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

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  • 1. An Empirical Study of the Returns on Defaulted Debt and the Discount Rate for Loss- Given-Default Michael Jacobs, Ph.D., CFA Senior Financial Economist Credit 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.
  • 2. 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
  • 3. 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
  • 4. 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
  • 5. 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
  • 6. 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%)
  • 7. 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 at default implies better performance (mispricing?) • Obligor characteristics: increase for more highly rated obligors at 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
  • 8. 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%
  • 9. 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?
  • 10. Advanced IRB & Other Supervisory Requirements • FSA (2003, page 68, Annex 3): quot;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): quot;Effective original loan rate (the rate that exactly discounts expected future cash payments or receipts through the expected life of the financial instrument).quot; • 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.”
  • 11. Theoretical Framework • A very general (not too useful) expression for expected LGD is: Cτ cs e dF c% ,τ ( c, s ) − sr ∫C s∫t D s EtP [ LGDτ ] ≡ ELGDt = 1 − c = = EADt • Where c(τ): uncertain recovery cash flows (times), Fc,τ(): their joint distribution, EAD: exposure-at-default, rsD: risk-adjusted discount rate (maybe time dependent, a function of risk drivers & random), P: physical probability measure. But in practice: T cs 1 ∑ LGDt = 1 − ( ) s 1 + rsD EADt s =t • 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
  • 12. 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: dVi ,t = μ dt + σ dW i i i ,t Vi ,t • 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,t is a standard Weiner process that decomposes as: dWi ,t = ρi , X dX t + 1 − ρi2, X dZ i ,t • The standard Weiners processes Xt & Zi,t are the systematic & idiosyncratic risk factors, respectively; and the factor loading ρi,X is either firm-specific or obligors in segment i
  • 13. Theoretical Framework (continued) • It follows that the instantaneous asset-value correlation (AVC) amongst firms (or segments) i and j is given by: ⎡ dVi ,t dV j ,t ⎤ 1 ⎥ = ρi , x ρ j , x Cori , j ⎢ V , ⎢ Vi ,t V j ,t ⎥ dt ⎣ ⎦ • 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,X2=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: ⎡ dV dV ⎤ Covi , M ⎢ i ,t , M ,t ⎥ ⎣ Vi ,t VM ,t ⎦ = β = σ i Ri σM ⎡ dVM ,t ⎤ i,M VarM ⎢ ⎥ VM ,t ⎦ ⎣
  • 14. Theoretical Framework (continued) • 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 : σ i Ri ( rM − rrf ) = rrf + βi,M MRP = rrf + δ i ri = rrf + D σM • 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: dWi ,R = ρi , X R dX tR + 1 − ρi2, X R dZ iRt t , • The standard Weiners XtR and Zi,tR 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
  • 15. Theoretical Framework (continued) • Assume the systematic factors on the PD and LGD “sides” to be standard and bivariate normally distributed with correlation r: ⎛⎛0⎞ ⎛1 r ⎞⎞ ( dX ) RT ~ N ⎜⎜ ⎟,⎜ ⎟⎟ , dX t t ⎝ 0⎠ ⎝ r 1⎠⎠ ⎝ • 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: ( PD , LGD , ρ ) T , ρs, X R , r r s r,X • 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: ( ) l drt ,r , lrt , s | PDr , ρ r , X , LGDs , ρ s , X R , r = ⎛ Φ −1 ( LGD ) − 1 − ρ 2 Φ −1 ( u ) ⎞ 1 − ρ 2 R ⎛ Φ −1 ( LGDs ) − 1 − ρ 2 R Φ −1 ( v ) ⎞ 1 − ρi2, X 11 φ⎜ ⎟Φ ( u, v | r ) dudv ∫ ∫ ρi , X φ ( u ) φ ⎜ ⎟ r i, X i, X i, X ⎟ ρi , X R φ ( v ) ⎜ ⎟2 ρi , X ρi , X R ⎜ ⎝ ⎠ ⎝ ⎠ 00
  • 16. 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 the1 time of resolution: ⎛ Pi ,E ,t E ⎞ tiE,s −tiD,s ri ,D = ⎜ D i ⎟ −1 s ⎜ Pi , s ,t D ⎟ s ⎝ ⎠ i • ith(sth) denotes loan (segment), PE (PD) price at emergence (default), tE (tD) respective times and ri,sD is the RDD • An estimate for the discount rate for the sth “LGD segment” is an arithmetic averages across NsD defaulted loans: ⎡E ⎤ 1 ⎢⎛ Pi , s ,tiE ⎞ tiEs −tiDs ⎥ N sD 1 , , rs = D ∑ ⎢⎜ D ⎟ − 1⎥ D N s i =1 ⎢⎜ Pi , s ,t D ⎟ ⎥ ⎝ ⎠ ⎣ ⎦ i
  • 17. 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: EtP ⎡ Pi ,E ,t E ⎤ ⎣ si⎦ = Pi ,D,t D (1 + ri,s ) D ti ,s −ti ,s E D s i • 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 + r ) D ti ,s −ti ,s E D −P E D Pi , s ,tiE i , s ,tiD i,s ε i,s ≡ % Pi ,D,t D × tiEs − tiDs , , si • Assume: pricing errors are standard normal & LGD uncertainty proportional to sqrt(tE-tD), then solve by maximum likelihood: ⎡⎛ E ⎞⎤ ⎢ ⎜ Pi , s ,tiE − Pi , s ,tiD × (1 + ri , s ) D ti ,s −ti ,s E D D D D Ns Ns ⎟⎥ ri , s = arg max LL = arg max ∑ log ⎡φ ( ε i , s ) ⎤ = arg max ∑ log ⎢φ ⎜ ⎣%⎦ D ˆ ⎟⎥ Pi ,D,t D × tiEs − tiDs ⎜ ⎟⎥ D D riD i =1 i =1 ⎢⎝ ri ,s ri ,s ,s ⎠⎦ ⎣ , , si
  • 18. 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.)
  • 19. 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.)
