized positive correlation & is the variable from this group to enter the regressions

• As in the tabular results, lower rank of seniority or collateral is associated with lower RDD with seemingly robust magnitudes, but this is not so in the multivariate regressions

• Percent debt below (above) has the “expected” positive (negative) correlation coefficient


Corr with RDD

Seniority Rank 3886 1.0000 1.7123 0.8953 -9.64%Collateral Rank 3886 6.0000 4.5844 1.6206 -9.97%Percent Debt Below 3886 10.13% 25.82% 30.19% 10.51%Percent Debt Above 3886 0.00% 21.51% 28.95% -6.51%Tranche Safety Index 3886 50.00% 52.16% 25.44% 9.69%

Table 8.5 - Summary Statistics on Instrument / Contractual Variables and Correlations with RDD


y = 0.515x + 0.046R² = 0.009

‐200%

0%

200%

400%

600%

800%

1000%

0% 20% 40% 60% 80% 100% 120%

RDD

TSI

Figure 12.7: Annualized Return on Defaulted Debt vs. Tranche Safety Index (MULGD Database 1987‐2007)

Correlation Analysis of RDD: Macro / Aggregate Market Covariates

• The two cyclical variables from this group to enter regressions are the Moody’s 12 mos. lagging speculative grade default rate by industry and 1-month T-bill yield, with positive & negative signs as in this table, respectively

• Equity market volatility is seemingly unrelated to RDD

• Long term interest rates have somewhat of an inverse univariate relation but does not make it to the regressions (same for long/short spread – not shown)

Variable Cnt Median Mean Maximum Std Dev

Corr with RDD

Moody's All-Corporate Quarterly Default Rate 1262 7.05% 7.38% 13.26% 3.28% 5.72%Moody's Speculative Quarterly Default Rate 1262 7.05% 7.40% 13.26% 3.24% 5.43%Moody's All-Corporate Quarterly Default Rate by Industry 1262 3.78% 4.13% 12.68% 2.70% 7.40%Moody's Speculative Quarterly Default Rate by Industry 1262 6.52% 7.03% 17.50% 4.19% 6.66%Fama-French Excess Return on Market Factor 3886 86.00% 33.35% 1030.00% 464.59% -0.07%Fama-French Relative Return on Small Stocks Factor 3886 31.00% 13.66% 843.00% 394.25% 2.37%Fama-French Excess Return on Value Stock Factor 3886 64.00% 81.98% 1380.00% 373.74% -3.62%Short-Term Interest Rates (1-Month Treasury Yields) 1262 32.00% 31.82% 79.00% 16.83% -10.41%Long-Term Interest Rates (10-Month Treasury Yields) 1111 535.00% 548.19% 904.00% 125.45% -6.69%Stock-Market Volatility (2-Year IDX) 1111 9.00% 9.98% 19.00% 3.84% -0.36%

Table 8.6 - Summary Statistics on Macroenonomic and Cyclical Variables and Correlations with RDD (Moody's Ultimate LGD Database 1987-2007)

• The Fama-French factors show little relationship to defaulted debt performance (implies large unsystematic component of RDD?)

y = 1.850x + 0.162R² = 0.004

‐200.00%

0.00%

200.00%

400.00%

600.00%

800.00%

1000.00%

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

RDD

MQSRDRI

Figure 12.8: Annualized Return on Defaulted Debt vs. Moody's Quarterly Speculative Grade Default Rate by Industry (MULGD Database 1987‐2007)

y = ‐0.720x + 0.521R² = 0.010

‐200.00%

0.00%

200.00%

400.00%

600.00%

800.00%

1000.00%

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

RDD

T1MTBY

Figure 12.9: Annualized Return on Defaulted Debt vs. 1‐Month Treasury Bill Yield (MULGD Database

1987‐2007)

Correlation Analysis of RDD: Vintage / Duration Covariates

• None of these appear in the regression models (and some we would not want – i.e., not known at default) and most no relation to RDD

• Time-in-distress (last cash-pay to default) no relationship to RDD

• Almost no vintage (time from origination or 1st rating to default or maturity) effect

• There is a clear “term-structure”effect – longer TTR-> lower RDD (uncertainty resolved?)


