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“A bank is a place that will lend you money if you can prove that you don’t need it.”. Bob Hope. Why New Approaches to Credit Risk Measurement and Management?. Why Now?. Structural Increase in Bankruptcy. Increase in probability of default - PowerPoint PPT Presentation
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Saunders & Cornett, Financial Institutions Management, 4th ed.
1
“A bank is a place that will lend you money if you can prove that
you don’t need it.”Bob Hope
Saunders & Cornett, Financial Institutions Management, 4th ed.
2
Why New Approaches to Credit Risk Measurement and
Management?
Why Now?
Saunders & Cornett, Financial Institutions Management, 4th ed.
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, J&J, Pfizer, UPS. Late 70s: 58 firms. Early 90s: 22 firms.
Saunders & Cornett, Financial Institutions Management, 4th ed.
4
Disintermediation
• Direct Access to Credit Markets– 20,000 US companies have access to US
commercial paper market.– Junk Bonds, Private Placements.
• “Winner’s Curse” – Banks make loans to borrowers without access to credit markets.
Saunders & Cornett, Financial Institutions Management, 4th ed.
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
Saunders & Cornett, Financial Institutions Management, 4th ed.
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 > $84 trillion.• All derivatives have credit exposure.• Credit Derivatives.
Saunders & Cornett, Financial Institutions Management, 4th ed.
7
Declining and Volatile Values of Collateral
• Worldwide deflation in real asset prices.– Ex: Japan and Switzerland– Lending based on intangibles – ex. Enron.
Saunders & Cornett, Financial Institutions Management, 4th ed.
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.
Saunders & Cornett, Financial Institutions Management, 4th ed.
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.
Saunders & Cornett, Financial Institutions Management, 4th ed.
10
Traditional Approaches to Credit Risk Measurement
20 years of modeling history
Saunders & Cornett, Financial Institutions Management, 4th ed.
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 >10%, 1992-1999: < 3% p.a. Altman & Saunders (2001)
– Non-monotonic relationship between interest rates & excess returns. Stiglitz-Weiss adverse selection & risk shifting.
Saunders & Cornett, Financial Institutions Management, 4th ed.
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?
Saunders & Cornett, Financial Institutions Management, 4th ed.
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 (<$5 billion in assets) use for small business loans. Mester (1997).
Saunders & Cornett, Financial Institutions Management, 4th ed.
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
Saunders & Cornett, Financial Institutions Management, 4th ed.
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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.
Saunders & Cornett, Financial Institutions Management, 4th ed.
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The Option Theoretic Model of Credit Risk Measurement
Based on Merton (1974)
KMV Proprietary Model
Saunders & Cornett, Financial Institutions Management, 4th ed.
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The Link Between Loans and Optionality: Merton (1974)
• Figure 4.1: Payoff on pure discount bank loan with face value=0B 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 < 0B then default. Bank receives assets.
Saunders & Cornett, Financial Institutions Management, 4th ed.
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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, , ) whereS=stock price, X=exercise price, r=risk-free rate, =equity
volatility,=time to maturity. Value of default option on risky loan = equation (4.2) =
f(A, B, r, A, ) whereA=market value of assets, B=face value of debt, r=risk-free
rate, A=asset volatility,=time to debt maturity.
Saunders & Cornett, Financial Institutions Management, 4th ed.
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$ Payoff
Assets0 A1 B A2
Figure 4.1 The payoff to a bank lender
Saunders & Cornett, Financial Institutions Management, 4th ed.
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$ Payoff
Stock Price (S)0
X
Figure 4.2 The payoff to the writer of a put option on a stock.
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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
Saunders & Cornett, Financial Institutions Management, 4th ed.
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Value ofAssets (A)
Value ofEquity (E)
($)
B
L
A1 A20
Figure 4.3 Equity as a call option on a firm.
Saunders & Cornett, Financial Institutions Management, 4th ed.
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B$80m
A$100m
t0 t1 Time(t)
Default Region
A
A
Figure 4.4 Calculating the theoretical EDF
Saunders & Cornett, Financial Institutions Management, 4th ed.
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Merton’s Theoretical PD
• Assumes assets are normally distributed.• Example: Assets=$100m, Debt=$80m, A=$10m• 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).
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Merton’s Bond Valuation Model
• B=$100,000, =1 year, =12%, r=5%, leverage ratio (d)=90%
• Substituting in Merton’s 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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KMV’s Empirical EDF
• Utilize database of historical defaults to calculate empirical PD (called EDF):
• Fig. 4.5
Number of firms that defaulted within a year with asset values of 2 from Empirical EDF = B at the beginning of the year Total population of firms with asset values of 2 from B at the beginning of the year
50 Defaults Empirical EDF = Firm population of 1, 000 = 5 percent
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5%
EmpiricalEDF
Figure 4.5default (DD): A hypothetical example.Empirical EDF and the distance to
0 Distanceto Default
(DD)
ProprieteryTrade-Off
2
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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 S&P/Moody’s obligor-level ratings=22%; Type 1 error on issue-specific rating=35%.
