12 Chapter - Credit Risk: Loan Portfolio and Concentration Risk
Chapter Twelve
Credit Risk: Loan Portfolio and Concentration Risk
Chapter Outline
Introduction
Simple Models of Loan Concentration Risk
Loan Portfolio Diversification and Modern Portfolio Theory
Moodys KMV Portfolio Manager Model
Partial Applications of Portfolio Theory
Regulatory Models
Summary
Appendix 12A: CreditMetrics
Appendix 12B: CreditRisk+
12-1
Chapter 12 - Credit Risk: Loan Portfolio and Concentration Risk
Solutions for End-of-Chapter Questions and Problems
1.
How do loan portfolio risks differ from individual loan risks?
Loan portfolio risks refer to the risks of a portfolio of loans as opposed to the risks of a single
loan. Inherent in the distinction is the elimination of some of the borrower-specific risks of
individual loans because of benefits from diversification.
2. What is migration analysis? How do FIs use it to measure credit risk concentration? What are
its shortcomings?
Migration analysis uses information from the market to determine the credit risk of an individual
loan or sectoral loans. With this method, FI managers track credit ratings, such as S&P and
Moodys ratings, of firms in particular sectors or ratings classes for unusual declines to
determine whether firms in a particular sector are experiencing repayment problems. This
information can be used to either curtail lending in that sector or to reduce maturity and/or
increase interest rates. A problem with migration analysis is that the information may be too late,
because ratings agencies usually downgrade issues only after the firm or industry has
experienced a downturn.
3. What does loan concentration risk mean?
Loan concentration risk refers to the extra risk borne by having too many loans concentrated
with one firm, industry, or economic sector. To the extent that a portfolio of loans represents
loans made to a diverse cross section of the economy, concentration risk is minimized.
4. A manager decides not to lend to any firm in sectors that generate losses in excess of 5
percent of capital.
a. If the average historical losses in the automobile sector total 8 percent, what is the
maximum loan a manager can lend to firms in this sector as a percentage of total
capital?
Concentration limit = (Maximum loss as a percent of capital) x (1/Loss rate) = .05 x 1/0.08
= 62.5 percent of capital is the maximum amount that can be lent to firms in the automobile
sector.
b. If the average historical losses in the mining sector total 15 percent, what is the
maximum loan a manager can lend to firms in this sector as a percentage of total
capital?
Concentration limit = (Maximum loss as a percent of capital) x (1/Loss rate) = .05 x
1/0.15= 33.3 percent of capital is the maximum amount that can be lent to firms in the
mining sector.
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Chapter 12 - Credit Risk: Loan Portfolio and Concentration Risk
5.
An FI has set a maximum loss of 2 percent of total capital as a basis for setting
concentration limits on loans to individual firms. If it has set a concentration limit of 25
percent to a firm, what is the expected loss rate for that firm?
Concentration limit = (Maximum loss as a percent of capital) x (1/Loss rate)25 percent = 2
percent x 1/Loss rate Loss rate = 0.02/0.25 = 8 percent
6.
Explain how modern portfolio theory can be applied to lower the credit risk of an FIs
portfolio.
The fundamental lesson of modern portfolio theory is that, to the extent that an FI manager holds
widely traded loans and bonds as assets or can calculate loan or bond returns, portfolio
diversification models can be used to measure and control the FIs aggregate credit risk
exposure. By taking advantage of its size, an FI can diversify considerable amounts of credit risk
as long as the returns on different assets are imperfectly correlated with respect to their default
risk adjusted returns. By fully exploiting diversification potential with bonds or loans whose
returns are negatively correlated or that have a low positive correlations with those in the
existing portfolio, the FI manager can produce a set of efficient frontier portfolios, defined as
those portfolios that provide the maximum returns for a given level of risk or the lowest risk for a
given level of returns. By choosing portfolios on the efficient frontier, an FI manager may be
able to reduce credit risk to the fullest extent. As shown in Figure 12-1, a managers selection of
a particular portfolio on the efficient frontier is determined by the risk-return trade-off.
7.
The Bank of Tinytown has two $20,000 loans that have the following characteristics: Loan
A has an expected return of 10 percent and a standard deviation of returns of 10 percent.
