2. 11-2
Overview
This chapter discusses types of loans,
and the analysis and measurement of
credit risk on individual loans. This is
important for purposes of:
Pricing loans and bonds
Setting limits on credit risk exposure
3. 11-3
Credit Quality Problems
Problems with junk bonds, LDC loans, residential and
farm mortgage loans.
More recently, credit card and auto loans.
Default of one major borrower can have significant
impact on value and reputation of many FIs
Emphasizes importance of managing credit risk
4. 11-4
Credit Quality Problems
Over the early to mid 1990s, improvements in
NPLs for large banks and overall credit quality.
Late 1990s concern over growth in low quality
auto loans and credit cards, decline in quality
of lending standards.
Late 1990s and early 2000s: telecom
companies, tech companies, Argentina, Brazil,
Russia, South Korea
Mid 2000s, economic growth accompanied by
reduction in NPLs
New types of credit risk related to loan
guarantees and off-balance-sheet activities.
Increased emphasis on credit risk evaluation.
7. 11-7
Types of Loans:
C&I loans: secured and unsecured
Syndication
Spot loans, Loan commitments (Fixed
Rate/floating)
Decline in C&I loans originated by commercial
banks and growth in commercial paper
market.
RE loans: primarily mortgages
Fixed-rate, ARM (Interest Rate cycle)
Mortgages can be subject to default risk when
loan-to-value declines.
10. 11-10
Consumer loans
Individual (consumer) loans: personal, auto,
credit card.
Nonrevolving loans
Automobile, mobile home, personal loans
Growth in credit card debt
Visa, MasterCard
Proprietary cards such as Sears, AT&T
usury ceilings
Bankruptcy Reform Act of 2005
11. 11-11
Other loans
Other loans include:
Farm loans
Other banks
Nonbank FIs
Broker margin loans
Foreign banks and sovereign governments
State and local governments
12. 11-12
Return on a Loan:
Number of factors impact promised return FI achieve on
any given dollar lent:
1) Interest rate on the loan
2) Any fees relating to the loan (of)
3) The credit risk premium on the loan (m)
4) The collateral backing of the loan
5) Compensating balance (b) & reserve requirements
(RR)
13. 11-13
Return on a Loan:
Return = inflow/outflow
1+k = 1+{of + (BR + m )}/(1-[b(1-RR)])
Expected return: E(r) = p(1+k) - 1
where p equals probability of repayment
Note that realized and expected return
may not be equal.
14. 11-14
Return on a Loan:
The numerator is the promised gross cash inflow to
the FI per dollar lent, reflecting direct fees ( of ) plus
the loan interest rate ( BR + of ).
In the denominator, for every $1 the FI lends, it retains
b as noninterest- bearing compensating balances.
Thus, 1-b is the net proceeds of each $1 of loans
received by the borrower from the FI, ignoring reserve
requirements.
However, since b (the compensating balance) is held
by the borrower at the FI in a demand deposit account,
the Federal Reserve requires depository institutions to
hold non- (or low) interest-bearing reserves at the rate
RR against the compensating balance.
15. 11-15
Return on a Loan:
Thus, the FI’s net benefit from requiring compensating
balances must consider the cost of holding additional
reserve requirements.
The net outflow by the FI per $1 of loans is
1 - [ b (1 -RR )], or 1 minus the reserve adjusted
compensating balance requirement.
17. 11-17
Return on a Loan: Practice Q1
Calculate the promised return ( k ) on a loan if the base
rate is 13 percent, the risk premium is 2 percent, the
compensating balance requirement is 5 percent, fees are
½ percent, and reserve requirements are 10 percent.
(16.23%)
20. 11-20
The true cost is the
= loan rate ÷ (1 – compensating balance rate)
= 9% ÷ (1.0 – 0.1)
= 10 percent.
For compensating balance rates of 15 percent and 20
percent, the true cost of the loan would be 10.59
percent and 11.25 percent respectively.
Note that as the compensating balance rate increases
by a constant amount, the true cost of the loan
increases at an increasing rate.