Corr with RDD

Time from Origination to Default 3365 2.8849 4.0128 3.7660 -0.67%Time from First Rating to Default 3178 5.7425 10.2523 11.3994 -0.51%Time from Last Cash-Pay Date to Default 3886 0.2411 0.3907 0.4849 0.22%Time from Default to Resolution 3886 1.1685 1.4594 1.3320 -13.72%Time from Origination to Maturity Date 3365 7.8219 8.9032 6.5084 -1.31%

Table 8.7 - Summary Statistics on Duration / Vintage Variables and Correlations with RDD


y = ‐0.113x + 0.484R² = 0.018

‐200%

0%

200%

400%

600%

800%

1000%

0% 100% 200% 300% 400% 500% 600% 700% 800% 900% 1000%

RDD

TTR

Figure 12.10: Annualized Return on Defaulted Debt vs. Time‐to‐Resolution (MULGD Database 1987‐2007)

Econometric Modeling of RDD: Beta-Link Generalized Linear Model• The distributional properties of LGD discount rate measures like RDD

creates challenges in applying standard statistical techniques • Non-normality of Basel parameters (RDD) in general (particular) - boundary bias• OLS clearly inappropriate (averaging across segments OK?)

• Borrow from the default prediction literature by adapting generalized linear models (GLMs) to RDD setting (continuous variable + bounded domain)• See Maddala (1981, 1983) for an introduction application to economics• Logistic regression in default prediction or PD modeling is a special case

• Follow Mallick and Gelfand (Biometrika 1994) in which the link function is taken as a mixture of cumulative beta distributions vs. logistic• See Jacobs (2007) or Huang & Osterlee (2008) for applications to LGD

• We may always estimate the underlying parameters consistently and efficiently by maximizing the log-likelihood function (albeit numerically)• Downside: computational overhead and interpretation of parameters

• Alternatives: robust / resistant statistics or modeling of LGD discount rate measures through quantile regression• See Jacobs (2008) or Moral (2006) for the case of EAD

Econometric Modeling of RDD: Beta-Link GLM (continued)

• Denote the ith observation of some LGD discount rate measure by εi in some limited domain (l,u), a vector of covariates xi, and a smooth, invertible function m() that links linear function of xi to the conditional expectation EP(εi|xi ):

• In this framework, the distribution of εi resides in the exponential family, membership in which implies a probability distribution function of the form:

[ ] ( ) ( ) ( )| |u

P i i i i i il

E p d mε μ ε ε υ ε η= = =∫x x ( )1Ti mη μ−= =β x

( ) ( ) ( ){ }p | , , , exp | | ,ii i i i i i i

i

AAAζε ζ ε θ γ τ ε

ζ⎡ ⎤⎛ ⎞

= − +⎢ ⎥⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

x β x β x β

τ, γ are smooth functions, Ai is a prior weight, ζ is a scale parameter

• The location function θ(.) is related to the linear predictor according to:

( ) ( )( ) ( )( )1 1| ( ') ( ') Ti i imθ γ μ γ− −= =x β x β x

Econometric Modeling of RDD: Beta-Link GLM (continued)

• Having a bounded random variable, with no loss of generality assume to be [0,1], conveniently modeled through a beta distribution, with density:

( )( ) ( ) ( )

( ) ( )1 11

p | , [0,1]; , :,

T Ti i

i ii i iT T

i i

R RB

α βε εε ε α β

α β

− −++−

= ∈ →⎡ ⎤⎣ ⎦

β x β x

x ββ x β x

[ ] ( ) ( )( ) ( )

11

0

, 1 yx ix yB x y u u du

x y−−Γ Γ

= = −Γ + ∫

• We follow Mallick and Gelfand (1994), in which the location function is taken as a mixture of cumulative beta distributions, taking the form:

( ) ( ) 11

1 0

1| , , ,

,

jji balkT

i i jj u j j

u udu

B a bθ φ

−−

= =

−= =

⎡ ⎤⎣ ⎦∑ ∫x β φ a b β x

• We may always estimate the underlying parameters consistently and efficiently by maximizing the log-likelihood function:

( ) ( )( ) ( ) ( ) ( ){ } [ ]1

|| , | , | , , | | ,

|

nii

i i i i i i i i i ii i i

Al AA

ζθ ζ ε εθ γ τ ε

ζ=

⎡ ⎤⎛ ⎞= − +⎢ ⎥⎜ ⎟

⎢ ⎥⎝ ⎠⎣ ⎦∑

β xβ x β x β x β x β x

β x

• Common approaches: transform Є to a normal variate through a beta inverse and perform OLS (Moody’s LossCalc™) or quasi-MLE of the above

