Credit Scores and Loan Portfolio Risk in Small Banks ∗
One of the major tasks for banks is to capture changes of their portfolio loan risk. Current
and past subprime crises and corresponding effect in the mortgage market accentuate the need
for measuring banks portfolio credit risk. Even though most large banks have their own models
to measure the risk of their loan portfolios, small and community banks do not have the
resources to measure the riskiness of their loan portfolios. This paper proposes a simple model
by using credit scores to measure the loan portfolio of small and community banks. It uses the
credit scores stored in the bank lending portfolio to measure and compare the bank loan portfolio
condition. The proposed model is tested by using credit scores of two branches of a commercial
bank. Discriminate analysis is applied to the credit scores to find out the risk differences of the
bank between the regions. The results capture the differences in the riskiness of two regions of a
Keywords: credit scores, loan portfolios, small banks, financial risk, charge-offs,
Don’t quote without the permission of the author.
The main goal of the paper is to use credit scores to test the proposed model of predicting
loan portfolio risk of two or more banks or branches of a bank in a given region. This model can
also be used to measure the loan portfolio credit risk of a bank by measuring the risk at two
different periods and test if the portfolio risk stays the same, increases or decreases over time.
Even though most large banks have their own risk models to measure their loan portfolio
riskiness, most medium, small, and community banks do not have the resources to have financial
risk management department to compare the risk of the branches of the bank.
Credit scoring systems can be found in virtually all types of credit analysis from
mortgages, consumer credit, to commercial loans. The current crisis of the subprime mortgages
emphasis the need to have simple models capable of capturing the financial institution
population risk. The idea is to find and pre-identify certain factors that determine the probability
of default for a given loan or credit by using quantitative scores. In some cases, the score can be
interpreted as a probability of default. The score may also be used to classify or quantify the
potential of default or to group a borrower into a “good” or “bad” category.
Credit scoring systems are also known as behavioral scoring in which the score tries to
predict behavioral trends in the customers. Credit scoring applies logic to behavioral results and
provides warning reports to portfolio management personnel on credits possessing undesirable
behavioral attributes deemed to be associated with greater potential loss. Attributes of credit
scoring systems may include, but not limited to, updates of loan accounting system information,
updates of loan deposit information, and information from personal and/or business credit bureau
files. With a credit scoring system, accounts can be queued to portfolio management personnel
for risk grade establishment and exposure assessment.
While credit scoring is used within mortgages and the small business lending industry, it
is still a relatively new process. Due to the emergence of mortgages and small business credit
scoring, the question of how to conduct a scorecard validation has become a concern for many
lenders. The need to forecast credit losses in the lender’s lending portfolio has become crucial for
the economy as a whole. There is a significant risk of error inherent in any credit loss forecast
due to its vulnerability to shifts in the industry, population, and the economy. The need to have a
robust loss forecasting model requires a sufficient number of delinquent and charges off accounts
to establish a relatively precise relationship between predictive account behavior characteristics
and account charge-offs.
This paper proposes a model for measuring bank portfolio loan risk and applies a
forecasting technique, descriminant analysis, to measure current risk exposure in the loan
portfolio risk and intends to capture the trend of potential charge-off risks for next periods. This
paper proposes using the credit score obtained by the financial institution when they provide
mortgages and loans to their clients. Most financial institutions, even small ones, will possess a
large number of credit scores accounts from their mortgage and lending portfolios.
LITERATURE REVIEW OF CREDIT SCORES AND SUBPRIMES
The most common measure of loan riskiness is the so called credit score, which can be
traced back to the beginnings of subprime rate loans. According to Mester (1997), a credit score
“is a method of evaluating the credit risk of loan applications.” 1 Mester shows that 97 percent of
the responding banks that used credit scoring lending operations use it in the credit card
applications. Avery (1996) explains it by saying, “Most credit scoring systems that are widely
used have adopted a scale with a range of scores between 300 and 900, with higher scores
corresponding to lower credit risk.” 2 Souphala and Pennington-Cross (1996) asserts, “Subprime
lending is a relatively new and rapidly growing segment of the mortgage market that expands the
pool of credit to borrowers who, for a variety of reasons, would otherwise be denied credit.” 3
They conclude that since the early nineties, many subprime loans have lowered their risk
exposure by limiting high risk loans and requiring a prepayment penalty to low credit score
clients who receive a loan. Kwan (2001) found the average annual growth rate of subprime
Mester, L. (1997) What’s the point of Credit Scoring? The Federal Reserve Bank of Philadelphia.