The expected return and standard deviation of returns for loan B are 12 percent and 20
percent, respectively.
a. If the correlation coefficient between loans A and B is .15, what are the expected return
and standard deviation of this portfolio?
XA = XB = $20,000/$40,000 = .5
Expected return = 0.5(10%) + 0.5(12%) = 11 percent
Standard deviation = [0.52(.10)2 + 0.52(.20)2 + 2(0.5)(0.5)(.10)(.20)(.15)] = 11.83 percent
b. What is the standard deviation of the portfolio if the correlation is -.15?
Standard deviation = [0.52(.10)2 + 0.52(.20)2 + 2(0.5)(0.5)(.10)(.20)(-0.15)] = 10.49 percent
c. What role does the covariance, or correlation, play in the risk reduction attributes of
modern portfolio theory?
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Chapter 12 - Credit Risk: Loan Portfolio and Concentration Risk
The risk of the portfolio as measured by the standard deviation is reduced when the
covariance is reduced. If the correlation is less than +1.0, the standard deviation of the
portfolio will always be less than the weighted average of the standard deviations of the
individual assets.
8.
Why is it difficult for small banks and thrifts to measure credit risk using modern portfolio
theory?
The basic premise behind modern portfolio theory is the ability to diversify and reduce risk by
eliminating diversifiable risk. Small banks and thrifts may not have the ability to diversify their
asset base, especially if the local markets which they serve have a limited number of industries.
The ability to diversify is even more acute if these loans cannot be traded easily.
9.
What is the minimum risk portfolio? Why is this portfolio usually not the portfolio chosen
by FIs to optimize the return-risk tradeoff?
The minimum risk portfolio is the combination of assets that reduces portfolio risk as measured
by the standard deviation of returns to the lowest possible level. This portfolio usually is not the
optimal portfolio choice because the returns on this portfolio are low relative to other alternative
portfolio selections. By accepting some additional risk, portfolio managers are able to realize a
higher level of return relative to the risk of the portfolio.
10.
The obvious benefit to holding a diversified portfolio of loans is to spread risk exposures so
that a single event does not result in a great loss to an FI. Are there any benefits to not
being diversified?
One benefit to not being diversified is that an FI that lends to a certain industrial or geographic
sector is likely to gain expertise about that sector. Being diversified requires that the FI becomes
familiar with many more areas of business. This may not always be possible, particularly for
small FIs.
11.
A bank vice president is attempting to rank, in terms of the risk-reward trade-off, the loan
portfolios of three loan officers. Information on the portfolios is noted below. How would
you rank the three portfolios?
Portfolio
A
B
C
Expected
Return
10%
12%
11%
Standard
Deviation
8%
9%
10%
Portfolio B dominates portfolio C because B has a higher expected return and a lower standard
deviation. Thus, C is clearly inferior. A comparison of portfolios A and B represents a risk-return
trade-off in that B has a higher expected return, but B also has higher risk. A crude comparison
12-4
Chapter 12 - Credit Risk: Loan Portfolio and Concentration Risk
may use the coefficient of variation or the Sharpe measure, but a judgment regarding which
portfolio is better would be based on the risk preference of the vice president.
12.
CountrySide Bank uses the KMV Portfolio Manager model to evaluate the risk-return
characteristics of the loans in its portfolio. A specific $10 million loan earns 2 percent per
year in fees and the loan is priced at a 4 percent spread over the cost of funds for the bank.
Because of collateral considerations, the loss to the bank if the borrower defaults will be 20
percent of the loans face value. The expected probability of default is 3 percent. What is
the anticipated return on this loan? What is the risk of the loan?
Expected return = AISi E(Li) = (0.02 + 0.04) (0.03 x 0.20) = .054 or 5.4 percent
Risk of the loan = Di x LGDi = [0.03(0.97)] x 0.20 = 0.0341 or 3.41 percent
13. Suppose that an FI holds two loans with the following characteristics.
Loan
1
2
Xi
.45
.55
Annual
Spread Between
Loan Rate and FI=s
Cost of Funds
5.5%
3.5
Annual
Fees
2.25%
1.75
Loss to FI
Given
Default
30%
20
Expected
Default
Frequency
3.5%
1.0
12 = -.15
Calculate of the return and risk on the two-asset portfolio using KMV Portfolio Manager.
