“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.
1
Why New Approaches to Credit
Risk Measurement and
Management?
Why Now?
Saunders & Cornett, Financial
Institutions Management, 4th ed.
2
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.
3
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.
4
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.
5
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.
6
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.
7
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.
8
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.
9
Traditional Approaches to Credit
Risk Measurement
20 years of modeling history
Saunders & Cornett, Financial
Institutions Management, 4th ed.
10
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
11
Institutions Management, 4th ed.
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.
12
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.
13
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.
14
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.
15
The Option Theoretic Model of
Credit Risk Measurement
Based on Merton (1974)
KMV Proprietary Model
Saunders & Cornett, Financial
Institutions Management, 4th ed.
16
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.
17
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
S=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, ) where
A=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.
18
Figure 4.1 The payoff to a bank lender
$ Payoff
0
A1
B
Saunders & Cornett, Financial
Institutions Management, 4th ed.
A2
Assets
19
Figure 4.2 The payoff to the w riter of a put option on a stock.
$ Payoff

0
X
Stock Price (S)

Saunders & Cornett, Financial
Institutions Management, 4th ed.
20
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.
21
Figure 4.3 Equity as a call option on a firm.
Value of
Equity (E)
($)
0
A1
B
A2
Value of
Assets (A)
L
Saunders & Cornett, Financial
Institutions Management, 4th ed.
22
Figure 4.4 Calculating the theoretical EDF
A
A $100m
A
B $80m
Default Region
t 0
t 1
Saunders & Cornett, Financial
Institutions Management, 4th ed.
Time (t)
23
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).
Saunders & Cornett, Financial
Institutions Management, 4th ed.
24
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%
Saunders & Cornett, Financial
Institutions Management, 4th ed.
25
KMV’s Empirical EDF
• Utilize database of historical defaults to
calculate empirical PD (called EDF):
Empirical EDF =
• Fig. 4.5
Empirical EDF
percent
=
at the beginning of the year
asset values of 2 from B
Total population of firms with
B at the beginning of the year
a year with asset values of 2 from
Number of firms that defaulted within
50 Defaults
Firm population of 1, 000
Saunders & Cornett, Financial
Institutions Management, 4th ed.
= 5
26
Figure 4.5 Empirical EDF and the distance to
default (DD): A hypothetical example.
Empirical
EDF
5%
Proprietery
Trade-Off
0
2
Saunders & Cornett, Financial
Institutions Management, 4th ed.
Distance
to Default
(DD )
27
Accuracy of KMV EDFs
Comparison 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%.
Saunders & Cornett, Financial
Institutions Management, 4th ed.
28
Figure 4.6 KMV expected default frequency
for Comdisco Inc.
Source:
TM
and agency rating
KMV.
KMV EDF Credit Measure
Agency Rating
20 CC
15
10 CCC
7
5
B
2
1.0
BB
.5
BBB
.20
.15
.10
.05
A
AA
.02 AAA
12/96 06/97 12/97 06/98 12/98 06/99 12/99 06/00 12/00 06/01
Figure 4.7 KMV expected default frequency
for USG Corp.
TM
and agency rating
Source: KMV.
KMV EDF Credit Measure
Agency Rating
20 CC
15
10 CCC
7
5
B
2
BB
1.0
.5
BBB
.20
.15
.10 A
.05
AA
.02 AAA
12/96 06/97 12/97 06/98 12/98 06/99 12/99 06/00 12/00 06/01
Saunders & Cornett, Financial
Institutions Management, 4th ed.
29
Monthly
EDF™ credit
measure
Agency Rating
Saunders & Cornett, Financial
Institutions Management, 4th ed.
30
Figure 4.8 KMV EDF Credit Measure vs.
agency ratings (1990-1999) for rated U.S. companies.
Source:
Kealhof er (2000).
100
90
80
70
60
50
40
30
EDF Power
20
S&P Company Power
S&P Implied Power
10
Moody s Implied Power
0
0
10
20
30
40
50
60
70
80
90
100
Percent of Population Excluded
Saunders & Cornett, Financial
Institutions Management, 4th ed.
31
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.
Saunders & Cornett, Financial
Institutions Management, 4th ed.
32
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.
33
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.
Saunders & Cornett, Financial
Institutions Management, 4th ed.
34
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.
35
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.
36
Figure 5.1 Yield curves.
Spot
Yield
16%
13.69%
14%
B Rated ZeroCoupon Bond
A Rated ZeroCoupon Bond
Zero-Coupon
Treasury Bond
10%
11.5%
8%
1 Yr.
2 Yr.
Saunders & Cornett, Financial
Institutions Management, 4th ed.
Time to Maturity
37
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.
38
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.
39
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.
40
Figure 5.2 The multiperiod loan migrates over
many periods.
A
B Risk
Grade
B
C
D
0
1
2
3
4
Time
Saunders & Cornett, Financial
Institutions Management, 4th ed.
41
Figure 5.3 Risky debt pricing.
Period 0
Period 1
$85.43
Period 2
94%
5.66%
1%
$67.14
94%
$80.28
$100 A Rating
1%
94%
$100 B Rating
0.34%
5%
5%
$0 Default
Saunders & Cornett, Financial
Institutions Management, 4th ed.
42
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
43
Institutions Management, 4th ed.
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.
44
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.
45
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.
46
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.
47
Figure 8.1 Comparison of credit risk plus
and CreditMetrics.
Credit Risk Plus
Default Rate
Possible Path of Default Rate
BBB Loan
Time Horizon
Default Rate
CreditMetrics
Possible Path
of Default Rate
BBB Loan
D
BBB
AAA
Time Horizon
Saunders & Cornett, Financial
Institutions Management, 4th ed.
48
Figure 8.2
The CSFP credit risk plus model.
Frequency
of Defaults
Severity
of Losses
Distribution of
Default Losses
Saunders & Cornett, Financial
Institutions Management, 4th ed.
49
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.
50
Figure 8.3 Distribution of losses w ith default
rate uncertainty and severity uncertainty.
Model 1
Probability
Actual
Distribution
of Losses
Losses
Saunders & Cornett, Financial
Institutions Management, 4th ed.
51
Figure 8.4 Capital requirement under the CSFP
credit risk plus model.
Expected
Loss
99th
Percentile
Loss Level
Probability
Economic
Capital
0
Loss
Saunders & Cornett, Financial
Institutions Management, 4th ed.
52
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.
53
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.
54
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.
55
Figure 8.5
Distribution of defaults: Band 1.
.224
.168
.05
.008
0
1
2
3
4
8
Defaults
Saunders & Cornett, Financial
Institutions Management, 4th ed.
56
Loss Probabilities for $20,000
Severity Band
Table 8.2 Calculation of the Probability of Default, Using the Poisson
Distribution
N
Probability
0
1
2
3
.
7
8
Probability
Cumulative
0.049787
0.149361
0.224042
0.224042
0.049789
0.199148
0.42319
0.647232
0.021604
0.008102
0.988095
0.996197
Saunders & Cornett, Financial
Institutions Management, 4th ed.
57
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.
58
Figure 8.6
Loss distribution for single loan portfolio
severity rate = $20,000 per $100,000 loan.
—
0.25
Expected
Loss
0.2
Unexpected
Loss
0.15
0.1
0.05
Economic
Capital
0
0
60,000 100,000 160,000 200,000 250,000 300,000 350,000 400,000
Amount of Loss in $
Saunders & Cornett, Financial
Institutions Management, 4th ed.
59
Figure 8.7
Single loan portfolio
per $100,000 loan.
—severity rate = $40,000
0.25
0.2
0.15
0.1
0.05
0
0
50,000 100,000 150,000 200,000 250,000 300,000 350,000 400,000
Amount of Loss in $
Saunders & Cornett, Financial
Institutions Management, 4th ed.
60
Calculating the Loss Distribution of a
Portfolio Consisting of 2 Bands:
$20,000 and $40,000 Loss Severity
Aggregate Portfolio
Loss ($)
0
20,000
40,000
60,000
80,000
(Loss on v = 1, Loss on v = 2)
in $20,000 units
Probability
(0,0)
(.0497 x .0497)
(1,0)
(.1493 x .0497)
[(2, 0) (0,1)]
[(.224 x .0497) + (.0497 x.1493)]
[(3, 0) (1, 1)]
[(.224 x .0497) + (.1493)2]
[(4, 0) (2,l) (0, 2)]
[(.168 x.0497) + (.224 x.1493) +
(.0497x.224)]
Saunders & Cornett, Financial
Institutions Management, 4th ed.
61
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.
62
Figure 8.8
Loss distribution for tw o loan portfolios w ith
severity rates of $20,000 and $40,000.
0.120
0.100
0.080
0.060
0.040
0.020
0.000
0
50,000 100,000 150,000 200,000 250,000 300,000 350,000 400,000
Amount of Loss in $
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Institutions Management, 4th ed.
63
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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Institutions Management, 4th ed.
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Loan Portfolio Selection and
Risk Measurement
Chapter 12
Saunders & Cornett, Financial
Institutions Management, 4th ed.
65
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.
Saunders & Cornett, Financial
Institutions Management, 4th ed.
66
Figure 10.1
The paradox of credit.
B
The Efficient
Frontier
Return
C
0
A
Risk
Saunders & Cornett, Financial
Institutions Management, 4th ed.
67
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
Saunders & Cornett, Financial
Institutions Management, 4th ed.
68
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:
r

