1
A bank is a place that will lend you money if
you can prove that you dont need it.

• Bob Hope

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Why New Approaches to Credit Risk Measurement and
Management?

• Why Now?

3
Structural Increase in Bankruptcy

• Increase in probability of default
• High yield default rates 5.1 (2000), 4.3
  (1999, 1.9 (1998). Source Fitch 3/19/01
• Historical Default Rates 6.92 (3Q2001), 5.065
  (2000), 4.147 (1999), 1998 (1.603), 1997
  (1.252), 10.273 (1991), 10.14 (1990). Source
  Altman
• Increase in Loss Given Default (LGD)
• First half of 2001 defaulted telecom junk bonds
  recovered average 12 cents per 1 (0.25 in
  1999-2000)
• Only 9 AAA Firms in US Merck, Bristol-Myers,
  Squibb, GE, Exxon Mobil, Berkshire Hathaway, AIG,
  JJ, Pfizer, UPS. Late 70s 58 firms. Early 90s
  22 firms.

4
Disintermediation

• Direct Access to Credit Markets
• 20,000 US companies have access to US commercial
  paper market.
• Junk Bonds, Private Placements.
• Winners Curse Banks make loans to borrowers
  without access to credit markets.

5
More Competitive Margins

• Worsening of the risk-return tradeoff
• Interest Margins (Spreads) have declined
• Ex Secondary Loan Market Largest mutual funds
  investing in bank loans (Eaton Vance Prime Rate
  Reserves, Van Kampen Prime Rate Income, Franklin
  Floating Rate, MSDW Prime Income Trust) 5-year
  average returns 5.45 and 6/30/00-6/30/01 returns
  of only 2.67
• Average Quality of Loans have deteriorated
• The loan mutual funds have written down loan value

6
The Growth of Off-Balance Sheet Derivatives

• Total on-balance sheet assets for all US banks
  5 trillion (Dec. 2000) and for all Euro banks
  13 trillion.
• Value of non-government debt bond markets
  worldwide 12 trillion.
• Global Derivatives Markets gt 84 trillion.
• All derivatives have credit exposure.
• Credit Derivatives.

7
Declining and Volatile Values of Collateral

• Worldwide deflation in real asset prices.
• Ex Japan and Switzerland
• Lending based on intangibles ex. Enron.

8
Technology

• Computer Information Technology
• Models use Monte Carlo Simulations that are
  computationally intensive
• Databases
• Commercial Databases such as Loan Pricing
  Corporation
• ISDA/IIF Survey internal databases exist to
  measure credit risk on commercial, retail,
  mortgage loans. Not emerging market debt.

9
BIS Risk-Based Capital Requirements

• BIS I Introduced risk-based capital using 8
  one size fits all capital charge.
• Market Risk Amendment Allowed internal models to
  measure VAR for tradable instruments portfolio
  correlations the 1 bad day in 100 standard.
• Proposed New Capital Accord BIS II Links
  capital charges to external credit ratings or
  internal model of credit risk. To be implemented
  in 2005.

10
Traditional Approaches to Credit Risk Measurement

• 20 years of modeling history

11
Expert Systems The 5 Cs

• Character reputation, repayment history
• Capital equity contribution, leverage.
• Capacity Earnings volatility.
• Collateral Seniority, market value volatility
  of MV of collateral.
• Cycle Economic conditions.
• 1990-91 recession default rates gt10, 1992-1999
  lt 3 p.a. Altman Saunders (2001)
• Non-monotonic relationship between interest rates
  excess returns. Stiglitz-Weiss adverse
  selection risk shifting.

12
Problems with Expert Systems

• Consistency
• Across borrower. Good customers are likely to
  be treated more leniently. A rolling loan
  gathers no loss.
• Across expert loan officer. Loan review
  committees try to set standards, but still may
  vary.
• Dispersion in accuracy across 43 loan officers
  evaluating 60 loans accuracy rate ranged from
  27-50. Libby (1975), Libby, Trotman Zimmer
  (1987).
• Subjectivity
• What are the optimal weights to assign to each
  factor?

13
Credit Scoring Models

• Linear Probability Model
• Logit Model
• Probit Model
• Discriminant Analysis Model
• 97 of banks use to approve credit card
  applications, 70 for small business lending, but
  only 8 of small banks (lt5 billion in assets)
  use for small business loans. Mester (1997).