The return and risk on loan 1 are:
R1 = (.055 + .0225) - [.035 .30] = 0.0670 or 6.70%
1 = [%
.035(.965)] .30 = .05513 or 5.513%
The return and risk on loan 2 are:
R2 = (.035 + .0175) - [.01 .20] = 0.0505 or 5.05%
2 = [%
.01(.99)] .20 = .01990 or 1.990%
The return and risk of the portfolio is then:
Rp = .45 (6.70%) + .55 (5.05%) = 5.7925%
p2 = (.45)2 (5.513%)2 + (.55)2 (1.990%)2 + 2 (.45) (.55)(-.15)(5.513%)(1.990%) = 6.53876%.
Thus, p = %
6.53876% = 2.56%.
14.
Suppose that an FI holds two loans with the following characteristics.
12-5
Chapter 12 - Credit Risk: Loan Portfolio and Concentration Risk
Loan
1
2
Xi
?
?
Annual
Spread Between
Loan Rate and FI=s
Cost of Funds
4.0%
2.5
Annual
Fees
1.50%
1.15
Loss to FI
Given
Default
?%
?
Expected
Default
Frequency
4.0%
1.5
12 = -.10
The return on loan 1 is R1 = 6.25%, the risk on loan 2 is 2 = 1.8233%, and the return of the
portfolio is Rp = 4.555%. Calculate of the loss given default on loans 1 and 2, the
proportions of loans 1 and 2 in the portfolio, and the risk of the portfolio, p, using KMV
Portfolio Manager.
R1 = .0625 = (.04 + .015) - [.040 LGD1] => LGD1 = (.0625 (.04 + .015))/(-.04) = .1875
=> 1 = [%
.04(.96)] .1875 = .03674 or 3.674%
2 = .018233 = [%
.015(.985)] LGD2 => LGD2 = .018233/[%
.015(.985)] = .15
=> R2 = (.025 + .0115) - [.015 .15] = .03425 or 3.425%
=> Rp = X1 (.0625) + (1 X1) (.03425) = .04555
=> X1 = (.04555 - .03425)/(.0625 - .03425) = .40 and X2 = 1 - .40 = .60
p2 = (.40)2 (.03674)2 + (.60)2 (.018233)2 + 2 (.40) (.60)(-.10)( .03674)( .018233) = .000303523.
Thus, p = %
.000303523= .0174 = 1.74%.
15.
What databases are available that contain loan information at national and regional levels?
How can they be used to analyze credit concentration risk?
Two publicly available databases are (a) the commercial bank call reports of the Federal Reserve
Board which contain various information supplied by banks quarterly and (b) the shared national
credit database, which provides information on loan volumes of FIs separated by two-digit SIC
(Standard Industrial Classification) codes. Such data can be used as a benchmark to determine
whether an FIs asset allocation is significantly different from the national or regional average.
16.
Information concerning the allocation of loan portfolios to different market sectors is given
below:
Allocation of Loan Portfolios in Different Sectors (%)
Sectors
National
Bank A
Bank B
Commercial
30%
50%
10%
Consumer
40%
30%
40%
Real Estate
30%
20%
50%
Bank A and Bank B would like to estimate how much their portfolios deviate from the
national average.
12-6
Chapter 12 - Credit Risk: Loan Portfolio and Concentration Risk
a. Which bank is further away from the national average?
Using Xs to represent portfolio holdings:
Bank A
(.50 - .30)2 = .0400
(.30 - .40)2 = .0100
(.20 - .30)2 = .0100
(X1j - X1 )2
(X2j - X2 )2
(X3j - X3 )2
n
i 1
( X ij X i ) 2
n
=
(X
i =1
ij
n =3
= .0600
i =1
Bank B
(.10 - .30)2 = .0400
(.40 - .40)2 = .0000
(.50 - .30)2 = .0400
n =3
= .0800
i =1
X i )2
n
= 14.14 percent
= 16.33 percent
Bank B deviates from the national average more than Bank A.
b. Is a large standard deviation necessarily bad for an FI using this model?
