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### An Empirical Study of Exposure at Default

Michael Jacobs, Ph.D., CFA

Senior Financial Economist

Risk Analysis Division / Credit Risk Modeling

Moody’s KMV Credit Practitioner’s Conference

September 9, 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

- Background and Motivation
- Introduction and Conclusions
- Review of the Literature
- Basel Requirements
- Methodology
- Measurement Issues
- Empirical Results
- Econometric Model & Out-of-Sample Validation
- Summary and Future Directions

Background and Motivation

Why the special interest in understanding risk of committed revolving (unfunded) credit facilities?

- Unique structural characteristics / complexities (optionality) and risk factors (adverse selection)
- Represents a large exposure to the banking system and historically high risk / return tradeoff
- Basel II requirements: Banks must empirically support assumptions on expected drawdowns given default
- Relatively unstudied as compared with other aspects of credit risk (capital, PD, LGD, etc.)
- Arises in many contexts / products (e.g., credit cards, market risk: trading CPC exposure, LCs)

But focus here is on “standard”, “traditional” revolvers for U.S. large-corporates

Formulation of the Research Problem: What Exactly is EAD?

- Basel II definition: “A Bank’s best estimate of the amount drawn down upon on a revolving credit upon default in a year”?
- Historical observation of a drawn (or fraction of previously undrawn) amount on a default in a reference data-set?
- A random variable (or distribution) of future $ drawn (or % fraction of undrawn) amounts conditional upon default?
- A feature of the EAD distribution (e.g., measure of central tendency or high quantile)?
- The distributional properties of this feature (if we are modeling parameter uncertainty)?
- A form modeling framework (structural or reduced form) understanding or predicting EAD?

We develop empirical methods potentially supporting EAD estimation in ALL of these senses

Introduction and Conclusions

- Empirical study of EAD for the large corporate defaulted (i.e., Chapter 11 & distress) universe (U.S., 1985-2007)
- Builds upon previous practitioner literature and current practices in the industry
- References issues in risk management and supervisory requirements (Basel II Advanced IRB)
- Application of advanced statistical methods (beta-link GLM)
- Highlights issues in measurement and data interpretation
- Exploration of alternative measures of EAD risk
- Confirms some previous findings: increased EAD risk with better rating, lower utilization or longer time-to-default
- “New” findings: EAD risk found to increase (decrease) with company size, intangibility,% bank or secured debt (leverage, profitability, collateral quality, percent debt cushion), and
- Counter-cyclicality: evidence that EAD risk is elevated during economic expansion periods

Review of the Literature

Limited previous work, but some well-regarded benchmarks

- The “classics”: Asarnow & Marker (1995 - ”The Citi Study”), Araten & Jacobs (2001 - “The Chase Study”)
- Still the standard in methodology & concept
- Multiple unpublished studies by financial institutions previously & in more recently preparation for Basel II
- Much variation in degree to which differs from the above
- Recent works in the academic & especially the supervisory / academic community (including this)
- Moral* (2006): alternative frameworks for estimating EAD (optimal in regulatory sense, i.e. LEQ > 0, reg. capital not under-estimated)
- Sufi (RFS, 2008): usage of credit lines in a corporate finance perspective (↑ historical profitability→more credit,revolvers=80% of all financing U.S.)
- Jimenez et at (S.F. FRB, 2008): empirical EAD study for Spanish credit register data (defaulted firms -> higher usage up to 5 yrs. to default)
- Loukoianova, Neftci & Sharma (J of Der., 2007): arbitrage-free valuation framework for contingent credit claims

*In “The Basel II Risk Parameters: Estimation, Validation, and Stress Testing”

Advanced IRB Requirements

- Within the Basel II framework EAD is a bank’s expected gross dollar exposure to a facility upon the borrower’s default
- EAD is meant to reflect the capital at risk
- The general ledger balance is appropriate for fixed exposures, like bullet and term loans (see Paragraph 134)
- But provides an allowance for allocated transfer risk reserve if the exposure is held available-for-sale
- In the case of variable exposures, like revolving commitments and lines of credit exposures, this is not appropriate: banks must estimate the EAD for each exposure in the portfolio
- But the guidance is not prescriptive about how to form this estimate
- Ideally use internal historical experience relevant to the current portfolio
- Note that there is no downward adjustment for amortization or expected prepayments
- EAD is floored at current outstanding
- At odds with empirical evidence (Banks seeing evidence ort paydowns)
- Implications for properties of estimators (i.e., LEQ>0 or EAD>drawn)

Methodology: The Loan Equivalency Factor (LEQ)

- EAD: time t expected $ utilization (= availability) default time τ:

- “Traditionally” estimated through an LEQ factor that is applied to the current unused:

- The LEQ factor conditional on a vector of features X can be estimated by observations of changes in utilization over unused to default (typically averaging over “homogenous segments”):

Methodology: The Credit Conversion Factor (CCF)

- An alternative approach estimates a credit conversion factor (CCF) to be applied to the current outstanding (used amount):

- The CCF is simply the expected gross percent change in the total outstanding:

- CCF can be estimated by averaging the observed percent changes in outstandings:

Methodology: The Exposure at Default Factor (EADF) & Modeling of Dollar EAD

- Alternatively, dollar EAD may be factored into the product of the current availability and an EAD factor:

- Where EADf is the expected gross change in the limit:

- May be estimated as the average of gross % limit changes:

- Most generally & least common, model dollar EAD as a function of used / unused & covariates (Levonian, 2007) :

- Where Y=(X,AVAIL,UTIL,T,t), L(.) is a loss metric, and EP is expectation with respect to physical (empirical) measure

Measurement Issues

- The process is saturated with judgment & labor intensive (importance of documentation, automation & double checking work
- Data on outstandings and limits extracted from SEC filings: Lack of consistent reporting & timing issues (the Basel 1-Year horizon?)
- Unit of observation: is it the same facility?
- Amendments to loan agreements (“stringing together”) over time
- Combining facilities for a given obligor
- Need of a sampling scheme: generally at 1-year anniversaries, rating changes, amendments or “significant” changes in exposure
- Avoid duplicative observations
- Data cleansing: elimination of clearly erroneous data points vs. modifying estimates (capping / flooring, Winsorization)
- When are extreme values deemed valid observations?
- Treatment of outliers and “non-credible” observations
- Repeat defaults of companies (“Chapter 22s”): look at spacing
- Determine if it is really a distinct instance of default
- Ratings: split between S&P & Moody’s?
- Take to worst rating (conservativism)

Empirical Results: Data Description

- Starting point: Moody’s Ultimate LGD Database™ (“MULGD”)
- February 2008 release
- Comprehensive database of defaults (bankruptcies and out-of-court settlements)
- Broad definition of default (“quasi-Basel”)
- Largely representative of the U.S. large corporate loss experience
- Most obligors have rated instruments (S&P or Moody’s) 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
- 3,886 defaulted instruments from 1985-2007 for 683 borrowers
- Revolving credits subset: 496 obligors, 530 defaults and 544 facilities

Empirical Results: Data Description (continued)

- MULGD has information on all classes of debt in the capital structure at the time of default, including revolvers
- 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
- 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 1: prices of traded debt or equity at default (30-45 day avg.)
- Sub-set 2: revolving loans with limits in 10K and 10Q reports

Empirical Results: Summary Statistics (EAD Risk Measures)

- Various $ exposure measures: EAD & ∆ to default, drawn/ undrawn, limits, “race to default” quantities
- LEQ (CCF & EADF) 2 (3 types)

- This conveys a sense of the extreme values observed here
- LEQ ranges in [-210,106], CCF (EADF) max at 704 (106)
- Shows that you need to understand extremes & the entire distribution
- Mean collared LEQ factor 42.2% in “ballpark” with benchmarks
- Median 33.3% OK but mean 16.1% raw seems too low
- Raw CCF, EADF better (natural flooring) but decide to Winsorize

Empirical Results: Distributions of EAD Risk Measures

- Raw LEQ distribution: akin to the return on an option?
- Collared LEQ: familiar “barbell” shape (like LGDs)
- Decide to go with collared measure
- Consistency with common practice
- Numerical instability of others -> estimation problems

Empirical Results: Distributions of EAD Risk Measures (continued)

- More stable than LEQs
- Natural floor at 0%
- Choose Winsorized measures
- As with LEQ, estimation issues with raw
- Multi-modality (especially EADF)?

Empirical Results: Estimation Regions of EAD Risk Measures

- About 1/3 LEQs <= 0% → paydowns effectuated?
- But 14% > 1 → additional drawdowns?
- 34% CCFs < 1 → balance shrinkage?
- But 56% > 1 → inflation
- 14% EADFs > 1 → larger limits?
- But 80 <1 → lower limits

- But this tendency to “quirky” values attenuated for worse rating and shorter time-to-default

Empirical Results: Summary Statistics (Covariates)

- Availability of fin. ratios limited vs. instrument, cap structure & macro

- Companies highly levered, unprofitable, intangible, negative cash flow
- Low LGDs (top of the capital structure)

Empirical Results: Distributions of LEQ by Rating

- Clear shift of probability mass from 1 to zero as grade worsens
- But similar bimodal shape across all grades

Empirical Results: Distributions of LEQ by Time-to-Default

- Clear shift of probability mass from zero to 1 as time-to-default lengthens
- But similar bimodal shape across all TTDs

Empirical Results: LEQ vs. Rating & Time-to-Default Grids

- Similar table to this in Araten et al (2001)
- Average LEQs decrease (increase) almost montonically in worsening grade (longer time-to-default)
- Results not as clear-cut for either non-collared LEQ or CCF, EADF

Empirical Results: EAD Risk Measures vs. Rating

- Generally a decrease in LEQ, CCF and EADF with worsening grade
- Does not hold monotonically for uncollared LEQ or un-Winsorized CCF, EADF

Empirical Results: EAD Risk Measures by Year of Observation

- Where is the ”downturn EAD”?
- How many banks look for it
- Define downturn as the default rate in the highest quintile
- → DR > 6.8% (‘91-92,’01-03)
- A countercyclical effect can be seen (i.e., ↑ factors in mid-90s)
- But 1st episode vs. 80s not so clear (thin observations)
- Do we really expect higher EAD risk in downturns (but then what is the story here?)
- Monitoring – “laxity” or ↑ cost in good periods?
- Moral Hazard - incentives to overextend during expansion?