Econometric Modeling of RDD: Estimation Results

Partial Effect P-Value



Intercept 0.3094 1.42E-03 0.51005 9.35E-04 0.4342 6.87E-03Moody's 12 Month Lagging Speculative Grade Default Rate by Industry 2.0501 1.22E-02 2.2538 6.94E-03 2.1828 1.36E-02Collateral Rank Secured 0.2554 7.21E-03 0.2330 1.25E-02 0.2704 9.36E-04Tranche Safety Index 0.4548 3.03E-02 0.4339 3.75E-02Loss Given Default 0.3273 1.44E-02 0.2751 3.88E-02Cumulative Abnormal Returns on Equity Prior to Default 0.3669 1.51E-03 0.3843 1.00E-03 0.4010 9.39E-04Total Liabilities to Total Assets 0.2653 5.22E-08Moody's Original Rating Investment Grade 0.2118 2.80E-02 0.2422 6.84E-03 0.1561 6.25E-021-Month Treasury Yield -0.4298 3.04E-02 -0.3659 1.01E-02 -0.4901 3.36E-02Size Relative to the Market -0.0366 4.76E-02 -0.0648 3.41E-03Market Value to Book Value 0.1925 2.64E-05 0.1422 5.63E-03Free-Asset Ratio -0.2429 2.25E-02Degrees of FreedomLog-LikelihoodMcFadden Pseudo R-Squared (In-Sample)McFadden Pseudo R-Squared (Out-Of-Sample) - Bootstrap MeanMcFadden Pseudo R-Squared (Out-Of-Sample) - Bootstrap Standard Error 2.28%

21.23% 12.11% 17.77%

-592.30 -594.71 -503.9932.48% 38.80% 41.73%

Table 9 - Beta-Link Generalized Linear Model for Annualized Returns on Defaulted Debt (Moody's Ultimate LGD Database 1987-2007)

Model 1 Model 2 Model 3

959 958 783

Variables

1.16% 1.70%

Econometric Modeling of RDD: Estimation Results (continued)

• Estimates generally significant (but some p-values marginal), signs all in line with univariate analysis & overall fit is fair (R^2’s ranging in 32-43%)

• Model selection process: a “judicious” alternating stepwise procedure (weighed relevant dimensions, parsimony, signs / significance & fit)

• All models show RDD ↑ (↓) in spec grade default rate, collateral dummy secured, CAR, investment grade dummy (1-Month T-Bill yield)

• Models 2&3 show RDD ↑ (↓) MV/BV (relative size), Model 3 shows inverse relationship to FAR, Models 1 & 2 show positive relationship with LGD

• Model selection by OOS/OOT: repeatedly rebuild models on bootstrapped (resampled with replacement) development & 1-year ahead evaluation samples (start from middle of period & move ahead annually to end)

• While Model 3 (1) performs best (worst) in sample by McFadden pseudo-rsquared of 41.7% (32.5%) - & #2 in the middle 38.8%; but this ordering is not preserved in out-of-sample & out-of-time (OOS/OOT) analysis

• Model 2 (3) differs from 1 (2) with MV/BV and size relative to market in lieu of TL/TA (no TS or LGD but has FAR)

• On a OOT/OOS basis Models 1-3 R^2’s = 21.2%, 12.1% & 17.8%, resp.

The Regulatory Capital Impact of the Discount Rate for LGD

• Exercise of treating our sub-set of the MULGD database as a hypothetical non-defaulted portfolio, for which we know the post-default cash-flows

• Compare 3 methods of discounting LGD: contractual coupon rate (CCR), RDD regression Model 1 & a punitive discount rate (PDR) of 25%

• The formula for regulatory capital (denoted by KR) that we compute is a version of the published formula (Basel II U.S. Final Rule, page 69335):

• LGD is calculated as the actual loss rate in the database, according to the different methods of discounting, and this is converted to a downturn LGD according to the supervisory formula:

• We estimate PD by the Moody’s long-run default rates associated with each observation, according to it’s rating at approximately one-year prior to default

• The correlation R is related to the PD according to the relationship prescribed in the Rule for wholesale non-HVCRE exposures:

( ) ( )1 1 0.9991

R DN PD RNK N PD LGD

R

− −⎛ ⎞⎛ ⎞+⎜ ⎟= − ×⎜ ⎟⎜ ⎟⎜ ⎟−⎝ ⎠⎝ ⎠

500.12 0.18 PDR e− ×= + ×

0.08 0.92DLGD LGD= + ×

The Regulatory Capital Impact of the Discount Rate for LGD (contd.)