No; a higher standard deviation is not necessarily bad for an FI because the FI could have
comparative advantages that are not required or available to a national well-diversified
bank. For example, an FI could generate high returns by serving specialized markets or
product niches that are not well diversified. Further, an FI could specialize in only one
product, such as mortgages, but be well-diversified within this product line by investing in
several different types of mortgages that are distributed both nationally and internationally.
This would still enable it to obtain portfolio diversification benefits that are similar to the
national average.
17.
Assume that, on average, national banks engaged primarily in mortgage lending have their
assets diversified in the following proportions: 60 percent residential, 15 percent
commercial, 5 percent international, and 20 percent mortgage-backed securities. A local
bank has the following distribution of mortgage loans: 50 percent residential, 30 percent
commercial, and 20 percent international. How does the local bank differ from national
banks?
Using Xs to represent portfolio holdings:
(X1j - X1 )2
(X2j - X2 )2
(X3j - X3 )2
(.50 - .60)2 = .0100
(.30 - .15)2 = .0225
(.20 - .05)2 = .0225
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Chapter 12 - Credit Risk: Loan Portfolio and Concentration Risk
(X4j - X4 )2
n
i =1
(.00 - .20)2 = .0400
n =4
( X ij X i )
n
=
(X
i =1
ij
= .0950
2
i =1
X i )2
= 15.41 percent
n
The banks standard deviation in its loan portfolio allocation is 15.41 percent. This suggests
that the bank is different from the national average. Whether it is significantly different
cannot be stated without comparing it to other banks.
18.
Over the last ten years, a bank has experienced the following loan losses on its C&I loans,
consumer loans, and total loan portfolio.
Year
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
C&I Loans
0.0080
0.0088
0.0100
0.0120
0.0104
0.0084
0.0072
0.0080
0.0096
0.0144
Consumer Loans
0.0165
0.0183
0.0210
0.0255
0.0219
0.0174
0.0147
0.0165
0.0201
0.0309
Total Loans
0.0075
0.0085
0.0100
0.0125
0.0105
0.0080
0.0065
0.0075
0.0095
0.0155
Using regression analysis on these historical losses, loan the bank has estimated the
following:
XC = 0.002 + 0.8XL and Xh = 0.003 + 1.8XL
where XC = loss rate in the commercial sector, Xh = loss rate in the consumer (household)
sector, XL = loss rate for its total loan portfolio.
a. If the banks total loan loss rates increase by 10 percent, what are the expected loss rate
increases in the commercial and consumer sectors?
Commercial loan loss rates will increase by 0.002 + 0.8(0.10) = 8.20 percent.
Consumer loan loss rates will increase by 0.003 + 1.8(0.10) = 18.30 percent.
b. In which sector should the bank limit its loans and why?
12-8
Chapter 12 - Credit Risk: Loan Portfolio and Concentration Risk
The bank should limit its loans to the consumer sector because the loss rates are
systematically higher than the loss rates for the total loan portfolio. Loss rates are lower for
the commercial sector. For a 10 percent increase in the total loan portfolio, the consumer
loss rate is expected to increase by 18.30 percent, as opposed to only 8.2 percent for the
commercial sector.
19.
What reasons did the Federal Reserve Board offer for recommending the use of subjective
evaluations of credit concentration risk instead of quantitative models? How did this
change in 2006?
The Federal Reserve Board recommended a subjective evaluation of credit concentration risk
instead of quantitative models because (a) current methods to identify credit concentrations were
not reliable and (b) there was insufficient data to develop reliable quantitative models. In June
2006 the Bank for International Settlements released guidance on sound credit risk assessment
and valuation for loans. The guidance addresses how common data and processes related to loans
may be used for assessing credit risk, accounting for loan impairment and determining regulatory
capital requirements and is structured around ten principles that fall within two broad categories:
i) supervisory expectations concerning sound credit risk assessment and valuation for loans and
ii) supervisory evaluation of credit risk assessment for loans, controls and capital adequacy.
20.
What rules on credit concentrations has the National Association of Insurance
Commissioners enacted? How are they related to modern portfolio theory?