R
p
f

p
Saunders & Cornett, Financial
Institutions Management, 4th ed.
69
Figure 10.2
The optimum risky loan portfolio
B
D
Return (Rp )
rf
A
C
Risk (p )
Saunders & Cornett, Financial
Institutions Management, 4th ed.
70
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
Saunders & Cornett, Financial
Institutions Management, 4th ed.
71
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 = EDF (1 EDF )
– LGD variable, but independent across borrowers: ULi =
EDFi(1  EDFi) LGDi2  EDFiVOL2i
– 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 =
EDFi(1  EDFi) LGDi2  EDFiVVOL2i  (1  EDFi)VVOL2i
Saunders & Cornett, Financial
Institutions Management, 4th ed.
72
Correlations
• Figure 11.2 – joint PD is the shaded area.
• GF = GF/GF
• GF =
JDFGF  ( EDFG EDFF )
EDFG (1  EDFG ) EDFF (1  EDFF )
• Correlations higher (lower) if isocircles are
more elliptical (circular).
• If JDFGF = EDFGEDFF then correlation=0.
Saunders & Cornett, Financial
Institutions Management, 4th ed.
73
Figure 11.2 Value correlation.
Market Value
of Assets - Firm G
Firm G
Market Value
of Assets - Firm F
Firm F
100(1-LGD)
Face Value of Debt
100
Firm F ’s
Debt Payoff
Saunders & Cornett, Financial
Institutions Management, 4th ed.
74