Avery, Robert; Bostic, Raphael; Calem, Paul; Canner, Glenn (1996) Credit Risk, Credit Scoring, and the
Performance of Home Mortgages. Federal Reserve Bulletin
Chomsisengphet, Souphala and Pennington-Cross, Anthony. (1996) The Evolution of the Subprime Mortgage
Market. Federal Reserve Bank of St. Louis Review, January/February 2006, 88(1), pp. 31-56.
mortgages was 26 percent. 4 Kwan concludes that subprime loans can affect credit values and the
loans that are tied in with them.
The issue here is not the subprime loans themselves, but the delinquency rate that comes
with many typical subprime loans. The study by the Joint Economic Committee (2007) explains
exactly why so many loans become delinquent. 5 They found that if loan institutions do not lower
the rate at which they give subprime loans out, then if the economy has a slump in the housing
market, then it could affect the economy badly as a whole. “In the current market, resets have
caused payments to rise by at least 30 percent, to an amount that borrowers can no longer afford.
As a result, the delinquency and foreclosure rates for subprime adjustable rates mortgages have
been sharply rising.” 6 The New York Times stated, “That was the highest rate since the group
started tracking prime and subprime mortgages separately in 1998. The delinquency and
foreclosure rate for all mortgages, 7.3 percent, is higher than at any time since the group started
tracking that data in 1979, largely as a result of the surge in subprime lending during the last few
years.” 7 Avery, Bostic, Calem, and Canner (1996) 8 examine the performance of home
mortgages and how it affected credit scoring, as well as how it becomes approved. Credit
scoring, as expressed in the paper, is based on credit history and other pertinent data which then
dictates the distribution and performance of the loans. 9 It is clear that if a person cannot commit
to pay back their loans, the lending organizations must draw a conclusion about the likelihood of
Data taken is nine years from Merrill Lynch and Fannie Mae
This study used data from years past to compare the subprime rate of delinquency to the prime rate of delinquency.
Maloney, Carolyn B. and Schumer, Charles E. 2007. The Subprime Lending Crisis: The Economic Impact on
Wealth, Property and Values and Tax Revenues, and How We Got Here. Recommendations by the Majority Staff of
the Joint Economic Committee. October, 2007.
Bajaj, Vikas and Story, Louise. Mortgage Crisis Spreads Past Subprime Loans. The New York Times. February
Robert Avery, Raphael Bostic, Paul Calem, and Glenn Canner., “Credit Risk, Credit Scoring, and the Performance
of Home Mortgages”, Federal Reserve Bulletin: July 1996. P. 621-648.
The data used was mostly from individual credit scores from a bank which was used to estimate the weights and
figures. The paper asserts that Banks should measure credit risk by gathering information about the potential
borrowers and analyzing their credit history
default for the borrower. Chatterjee, Corbae, and Rull (Jan. 2005)10 found that people with
higher credit scores are, if fact, less likely to default on their loans than those with low scores.
Walters and Hermanson (2001) 11 found that over 75 percent of all home mortgage loan decisions
made by lenders used credit scoring to determine the likelihood of a consumer to repay on their
mortgage loan as agreed. 12
Let Yt-1 be the principal amount in dollars lent to an applicant at t-1. Let APt be the amount in
dollars paid out to the principal at time t. Then, in case of default, the charge-off amount, COt at
time t, is given by:
COt = Yt-1 – APt (1)
Where, Yt-1 = Σ yi = sum of future payments.
The individual risk of a given account to charge-off is estimated by the credit score of the
St-1 = p(COt) (2)
Where St-1 is the risk measure or credit score that the loan application received when it was
accepted by the lender and p(COt) measures the probability of a charge-off at time t. The
probability of charge-off is determined by several predictable variables that in turn provides a
credit score. Notice that the credit score for a loan was given at St-1 at the same time the loan was
approved, i.e. Yt-1.