The NAIC set a maximum limit of 3% that life insurers can hold in securities belonging to a
single issuer. Similarly, the limit is 5% for property-casualty (PC) insurers. This forces life
insurers to hold a minimum of 33 different securities and PC insurers to hold a minimum of 20
different securities. Modern portfolio theory shows that by holding well-diversified portfolios,
investors can eliminate undiversifiable risk and be subject only to market risk. This enables
investors to hold portfolios that provide either high returns for a given level of risk or low risks
for a given level of returns.
21.
An FI is limited to holding no more than 8 percent of its assets in securities of a single
issuer. What is the minimum number of securities it should hold to meet this requirement?
What if the requirements are 2 percent, 4 percent, and 7 percent?
If an FI is limited to holding a maximum of 8 percent of securities of a single issuer, it will be
forced to hold 100/8 = 12.5, or 13 different securities.
For 2%, it will be 100/2, or 50 different securities.
For 4%, it will be 100/4, or 25 different securities.
For 7%, it will be 100/7, or 15 different securities.
The questions and problems that follow refer to Appendixes 12A and 12B. Refer to the information
in Appendix 12A for problems 22 through 24. Refer to Appendix 12B for problem 25.
12-9
Chapter 12 - Credit Risk: Loan Portfolio and Concentration Risk
22.
From Table 12A-1, what is the probability of a loan upgrade? A loan downgrade?
The probability of an upgrade is 5.95% + 0.33% + 0.02% = 6.30%. The probability of a
downgrade is 5.30% + 1.17% + 0.12% = 6.59%.
a. What is the impact of a rating upgrade or downgrade?
The effect of a rating upgrade or downgrade will be reflected on the credit-risk spreads or
premiums on loans and thus on the implied market value of the loan. A downgrade should
cause this credit-risk spread premium to rise.
b. How is the discount rate determined after a credit event has occurred?
The discount rate for each year in the future in which cash flows are expected to be
received includes the forward rates from the current Treasury yield curve plus the annual
credit spreads for loans of a particular rating class for each year. These credit spreads are
determined by observing the spreads of the corporate bond market over Treasury securities.
c. Why does the probability distribution of possible loan values have a negative skew?
The negative skew occurs because the probability distribution is non-normal. The potential
downside change in a loans value is greater than the possible upside change in value.
d. How do the capital requirements of the CreditMetrics approach differ from those of the
BIS and Federal Reserve System?
The Fed and the BIS require the capital reserve to be 8 percent of the risk-weighted book
value of a loan. Under CreditMetrics each loan is likely to have a different VAR and thus a
different implied capital requirement. Further, this required capital is likely to be greater
than 8 percent of the risk-weighted book value because of the non-normality of the
probability distributions.
23.
A five-year fixed-rate loan of $100 million carries a 7 percent annual interest rate. The
borrower is rated BB. Based on hypothetical historical data, the probability distribution
given below has been determined for various ratings upgrades, downgrades, status quo, and
default possibilities over the next year. Information also is presented reflecting the forward
rates of the current Treasury yield curve and the annual credit spreads of the various
maturities of BBB bonds over Treasuries.
Rating
AAA
Probability
Distribution
0.01%
New Loan
Value plus
Coupon $
$114.82m
Forward Rate Spreads at Time t
t
rt %
st% .
1
3.00%
0.72%
12-10
Chapter 12 - Credit Risk: Loan Portfolio and Concentration Risk
AA
A
BBB
BB
B
CCC
Default
0.31
1.45
6.05
85.48
5.60
0.90
0.20
114.60m
114.03m
2
3
4
3.40
3.75
4.00
0.96
1.16
1.30
108.55m
98.43m
86.82m
54.12m
a. What is the present value of the loan at the end of the one-year risk horizon for the case
where the borrower has been upgraded from BB to BBB?
PV = $7 m +
$7 m
$7 m
$7 m
$107 m
+
+
+
= $113.27 million
2
3
1.0372 (1.0436) (1.0491) (1.0530) 4
b. What is the mean (expected) value of the loan at the end of year one?
The solution table on the following page reveals a value of $108.06.
c. What is the volatility of the loan value at the end of the year?
The volatility or standard deviation of the loan value is $4.19.
d. Calculate the 5 percent and 1 percent VARs for this loan assuming a normal
distribution of values.