14
Linear Discriminant Analysis The Altman Z-Score
Model

• Z-score (probability of default) is a function
  of
• Working capital/total assets ratio (1.2)
• Retained earnings/assets (1.4)
• EBIT/Assets ratio (3.3)
• Market Value of Equity/Book Value of Debt (0.6)
• Sales/Total Assets (1.0)
• Critical Value 1.81

15
Problems with Credit Scoring

• Assumes linearity.
• Based on historical accounting ratios, not market
  values (with exception of market to book ratio).
• Not responsive to changing market conditions.
• 56 of the 33 banks that used credit scoring for
  credit card applications failed to predict loan
  quality problems. Mester (1998).
• Lack of grounding in economic theory.

16
The Option Theoretic Model of Credit Risk
Measurement

• Based on Merton (1974)
• KMV Proprietary Model

17
The Link Between Loans and Optionality Merton
(1974)

• Figure 4.1 Payoff on pure discount bank loan
  with face value0B secured by firm asset value.
• Firm owners repay loan if asset value (upon loan
  maturity) exceeds 0B (eg., 0A2). Bank receives
  full principal interest payment.
• If asset value lt 0B then default. Bank receives
  assets.

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Using Option Valuation Models to Value Loans

• Figure 4.1 loan payoff Figure 4.2 payoff to the
  writer of a put option on a stock.
• Value of put option on stock equation (4.1)
• f(S, X, r, ?, ?) where
• Sstock price, Xexercise price, rrisk-free
  rate, ?equity volatility,?time to maturity.
• Value of default option on risky loan
  equation (4.2)
• f(A, B, r, ?A, ?) where
• Amarket value of assets, Bface value of debt,
  rrisk-free rate, ?Aasset volatility,?time to
  debt maturity.

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Problem with Equation (4.2)

• A and ?A are not observable.
• Model equity as a call option on a firm. (Figure
  4.3)
• Equity valuation equation (4.3)
• E h(A, ?A, B, r, ?)
• Need another equation to solve for A and ?A
• ?E g(?A) Equation (4.4)
• Can solve for A and ?A with equations (4.3) and
  (4.4) to obtain a Distance to Default (A-B)/ ?A
  Figure 4.4

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Mertons Theoretical PD

• Assumes assets are normally distributed.
• Example Assets100m, Debt80m, ?A10m
• Distance to Default (100-80)/10 2 std. dev.
• There is a 2.5 probability that normally
  distributed assets increase (fall) by more than 2
  standard deviations from mean. So theoretical PD
  2.5.
• But, asset values are not normally distributed.
  Fat tails and skewed distribution (limited upside
  gain).

25
Mertons Bond Valuation Model

• B100,000, ?1 year, ?12, r5, leverage ratio
  (d)90
• Substituting in Mertons option valuation
  expression
• The current market value of the risky loan is
  93,866.18
• The required risk premium 1.33

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KMVs Empirical EDF

• Utilize database of historical defaults to
  calculate empirical PD (called EDF)
• Fig. 4.5

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Accuracy of KMV EDFsComparison to External
Credit Ratings

• Enron (Figure 4.8)
• Comdisco (Figure 4.6)
• USG Corp. (Figure 4.7)
• Power Curve (Figure 4.9) Deny credit to the
  bottom 20 of all rankings Type 1 error on KMV
  EDF 16 Type 1 error on SP/Moodys
  obligor-level ratings22 Type 1 error on
  issue-specific rating35.

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Monthly EDF credit measure
Agency Rating
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Problems with KMV EDF

• Not risk-neutral PD Understates PD since
  includes an asset expected return gt risk-free
  rate.
• Use CAPM to remove risk-adjusted rate of return.
  Derives risk-neutral EDF (denoted QDF). Bohn
  (2000).
• Static model assumes that leverage is
  unchanged. Mueller (2000) and Collin-Dufresne and
  Goldstein (2001) model leverage changes.
• Does not distinguish between different types of
  debt seniority, collateral, covenants,
  convertibility. Leland (1994), Anderson,
  Sundaresan and Tychon (1996) and Mella-Barral and
  Perraudin (1997) consider debt renegotiations and
  other frictions.
• Suggests that credit spreads should tend to zero
  as time to maturity approaches zero. Duffie and
  Lando (2001) incomplete information model. Zhou
  (2001) jump diffusion model.

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Term Structure Derivation of Credit Risk Measures

• Reduced Form Models KPMGs Loan Analysis System
  and Kamakuras Risk Manager

34
Estimating PD An Alternative Approach

• Mertons OPM took a structural approach to
  modeling default default occurs when the market
  value of assets fall below debt value
• Reduced form models Decompose risky debt prices
  to estimate the stochastic default intensity
  function. No structural explanation of why
  default occurs.

