** Expected Standard**
**Portfolio** **Return** **Deviation**
A 10% 8%
B 12% 9%
C 11% 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 a higher risk measure. A crude comparison may use the coefficient of variation or the Sharpe measure, but a judgement regarding which portfolio is “better” would be based on the risk preference of the judge.
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 loan’s 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 = AIS_{i} – E(L_{i}) = (0.02 + 0.04) – (0.03 x 0.20) = .054 or 5.4 percent
Risk of the loan = _{Di} x LGD_{i} = [0.03(0.97)]^{½} x 0.20 = 0.0341 or 3.41 percent
13. What databases are available that contain loan information at national and regional levels? How can they be utilized 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 a bank’s asset allocation is significantly different from the national or regional average.
14. 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.
a. Which bank is further away from the national average?
Using Xs to represent portfolio holdings:
__Bank A__ __Bank B__
(*X*_{1j } - *X*_{1 })^{2 }(.50 - .30)^{2 }= 0.04 (.10 - .30)^{2 } = 0.04
(*X*_{2j } - *X*_{2 })^{2 }(.30 - .40)^{2 }= 0.01 (.40 - .40)^{2 } = 0.00
__(____X___{3j }__ - ____X___{3 }__)__^{2}^{ }__(.20 - .30)__^{2 }__= 0.01__ __(.50 - .30)__^{2 }__ = 0.04__
= 0.1414 or 14.14 percent = 0.1633 or 16.33 percent
Bank B deviates from the national average more than Bank A.
b. Is a large standard deviation necessarily bad for a bank using this model?
No, a higher standard deviation is not necessarily bad for an FI because it could have comparative advantages that are not required or available to a national well-diversified bank. For example, a bank could generate high returns by serving specialized markets or product niches that are not well diversified. Or, a bank 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.
15. Assume that the averages for national banks engaged primarily in mortgage lending have their assets diversified in the following proportions: 20 percent residential, 30 percent commercial, 20 percent international, and 30 percent mortgage-backed securities. A local bank has the following ratios: 30 percent residential, 40 percent commercial, and 30 percent international. How does the local bank differ from the national banks?
Using Xs to represent portfolio holdings:
(*X*_{1j } - *X*_{1 })^{2 }(.30 - .20)^{2 } = 0.01
(*X*_{2j } - *X*_{2 })^{2 }(.40 - .30)^{2 } = 0.01
(*X*_{3j } - *X*_{3 })^{2 }(.30 - .20)^{2 }= 0.01
__(____X___{4j }__ - ____X___{4 }__)__^{2}^{ }__(.0 - .30)__^{2 }__ = 0.09__
= 0.1732 or 17.32 percent
The bank’s standard deviation is 17.32 percent, suggesting that it is different from the national average. Whether it is significantly different cannot be stated without comparing it to another bank.
16. Using regression analysis on historical loan losses, a bank has estimated the following:
X_{C }= 0.002 + 0.8X_{L}, and X_{h }= 0.003 + 1.8X_{L}
where X_{C} = loss rate in the commercial sector, X_{h} = loss rate in the consumer (household) sector, X_{L} = loss rate for its total loan portfolio.
a. If the bank’s total loan loss rates increase by 10 percent, what are the increases in the expected loss rates 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?
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.
17. What reasons did the Federal Reserve Board offer for recommending the use of subjective evaluations of credit concentration risk instead of quantitative models?
The Federal Reserve Board recommended a subjective evaluation of credit concentration risk instead of quantitative models because (a) current methods to identify credit concentrations are not reliable, and (b) there is insufficient data to develop reliable quantitative models.
18. What rules on credit concentrations have the National Association of Insurance Commissioners proposed? How are they related to modern portfolio theory?
The NAIC has set a maximum limit of 3% that life and health insurers can hold in securities belonging to a single issuer. Similarly, the limit is 5% for property-casualty (P/C) insurers. This forces life insurers to hold a minimum of 34 different securities and P/C 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.
19. An FI is limited to holding no more than 8 percent of 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.
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