24. 11-24
Expected Return on a loan
Expected return: E(r) = p(1+k) - 1
where p equals probability of repayment
To the extent that p is less than 1, default risk is
present. This means the FI manager must
1) set the risk premium sufficiently high to compensate
for this risk
2) recognize that setting high risk premiums as well as
high fees and base rates may actually reduce the
probability of repayment ( p )
25. 11-25
Lending Rates and Rationing
At retail: Usually a simple accept/reject
decision rather than adjustments to the
rate.
Credit rationing.
If accepted, customers sorted by loan
quantity not pricing
For mortgages, discrimination via loan to
value rather than adjusting rates
At wholesale:
Use both quantity and pricing adjustments.
27. 11-27
Measuring Credit Risk
Availability, quality and cost of information are critical
factors in credit risk assessment
Facilitated by technology and information
The availability of more information, along with the
lower average cost of collecting such information,
allows FIs to use more sophisticated and usually more
quantitative methods in assessing default probabilities
for large borrowers compared with small borrowers.
Also, bonds, like loans, include covenants restricting
or encouraging various actions to enhance the
probability of repayment. Covenants can include limits
on the type and amount of new debt, investments, and
asset sales the borrower may undertake while the loan
or bonds are outstanding.
28. 11-28
Measuring Credit Risk
Default Risk Models:
1) Qualitative Models
a) Borrower Specific Factors
b) Market Specific Factors
2) Quantitative Models
a) Credit Scoring Models
i. Linear Probability Models
ii. Logit Models
iii. Linear Discriminant Analysis
3) Newer Models of Credit Risk Measurement
29. 11-29
Measuring Credit Risk – Qualitative Models
Qualitative models: borrower specific
factors are considered as well as market
or systematic factors.
Borrower specific factors include:
reputation
leverage
volatility of earnings
collateral
Market specific factors include:
business cycle
interest rate levels.
30. 11-30
Measuring Credit Risk – Credit Scoring Models
Credit scoring models are quantitative models that use
observed borrower characteristics either to calculate a
score representing the applicant’s probability of
default or to sort borrowers into different default risk
classes.
This enables FI to:
1) Numerically establish which factors are important in
explaining default risk.
2) Evaluate the relative degree or importance of these
factors.
3) Improve the pricing of default risk.
4) Be better able to screen out bad loan applicants.
5) Be in a better position to calculate any reserves
needed to meet expected future loan losses.
31. 11-31
Measuring Credit Risk – Credit Scoring Models
Three types of Credit Scoring Models:
1) Linear Probability Models
2) Logit Models
3) Linear discriminant analysis
32. 11-32
Measuring Credit Risk – Credit Scoring Models
Linear Probability Models:
The linear probability model uses past data, such as
financial ratios, as inputs into a model to explain
repayment experience on old loans.
The relative importance of the factors used in
explaining past repayment performance then forecasts
repayment probabilities on new loans.
That is, factors explaining past repayment
performance can be used for assessing p, the
probability of repayment (a key input in setting the
credit premium on a loan or determining the amount to
be lent) and the probability of default (PD).
33. 11-33
Credit Scoring Models
Linear probability models:
Zi =
Statistically unsound since the Z’s obtained
are not probabilities at all.
*Since superior statistical techniques are
readily available, little justification for
employing linear probability models.
n
j
j
i
j X
1
, error
39. 11-39
Credit Scoring Models – Practice Q6
PD = 0.3(2.5) + 0.2(.25) - 0.05(.10)
= 0.795
The expected probability of repayment is 1 - 0.795 = 0.205.
40. 11-40
Credit Scoring Models – Logit Model
While linear probability model technique is
straightforward as long as current information on the X
ij is available for the borrower, its major weakness is
that the estimated probabilities of default can often lie
outside the interval 0 to 1.
The logit model overcomes this weakness by
restricting the estimated range of default probabilities
from the linear regression model to lie between 0 and
1.