  • 20. Empirical Results: RDD by Instrument & Default Event Type 1 2 Table 1.1 - RDD and MLDR Observations by Default and Instrument Type (Moody's Ultimate LGD Database 1987-2007) Bankruptcy Out-of-Court Total MLDR RDD MLDR RDD MLDR RDD MLE MLE MLE MLE Std Std Std Est. Err Avg Std Dev Min Max Cnt MLE Est. Err Avg Std Dev Min Max MLE Est. Err Avg Std Dev Min Max Cnt Cnt 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% • 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%)
  • 21. Empirical Results: Distributions of RDD by Instrument & Default Event • RDD is “naturally” floored Figure 1: Dis tribution of Return on Defaulted Debt (All Ins trum en at -100% but has an extremely long right tail 0.5 • There were a few credible cases where 0.4 debt selling for pennies at default went for close to 0.3 par at emergence! • As we have a prior that 0.2 this is probably the best case, we expect a limited 0.1 domain, so something “like” a beta distribution 0.0 might be best to model 0 2 4 6 8 10 RDD.Ann.0 the distribution of RDD Moody's Ultimate LGD Database 1987-2007
  • 22. Distributions of RDD by Instrument & Default Event (continued) • While out-of-court Figure 2.1: Distribution of Return on Def aulted Debt (Bankruptcies) settlements have a long 0.5 tail, the distribution is less 0.4 peaked & possibly multi- 0.3 modal vs. bankruptcies 0.2 0.1 • Bankruptcies clearly have 0.0 more mass near zero as 0 2 4 6 8 10 RDD.Data.Bnkrpt[, 1] compared to out-of-court Moody's Ultimate LG D Database 1987-2007 Figure 2.2: Distribution of Return on Def aulted Debt (Out-of -Court Settlements • Studying various features 0.30 of the distributions, and 0.20 prior considerations 0.10 (amount of uncertainty present at default), lead us 0.0 to believe that these are 0 2 4 6 8 10 RDD.Data.O utcrt[, 1] Moody's Ultimate LG D Database 1987-2007 fundamentally different • KS test for difference in distributions significant (p-value = 0.0024)
  • 23. Distributions of RDD by Instrument & Default Event (continued) • Bonds share the long tail, Figure 3.1: Distribution of Return on Def aulted Debt (Bonds) but the distribution is 0.4 slightly more peaked as 0.3 compared with loans 0.2 • Bonds have some more 0.1 mass near zero as 0.0 0 2 4 6 8 10 compared to loans RDD.Data.Bond[, 1] Moody's Ultimate LG D Database 1987-2007 Figure 3.2: Distribution of Return on Def aulted Debt (Loans) • Studying various features 0.30 of the distributions, and prior considerations, lead 0.20 us to believe that these 0.10 are not so fundamentally 0.0 different as to necessitate 0 2 4 6 8 10 separating them in further RDD.Data.Outcrt[, 1] Moody's Ultimate LG D Database 1987-2007 analysis • KS test for difference in distributions insignificant (p-value = 0.2792)
  • 24. Empirical Results: RDD and MLDR by Collateral & Seniority • Central tendencies generally Table 2.1 - Central Tendency and Dispersion Measures of RDD and MLDR by decrease for lower seniorities Seniority Rank (Moody's Ultimate LGD Database 1987-2007) ranks (but peak at sen. sec.) Revolving Senior Senior Senior Credit / Secured Unsecured Subordinated Subordinated Total • Dispersions pattern not as clear: Term Loan Bonds Bonds Bonds Bonds Instrument Count 374 142 437 179 130 1262 overall seems to decline for MLDR Mean of (not so much RDD) but peaks at RDD 43.3% 50.7% 22.5% 23.9% -5.0% 29.2% MLE of senior sen. sec. (sen. sub.) MLDR 14.5% 38.4% 20.9% 21.9% 16.5% 21.3% Std Dev of • Mean RDD & MLE of MLDR RDD 106.7% 116.4% 104.5% 158.6% 104.1% 116.5% MLE Std Err higher for secured vs. unsecured, of MLRD 32.8% 101.3% 17.4% 13.7% 15.1% 114.2% but not clear ranks (RDD peaks @ Table 2.2 - Central Tendency and Dispersion Measures of RDD and MLDR by Major CA/CS but MLDR little difference) Collateral Category (Moody's Ultimate LGD Database 1987-2007) Cash, Inventory, All Current • Similar pattern for dispersion Accounts Most Assets & Assets & PPE & Receivables Assets & Real Capital Second Total Total Total & Guarantees Equipment Estate Stock Lien Secured Unsecured Collateral measures – higher for secured but Count 7 19 323 84 54 500 762 1262 Mean of across groups non-monotonic RDD 27.8% 31.1% 43.4% 59.6% 54.8% 46.4% 17.9% 29.2% MLE of • “Counterintuitive story” – greater MLDR 33.3% 20.6% 30.4% 34.0% 33.7% 31.7% 18.3% 21.3% Std Dev of recovery risk in better ranked / RDD 36.9% 31.5% 118.6% 104.5% 104.3% 118.0% 112.0% 116.5% MLE Std Err secured loans? of MLRD 13.4% 7.8% 44.5% 9.2% 10.4% 28.8% 10.8% 114.2%
  • 25. RDD and MLDR by Collateral & Seniority (continued) Figure 5.1: Central Tendency Measures of RDD and MLDR  Figure 6.1: Central Tendency Measures of RDD and MLDR  Observations by Seniority Rank                            Observations by  Collateral  Category                      (MULGD Database 1987‐2007) (MULGD Database 1987‐2007) 60.0% 70.0% 60.0% 50.0% 50.0% 40.0% Mean of RDD MLE of MLDR 40.0% 30.0% 30.0% 20.0% 20.0% Mean of RDD MLE of MLDR 10.0% 10.0% 0.0% 0.0% Cash, Accounts Inventory, Most All Assets & Non‐Current PPE & Second Total Secured Total Unsecured Total Collateral Revolving Credit / Senior Secured Senior Unsecured Senior Subordinated Total Instrument Receivables & Assets & Real Estate Assets & Lien Term Loan Bonds Bonds Subordinated Bonds Guarantees Equipment Capital Stock Bonds ‐10.0% • 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