The risk of individual loan application is measured through credit scoring. Every loan
application get a score Sk, at the time the borrower submit his/her application, that is at time t-1.
Sk measures or indicates the risk of the loan application.
Sk,t-1 = αk,t-1( Zk,t-1, Xk,t-1, Uk,t-1, Vk,t-1, …)
Satyajit Chatterjee, Dean Corbae, Jos´e-V´ıctor R´ıos-Rull., “Credit Scoring and Competitive Pricing of Default
Risk”, Federal Reserve Bank of Philadelphia: Dec. 2005. p. 112
Hermanson, Sharon and Walters, Neal. “Credit Scores and Mortgage Lending.” Public Policy Institute Aug 2001:
IB Number 52.
A recent industry study indicates consumers with low credit scores are more likely to have been delinquent in
their mortgage payments.
Where, Zk, Xk, Uk, Vk, represents predictive variables such as maximum potential exposure
(MPE), expected revenues, personal bureau credit risk, commercial bureau credit risk, and so on.
The individual loan applicant is going to be accepted or declined depending on his/her
position with respect to a cut-off value, Sco. A low value of Sk, implies the probability of charge-
off is high. If Sk is lower than Sco, the loan is expected to be rejected. A high value of Sk, implies
the probability of charge-off is low. If Sk is greater than Sco, the loan is expected to be accepted.
Loan applications that have a score below Sco have a higher probability to become delinquent and
We are assuming that the credit score for each individual application is the same for the
duration of the loan.
St-1 = St = St+1 = St+2 = St+3 … (3)
This implies that the credit scoring is done once. So, even if the account becomes
delinquent or charged-off, the score given when the loan application was approved will remain
the same throughout the life of the account.
The probability that a borrower is going to payback or not the whole amount is given by
PBt such that:
PBt = α Yt-1 + (1- α) COt (4)
If we concentrate only in the charge off side of equation (4), then we can get that
(1- α) COt or COt = αCOt,
So the probability of charge-off for an individual account can be shown as:
COt = αCOt + εt (5)
Where εt provides the unexpected loan risk of the charge-off that could not be known to the
lender when the loan was approved. This error term also measures hidden information not given
by the borrower when the loan was processed. If the lender would have known the information
contained on εt, the credit score given to that application would have been lower than the cut-off
value, which in turn would have rejected the loan application.
If we assume that the bank has N accounts, then the portfolio charge-off can be obtained
PCOt = α1CO1 + α2CO2 + α3CO3 + α4CO4 + α5CO5 + …+ αNCON + vt (6)
Where, PCOt = is the charge-offs at time t for the entire portfolio of the bank
i = 1 … N, is the number of individual charge-offs in a given period t.
Σαi = 1
In the case that Σαi = 1, the total sum of the charge off will be equal to the total payment of the
loan or principal.
The error term, vt, provides the unexpected market loan risk of the charge-off for the bank
portfolio. This error term also measures the market hidden information not given by the
borrowers or any other market risk which information was not available when the loans were
Since the probability of charge-offs are measured by the credit score that each loan
application receives which in turn measures the risk for each borrower, we can estimate the risk
of the entire bank portfolio by using the individual credit score assigned to each loan. Using the
estimates for αs, we can then find the weights that can be assigned to the risks found in previous
periods. We can then forecast the next period risk level by using the previous average weighted
risk levels using the following equation:
St+1 = ά1 S1 + ά2S2 + ά3S3 + … άn Sn + έt (7)
St = ΣSj / Ns , (8)
Where j = 1 … Ns, is the number of individual scores in a given period t and άts are
The term ΣNi co = ΣNj s, indicates that all charge-offs are scored.
Notice that to equation (7), an interest rate spread, rt, can be added to measure the
market expectation for the next period such that:
rt = rt - rt-1. (10)
In order to capture the immediate effect on the market, a short-term rate, rt, may be used
such as money market rates or ninety day treasury bill. If rt increases, it will imply that the
market risk has increased, increasing the expected score for St+1.