41. 11-41
Credit Scoring Models – Linear Discriminant Models
While linear probability and logit models project a
value for the expected probability of default if a loan is
made, discriminant models divide borrowers into high
or low default risk classes contingent on their
observed characteristics ( X ij ).
Similar to linear probability models, linear discriminant
models use past data as inputs into a model to explain
repayment experience on old loans. The relative
importance of the factors used in explaining past
repayment performance then forecasts whether the
loan falls into the high or low default class.
42. 11-42
Altman’s Linear Discriminant Model:
Z = 1.2X1+ 1.4X2 +3.3X3 + 0.6X4 +1.0X5
Critical value of Z = 1.81.
X1 = Working capital/total assets.
X2 = Retained earnings/total assets.
X3 = EBIT/total assets.
X4 = Market value equity/ book value LT debt.
X5 = Sales/total assets.
43. 11-43
Altman’s Linear Discriminant Model:
The indicator variable Z is an overall measure of the
default risk classification of a commercial borrower.
This in turn depends on the values of various financial
ratios of the borrower ( X ij ) and the weighted
importance of these ratios based on the past observed
experience of defaulting versus non-defaulting
borrowers derived from a discriminant analysis model.
According to Altman’s credit scoring model, any firm
with a Z score of less than 1.81 should be considered a
high default risk firm; between 1.81 and 2.99, an in-
determinant default risk firm; and greater than 2.99, a
low default risk firm.
44. 11-44
Altman’s Linear Discriminant Model:
Example
Suppose that following are the financial ratios of
potential borrowing firm. Calculate z-score
46. 11-46
Linear Discriminant Model
Problems:
Only considers two extreme cases
(default/no default).
Weights need not be stationary over time.
Ignores hard to quantify factors including
business cycle effects.
Database of defaulted loans is not available
to benchmark the model.
54. 11-54
Term Structure derivation of credit risk
Because Treasury strips and zero-coupon corporate
bonds are single-payment discount bonds, it is
possible to extract required credit risk premiums and
implied probabilities of default from actual market data
on interest rates.
That is, the spreads between risk-free discount bonds
issued by the Treasury and discount bonds issued by
corporate borrowers of differing quality reflect
perceived credit risk exposures of corporate
borrowers for single payments at different times in the
future.
FIs can use these credit risk probabilities on existing
debt to decide whether or not to issue additional debt
to a particular credit risk borrower.
55. 11-55
Term Structure derivation of credit risk – One year case
Assume that the FI requires an expected return on a
one-year (zero-coupon) corporate debt security equal
to at least the risk-free return on one-year (zero-
coupon) Treasury strips.
Let p be the probability that the corporate debt will be
repaid in full; therefore, (1-p) is the probability of
default.
If the borrower defaults, the FI is assumed to get
nothing (i.e., the recovery rate is zero or the loss given
default is 100 percent).