  • 26. Empirical Results: RDD and MLDR Measures by Year of Default • Identify “downturn periods” as 1 2 3 4 5 Table 3 - RDD , MLDR , LGD , Default Rate , Dollar Loss and 6 Duration of Defaulted Instruments by Cohort Year 1990-91 and 2000-02 when (Moody's Ultimate LGD Database 1987-2007) Moody’s default rate is elevated Average of Average Moody's • RDD & MLDR somewhat of Total Average of Speculati MLE Std Average ve Grade Defaulted Time-to- MLE elevated in bad periods (but LGD at Default Amount Resolution Count Average Std Dev Est of Err of 2 4 5 Year of RDD of RDD of RDD MLDR MLDR Default Rate ($MM) (Yrs.) lagging a little in recent one) 1987 5 -5.03% 10.81% -2.90% 202.18% 70.08% 4.71% 3,803 2.0379 1988 11 -1.34% 50.08% 9.07% 12.37% 63.80% 3.32% 3,697 2.0123 • Similar pattern for dispersions 1989 14 29.07% 108.33% 35.47% 29.34% 74.55% 4.80% 7,915 2.2638 1990 64 46.40% 143.41% 17.58% 91.36% 75.63% 10.36% 26,148 1.6991 (but now lagging more / less 1991 92 43.75% 117.69% 39.44% 35.02% 57.15% 9.85% 25,252 1.6074 1992 27 32.54% 172.26% 5.33% 15.73% 58.89% 6.13% 6,340 1.7309 prominent for RDD / MLDR) 1993 10 1.32% 91.31% 13.38% 31.14% 51.10% 3.02% 3,912 1.1740 1994 6 -27.64% 40.67% 12.11% 20.54% 70.57% 2.42% 3,926 0.9574 1995 35 27.45% 107.80% 11.27% 26.85% 41.96% 3.19% 8,966 2.0764 • The story for cyclicality be? – 1996 25 27.43% 73.00% 20.42% 19.46% 44.32% 2.18% 5,223 1.3572 1997 17 9.14% 61.15% -1.27% 12.81% 46.65% 2.27% 4,386 1.3159 the market over-reacts and 1998 33 -37.79% 49.62% -25.43% 9.69% 57.05% 3.77% 8,837 1.3471 1999 92 6.83% 53.26% 10.74% 6.53% 65.01% 6.12% 28,296 1.3468 overly beats this debt down at 2000 105 ‐3.95% 67.96% 7.59% 60.25% 62.63% 7.93% 34,383 1.7394 2001 257 16.15% 101.98% 24.59% 10.97% 58.25% 11.39% 96,929 1.7314 around contraction periods? 2002 207 50.77% 147.80% 32.83% 17.41% 61.61% 7.89% 183,801 1.3021 2003 106 64.24% 161.24% 46.20% 15.92% 49.34% 5.83% 43,151 0.9826 • Beware: censoring problem 2004 75 46.60% 88.50% 15.73% 8.63% 33.12% 3.31% 22,863 0.7811 2005 63 42.59% 118.00% 50.84% 53.22% 35.58% 2.33% 43,461 1.1160 (low counts in beginning & end 2006 9 29.65% 88.81% -6.25% 20.82% 32.50% 1.73% 2,355 0.5652 2007 9 9.98% 46.68% -31.19% 8.24% 18.97% 1.26% 3,388 0.2189 Total 1,262 29.21% 116.49% 22.38% 107.83% 55.78% 7.14% 567,520 1.4594 of sample)
  • 27. RDD and MLDR Measures by Year of Default (continued) Figure 7.2: Dispersion Measures of RDD and MLDR Observations by  Figure 7.1: Central Tendency Measures of RDD and MLDR  Year  of Default                                                      Observations by Year of Default                           (MULGD Database 1987‐2007) (MULGD Database 1987‐2007) 250.00% 80.00% 60.00% 200.00% Std Dev of RDD MLE Std Err of MLDR 40.00% 150.00% 20.00% 100.00% 0.00% 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 Total ‐20.00% 50.00% ‐40.00% 0.00% 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 ‐60.00% • 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)
  • 28. Empirical Results: Term Structures of RDD and MLDR • TTR (TID): time from default (last Table 3.1 - Central Tendency Measures of RDD and MLDR Observations by Quintiles of Time-to-Resolution cash pay) date to resolution (default) (Moody's Ultimate LGD Database 1987-2007) 1st 2nd 3rd 4th 5th • RDD generally falls in TTR while Quintile Quintile Quintile Quintile Quintile TTR TTR TTR TTR TTR Total MLDR peaks at 4th quintile Mean of RDD 70.8% 41.4% 17.8% 26.4% 7.5% 29.2% MLE of • Both show non-monotone decline in MLDR 23.6% 16.8% 21.4% 42.9% 18.5% 21.3% Std Dev dispersion of RDD 178.5% 156.6% 91.3% 84.7% 45.0% 116.5% MLE Std • Both mean RDD & MLE of MLDR Err of MLRD 96.6% 5.7% 7.6% 18.3% 6.7% 114.2% show a bumpy overall decline in TID Table 3.2 - Central Tendency Measures of RDD and MLDR • But dispersion of RDD (MLDR) U- Observations by Quintiles of Time-in-Distress (Moody's Ultimate LGD Database 1987-2007) shaped (humped) in TID 1st 2nd 3rd 4th 5th Quintile Quintile Quintile Quintile Quintile • Story for what are kind of seeing – TID TID TID TID TID Total Mean of uncertainty gets more “settled” RDD 41.3% 27.6% 31.0% 29.8% 21.3% 29.2% MLE of longer under “watch” prior to default MLDR 27.6% 16.7% 25.9% 24.2% 13.3% 21.3% Std Dev or as bankruptcy proceeds? of RDD 145.6% 94.5% 93.1% 120.1% 133.0% 116.5% MLE Std • TID shows no univariate correlation Err of MLRD 24.7% 6.6% 53.5% 5.5% 26.9% 114.2% & neither in regressions (OK for TTR)
  • 29. Term Structures of RDD and MLDR (continued) Figure 8.1: Central Tendency and Dispersion  Figure 8.2: Central Tendency and Dispersion  Measures of RDD and MLDR Observations by  Measures of RDD and MLDR Observations by  Quintiles of Time‐to‐Resolution  Quintiles of Time‐in‐Distress (MULGD Database 1987‐2007) (MULGD Database 1987‐2007) 160.0% 200.0% Mean of RDD MLE of MLDR Std Dev of RDD MLE Std Err of MLRD Mean of RDD MLE of MLDR Std Dev of RDD MLE Std Err of MLRD 180.0% 140.0% 160.0% 120.0% 140.0% 100.0% 120.0% 80.0% 100.0% 80.0% 60.0% 60.0% 40.0% 40.0% 20.0% 20.0% 0.0% 0.0% 1st Quintile TTR 2nd Quintile TTR 3rd Quintile TTR 4th Quintile TTR 5th Quintile TTR Total 1st Quintile TID 2nd Quintile TID 3rd Quintile TID 4th Quintile TID 5th Quintile TID Total • We get some sense of the bumpy downward path in discount rate measures and their volatilities in these duration buckets