• Discounting by RDD the model results in higher estimates of LGD & higher regulatory capital vs. contractual or constant punitive rates

• The RDD model discount has a higher quantiles of LGD across the board than the other methods (distribution is shifted right); e.g.,higher mean of 64.1% vs. at 59.0% punitive rate & 52.1% under the contract rate

• Capital under the RDD model is 8.04% (the mean), 73 bps (113 bps) higher than under a punitive (contract) where capital is 7.31% (6.91%)

25th Percentile Median Mean

75th Percentile

Standard Deviation Skewness Kurtosis

Discounted LGD - Contractual Coupon Rate2 13.68% 54.97% 52.07% 88.17% 35.86% -0.0569 -1.5467Discounted LGD - RDD Regression Model3 33.29% 72.10% 64.05% 95.07% 33.03% -0.3122 -1.2998Discounted LGD - Punitive Discount Rate4 33.08% 62.12% 59.03% 89.62% 31.53% -0.2133 -1.3288Regulatory Capital - Contractual Coupon Rate 0.78% 2.66% 6.91% 9.91% 9.18% 1.9366 4.3220Regulatory Capital - RDD Regression Model 1.00% 3.72% 8.04% 10.87% 9.86% 1.7132 3.3883Regulatory Capital - Punitive Discount Rate 0.94% 3.14% 7.31% 10.14% 9.26% 1.8544 3.9928

Table 10 - Summary Statistics on Discounted LGD and Regulatory Capital for Different Discounting Methodologies


• The model for RDD is discounting at a much higher rate types of loans that have larger recovery cash flows & increased recovery risk

• Furthermore, one can argue that the market is impounding other material direct and indirect costs into this empirical measure, such as workout costs


• While all 3 provide highly correlated estimates of LGD (R^2’s 0.79 and 0.78 RDD vs. contract & punitive, respectively), the RDD model is shifted considerably upward (respective intercepts 0.22 and 0.08)

Figure 13.1: Discounted LGD by Regression Model for RDD vs. Pre-petition Coupon Rate (MULGD Database 1987-2007)

y = 0.8166x + 0.2152R2 = 0.786

0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

120.00%

0.00% 20.00% 40.00% 60.00% 80.00% 100.00% 120.00%

LGD Discounted by Contractual by Coupon Rate

LGD Discounted by RDD Model

Figure 13.2: Discounted LGD by Regression Model for RDD vs. Punitive Discount Rate (MULGD Database 1987-2007)

y = 0.9401x + 0.0818R2 = 0.7785

0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

120.00%

0.00% 20.00% 40.00% 60.00% 80.00% 100.00% 120.00%

LGD Discounted by Punitive Discount Rate

LGD Discounted by RDD Model

• Note that in the comparison of the RDD model to the contract rate all the cases where the latter would yield a zero LGD, yet by a risk sensitive discount we get a non-zero (and sometimes a very large) LGD


• Examining the distributions of LGD (dashed lines) in this portfolio, it is clear that under RDD model discounting there is a shift in probability mass to the right, compared with either the contract rate or a punitive rate

• Note how the mode at near zero under the contract rate is diminished by either a punitive or RDD model discounting

0.0 0.2 0.4 0.6 0.8 1.0 1.20.0

0.5

1.0

1.5

2.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2Figure 13.3: Densities of LGD Discounted by RDD Model vs. Contract Rate

Contractual Discount Rate (mean = 52.1%)RDD Model Discount Rate (mean = 64.1%)

0.0 0.2 0.4 0.6 0.8 1.0 1.20.0

0.5

1.0

1.5

2.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2Figure 13.4: Densities of LGD Discounted by RDD Model vs. Punitive Rate

Punitive Discount Rate (mean = 59.0%)RDD Model Discount Rate (mean = 64.1%)


• Examining the distributions of portfolio regulatory capital in Figures 13.5 and 13.6, where we see that the density mass is shifted right-ward under the RDD model relative to either the contract rate or the 25% punitive discount rate.