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12/96 06/97 12/97 06/98 12/98 06/99 12/99 06/00 12/00 06/01
20 CCCCC
B
KMV EDF Credit Measure
Source: KMV.
Agency Rating
BB
BBB
A
AA
AAA
151075
2
1.0
.5
.20
.15
.10
.05
.02
Figure 4.6 KMV expected default frequency TM and agency rating for Comdisco Inc.
12/96 06/97 12/97 06/98 12/98 06/99 12/99 06/00 12/00 06/01
20 CCCCC
B
KMV EDF Credit Measure Agency Rating
BB
BBB
A
AA
AAA
151075
2
1.0
.5
.20
.15
.10
.05
.02
Source: KMV.
Figure 4.7 KMV expected default frequency TM and agency rating for USG Corp.
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Monthly EDF™ credit measure
Agency Rating
Saunders & Cornett, Financial Institutions Management, 4th ed.
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1009080706050
Percent of Population Excluded
40302010
100
90
80
70
60
50
40
30
20
10
00
Figure 4.8
Source: Kealhofer (2000).
agency ratings (1990-1999) for rated U.S. companies.KMV EDF Credit Measure vs.
EDF Power
S&P Company Power
S&P Implied Power
Moodys Implied Power
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Problems with KMV EDF
• Not risk-neutral PD: Understates PD since includes an asset expected return > 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: KPMG’s Loan Analysis System and Kamakura’s Risk Manager
Saunders & Cornett, Financial Institutions Management, 4th ed.
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Estimating PD: An Alternative Approach
• Merton’s 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 Example:Deriving Risk-Neutral Probabilities of Default
• B rated $100 face value, zero-coupon debt security with 1 year until maturity and fixed LGD=100%. Risk-free spot rate = 8% p.a.
• Security P = 87.96 = [100(1-PD)]/1.08 Solving (5.1), PD=5% p.a.
• Alternatively, 87.96 = 100/(1+y) where y is the risk-adjusted rate of return. Solving (5.2), y=13.69% p.a.
• (1+r) = (1-PD)(1+y) or 1.08=(1-.05)(1.1369)
Saunders & Cornett, Financial Institutions Management, 4th ed.
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Multiyear PD Using Forward Rates
• Using the expectations hypothesis, the yield curves in Figure 5.1 can be decomposed:
• (1+0y2)2 = (1+0y1)(1+1y1) or 1.162=1.1369(1+1y1) 1y1=18.36% p.a.
• (1+0r2)2 = (1+0r1)(1+1r1) or 1.102=1.08(1+1r1) 1r1=12.04% p.a.
• One year forward PD=5.34% p.a. from:
(1+r) = (1- PD)(1+y) 1.1204=1.1836(1 – PD)
• Cumulative PD = 1 – [(1 - PD1)(1 – PD2)] = 1 – [(1-.05)(1-.0534)] = 10.07%
Saunders & Cornett, Financial Institutions Management, 4th ed.
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16%
14%
10%
8%
1 Yr. 2 Yr. Time to Maturity
SpotYield
Zero-CouponTreasury Bond
A Rated Zero-Coupon Bond
B Rated Zero-Coupon Bond
11.5%
13.69%
Figure 5.1 Yield curves.
Saunders & Cornett, Financial Institutions Management, 4th ed.
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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.
Saunders & Cornett, Financial Institutions Management, 4th ed.
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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.
Saunders & Cornett, Financial Institutions Management, 4th ed.
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KPMG’s 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 LGD=100% 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/[(1.08+CS)(1.1204+CS)] to get CS=5.8% p.a.
Saunders & Cornett, Financial Institutions Management, 4th ed.
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0 1 2 3
Time
4D
C
B
B RiskGrade
A
Figure 5.2 The multiperiod loan migrates overmany periods.
Saunders & Cornett, Financial Institutions Management, 4th ed.
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Period 1Period 0
Figure 5.3 Risky debt pricing.
Period 2
$100 A Rating
$100 B Rating
$85.43
$67.14$80.28
$0 Default
5%5%
0.34%
94%
94%
1%5.66%
94%
1%
Saunders & Cornett, Financial Institutions Management, 4th ed.
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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
Saunders & Cornett, Financial Institutions Management, 4th ed.
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Mortality Rate Derivation of Credit Risk Measures
The Insurance Approach:
Mortality Models and the CSFP Credit Risk Plus Model
Saunders & Cornett, Financial Institutions Management, 4th ed.
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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.
Saunders & Cornett, Financial Institutions Management, 4th ed.
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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 x…x 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
Saunders & Cornett, Financial Institutions Management, 4th ed.
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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 portfolio’s 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 +.
Saunders & Cornett, Financial Institutions Management, 4th ed.
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Default Rate
BBB Loan
Credit Risk Plus
CreditMetrics
Possible Path of Default Rate
Time Horizon
Default Rate
BBB Loan
Possible Pathof Default Rate D
BBB
AAA
Time Horizon
Figure 8.1Comparison of credit risk plusand CreditMetrics.