  • 30. Empirical Results: RDD and MLDR by Original Credit Rating Figure 9.1: Central Tendency Measures of RDD and  1 2 Table 5 - RDD and MLDR of Defaulted Instruments by Credit MLDR Observations by Credit Rating at Origination (MULGD Database 1987‐2007) Rating at Origination 120.00% (Moody's Ultimate LGD Database 1987-2007) 100.00% MLE Standard MLE Standard 80.00% Average Deviation Estimate Error of Average of RDD MLE Estimate of MLDR Count of RDD RDD of MLDR MLDR 60.00% AA-A 130 26.43% 63.36% 20.67% 28.16% BBB 58 48.62% 110.94% 111.61% 51.45% Rating Groups 40.00% BB 299 18.10% 91.67% 22.13% 7.18% B 497 32.06% 140.92% 13.24% 13.68% 20.00% CC-CCC 89 19.58% 78.55% 18.30% 7.93% Investment Grade (BBB-A) 188 33.28% 80.75% 23.70% 25.89% 0.00% Junk Grade (CC-BB) 885 26.09% 212.83% 18.48% 8.10% AA‐A BBB BB  B CC‐CCC Investment Junk Grade (CC‐ Total Total 1262 29.21% 116.49% 21.31% 114.15% Grade (BBB‐A) BB) Rating Groups • Discount rate measures generally higher Figure 9.2: Dispersion Measures of RDD and MLDR  for better rated: RDD (MLDR) 33.3%- Observations by Credit Rating at Origination (MULGD Database 1987‐2007) 26.1% (23.7%-18.5%) inv. gr.-junk 250.00% • Pattern non-monotonic by finer 200.00% Standard Deviation RDD MLE Standard Error of MLDR categories: RDD / MLDR peak at BBB 150.00% • Disagreement in dispersion pattern: 100.00% MLDR(RDD) higher inv. gr. (junk) 50.00% • “Fighting spirit” vs. more recovery risk 0.00% AA‐A BBB BB  B CC‐CCC Investment Junk Grade (CC‐ Total for ”fallen angels”? Grade (BBB‐A) BB) Rating Groups
  • 31. Empirical Results: RDD and MLDR by Tranche Safety & Position Figure 10.1: Central Tendency Measures of RDD & MLDR  1 2 Table 6 - RDD and MLDR of Defaulted Instruments by by Tranche Safety Index & Debt Position Categories 3 (MULGD Database 1987‐2007) Tranche Safety Index (TSI) Quintiles and Categories 60.00% (Moody's Ultimate LGD Database 1987-2007) Standard 50.00% Average Deviation MLE Std 40.00% Count RDD RDD MLDR Err MLDR 1st Quintile TSI 154 33.03% 162.52% 33.84% 28.96% 30.00% 2nd Quintile TSI 324 9.55% 97.95% 21.29% 20.71% Debt Tranche Groups 3rd Quintile TSI 372 26.55% 109.95% 14.38% 38.66% 20.00% 4th Quintile TSI 326 43.63% 116.28% 25.05% 3.22% Average RDD MLDR 10.00% 5th Quintile TSI 86 53.23% 99.63% 29.62% 32.06% 4 NDA / SDB 427 44.16% 103.17% 25.29% 6.87% 0.00% 5 1st 2nd 3rd 4th 5th NDA / SDB4 SDA / SDB5 NDA / NDB / SDA7 Total SDA / SDB 232 25.08% 124.31% 35.39% 8.46% Quintile Quintile Quintile Quintile Quintile NDB6 6 TSI TSI TSI TSI TSI NDA / NDB 154 26.30% 122.01% 12.03% 93.37% 7 Debt Tranche Groups NDB / SDA 449 18.12% 121.14% 19.72% 17.73% Total 1262 29.21% 116.49% 21.31% 114.15% Figure 10.2: Dispersion Measures of RDD & MLDR by  Tranche Safety Index & Debt Position Categories 1 [% Debt Below − % Debt Above + 1] TSI ≡ (MULGD Database 1987‐2007) 2 180.00% • Both measures are U-shaped in quintiles of 160.00% Standard Deviation RDD MLE Std Err MLDR 140.00% TSI, but RDD shows overall increase 120.00% 100.00% • RDD higher for NDA/SDB (best) vs. NDB 80.00% 60.00% /SDA (worst) group, but not so MLDR 40.00% 20.00% • St dev RDD increasing in worst tranches, 0.00% 1st 2nd 3rd 4th 5th NDA / SDB4 SDA / SDB5 NDA / NDB / SDA7 Total Quintile Quintile Quintile Quintile Quintile NDB6 but not as clear for MLDR TSI TSI TSI TSI TSI Debt Tranche Groups
  • 32. Empirical Results: RDD and MLDR Measures by Obligor Industry Figure 11.1: Central Tendency Measures of RDD & MLDR by Industry  1 2 Table 7 - RDD and MLDR of Defaulted Instruments by Industry (MULGD Database 1987‐2007) (Moody's Ultimate LGD Database 1987-2007) 45.00% RDD MLDR 40.00% MLE 35.00% Standard MLE Standard Count Average Deviation Estimate Error 30.00% Industry Group Aerospace / Auto / Capital Goods / Equipment 156 41.30% 122.21% 22.29% 22.80% 25.00% Consumer / Service Sector 235 34.27% 121.28% 28.84% 61.19% 20.00% Energy / Natural Resources 183 26.56% 55.42% 20.35% 34.96% Healthcare / Chemicals 93 24.03% 90.98% 17.99% 10.77% 15.00% RDD Average MLDR MLE Estimate High Technology / Telecommunications 225 40.98% 159.31% 17.92% 6.94% 10.00% Leisure Time / Media 114 36.58% 114.81% 26.42% 13.25% Transportation 236 6.02% 99.95% 5.76% 16.04% 5.00% Forest / Building Products / Homebuilders 20 23.01% 128.62% 34.94% 21.06% 0.00% Grand Total 1,262 29.21% 116.49% 22.38% 107.83% Aerospace / Auto / Consumer / Service Energy / Natural Healthcare / High Technology / Leisure Time / Media Transportation Forest / Building Grand Total Capital Goods / Sector Resources Chemicals Telecommunications Products / Equipment Homebuilders • Difficult to discern a “story” & lack of Figure 11.2: Dispersion Measures of RDD & MLDR by Industry agreement between RDD / MLDR (MULGD Database 1987‐2007) 180.00% 160.00% • High RDD: Aerospace/…,High 140.00% Tech/…,Leisure/… but high MLDR 120.00% 100.00% Consumer/…,Leisure/… 80.00% RDD Standard Deviation MLDR MLE Standard Error 60.00% • Low in both: Healthcare/… & 40.00% Transportation 20.00% 0.00% Aerospace / Auto / Consumer / Service Energy / Natural Healthcare / High Technology / Leisure Time / Media Transportation Forest / Building Grand Total Capital Goods / Sector Resources Chemicals Telecommunications Products / Equipment Homebuilders