The estimate error term, έt, provides the information of the charge-off accounts for which
the scores did not capture the risk involved on the underlying accounts.
Data and Methodology
Actual data from individual credit scores from two branches from a commercial bank are
used to estimate the coefficients of the model. These branches are located in two nearby cities of
a southern state.
Discriminant analysis is used to test this model. Discriminant analysis is a statistical
method that is used by researchers to help them understand the relationship between a dependent
variable and one or more independent variables, in our case, credit scores.
In general, in the two group case we fit a linear equation of the type:
Group (D) = a + b1*x1 + b2*x2 +…+ bm*xm
Where: a is a constant, and b1 through bm are regression coefficients.
D = discriminant function score,
B, = discriminant function coefficient relating independent (credit scores) variables i to the
discriminant function score,
X = value of independent variable i, (credit scores).
The discriminant function is treated as a standardized variable, so it has a mean of zero
and a standard deviation of one. The magnitudes of the coefficients tell us about the relative
contributions of the credit scores to the dependent variable. The closer the value of credit scores
coefficients is to zero, the weaker it is as a predictor of the dependent variable. On the other
hand, the closer the value of credit scores coefficient is to either 1.0 or -1.0, the stronger it is as a
predictor of the dependent variable.
Again, the main goal of the paper is to use credit scores to test the proposed model of
predicting loan portfolio risk of two or more banks or branches of a bank in a given region. This
model can also be used to measure the loan portfolio credit risk of a bank by measuring the risk
at two different periods and test if the portfolio risk stays the same, increases or decreases over
time. In this paper, we will name two banks which we call them; Northern Bank and Southern
Testing the Model -Results
The Northern Bank’s approved amount for each loan is determined by the client’s credit
score. In order words, the higher the credit score of the client, the higher approved amount of a
loan that the client may receive. When we run the discriminant multivariate function, we use the
credit scores as the predictor for the Approved Amount. First, we classify the credit scores from
individual clients into groups of approved loan amounts from $1,000 to $500,000. Table-1 shows
how we classified the Approval Amount into five groups.
Table-1 –Grouping “Approval Amount” Value for Northern and Southern Bank
Group Approval Amount
1 $1,000 - $10,000
2 $10,000 - $20,000
3 $20,000 - $30,000
4 $30,000 - $50,000
5 $50,000 - $500,000
For the Northern Bank, the discriminant results found that there are 43 loans out of 195
loans that have the right approved amount given to the right credit scores. The Total Proportion
Correct equals 0.221 (43/195 = 0.221), which means that there is a 22.1% chance that the
Northern Bank would correctly assign an approved amount of loans to the right credit score
(77.9% of chance that this bank would incorrectly approve certain amount of loans to the
inappropriate credit score).
The discriminant summary report (see Appendix, Table A-2) also shows that the
regression coefficients of the credit scores of the multiple discriminant analysis equal Group (1)
= 0.0782, Group (2) = 0.0792, Group (3) = 0.0822, Group (4) = 0.0820, Group (5) = 0.0765.
Therefore, we apply the model proposed (see equation 9) to forecast the bank loan portfolio
credit risk (measure the risk level) based on a discriminant function of the form:
S (t+1) = 0.0782*X1 + 0.0792*X2 + 0.0822*X3 + 0.0820*X4 + 0.0765*X5 (13)
The groups with the largest linear discriminant function, or regression coefficients,
contribute most to the classification of observations. For this data, Group (3) has the highest
linear discriminant function (0.0822), indicating that Group (3) contributes more than Group 1,
2, 3, or 4 to the classification of group membership.
For the Southern Bank, the discriminant results show that there are 34 loans out of 129
loans that have the right approved amount given to the right credit scores. The Total Proportion
Correct equal 0.264 (43/195 = 0.264) means there is a 26.4% chance that the Southern Bank
would correctly make approved amount of loans to the right credit score (73.6% chance that this
bank would incorrectly approved certain amount of loans to the inappropriate credit score).