The 5 percent VAR is 1.65 x $4.19 = $6.91.
The 1 percent VAR is 2.33 x $4.19 = $9.76.
Year-end
Rating
AAA
AA
A
BBB
BB
B
CCC
Default
Probability
0.0001
0.0031
0.0145
0.0605
0.8548
0.056
0.009
0.002
1.000
Value
(m of $)
$114.82
114.60
114.03
113.27
108.55
98.43
86.82
54.12
Mean =
Probability
x Value
Deviation
$0.01
6.76
0.36
6.54
1.65
5.97
6.85
5.21
92.79
0.49
5.51
-9.63
0.78
-21.24
0.11
-53.94
$108.06m Variance =
Standard Deviation =
12-11
Probability
x Deviation
Squared
0.0046
0.1325
0.5162
1.6402
0.2025
5.1968
4.0615
5.8197
17.5740
$4.19m
Chapter 12 - Credit Risk: Loan Portfolio and Concentration Risk
e. Estimate the approximate 5 percent and 1 percent VARs using the actual distribution
of loan values and probabilities.
5% VAR = 95% of actual distribution = $108.06m - $98.43m = $9.63m
1% VAR = 99% of actual distribution = $108.06m - $86.82m = $21.24m
where:
5% VAR is approximated by 0.056 + 0.009 + 0.002 = 0.067 or 6.7 percent, and
1% VAR is approximated by 0.009 + 0.002 = 0.011 or 1.1 percent.
Using linear interpolation, the 5% VAR = $10.65 million and the 1% VAR = $19.31
million. For the 1% VAR, $19.31m = (1 0.1/1.1) x $21.24m.
f. How do the capital requirements of the 1 percent VARs calculated in parts (d) and (e)
above compare with the capital requirements of the BIS and Federal Reserve System?
The Fed and BIS systems would require 8 percent of the loan value, or $8 million. The 1
percent VAR would require $19.31 million under the approximate method, and $9.76
million (2.33 x $4.19m) in capital under the normal distribution assumption. In each case,
the amounts exceed the Fed/BIS amount.
24.
How does the Credit Risk+ model of Credit Suisse Financial Products differ from the
CreditMetrics model of J.P. Morgan Chase?
CreditRisk+ attempts to estimate the expected loss of loans and the distribution of these losses
with the focus on calculating the required capital reserves necessary to meet these losses. The
method assumes that the probability of any individual loan defaulting is random and that the
correlation between the defaults on any pair of loan defaults is zero. CreditMetrics focuses on
estimating a complete VAR framework.
25.
An FI has a loan portfolio of 10,000 loans of $10,000 each. The loans have a historical
average default rate of 4 percent and the severity of loss is 40 cents per dollar.
a. Over the next year, what are the probabilities of having default rates of 2, 3, 4, 5, and 8
percent?
e m m n ( 2.71828) 4 x 4 2 0.018316 x16
Pr obability of 2 defaults =
=
=
= 0.1465 = 14.65%
n!
1x 2
2
n
Probability
2
14.65%
3
19.54%
4
19.54%
5
15.63%
8
2.98%
.
b. What would be the dollar loss on the portfolios with default rates of 4 and 8 percent?
Dollar loss of 4 loans defaulting = 4 x 0.40 x $10,000 = $16,000
Dollar loss of 8 loans defaulting = 8 x 0.40 x $10,000 = $32,000
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Chapter 12 - Credit Risk: Loan Portfolio and Concentration Risk
c. How much capital would need to be reserved to meet the 1 percent worst-case loss
scenario? What proportion of the portfolios value would this capital reserve be?
The probability of 8 defaults is ~3 percent. The probability of 10 defaults is 0.00529 or
close to 1 percent. The dollar loss of 10 loans defaulting is $40,000. Thus, a 1 percent
chance of losing $40,000 exists.
A capital reserve should be held to meet the difference between the unexpected 1 percent
loss rate and the expected loss rate of 4 defaults. This difference is $40,000 minus $16,000
or $24,000. This amount is 0.024 percent of the total portfolio.