  • 33. Correlation Analysis of RDD: Financial / Valuation Covariates • Book leverage & market / book strong Table 8.1 - Summary Statistics on Financial positive drivers (appear in regressions) Statement and Market Valuation Variables and Correlations with RDD (Moody's Ultimate LGD • Size by market value of total assets Database 1987-2007) inversely correlated (somewhat less extent Corr with by net sales & book value assets) Variable Cnt Median Mean Std Dev RDD • Cash-flow measures inversely correlated BVTL / BVTA 1111 117.00% 138.89% 73.94% 17.18% BVTL / MVTA 1111 97.00% 91.23% 12.02% -1.23% (FAR makes one of the regressions) MVTA 790 2.0913 2.0691 0.9462 -8.15% Net Sales 980 2.8596 2.8035 0.6744 -2.69% • Some profitability measures negatively BVA 983 3.0659 3.0362 0.5958 -1.83% Tobin's Q 735 84.01% 100.69% 61.21% -0.12% related to RDD (NI/TA, ROA & ROE) MVTA / BVTA 1111 127.00% 153.82% 83.03% 18.50% BVI / BVTA 773 18.34% 21.02% 20.98% 2.00% • Liquidity dimension: only ICR has a PE Ratio 791 -0.3084 -2.2438 14.8584 4.02% CR 911 113.41% 133.57% 84.43% 2.33% significantly inverse relationship ICR 982 0.01 (1.43) 4.56 -6.57% WC / BVTA 914 2.86% -5.88% 38.10% 2.87% Figure 12.1: Annualized Return on Defaulted Debt vs.  CF / CL 902 -0.06% -31.79% 122.08% -2.98% Market‐to‐Book Value (MULGD Database 1987‐2007) FAR 881 13.30% 9.27% 35.02% -12.56% 1000.00% FCF / BVTA 946 0.06% -8.02% 20.07% -4.03% 800.00% CFO / BVTA 954 0.47 102.76 988.72 1.26% NI / BVTA 1111 -8.00% -20.71% 38.64% -2.85% 600.00% NI / MVTA 1111 -4.00% -11.67% 17.93% 0.21% RDD 400.00% RE / BVTA 971 -22.57% -55.95% 97.26% -6.69% ROA 971 -7.08% -19.29% 27.95% -8.13% 200.00% y = 0.258x ‐ 0.107 R² = 0.034 ROE 971 -1.85% 17.41% 568.41% -2.78% 0.00% 0 1 2 3 4 5 6 ‐200.00% MV / BV
  • 34. Correlation Analysis of RDD: Firm Level Equity Price Covariates • CARs (only variable here in the Table 8.2 - Summary Statistics on Equity Price Performance Variables and Correlations with RDD regressions) in the 90 days to the (Moody's Ultimate LGD Database 1987-2007) 1-year horizon to default has strong Corr with positive correlation Variable Cnt Median Mean Std Dev RDD 1-Yr Expected Equity Return 1111 -81.00% -73.93% 41.35% -6.36% • 1-year expected return (just avg. to 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% 1 yr. prior to default) is mildly 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% negatively correlated Cumulative Abnormal Returns 1111 0.00% -5.13% 29.42% 10.90% • 1 month equity volatility has a weak Figure 12.4: Annualized Return on Defaulted Debt vs.  positive relationship Cumulative Abnormal Equity Returns (MULGD Database  1987‐2007) • Relative larger defaulted firms, in terms 1000% or either market cap or stock price, 800% have poorer debt performance 600% RDD • Firms trading nearer to the high point of 400% their 3-year trading range also tend to 200% y = 0.430x + 0.313 R² = 0.011 have lower RDDs, but it is a weak 0% ‐150% ‐100% ‐50% 0% 50% 100% 150% 200% correlation ‐200% CAR
  • 35. Correlation Analysis of RDD: Firm Level Capital Structure Covariates • No variables from this group are in Table 8.3 - Summary Statistics on Capital Structure Variables the final regression models and Correlations with RDD (Moody's Ultimate LGD Database 1987-2007) • Note generally very little change in Corr with these from 1 yr. prior to default Variable Cnt Median Mean Std Dev RDD Number of Instruments 3886 6.0000 10.5252 12.8458 -4.01% • Strongest relationship is a positive 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% one for proportion of secured debt Percent Bank Debt 3886 39.92% 40.78% 30.84% 7.32% Percent Subordinated Debt 3886 38.81% 40.34% 31.23% 5.60% • Percent bank and sub debt also a Figure 12.5: Annualized Return on Defaulted Debt vs.  mild direct association with RDD Percent Secured Debt (MULGD Database 1987‐2007) 1000% • Measures of “capital structure 800% complexity”, number of instruments or of major creditor classes, have 600% small negative correlations with RDD RDD 400% • Work-in-progress: analysis of bank 200% y = 0.349x + 0.146 lender concentration by Herfindahl R² = 0.008 0% 0% 20% 40% 60% 80% 100% 120% index: expected relationship?(evidence ‐200% PBD that lower → ↑ firmwide recoveries)