56. 11-56
Term Structure derivation of credit risk – One year case
By denoting the contractually promised return on the
one-year corporate debt strip as 1+k and on the credit
risk–free one-year Treasury strip as 1 + i, the FI
manager would just be indifferent between corporate
and Treasury securities when:
p(1 + k) = 1 + i
60. 11-60
Term Structure derivation of credit risk – One year case
Practice Q9
One year AA Rated Zero coupon bond:
P = (1 + 0.06) / (1 + 0.095)
= 0.968
Market Risk Premium = 0.095 – 0.06
= 0.035 or 3.5 %
61. 11-61
Term Structure derivation of credit risk – One year case
Practice Q9
One year BB Rated Zero coupon bond:
P = (1 + 0.06) / (1 + 0.135)
= 0.9339
Market Risk Premum = 0.135 – 0.06
= 0.075 or 7.5%
62. 11-62
Term Structure derivation of credit risk – One year case
Recovery rate is not equal to zero
Then FI manager will be indifferent between Corporate
& treasury security when:
Expected Return on Corporate = Expected return on
Treasury
When,
Expected Return on Corporate loan
= (1-P)(Return in case of default) + (p*(1+k)) - 1
= (1-P)(Recovery rate*(1+k)) + (p*(1+k)) - 1
64. 11-64
Term structure derivation of credit risk –
Practice Q10
Expected Return on loan
= (1-P)(Recovery rate*(1+k)) + (p*(1+k)) - 1
= [(0.05)(0.5)(1.10)] + [(0.95*(1.1)] - 1
= 0.0275 + 1.045 - 1
= 7.25%
65. 11-65
Term Structure derivation of credit risk – One year case
Recovery rate is not equal to zero
Then FI manager will be indifferent between Corporate
& treasury security when:
Expected Return on Corporate = Expected return on
Treasury
Credit Risk Premium (k – i)
66. 11-66
Term Structure derivation of credit risk – One year case
Recovery rate is not equal to zero (Example)
I = 5.05%, p = 0.948, recovery rate = 0.9, Solve for credit
risk premium
67. 11-67
Term Structure derivation of credit risk – One year case
Recovery rate is not equal to zero (Example)
I = 5.05%, p = 0.948, recovery rate = 0.9, Solve for credit
risk premium
K – i
= [(1 + 0.0505) / (0.9 + 0.948 – (0.948*0.9))] – (1.0505)
= 1.05599 – 1.0505
= 0.55%
70. 11-70
Term Structure derivation of credit risk – Practice Q12
percent
or
k
i
p 47
.
94
9447
.
0
5
.
0
1
5
.
0
085
.
1
055
.
1
1
1
1
71. 11-71
Term Structure derivation of credit risk – Practice Q12
percent
or
k
i
p 00
.
50
5000
.
0
9447
.
0
1
9447
.
0
085
.
1
055
.
1
1
1
1
72. 11-72
Term Structure Based Methods – Multi
Period Case
Marginal Probability of default
Probability that a borrower will default in
any given year
Cumulative probability of default
Probability that a borrower will default over
a specified multi year period
74. 11-74
Term structure based methods -
Example
P1 = 0.95
P2 = 0.93
CP = 1 – [(0.95)(0.93)]
= 0.1165
There is 11.65% probability of default over
two years.
87. 11-87
Term structure based methods –
Practice Q14
One year forward rate on the treasuries:
f1 = [(1.055)^2 / (1.0465)] – 1
= 6.509%
One year forward corporate bond rate:
C1 = [(1.1025)^2/(1.085)] – 1
= 12.02%
88. 11-88
Term structure based methods –
Practice Q14
Marginal Probability of repayment in year 1:
P1 = [(1.0465) / (1.085)]
= 0.9645
Marginal Probability of repayment in year 2:
P2 = [(1.065)/(1.12)]
= 0.9508
91. 11-91
Term structure based methods –
Practice Q15
One year forward rate on the treasuries:
f1 = [(1.061)^2 / (1.05)] – 1
= 7.21%
One year forward corporate bond rate:
C1 = [(1.082)^2/(1.07)] – 1
= 9.41%
92. 11-92
Term structure based methods –
Practice Q15
Two year forward rate on the treasuries:
f2 = [(1.07)^3/ (1.061)^2] – 1
= 8.82%
Two year forward corporate bond rate:
C2 = [(1.093)^3/(1.082)^2] – 1
= 11.53%
93. 11-93
Term structure based methods –
Practice Q15
Marginal Probability of repayment in year 1:
P1 = [(1.05) / (1.07)]
= 0.9813
Marginal Probability of repayment in year 2:
P2 = [(1.0721)/(1.0941)]
= 0.9799
Marginal Probability pf repayment in year 3:
P3 = [1.0882/1.1153]
= 0.9757
94. 11-94
Term structure based methods –
Practice Q15
CP2 = 1 – (0.9813)(0.9799)
= 0.0384 Or 3.84%
CP3 = 1 – (0.9813)(0.9799)(0.9757)
= 0.0617 Or 6.17%
95. 11-95
Mortality Rate Derivation of credit Risk
Rather than extracting expected default rates from the
current term structure of interest rates, the FI manager
may analyze the historic or past default risk
experience, the mortality rates , of bonds and loans of
a similar quality.