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A Discrete ExampleDeriving Risk-Neutral
Probabilities of Default

• B rated 100 face value, zero-coupon debt
  security with 1 year until maturity and fixed
  LGD100. Risk-free spot rate 8 p.a.
• Security P 87.96 100(1-PD)/1.08 Solving
  (5.1), PD5 p.a.
• Alternatively, 87.96 100/(1y) where y is the
  risk-adjusted rate of return. Solving (5.2),
  y13.69 p.a.
• (1r) (1-PD)(1y) or 1.08(1-.05)(1.1369)

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Multiyear PD Using Forward Rates

• Using the expectations hypothesis, the yield
  curves in Figure 5.1 can be decomposed
• (10y2)2 (10y1)(11y1) or 1.1621.1369(11y1)
  1y118.36 p.a.
• (10r2)2 (10r1)(11r1) or 1.1021.08(11r1)
  1r112.04 p.a.
• One year forward PD5.34 p.a. from
• (1r) (1- PD)(1y) 1.12041.1836(1 PD)
  
• Cumulative PD 1 (1 - PD1)(1 PD2) 1
  (1-.05)(1-.0534) 10.07

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The Loss Intensity Process

• Expected Losses (EL) PD x LGD
• If LGD is not fixed at 100 then
• (1 r) 1 - (PDxLGD)(1 y)
• Identification problem cannot disentangle PD
  from LGD.

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Disentangling PD from LGD

• Intensity-based models specify stochastic
  functional form for PD.
• Jarrow Turnbull (1995) Fixed LGD,
  exponentially distributed default process.
• Das Tufano (1995) LGD proportional to bond
  values.
• Jarrow, Lando Turnbull (1997) LGD proportional
  to debt obligations.
• Duffie Singleton (1999) LGD and PD functions
  of economic conditions
• Unal, Madan Guntay (2001) LGD a function of
  debt seniority.
• Jarrow (2001) LGD determined using equity
  prices.

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KPMGs Loan Analysis System

• Uses risk-neutral pricing grid to mark-to-market
• Backward recursive iterative solution Figure
  5.2.
• Example Consider a 100 2 year zero coupon loan
  with LGD100 and yield curves from Figure 5.1.
• Year 1 Node (Figure 5.3)
• Valuation at B rating 84.79 .94(100/1.1204)
  .01(100/1.1204) .05(0)
• Valuation at A rating 88.95 .94(100/1.1204)
  .0566(100/1.1204) .0034(0)
• Year 0 Node 74.62 .94(84.79/1.08)
  .01(88.95/1.08)
• Calculating a credit spread
• 74.62 100/(1.08CS)(1.1204CS) to get
  CS5.8 p.a.

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Noisy Risky Debt Prices

• US corporate bond market is much larger than
  equity market, but less transparent
• Interdealer market not competitive large
  spreads and infrequent trading Saunders,
  Srinivasan Walter (2002)
• Noisy prices Hancock Kwast (2001)
• More noise in senior than subordinated issues
  Bohn (1999)
• In addition to credit spreads, bond yields
  include
• Liquidity premium
• Embedded options
• Tax considerations and administrative costs of
  holding risky debt

44
Mortality Rate Derivation of Credit Risk Measures

• The Insurance Approach
• Mortality Models and the CSFP Credit Risk Plus
  Model

45
Mortality Analysis

• Marginal Mortality Rates (total value of
  B-rated bonds defaulting in yr 1 of issue)/(total
  value of B-rated bonds in yr 1 of issue).
• Do for each year of issue.
• Weighted Average MMR MMRi ?tMMRt x w where w
  is the size weight for each year t.

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Mortality Rates - Table 11.10

• Cumulative Mortality Rates (CMR) are calculated
  as
• MMRi 1 SRi where SRi is the survival rate
  defined as 1-MMRi in ith year of issue.
• CMRT 1 (SR1 x SR2 xx SRT) over the T years
  of calculation.
• Standard deviation ?MMRi(1-MMRi)/n As the
  number of bonds in the sample n increases, the
  standard error falls. Can calculate the number
  of observations needed to reduce error rate to
  say std. dev. .001
• No. of obs. MMRi(1-MMRi)/?2
  (.01)(.99)/(.001)2 9,900

47
CSFP Credit Risk Plus Appendix 11B

• Default mode model
• CreditMetrics default probability is discrete
  (from transition matrix). In CreditRisk ,
  default is a continuous variable with a
  probability distribution.
• Default probabilities are independent across
  loans.
• Loan portfolios default probability follows a
  Poisson distribution. See Fig.8.1.
• Variance of PD mean default rate.
• Loss severity (LGD) is also stochastic in Credit
  Risk .