• But there is less peakedness and skewness under the RDD model as compared to the other discounting, so most of the difference is from the body & not the tails of the distribution (although the standard deviation is higher)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

2

4

6

8

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7Figure 13.5: Densities of Regulatory Credit Capital (MULGD 1987-2007)

Capital for LGD Discounted at Contractual Coupon Rate (mean = 6.91%)Capital for LGD Discounted by RDD Regression Model (mean = 8.04%)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

2

4

6

8

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7Figure 13.6: Densities of Regulatory Credit Capital (MULGD 1987-2007)

Capital for LGD Discounted at Punitive Discount Rate (mean = 7.31%)Capital for LGD Discounted by RDD Regression Model (mean = 8.04%)

Benchmarking Alternative LGD Discount Rate Frameworks

DataModel for LGD Correlation to Systematic Factor Source / Reference

Discount Rate1

LGD Correlation (qi,m)2

Asset Value Volatility (σi)3

Market Volatility (sig_m)4

LGD Beta5 MRP6

Risk-Free Rate (R_f)7

Sample of Bid Quotes on 90 Defualted Bonds & S&P 500 Index Returns (4/02-8/03) Linear Regression Machlachan (2004) 7.23% N/A N/A N/A 37.10% 6.00% 5.00%

Monthly Altman Defaulted Bond Index & S&P 500 Index Returns (1986-2002) Linear RegressionAltman & Jha (2003), Machlachan (2004) 11.05% 20.30% 32.00% 18.74% 76.92% 7.87% 5.00%

Default Rates and Market Implied LGD (Moody's DRS Databases 1982-1999 ) 1-Factor Structural Model MLE Calibration Frye (2000), Machlachan (2004) 7.28% 17.00% 32.00% 18.74% 29.02% 7.87% 5.00%p ( y )

Loans7 2-Factor Structural Model MLE Calibration Jacobs (2008) 7.96% 22.03% 32.00% 18.74% 37.61% 7.87% 5.00%Default Rates and Market Implied LGD (Moody's DRS & MULGD Databases 1987-2007) - Senior Secured Bonds7 2-Factor Structural Model MLE Calibration Jacobs (2008) 9.92% 36.64% 32.00% 18.74% 62.56% 7.87% 5.00%Monthly RDD (Moody's DRS & MULGD Databases 1987-2007) and Fama-French Market Factor - Bonds Linear Regression Jacobs (2008) 6.78% 13.23% 32.00% 18.74% 22.59% 7.87% 5.00%Monthly RDD (Moody's DRS & MULGD Databases 1995-2007) and Fama-French Market Factor - Loans Linear Regression Jacobs (2008) 6.58% 11.76% 32.00% 18.74% 20.07% 7.87% 5.00%Monthly RDD and Trailing 12-Month Speculative Grade Default Rate (Moody's DRS & MULGD Databases 1987-2007) - Bonds Linear Regression Jacobs (2008) 8.85% 28.66% 32.00% 18.74% 48.93% 7.87% 5.00%Monthly RDD and Trailing 12-Month Speculative Grade Default Rate (Moody's DRS & MULGD Databases 1995-2007) - Loans Linear Regression Jacobs (2008) 7.89% 21.50% 32.00% 18.74% 36.70% 7.87% 5.00%Monthly Altman Public Bond Index & S&P 500 Return (1/99-9/08) Linear Regression Jacobs (2008) 10.50% 40.93% 32.00% 18.74% 69.87% 7.87% 5.00%Monthly Altman Bank Loan Index & S&P 500 Return (1/99-9/08) Linear Regression Jacobs (2008) 6.53% 11.41% 32.00% 18.74% 19.48% 7.87% 5.00%

Most Likely Discount Rate (S&P LossStats & CreditPro Databases 1985-2004) N/A Brady et al (2006) 14.00% N/A N/A N/A N/A N/A N/A

Ex Post Realized Returns (Moody's Bankrupt Bond Index 1988-1998) N/AHamilton & Berthault (2000), Araten (2004) 15.00% N/A N/A N/A N/A N/A N/A

Return on Defaulted Debt (Moody's DRS & MULGD Databases 1987-2007) N/A Jacobs (2008) 29.20% N/A N/A N/A N/A N/A N/A