  • 36. Correlation Analysis of RDD: Firm Level Credit Quality Covariates • Although the univariate correlation Table 8.4 - Summary Statistics on Credit Quality / Credit Market Variables is modest in size, a result from this and Correlations with RDD (Moody's Ultimate LGD Database 1987-2007) group result that carries over to the Corr with regressions is that higher LGD at Variable Cnt Median Mean Std Dev RDD Altman Z-Score 733 0.5266 -0.1010 2.2087 -11.23% default is indicative of higher RDD Credit Spread 1262 8.70% 8.11% 3.95% -5.66% Contractual Coupon Rate 3886 9.00% 8.64% 3.89% -5.76% • A higher spread over risk-free rate 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% or contractual coupon is inversely 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% correlated at similar magnitude but Moody's Long Run Default Rate (Minor Code) 3178 0.0249 0.0337 0.0461 0.29% not appearing in the regressions Figure 12.6: Annualized Return on Defaulted Debt  • The investment grade dummy has only vs. Loss‐Given‐Default (MULGD Database 1987‐ 2007) a small positive correlation here but 1000% appears significantly in regressions 800% • Altman Z: relatively sizable negative 600% correlation but not in any regressions RDD 400% (issues: limited availability & over-lap) 200% y = 0.399x + 0.066 R² = 0.012 • 0% Caveat on LGD at default in RDD ‐20% 0% 20% 40% 60% 80% 100% 120% model: 1-year horizon issue ‐200% LGD
  • 37. Correlation Analysis of RDD: Instrument / Contractual Covariates Table 8.5 - Summary Statistics on Instrument / • The TSI has a decently sized positive Contractual Variables and Correlations with RDD (Moody's Ultimate LGD Database 1987-2007) correlation & is the variable from this Corr group to enter the regressions with Variable Cnt Median Mean Std Dev RDD Seniority Rank 3886 1.0000 1.7123 0.8953 -9.64% • Percent debt below (above) has the Collateral Rank 3886 6.0000 4.5844 1.6206 -9.97% “expected” positive (negative) Percent Debt Below 3886 10.13% 25.82% 30.19% 10.51% Percent Debt Above 3886 0.00% 21.51% 28.95% -6.51% correlation coefficient Tranche Safety Index 3886 50.00% 52.16% 25.44% 9.69% Figure 12.7: Annualized Return on Defaulted Debt vs.  • As in the tabular results, lower rank of Tranche Safety Index (MULGD Database 1987‐2007) 1000% seniority or collateral is associated with lower RDD with seemingly robust 800% magnitudes, but this is not so in the 600% multivariate regressions RDD 400% 200% y = 0.515x + 0.046 R² = 0.009 0% 0% 20% 40% 60% 80% 100% 120% ‐200% TSI
  • 38. Correlation Analysis of RDD: Macro / Aggregate Market Covariates • The two cyclical variables from Table 8.6 - Summary Statistics on Macroenonomic and Cyclical Variables and Correlations with RDD (Moody's Ultimate LGD Database 1987-2007) this group to enter regressions Corr with Variable Cnt Median Mean Maximum Std Dev RDD are the Moody’s 12 mos. lagging 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% speculative grade default rate by 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% industry and 1-month T-bill yield, 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% with positive & negative signs as 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% in this table, respectively Figure 12.8: Annualized Return on Defaulted Debt  vs. Moody's Quarterly Speculative Grade Default  • The Fama-French factors show little relationship to Rate by Industry (MULGD Database 1987‐2007) 1000.00% defaulted debt performance (implies large 800.00% 600.00% unsystematic component of RDD?) RDD 400.00% y = 1.850x + 0.162 200.00% R² = 0.004 • Long term interest rates have somewhat of an 0.00% 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 ‐200.00% inverse univariate relation but does not make it to MQSRDRI Figure 12.9: Annualized Return on Defaulted Debt  vs. 1‐Month Treasury Bill Yield (MULGD Database  the regressions (same for long/short spread – not 1987‐2007) 1000.00% shown) 800.00% 600.00% • Equity market volatility is seemingly unrelated to RDD 400.00% 200.00% y = ‐0.720x + 0.521 R² = 0.010 RDD 0.00% 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 ‐200.00% T1MTBY
  • 39. Correlation Analysis of RDD: Vintage / Duration Covariates • None of these appear in the Table 8.7 - Summary Statistics on Duration / Vintage Variables and regression models (and some Correlations with RDD (Moody's Ultimate LGD Database 1987-2007) we would not want – i.e., not Corr known at default) and most no with Variable Cnt Median Mean Std Dev RDD relation to 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% • There is a clear “term-structure” 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% effect – longer TTR-> lower RDD (uncertainty resolved?) Figure 12.10: Annualized Return on Defaulted Debt vs.  Time‐to‐Resolution (MULGD Database 1987‐2007) • Almost no vintage (time from 1000% origination or 1st rating to default or 800% maturity) effect 600% • Time-in-distress (last cash-pay to RDD 400% default) no relationship to RDD 200% y = ‐0.113x + 0.484 0% R² = 0.018 0% 100% 200% 300% 400% 500% 600% 700% 800% 900% 1000% ‐200% TTR
  • 40. 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
  • 41. 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 ): u η = βT xi = m−1 ( μ ) EP [ε i | xi ] = μ = p ( ε i | xi )ε i dυ ( ε i ) = m (η ) ∫ l • In this framework, the distribution of εi resides in the exponential family, membership in which implies a probability distribution function of the form: τ, γ are smooth functions, ⎡A ⎛ ζ ⎞⎤ p ( ε i | xi , β, Ai , ζ ) = exp ⎢ i {ε iθ ( xi | β ) − γ ( xi | β )} + τ ⎜ ε i , ⎟ ⎥ Ai is a prior weight, ζ is a ⎢ζ ⎝ Ai ⎠ ⎥ scale parameter ⎣ ⎦ • The location function θ(.) is related to the linear predictor according to: ( ) θ ( xi | β ) = (γ ') −1 ( μ ( xi ) ) = (γ ') −1 m ( βT xi )