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Distribution of Losses

• Combine default frequency and loss severity to
  obtain a loss distribution. Figure 8.3.
• Loss distribution is close to normal, but with
  fatter tails.
• Mean default rate of loan portfolio equals its
  variance. (property of Poisson distrib.)

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Pros and Cons

• Pro Simplicity and low data requirements just
  need mean loss rates and loss severities.
• Con Inaccuracy if distributional assumptions are
  violated.

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Divide Loan Portfolio Into Exposure Bands

• In 20,000 increments.
• Group all loans that have 20,000 of exposure
  (PDxLGD), 40,000 of exposure, etc.
• Say 100 loans have 20,000 of exposure.
• Historical default rate for this exposure class
  3, distributed according to Poisson distrib.

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Properties of Poisson Distribution

• Prob.(n defaults in 20,000 severity band)
  (e-mmn)/n! Where mmean number of defaults.
  So if m3, then prob(3defaults) 22.4 and
  prob(8 defaults)0.8.
• Table 8.2 shows the cumulative probability of
  defaults for different values of n.
• Fig. 8.5 shows the distribution of the default
  probability for the 20,000 band.

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Loss Probabilities for 20,000 Severity Band
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Economic Capital Calculations

• Expected losses in the 20,000 band are 60,000
  (3x20,000)
• Consider the 99.6 VaR The probability that
  losses exceed this VaR 0.4. That is the
  probability that 8 loans or more default in the
  20,000 band. VaR is the minimum loss in the
  0.4 region 8 x 20,000 160,000.
• Unexpected Losses 160,000 60,000 100,000
  economic capital.

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Calculating the Loss Distribution of a Portfolio
Consisting of 2 Bands20,000 and 40,000 Loss
Severity
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Add Another Severity Band

• Assume average loss exposure of 40,000
• 100 loans in the 40,000 band
• Assume a historic default rate of 3
• Combining the 20,000 and the 40,000 loss
  severity bands makes the loss distribution more
  normal. Fig. 8.8.

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Oversimplifications

• The mean default rate was assumed constant in
  each severity band. Should be a function of
  macroeconomic conditions.
• Ignores default correlations particularly
  during business cycles.

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Loan Portfolio Selection and Risk Measurement

• Chapter 12

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The Paradox of Credit

• Lending is not a buy and holdprocess.
• To move to the efficient frontier, maximize
  return for any given level of risk or
  equivalently, minimize risk for any given level
  of return.
• This may entail the selling of loans from the
  portfolio. Paradox of Credit Fig. 10.1.

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Managing the Loan Portfolio According to the
Tenets of Modern Portfolio Theory

• Improve the risk-return tradeoff by
• Calculating default correlations across assets.
• Trade the loans in the portfolio (as conditions
  change) rather than hold the loans to maturity.
• This requires the existence of a low transaction
  cost, liquid loan market.
• Inputs to MPT model Expected return, Risk
  (standard deviation) and correlations

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The Optimum Risky Loan Portfolio Fig. 10.2

• Choose the point on the efficient frontier with
  the highest Sharpe ratio
• The Sharpe ratio is the excess return to risk
  ratio calculated as

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Problems in Applying MPT to Untraded Loan
Portfolios

• Mean-variance world only relevant if security
  returns are normal or if investors have quadratic
  utility functions.
• Need 3rd moment (skewness) and 4th moment
  (kurtosis) to represent loan return
  distributions.
• Unobservable returns
• No historical price data.
• Unobservable correlations

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KMVs Portfolio Manager

• Returns for each loan I
• Rit Spreadi Feesi (EDFi x LGDi) rf
• Loan Risksvariability around ELEGF x LGD UL
• LGD assumed fixed ULi
• LGD variable, but independent across borrowers
  ULi
• VOL is the standard deviation of LGD. VVOL is
  valuation volatility of loan value under MTM
  model.
• MTM model with variable, indep LGD (mean LGD)
  ULi

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Correlations

• Figure 11.2 joint PD is the shaded area.
• ?GF ?GF/?G?F
• ?GF
• Correlations higher (lower) if isocircles are
  more elliptical (circular).
• If JDFGF EDFGEDFF then correlation0.

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