Return on Defaulted Debt (Moody's DRS & MULGD Databases 1987-2007) - Loans N/A Jacobs (2008) 43.30% N/A N/A N/A N/A N/A N/AMost Likely Discount Rate (Moody's DRS & MULGD Databases 1987-2007) N/A Jacobs (2008) 21.30% N/A N/A N/A N/A N/A N/AMost Likely Discount Rate (Moody's DRS & MULGD Databases 1987-2007) - Loans N/A Jacobs (2008) 14.50% N/A N/A N/A N/A N/A N/A

Contractual Rate (incluyding penalty) N/AAsarnow & Edwards (1995) N/A N/A N/A N/A N/A N/A N/A

Lender's Cost of Equity N/A Eales & Bosworth (1998) N/A N/A N/A N/A N/A N/A N/A

Coupon Rate N/AFriedman & Sandow (2003) N/A N/A N/A N/A N/A N/A N/A

Risk-free rate of Return N/A Carey & Gordy (2006) N/A N/A N/A N/A N/A N/A N/A

Price of Traded Debt On-Month post Default Implied N/A Gupton & Stein (2002) N/A N/A N/A N/A N/A N/A N/AContactual Loan Rate N/A Carty et al (1998) N/A N/A N/A N/A N/A N/A N/A

Empi

rical

Mod

els

Table 11: Benchmark Comparison of Alternative Methodologies for Deriving the Discount Rate for Workout Recoveries

Mar

ket /

Stru

ctur

al B

ased

Mod

els

Mod

el-F

ree

Benchmarking Alternative LGD Discount Rate Frameworks (contd.)• Two types of model-based approaches that involve systematic recovery risk:

calibration to default/loss data with latent factors, single (Frye, 2000) & two-factor (developed herein) vs. regression models with observable proxies

• Model based approaches produce a correlation of the recovery process to thesystematic risk factor from estimation / calibration, a version of the inter-temporal CAPM & some simplifying assumptions: rf = 5%, σi = 32% (Frye, 2000), σM = 18.7% & MRP = 7.9% from Fama-French data 7/26-3/08

• Model based approaches, structural or regression, generate discount rate estimates significantly (7-11%) lower than empirical approaches (15-40%), lower for loans vs. bonds, & not too sensitive to the correlation estimate

• Estimate of 7.2% from Machlachlan’s regression of 90 defaulted bond bid quotes on the S&P 500 return 4/02-8/03 on the low end

• Altman and Jha (2003) is on high end: 11.1% rate (20.3% corr.) regressing Altman / Solomon Center defaulted bond index on S&P500 1986-2002

• Herein regression of RDDs on the Fama-French market factor lowest & little difference bond/loan: discount rate estimates 6.8% (6.6%) based on correlations of 13.2% (11.8%) bonds (loans) 1987-2007 (1995-2007)

Benchmarking Alternative LGD Discount Rate Frameworks (contd.)• RDD & Moody’s trailing 12-month spec grade default rate in lieu equity index

same period get 8.9% (7.9)% with 28.7% (21.5%) correlation bonds (loans)• Solomon Center / Altman & S&P 500 for updated period 1/99-9/08 (recently

circulated data) yields higher estimates for bonds: discount rates of 10.5% (6.5%) for bonds (loans) based on 40.9% (11.4%) correlation

• Single-factor model of Frye (2000) calibration on Moody’s loss data 1982-1999 yields a discount rate estimate of 7.3% (17% LGD-PD correlation)

• 2-factor version of the structural model using Moody’s data from 1987-2007 finds higher estimates: 8.0% (9.9%) for bank loans (senior secured bonds)

• Well cited 15% cited of JPMC based upon ex-post realized returns of the Moody’s Bankrupt Bond Index 1988-1998 (17.4%) & commonly quoted required rate of return for vulture investors (close to loan MLDR 14.5% here)

• MLDR estimate here is 21.3% (14.5%) bonds (loans) vs. Brady et al (2006) 14% based S&P LossStats database 1985-2004

• The 10% figure, some studies come close to (Altman & Jha, 2003), being cited by several banks based upon WACC, cost of equity, etc.

• RDD 29.3% (43.3%) bonds (loans) off the charts compared with any of these

Benchmarking Alternative LGD Discount Rate Frameworks (contd.)

• We calibrate a 2-factor version of the Basel capital model with systematic recovery risk to Moody’s annual default and loss rate data 1987-2007

• Consider only 1 rating and 2 seniority segments

• Recovery process correlation estimates 22% (37%) loans (bonds) higher than Frye (2000) single factor model 17%.