  • 42. 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: α ( β x ) −1 (1 − ε )β (β x )−1 Γ ( x)Γ( y) 1 T T ε i i ε i ∈ [0,1];α , β : R → R ++ B [ x, y ] = = u x −i (1 − u ) y −1 ∫ p ( ε i | xi , β ) = i i du Γ( x + y) ( )( ) B ⎡α β xi , β β xi ⎤ T T ⎣ ⎦ 0 • Common approaches: transform Є to a normal variate through a beta inverse and perform OLS (Moody’s LossCalc™) or quasi-MLE of the above • We follow Mallick and Gelfand (1994), in which the location function is taken as a mixture of cumulative beta distributions, taking the form: (1 − u ) b j −1 a j −1 li k u θ ( x i | β , φ, a , b ) = β T x i = ∑ φ j ∫ du B ⎡a j , bj ⎤ ⎣ ⎦ j =1 u =0 • We may always estimate the underlying parameters consistently and efficiently by maximizing the log-likelihood function: ⎛ ζ [β | xi ] ⎞⎤ n⎡ l (θ ( β | xi ) ,ζ ( β | xi ) , β | xi ,εi , Ai ) = ∑⎢ {εiθi (β | xi ) −γ (β | xi )} +τ ⎜εi , A ⎟⎥ Ai i=1 ⎢ζ ( β | xi ) ⎠⎥ ⎝ ⎣ ⎦ i
  • 43. Econometric Modeling of RDD: Estimation Results 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 Partial Partial Partial Effect P-Value Effect P-Value Effect P-Value Variables Intercept 0.3094 1.42E-03 0.51005 9.35E-04 0.4342 6.87E-03 Moody's 12 Month Lagging Speculative Grade Default Rate by Industry 2.0501 1.22E-02 2.2538 6.94E-03 2.1828 1.36E-02 Collateral Rank Secured 0.2554 7.21E-03 0.2330 1.25E-02 0.2704 9.36E-04 Tranche Safety Index 0.4548 3.03E-02 0.4339 3.75E-02 Loss Given Default 0.3273 1.44E-02 0.2751 3.88E-02 Cumulative Abnormal Returns on Equity Prior to Default 0.3669 1.51E-03 0.3843 1.00E-03 0.4010 9.39E-04 Total Liabilities to Total Assets 0.2653 5.22E-08 Moody's Original Rating Investment Grade 0.2118 2.80E-02 0.2422 6.84E-03 0.1561 6.25E-02 1-Month Treasury Yield -0.4298 3.04E-02 -0.3659 1.01E-02 -0.4901 3.36E-02 Size Relative to the Market -0.0366 4.76E-02 -0.0648 3.41E-03 Market Value to Book Value 0.1925 2.64E-05 0.1422 5.63E-03 Free-Asset Ratio -0.2429 2.25E-02 959 958 783 Degrees of Freedom -592.30 -594.71 -503.99 Log-Likelihood 32.48% 38.80% 41.73% McFadden Pseudo R-Squared (In-Sample) 21.23% 12.11% 17.77% McFadden Pseudo R-Squared (Out-Of-Sample) - Bootstrap Mean McFadden Pseudo R-Squared (Out-Of-Sample) - Bootstrap Standard Error 2.28% 1.16% 1.70%
  • 44. 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) • 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) • 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 • 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 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) • On a OOT/OOS basis Models 1-3 R^2’s = 21.2%, 12.1% & 17.8%, resp.
  • 45. 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): ⎛ ⎛ N −1 ( PD ) + RN −1 ( 0.999 ) ⎞ ⎞ ⎜N⎜ ⎟ × LGD D K= ⎟ − PD R ⎜⎜ ⎟ ⎟ 1− R ⎝⎝ ⎠ ⎠ • 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 • 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: LGD D = 0.08 + 0.92 × LGD • The correlation R is related to the PD according to the relationship prescribed in the Rule for wholesale non-HVCRE exposures: R = 0.12 + 0.18 × e −50× PD
  • 46. The Regulatory Capital Impact of the Discount Rate for LGD (contd.) • Discounting by RDD the Table 10 - Summary Statistics on Discounted LGD and Regulatory Capital for model results in higher Different Discounting Methodologies (Moody's Ultimate LGD Database 1987-2007) estimates of LGD & 25th 75th Standard Percentile Median Mean Percentile Deviation Skewness Kurtosis higher regulatory capital 2 Discounted LGD - Contractual Coupon Rate 13.68% 54.97% 52.07% 88.17% 35.86% -0.0569 -1.5467 Discounted LGD - RDD Regression Model3 33.29% 72.10% 64.05% 95.07% 33.03% -0.3122 -1.2998 vs. contractual or 4 Discounted LGD - Punitive Discount Rate 33.08% 62.12% 59.03% 89.62% 31.53% -0.2133 -1.3288 Regulatory Capital - Contractual Coupon Rate 0.78% 2.66% 6.91% 9.91% 9.18% 1.9366 4.3220 constant punitive rates Regulatory Capital - RDD Regression Model 1.00% 3.72% 8.04% 10.87% 9.86% 1.7132 3.3883 Regulatory Capital - Punitive Discount Rate 0.94% 3.14% 7.31% 10.14% 9.26% 1.8544 3.9928 • 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%) • 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
  • 47. The Regulatory Capital Impact of the Discount Rate for LGD (contd.) Figure 13.1: Discounted LGD by Regression Model for RDD vs. Pre-petition Figure 13.2: Discounted LGD by Regression Model for RDD vs. Punitive Coupon Rate (MULGD Database 1987-2007) LGD Discounted by Discount Rate (MULGD Database 1987-2007) RDD Model LGD Discounted by RDD Model 120.00% 120.00% 100.00% 100.00% 80.00% 80.00% y = 0.8166x + 0.2152 y = 0.9401x + 0.0818 R2 = 0.786 R2 = 0.7785 60.00% 60.00% 40.00% 40.00% 20.00% 20.00% 0.00% 0.00% 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 Contractual by Coupon Rate • 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) • 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