It is found that the regression coefficients of the credit scores of the multiple discriminant
analysis are Group (1) = 0.0062, Group (2) = 0.0069, Group (3) = 0.0071, Group (4) = 0.0069,
Group (5) = 0.0100. Therefore, we again apply the model proposed (see equation 9) to forecast
the bank loan portfolio credit risk (measure the risk level) based on a discriminant function of the
S (t+1) = 0.0062*X1 + 0.0069*X2 + 0.0071*X3 + 0.0069*X4 + 0.0100*X5 (14)
The groups with the largest linear discriminant function, or regression coefficients,
contribute most to the classification of observations. For this data, Group (5) has the highest
linear discriminant function (0.01), indicating that group 5 contributes more than Group 1, 2, 3,
or 4 to the classification of group membership.
When comparing the proportion correct between the Northern Bank and the Southern
Bank, we can see that the Southern Bank has higher a proportion correct than Northern Bank.
However, this does not mean that Southern Bank is less risky than the Northern Bank, because
Southern Bank approved fewer loans than the Northern Bank (195 loans of Northern compare
with 129 loans of Southern). Also, the range of the amount of loans approved of Southern Bank
is smaller than the Northern Bank (Northern Bank’s amount ranged from $1850 - $500,000,
while Southern Bank’s amount only ranged from $3,000 to $300,000). To find out which bank
has higher risk, we must compare the credit score between them using the Discriminant function
that we have constructed above (1) (2). The bank that has higher credit score is likely to match
more correct loans to the right credit scores less risky than the bank that has lower credit score.
Group 1 Group2 Group 3 Group 4 Group 5
(X1) (X2) (X3) (X4) (X5)
Group Average 208 215.5 223.76 223.03 208.2
S (t+1) = 0.0782*X1 + 0.0792*X2 + 0.0822*X3 + 0.0820*X4 + 0.0765*X5
=0.0782*(208) + 0.0792*(215.5) + 0.0822*(223.76) + 0.0820*(223.03) + 0.0765*(208.2)
This value represents the northern bank loan portfolio credit score measurement.
Group 1 Group 2 Group 3 Group 4 Group 5
(X1) (X2) (X3) (X4) (X5)
Group Average 201.09 224.56 230.55 223.36 325.14
S (t+1) = 0.0062*X1 + 0.0069*X2 + 0.0071*X3 + 0.0069*X4 + 0.0100*X5
=0.0062*(201.09) + 0.0069*(224.56) + 0.0071*(230.55) + 0.0069*(223.36) +
This value represents the Southern bank loan portfolio credit score measurement.
When we compare both loan portfolio credit scores, we find out that the loan portfolio
credit score of Northern Region = 85.94, is greater than the loan portfolio credit score of
Southeast Region = 9.23. These results indicate that the Southern bank loan portfolio is riskier
than the Northern bank loan portfolio.
Some applications of this model is to compare the riskiness several banks in a given
region or region. This will provide a score measurement of the population risk of the banks. A
given bank also can apply this model to different periods to find out if their loan portfolio risk
has changed over time. Finally, a given central bank district can get sufficient credit score data to
create a cut-off credit score value to find out what regions are lower or higher of this value and
estimate possible changes in risk in the region.
This paper proposes a simple test to measure and compare the risk of two banks, using
discriminant analysis; this paper evaluated the regression coefficients and the probability of
correct group classification. We used data from two branches which we call: Northern and
Southern Bank to forecast the credit score and evaluate the risk level. The Northern and Southern
Bank estimate the risk of the entire bank portfolio by using the credit score assigned to the loan.
If the Credit Score is low, that means the bank has higher risk and vice-versa. After evaluating
the value of the Credit Score for each bank, we multiplied each group average with its
coefficient, resulting in the credit score for Northern bank equal to 85.94 which is greater than
the credit score of the Southeast ban which is 9.23. The low credit score shows that Southeast
Region Bank has lent more money for clients with bad credit (or loaned less money to clients
with good credit) than the Northern Region Bank. Therefore, we can conclude that the Southern
Bank has a higher risk of making bad loans to the clients than the Northern Bank.
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