Integrated Mini Case: Loan Portfolio Analysis
As a senior loan officer at MC Financial Corp, you have a loan application from a firm in the
biotech industry. While the loan has been approved on the basis of an individual loan, you must
evaluate the loan based on its impact on the risk of the overall loan portfolio. The FI uses the
following three methods to assess its loan portfolio risk.
1. Concentration Limits - The FI currently has lent an amount equal to 40 percent of its capital
to the biotech industry and does not lend to a firm in any sector that generates losses in excess
of 2 percent of capital. The average historical losses in the biotech industry total 5 percent.
Concentration limit = (Maximum loss as a percent of capital) x (1/Loss rate) = .02 x
1/0.05 = 40 percent of capital is the maximum amount that can be lent to firms in the
biotech sector.
MC Financial already has 40 percent of its capital lent out to the biotech industry. To give out
this new loan would put the FI over its concentration limit. Thus, MC Financial should not grant
this loan.
2. Loan Volume-based Model - National and MC Financials loan portfolio allocations are as
follows.
Allocation of Loan Portfolios in Different Sectors (%)
Sectors
National
MC Financial
Commercial
30%
40%
Real Estate
50%
45%
Consumer
20%
15%
MC Financial does not want to deviate from the national average by more than 12.25 percent.
Using Xs to represent portfolio holdings:(X1j - X1 )2
12-13
(.40 - .30)2 = .0100
Chapter 12 - Credit Risk: Loan Portfolio and Concentration Risk
(X2j - X2 )2
(X3j - X3 )2
n
i =1
(.45 - .50)2 = .0025
(.15 - .20)2 = .0025
n =3
( X ij X i )
n
=
(X
i =1
ij
= .0150
2
X i )2
i =1
= 12.25 percent
n
The FIs standard deviation in its loan portfolio allocation is 12.25 percent. To issue
another C&I loan would push MC Financial even further from the national average. Thus,
the FI would not want to give out the loan
3. Loan Loss Ratio-based Model - Based on regression analysis on historical loan losses, the FI
estimates the following loan loss ratio models:
XC&I = 0.001 + 0.85XL and Xcon = 0.003 + .65XL
where XC&I = loss rate in the commercial sector, Xcon = loss rate in the consumer
(household) sector, XL = loss rate for its total loan portfolio.
MC Financials total increase in the loan loss ratio is expected to be 12 percent next year.
Commercial loan loss rates will increase by 0.001 + 0.85(0.12) = 10.30 percent.
Consumer loan loss rates will increase by 0.003 + .65(0.12) = 8.10 percent.
MC Financial should limit its loans to the commercial sector because the loss rates are
systematically higher than the loss rates for the total loan portfolio. Loss rates are lower for the
consumer sector. For a 12 percent increase in the total losses in the loan portfolio, the
commercial loss rate is expected to increase by 10.30 percent, as opposed to only 8.1 percent for
the consumer sector. Thus, MC Financial should not issue this loan.
Should MC Financial Corp. grant this loan?
Based on all three models, from an overall loan portfolio perspective, MC Financial would not
want to issue this loan to a firm in the biotech sector.
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Chapter 12 - Credit Risk: Loan Portfolio and Concentration Risk
Additional Example for Chapter 12
Sectors
Commercial
Consumer
Real Estate
Allocation of Loan Portfolios in Different Sectors (%)
National
Bank A
Bank B
20%
50%
30%
40%
20%
40%
40%
30%
30%
How different are Banks A and B from the national benchmark? When using this example, note
that there is an implied assumption that Bank A and B belong to a certain size class or have some
common denominator linking them to the national benchmark. If that is the case, then the
solution is to estimate the standard deviation.
We use Xs to represent the portfolio concentrations. X1, X2 and X3 are the national benchmark
percentages
Bank A
Bank B
2
2 = 900
(X1j - X1 )
(50 - 20)
(30 - 20)2 = 100
(X2j - X2 )2
(20 - 40)2 = 400
(40 - 40)2 = 0
(X3j - X3 )2
(30 - 40)2 = 100
(30 - 40)2 = 100
n
i =1
n =3
( X ij X i )
n
=
(X
i =1
ij
2
X i )2
n =3
=1,400
= 200
= 37.42 percent
= 14.14 percent
i =1
i =1
n
Thus we can see here that Bank A is significantly different from the national benchmark.
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