  • 48. The Regulatory Capital Impact of the Discount Rate for LGD (contd.) Figure 13.3: Densities of LGD Discounted by RDD Model vs. Contract Rate Figure 13.4: Densities of LGD Discounted by RDD Model vs. Punitive Rate 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 2.0 2.0 Punitive Discount Rate (mean = 59.0%) Contractual Discount Rate (mean = 52.1%) RDD Model Discount Rate (mean = 64.1%) RDD Model Discount Rate (mean = 64.1%) 1.5 1.5 1.0 1.0 0.5 0.5 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 • 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
  • 49. The Regulatory Capital Impact of the Discount Rate for LGD (contd.) Figure 13.5: Densities of Regulatory Credit Capital (MULGD 1987-2007) Figure 13.6: Densities of Regulatory Credit Capital (MULGD 1987-2007) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Capital for LGD Discounted at Punitive Discount Rate (mean = 7.31%) Capital for LGD Discounted at Contractual Coupon Rate (mean = 6.91%) Capital for LGD Discounted by RDD Regression Model (mean = 8.04%) Capital for LGD Discounted by RDD Regression Model (mean = 8.04%) 8 8 6 6 4 4 2 2 0 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 • 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)
  • 50. Benchmarking Alternative LGD Discount Rate Frameworks Table 11: Benchmark Comparison of Alternative Methodologies for Deriving the Discount Rate for Workout Recoveries Risk- Market Free LGD Discount Correlation Asset Value Volatility LGD Rate Model for LGD Correlation to Systematic 1 4 5 6 7 3 2 Data Factor Source / Reference Rate Volatility (σi) (sig_m) Beta MRP (R_f) (qi,m) 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% Altman & Jha (2003), Market / Structural Based Models Monthly Altman Defaulted Bond Index & S&P 500 Index Returns (1986-2002) Linear Regression Machlachan (2004) 11.05% 20.30% 32.00% 18.74% 76.92% 7.87% 5.00% Frye (2000), Default Rates and Market Implied LGD (Moody's DRS Databases 1982-1999 ) 1-Factor Structural Model MLE Calibration Machlachan (2004) 7.28% 17.00% 32.00% 18.74% 29.02% 7.87% 5.00% p ( y ) 7 Loans 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) - 7 Senior Secured Bonds 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 Empirical Models Hamilton & Berthault Ex Post Realized Returns (Moody's Bankrupt Bond Index 1988-1998) N/A (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/A Most 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/A Most 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 Asarnow & Edwards Contractual Rate (incluyding penalty) N/A (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 Model-Free Friedman & Sandow Coupon Rate N/A (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/A Contactual Loan Rate N/A Carty et al (1998) N/A N/A N/A N/A N/A N/A N/A
  • 51. 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 the systematic 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)
  • 52. 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
  • 53. Benchmarking Alternative LGD Discount Rate Frameworks 2-factor version of (contd.) • We calibrate a the Basel capital model with Table 11.1: Simultaneous Full-Information Maximum Likelihood Estimation of 2-Factor Structural Credit Model systematic recovery risk to Moody's DRS Annual Speculative-Grade Default Rates and MULGD Moody’s annual default and loss Market Implied Loss-Given-Default (1987-2007) 2 .5 Asset Value Process for Rating Class r: At,r = ρrXt + (1-ρr ) Zt,r, Idiosyncratic PD rate data 1987-2007 Variable: Zt,r ~ NID(0,1), Systematic PD Variable: Xt , Asset Value Factor Loading 2 • Consider only 1 rating and 2 (Correlation): ρr (ρr ) 2 .5 Loss Rate Process for Seniority Class s: Lt,s = ρsYt + (1-ρs ) Zt,s , Idiosyncratic LGD seniority segments Variable: Zt,s ~ NID(0,1), Systematic LGD Variable: Yt , Recovery Value Factor 2 Loading (Correlation):ρs (ρs ) • Recovery process correlation -1 2 .5 Conditional Default Rate: R(Xt | PDr,ρr) = Φ[ (Φ [PDr]-ρrXt)/(1-ρr ) ], PDr: Long-Run estimates 22% (37%) loans (Expected) Probability of Default for Rating Class r -1 2 .5 Conditional Loss Rate: L(Yt | LGDs,ρs) = Φ[ (Φ [LGDs]-ρsYt)/(1-ρs ) ], LGDs: Long- (bonds) higher than Frye (2000) Run (Expected) Loss-Given-Default for Seniority Classs s single factor model 17%. T T T Zt,r , Zt,s ~ NID(0,1); (Xt, Yt) ~ N2 ([0,0] , [(1,rX,Y) ,(rX,Y,1) ] MLE Standard • 8% AVC estimate in ballpark Estimate Error Parameter with previous literature that Asset Value Correlation (ρr) 8.01% 4.66% Long-Run Probability of Default (PDr) 4.96% 3.01% calibrates to loss data 2 Recovery Value Correlation for Loans (ρl ) 22.03% 4.79% Loans Bank • High 64% correlation between Long-Run Loss-Given-Default for Loans (LGDl) 28.90% 13.23% systematic risk factor estimates Secured 2 Recovery Value Correlation for Bonds (ρb ) 36.64% 11.10% Senior Bonds support single factor model a Long-Run LGD for Bonds (LGDb) 44.61% 26.06% Correlation between Systematic Factors in Default and Loss reasonable approximation Rate (PD-LGD) Processes (rxy) 64.42% 18.83%
  • 54. 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 • Evidence that RDD is higher for better collateral quality ranking or better protected tranches, higher credit rating, more financially leverage, 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. • 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)
  • 55. 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)