Chapter Twelve
Credit Risk: Loan Portfolio and Concentration Risk
Chapter Outline
Introduction
Simple Models of Loan Concentration
Loan Portfolio Diversification and Modern Portfolio Theory (MPT)
∙KMV Portfolio Manager
∙Partial Applications of Portfolio Theory
∙Loan Loss Ratio-Bad Models
∙Regulatory Models
Summary
Solutions for End-of-Chapter Questions and Problems: Chapter Twelve
1. How do loan portfolio risks differ from individual loan risks?
Loan portfolio risks refer to the risks of a portfolio of loans as oppod to the risks of a single loan. Inherent in the distinction is the elimination of some of the risks of individual loans becau of benefits from diversification.
end是啥意思
2.What is migration analysis? How do FIs u it to measure credit risk concentration? What are its shortcomings?
Migration analysis us information from the market to determine the credit risk of an individual loan or ctoral loans. For example, bankers can u S&P and Moody’s ratings to determine whether firms in a particular ctor are experiencing repayment problems. This information can be ud to either curtail lending in that ctor or to reduce maturity and/or increa interest rates. A problem with migration analysis is that the information may be too late, becau 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 ctor. To the extent that a portfolio of loans reprents loans made to a diver cross ction of the economy, concentration risk is minimized.
4.A manager decides not to lend to any firm in ctors that generate loss in excess of 5 percent of equity.
a. If the average historical loss in the automobile ctor total 8 percent, what is the maximum loan a manager can lend to a firm in this ctor as a percentage of total capital?
Maximum limit = (Maximum loss as a percent of capital) x (1/Loss rate) = .05 x 1/0.08
= 62.5 percent is the maximum limit that can be lent to a firm in the
automobile ctor.大连翻译公司
b. If the average historical loss in the mining ctor total 15 percent, what is the maximum loan a manager can lend to a firm in this ctor as a percentage of total capital?
词霸搜索 Maximum limit = (Maximum loss as a percent of capital) x (1/Loss rate) = .05 x 1/0.15
= 33.3 percent is the maximum limit that can be lent to a firm in the mining ctor.
5. An FI has t a maximum loss of 12 percent of total capital as a basis for tting concentration limits on loans to individual firms. If it has t a concentration limit of 25 percent to a firm, what is the expected loss rate for that firm? few和little的区别
Maximum limit = (Maximum loss as a percent of capital) x (1/Loss rate)
25 percent = 12 percent x 1/Loss rate Loss rate = 0.12/0.25 = 48 percent
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6. Explain how modern portfolio theory can be applied to lower the credit risk of an FI’s portfolio.
Modern portfolio theory has demonstrated that a well-diversified portfolio can provide opportunities for individuals to invest in a t of efficient frontier portfolios, defined as tho 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, a banker may be able to reduce credit risk to the fullest extent. As shown in Figure 11.1, a manager’s lection of a particular portfolio on the efficient frontier is determined by his or her 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 covariance between A and B is .015 (1.5 percent), what are the expected ret
urn and standard deviation of this portfolio?
西安课外辅导 Expected return = 0.5(10%) + 0.5(12%) = 11 percent
Standard deviation = [0.5ntest2(0.102) + 0.52(0.202) + 2(0.5)(0.5)(0.015)]½ = 14.14 percent
b. What is the standard deviation of the portfolio if the covariance is -.015 (-1.5 percent)?
国际教育机构 Standard deviation = [0.52(0.102) + 0.52(0.202) + 2(0.5)(0.5)(-0.015)]½ = 7.07 percent
c. What role does the covariance, or correlation, play in the risk reduction attributes of modern portfolio theory?
whca 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 always will be less than the weighted average standard deviations of the individual asts.
8. Why is it difficult for small banks and thrifts to measure credit risk using modern portfolio theory?
The basic premi 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 ast ba, especially if the local markets in which they rve have a limited number of industries. The ability to diversify is even more acute if the loans cannot be traded easily.
9. What is the minimum risk portfolio? Why is this portfolio usually not the portfolio chon by FIs to optimize the return-risk tradeoff?