• 8% AVC estimate in ballpark with previous literature that calibrates to loss data

• High 64% correlation between systematic risk factor estimates support single factor model a reasonable approximation

MLE Estimate

Standard Error

8.01% 4.66%

4.96% 3.01%

Recovery Value Correlation for Loans (ρl2) 22.03% 4.79%

Long-Run Loss-Given-Default for Loans (LGDl) 28.90% 13.23%

Recovery Value Correlation for Bonds (ρb2) 36.64% 11.10%

Long-Run LGD for Bonds (LGDb) 44.61% 26.06%

64.42% 18.83%Correlation between Systematic Factors in Default and Loss Rate (PD-LGD) Processes (rxy)

Parameter

Long-Run Probability of Default (PDr)Asset Value Correlation (ρr)

Table 11.1: Simultaneous Full-Information Maximum Likelihood Estimation of 2-Factor Structural Credit Model

Bank

Lo

ans

Seni

or

Secu

red

Bond

s

Zt,r , Zt,s ~ NID(0,1); (Xt, Yt) ~ N2 ([0,0]T, [(1,rX,Y)T,(rX,Y,1)T]

Conditional Loss Rate: L(Yt | LGDs,ρs) = Φ[ (Φ-1[LGDs]-ρsYt)/(1-ρs2).5 ], LGDs: Long-

Run (Expected) Loss-Given-Default for Seniority Classs s

Conditional Default Rate: R(Xt | PDr,ρr) = Φ[ (Φ-1[PDr]-ρrXt)/(1-ρr2).5 ], PDr: Long-Run

(Expected) Probability of Default for Rating Class r

Loss Rate Process for Seniority Class s: Lt,s = ρsYt + (1-ρs2).5Zt,s , Idiosyncratic LGD

Variable: Zt,s ~ NID(0,1), Systematic LGD Variable: Yt , Recovery Value Factor Loading (Correlation):ρs (ρs

2)

Asset Value Process for Rating Class r: At,r = ρrXt + (1-ρr2).5Zt,r, Idiosyncratic PD

Variable: Zt,r ~ NID(0,1), Systematic PD Variable: Xt , Asset Value Factor Loading (Correlation): ρr (ρr

2)

Moody's DRS Annual Speculative-Grade Default Rates and MULGD Market Implied Loss-Given-Default (1987-2007)

Summary of Contributions and Major Findings

• Addressed questions surrounding the discount rate for workout recoveries for both Basel II & internal credit risk measurement

• Comprehensive analysis of empirical discount rates for LGD (RDD & MLDR) from market prices of defaulted debt in MULGD

• Examine the distributional properties of the discount rate measures across different segmentations in the dataset & develop a BLGLM regression model for RDD

• Quantify the effect of discounting on the distribution of economic LGD & on regulatory capital, for a hypothetical portfolio (more capital for RDD model vs. contractual or punitive rate)

• Perform a benchmarking analysis, comparing the empirical RDD & MLDR methods developed to alternative techniques, including model / market based approaches (latter imply lower rates)

• Evidence that RDD is higher for better collateral quality ranking or better protected tranches, higher credit rating, more financiallyleverage, higher CARs and higher market implied LGD at default

• Also evidence that LGD discount rates vary pro-cyclically and they are inversely related to short-term interest rates.

Directions for Future Research• This research opens up further questions regarding which

discount rate for workout recoveries is optimal in some sense, from either a supervisory or risk measurement perspective

• A great challenge in this regard we see as somehow reconciling the results of this empirical exercise, the implications of structural credit models as well as common industry practice

• Generalizations of the ARF framework: incorporating stochastic duration of bankruptcy resolution, simultaneous calibration by rating and seniority class, or incorporating strategic bankruptcy

• On the empirical side, better quantify the undiversifiable & non-systematic component of recovery risk, as that would help us sharpen our bound on the “appropriate” discount

• With a view towards the evolution of supervisory requirements, an examination of the impact of this choice upon economic credit, or even integrated, risk capital

• Final thought: as a methodological suggestion, banks can measures implicit discount rates from expected LGDs and realized workout cash flows (even if non-marketable loans)

An Empirical Study of the Returns on Defaulted Debt and the Discount Rate for Loss-Given-Default

Economy & Finance

Transcript of An Empirical Study of the Returns on Defaulted Debt and the Discount Rate for Loss-Given-Default