Empirical Results: EAD Risk Measures by Year of Default

- Grouping by default year and taking the observation 1-year back is akin to the “cohort approach” (CA) to EAD
- Pure CA analogous to rating agency default rate estimation
- Same story here: still the cycle to hard to detect in the “expected” direction
- But why do people expect to see this?
- Evidence of countercyclicality here, mainly from the 2nd downturn
- EAD risk measures higher in the benign mid-90’s

Empirical Results: EAD Risk Measures by Collateral & Seniority

- EAD risk is generally lower for better secured and more senior loans

- Mean LEQ 41% vs. 57% (39% vs. 51%) for secured vs. unsecured (senior vs. sub)

- Finally an “intuitive” result? (basis for some segmentations)

- However, ample judgment applied in forming these high level collateral groupings from lower level labels

Empirical Results: EAD Risk Measures by Obligor Industry

- Difficult to discern an explainable pattern

- Utilities, Tech, Energy & Transportation above average for LEQ

- Homebuilders & Consumer / Service below for LEQ

- But rankings not completely consistent across measures

- What could be the story? (e.g., tangibility & LGD)

Empirical Results: Correlations of EAD Risk Measures to Covariates

- Utilization strongest driver except in EADF

- TTD (rating) strongly + (-) → EAD risk

- Leverage, liquidity, profitability, tangibility (size) - (+) → EAD risk

- Better collateral rank, higher seniority, more debt cushion → lower EAD risk

- More % bank, secured debt -> higher EAD risk (monitoring/coordination story?)

- Countercyclical by speculative grade default rate (by industry too, but weaker)

- Cash flow → +EAD risk for LEQ & EADF (but weak & not in regressions)

- Equity markets – risk free rate & Fama French factors negative & small / weak

- Drawn (undrawn – ex EADF) + (-) EAD risk

- CARs neg. corr but not in regressions

Econometric Modeling of EAD: Beta-Link Generalized Linear Model

- The distributional properties of EAD risk measures creates challenges in applying standard statistical techniques

- Non-normality of EAD in general and collared LEQ factors in particular (boundary bias)

- OLS or even averaging across segments inappropriate or misleading

- Here we borrow from the default prediction literature by adapting generalized linear models (GLMs) to the EAD setting

- See Maddalla (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 on raw LEQ, modeling of dollar EAD measures through quantile regression (Moral, 2006)

Econometric Modeling of EAD: Estimation Results (BLGLM Models)

- Estimates generally significant (but some p-values marginal), signs in line with univariate analysis & “good” fit

- Model selection process: alternating stepwise procedure applied judiciously (i.e., judgment again)

- Utilization the strongest factor but only for LEQ and EADF

- Cutback Rate, Drawn and Undrawn in only one model?

- Different measure of leverage (book vs. market) in EADF model?

- Financials: larger, intangible, illiquid, unprofitable → higher EAD risk

- CCF: best fit in-sample, but LEQ forecasts $ EAD the best

- Estimates supports countercyclicality

Econometric Modeling of EAD: Out-of-Sample & Out-of-Time Validation

- This shows how in-sample results can be misleading: massive divergence in performance across runs

- LEQ best by Pseudo R^2 (highest median, least dispersion)

- But hard to tell which is best by Spearman correlation (CCF/EADF higher/lower median but more/less dispersed)

- Non-normality of bootstrapped sampling distributions for statistics

Summary of Contributions and Major Findings

- Defined several metrics which in principle should all give the correct answer, but with different properties

- Empirically investigated the determinants of, and built predictive econometric models for, measuring EAD risk

- Built upon a limited practitioner literature, extending the prior empirical work of Araten et al (2001) and Asarnow et al (1995)

- Incorporate accounting, macro, capital structure, pre-default exposure determinants in addition to rating, utilization and tenor

- Various measures of EAD risk compared through a multiple regression model (BLGLM) & validated out-of-sample & -time

- “New Findings”: EAD risk found to increase (decrease) with company size, intangibility, % bank or secured debt (leverage, profitability, collateral quality, % debt cushion, seniority) & counter-cyclicality (i.e., elevated in expansions)

- CCF found to fit best in sample but LEQ measure found to forecast $ EAD best & best distribution of R2 out of sample

Directions for Future Research

Expand data-set (private companies, international) or type of instruments (e.g., trade or financial letters of credit)

- A more general framework to encompass all 3 measures of EAD risk (e.g., directly model dollar EAD)

- Alternatively, pursue econometric designs better capable of dealing with outliers (e.g., robust / resistant regression)

- A theoretical model, wherein the parameter restrictions or functional forms could be subject to empirical falsification

- Joint estimation of EAD with PD or LGD risk measures

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