Saunders & Cornett, Financial Institutions Management, 4th ed.
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Frequencyof Defaults
Distribution ofDefault Losses
Severityof Losses
Figure 8.2 The CSFP credit risk plus model.
Saunders & Cornett, Financial Institutions Management, 4th ed.
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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.)
Saunders & Cornett, Financial Institutions Management, 4th ed.
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Probability
Model 1
ActualDistributionof Losses
Losses
Figure 8.3 Distribution of losses with defaultrate uncertainty and severity uncertainty.
Saunders & Cornett, Financial Institutions Management, 4th ed.
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Probability
ExpectedLoss
EconomicCapital
99thPercentileLoss Level
Loss0
Figure 8.4 Capital requirement under the CSFPcredit risk plus model.
Saunders & Cornett, Financial Institutions Management, 4th ed.
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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.
Saunders & Cornett, Financial Institutions Management, 4th ed.
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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.
Saunders & Cornett, Financial Institutions Management, 4th ed.
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Properties of Poisson Distribution
• Prob.(n defaults in $20,000 severity band) = (e-mmn)/n! Where: m=mean number of defaults. So: if m=3, 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.
Saunders & Cornett, Financial Institutions Management, 4th ed.
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.008
.05
.168
.224
Defaults
843210
Figure 8.5 Distribution of defaults: Band 1.
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Loss Probabilities for $20,000 Severity Band
Table 8.2 Calculation of the Probability of Default, Using the Poisson Distribution N Probability Cumulative Probability 0 0.049787 0.049789 1 0.149361 0.199148 2 0.224042 0.42319 3 0.224042 0.647232 . 7 0.021604 0.988095 8 0.008102 0.996197
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Economic Capital Calculations
• Expected losses in the $20,000 band are $60,000 (=3x$20,000)
• 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.
Saunders & Cornett, Financial Institutions Management, 4th ed.
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0
0.25
0.15
0.05
0.1
0.2
0
Amount of Loss in $
ExpectedLoss
EconomicCapital
UnexpectedLoss
350,000400,000250,000300,000160,000200,00060,000 100,000
Figure 8.6 Loss distribution for single loan portfolio —severity rate = $20,000 per $100,000 loan.
Saunders & Cornett, Financial Institutions Management, 4th ed.
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0
0.25
0.15
0.05
0.1
0.2
0
Amount of Loss in $
350,000400,000250,000300,000150,000200,00050,000 100,000
Figure 8.7 Single loan portfolio — severity rate = $40,000per $100,000 loan.
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Calculating the Loss Distribution of a Portfolio Consisting of 2 Bands:
$20,000 and $40,000 Loss Severity
Aggregate Portfolio (Loss on v = 1, Loss on v = 2) Loss ($) in $20,000 units Probability 0 (0,0) (.0497 x .0497) 20,000 (1,0) (.1493 x .0497) 40,000 [(2, 0) (0,1)] [(.224 x .0497) + (.0497 x.1493)] 60,000 [(3, 0) (1, 1)] [(.224 x .0497) + (.1493)2] 80,000 [(4, 0) (2,l) (0, 2)] [(.168 x.0497) + (.224 x.1493) + (.0497x.224)]
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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.
Saunders & Cornett, Financial Institutions Management, 4th ed.
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0
0.120
0.060
0.020
0.040
0.080
0.100
0.000
Amount of Loss in $
350,000400,000250,000300,000150,000200,00050,000 100,000
Figure 8.8 Loss distribution for two loan portfolios withseverity rates of $20,000 and $40,000.
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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 hold”process.
• 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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Return
The EfficientFrontier
A
B
C
Risk0
Figure 10.1 The paradox of credit.
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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:
p
fp rR
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Return (Rp)rf
A
BD
C
Risk (p)
Figure 10.2 The optimum risky loan portfolio
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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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KMV’s Portfolio Manager
• Returns for each loan I:– Rit = Spreadi + Feesi – (EDFi x LGDi) – rf
• Loan Risks=variability around EL=EGF 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 =
)1( EDFEDF
22)1( ii EDFiVOLLGDEDFiEDFi
222 )1()1( iii VVOLEDFiEDFiVVOLLGDEDFiEDFi
Saunders & Cornett, Financial Institutions Management, 4th ed.
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Correlations
• Figure 11.2 – joint PD is the shaded area.GF = GF/GF
GF =
• Correlations higher (lower) if isocircles are more elliptical (circular).
• If JDFGF = EDFGEDFF then correlation=0.
)1()1(
)(
FFGG
FGGF
EDFEDFEDFEDF
EDFEDFJDF
Saunders & Cornett, Financial Institutions Management, 4th ed.
74
Firm F
Firm G
Firm F’sDebt Payoff
100
100(1-LGD)
Market Valueof Assets - Firm G
Market Valueof Assets - Firm F
Face Value of Debt
Figure 11.2 Value correlation.