Solutions for End-of-Chapter Questions and Problems:Chapter Eleven
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9，County Bank offers one-year loans with a stated rate of9percent but requires a compensating balance of10percent.What is the true cost of this loan to the borrower? How does the cost change if the compensating balance is15percent?If the compensating balance is20percent?
The true cost is the loan rate÷(1–compensating balance rate)=9%÷(1.0–0.1)=10 percent.For compensating balance rates of15percent and20percent,the true cost of the loan would be10.59percent and11.25percent respectively.Note that as the compensating balance rate increas by a constant amount,the true cost of the loan increas at an increasing rate.
10，Metrobank offers one-year loans with a9percent stated or ba rate,charges a0.25 percent loan origination fee,impos a10percent compensating balance requirement,and must pay a6percent rerve requirement to the Federal Rerve.The loans typically are repaid at maturity.
此致是什么意思A，If the risk premium for a given customer is2.5percent,what is the simple promid interest return on the loan?
The simple promid interest return on the loan is BR+m=0.09+0.025=0.115or11.5 percent.
b.What is the contractually promid gross return on the loan per dollar lent?
C，Which of the fee items has the greatest impact on the gross return?
The compensating balance has the strongest effect on the gross return on the loan. Without the compensating balance,the gross return would equal11.75percent,a reduction of1.22percent.Without the origination fee,the gross return would be12.69 percent,a reduction of only0.28percent.Eliminating the rerve requirement would cau the gross return to increa to13.06percent,an increa of0.09percent.
18，Suppo the estimated linear probability model is PD=0.3X1+0.2X2-.05X3+error, where X1=0.75is the borrower's debt/equity ratio;X2=0.10is the volatility of borrower earnings;and X3=0.10is the borrower’s profit ratio.
a.What is the projected probability of default for the borrower?
PD=0.3(.75)+0.2(.25)-0.05(.10)=0.27
b.What is the projected probability of repayment if the debt/equity ratio is2.5?
PD=0.3(2.5)+0.2(.25)-0.05(.10)=0.795
The expected probability of repayment is1-0.795=0.205.
C，What is a major weakness of the linear probability model?
A major weakness of this model is that the estimated probabilities can be below0or above
公司过户1.0,an occurrence that does not make economic or statistical n.
22，If the rate of one-year T-Bills currently is6percent,what is the repayment probability for each of the following two curities?Assume that if the loan is defaulted,no payments are expected.What is the market-determined risk premium for the corresponding probability of default for each curity?
A，One-year AA rated bond yielding9.5percent?
Probability of repayment=p=(1+I)/(1+k)
For an AA-rated bond=(1+.06)/(1+.095)=0.968,or96.8percent
The market determined risk premium is0.095–0.060=0.035or3.5percent
b.One-year BB rated bond yielding13.5percent?
Probability of repayment=p=(1+I)/(1+k)醒着做梦
For BB-rated bond=(1+.06)/(1+.135)=93.39percent
The market determined risk premium is0.135–0.060=0.075or7.5percent
23，A bank has made a loan charging a ba lending rate of10percent.It expects a probability of default of5percent.If the loan is defaulted,it expects to recover50percent
of its money through the sale of its collateral.What is the expected return on this loan?
24，Assume a one-year T-Bill is currently yielding5.5percent,and a AAA-rated discount bond with similar maturity is yielding8.5percent.
a，If the expected recovery from collateral in the event of default is50percent of principal and interest,what is the probability of repayment of the AAA-rated bond?What is the probability of default?
Therefore the probability of default is1.0-.9447=0.0553or5.53percent.
b，What is the probability of repayment of the AAA-rated bond if the expected recovery from collateral in the ca of default is94.47percent of principal and interest?What is the probability of default?
Therefore the probability of default is1.0–0.5000=0.5000or50.00percent.
c，What is the relationship between the probability of default and the proportion of principal and interest that may be recovered in the ca of default on the loan?
四年级下册语文教学计划The proportion of the loan’s principal and interest that is collectible on default is a perfect substitute f
or the probability of repayment should such defaults occur.
26，Calculate the term structure of default probabilities over three years using the following spot rates from the Treasury and corporate bond(pure discount)yield curves.Be sure to calculate both the annual marginal and the cumulative default probabilities.
spot spot spot
27，The bond equivalent yields for U.S.Treasury and A-rated corporate bonds with maturities of93and175days are given below:
32，A bank is planning to make a loan of$5,000,000to a firm in the steel industry.It expects to charge a rvicing fee of50basis points.The loan has a maturity of8years and a duration of7.5years.The cost of funds(the RAROC benchmark)for the bank is10 percent.Assume the bank ha
s estimated the maximum change in the risk premium on the steel manufacturing ctor to be approximately4.2percent,bad on two years of historical data.The current market interest rate for loans in this ctor is12percent.
a.Using the RAROC model,determine whether the bank should make the loan?
植物的日记RAROC=Fees and interest earned on loan/Loan or capital risk
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S olutions for End-of-Chapter Questions and Problems:Chapter Twelve
5，An FI has t a maximum loss of12percent of total capital as a basis for tting concentration limits on loans to individual firms.If it has t a concentration limit of25 percent to a firm,what is the expected loss rate for that firm?
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Maximum limit=(Maximum loss as a percent of capital)x(1/Loss rate)25percent=12 percent x1/Loss rate Loss rate=0.12/0.25=48percent
7，The Bank of Tinytown has two$20,000loans that have the following characteristics:
Loan A has an expected return of10percent and a standard deviation of returns of10 percent.The expected return and standard deviation of returns for loan B are12percent
and20percent,respectively.
a.If the covariance between A and B is.015(1.5percent),what are the expected return
and standard deviation of this portfolio?
Expected return=0.5(10%)+0.5(12%)=11percent
Standard deviation=[0.52(0.102)+0.52(0.202)+2(0.5)(0.5)(0.015)]½=14.14percent
b.What is the standard deviation of the portfolio if the covariance is-.015(-1.5percent)? Standard deviation=[0.52(0.102)+0.52(0.202)+2(0.5)(0.5)(-0.015)]½=7.07percent
c.What role does the covariance,or correlation,play in the risk reduction attributes of modern portfolio theory?
The risk of the portfolio as measured by the standard deviation is reduced when the covariance is re
duced.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.