Consider calculating p1 and p2 using the mortality rate
model.
Here, p1 is the probability of a grade B bond or loan
surviving the first year of its issue; thus 1- p1 is the
marginal mortality rate , or the probability of the bond
or loan defaulting in the first year of issue.
96. 11-96
Mortality Rate Derivation of credit Risk
While p2 is the probability of the loan surviving in the
second year given that default has not occurred during
the first year, 1 - p 2 is the marginal mortality rate for
the second year.
Thus, for each grade of corporate borrower quality, a
marginal mortality rate (MMR) curve can show the
historical default rate experience of bonds in any
specific quality class in each year after issue on the
bond or loan.
97. 11-97
Mortality Rate Models
Similar to the process employed by
insurance companies to price policies. The
probability of default is estimated from past
data on defaults.
Marginal Mortality Rates:
101. 11-101
RAROC Models
The essential idea behind RAROC is that rather than
evaluating the actual or contractually promised annual
ROA on a loan, the lending officer balances expected
interest and fee income less the cost of funds against
the loan’s expected risk.
A loan is approved only if RAROC is sufficiently high
relative to a benchmark return on capital (ROE) for the
FI, where ROE measures the return stockholders
require on their equity investment in the FI.
The idea here is that a loan should be made only if the
risk-adjusted return on the loan adds to the FI’s equity
value as measured by the ROE required by the FI’s
stockholders.
102. 11-102
RAROC Models
Risk adjusted return on capital. This is one
of the most widely used models.
RAROC =
(one year net income on loan)/(loan risk)
Loan risk estimated from loan default rates,
or using duration.
103. 11-103
RAROC Models
One year Net income on loan:
= (Spread + fees) * dollar value of the loan outstanding
108. 11-108
RAROC Models – Practice Q18
Capital at risk:
DLN = -DLN x LN x (DR/(1+R))
= - 4.3 * 5,000,000 * (0.012/1.08)
= -238,889
Net Income = ??
109. 11-109
RAROC Models – Practice Q18
Capital at risk:
DLN = -DLN x LN x (DR/(1+R))
= - 4.3 * 5,000,000 * (0.012/1.08)
= -238,889
Net Income = (0.003+0.0025) * 5,000,000
= 27,500
RAROC = ??
110. 11-110
RAROC Models – Practice Q18
Capital at risk:
DLN = -DLN x LN x (DR/(1+R))
= - 4.3 * 5,000,000 * (0.012/1.08)
= -238,889
Net Income = (0.003+0.0025) * 5,000,000
= 27,500
RAROC = 27,500 / 238,889
= 11.51%
112. 11-112
RAROC Models – Practice Q19
Capital at risk:
DLN = -DLN x LN x (DR/(1+R))
= - 7.5 * 5,000,000 * (0.042/1.12)
= -1,406,250
Net Income = (0.005+0.02) * 5,000,000
= 125,000
RAROC = 125000 / 1406250
= 8.89%
113. 11-113
RAROC Models – Practice Q19
0.10 = 125000 / Capital at Risk
Capital at Risk = 125000/0.10
= 1,250,000
Capital at risk:
DLN = -DLN x LN x (DR/(1+R))
1,250,000 = - Duration * 5,000,000 * (0.042/1.12)
Duration = 1250,000/(5000,000 * 0.0375)
= 6.67 years
114. 11-114
RAROC Models – Practice Q19
0.10 = Net income on loan / 1406,250
Net income on loan = 0.10 * 1,406,250
= 140,625
Additional Income = 140,625 – 125,000
= 15,625
115. 11-115
RAROC Models – Practice Q19
Net income on loan = 0.10 * 1,406,250
= 140,625
140,625 = (0.005 + Spread) * 5,000,000
Spread = (140,625/5,000,000) – 0.005
= 2.31%
Loan Rate must be increased to 12.31% from 12% to
make the loan acceptable.
