1. An insurance company has issued $675,000,000 in short-term notes with a 1-year maturity to finance the purchase of $675,000,000 short-term investments with a 6-year maturity. The insurance company must pay 6.7% annual interest on the notes but earns 7.5% annual interest on the investments.
a. Calculate the insurance company’s profit spread and dollar value of profit at the end of Year 1.
(5 points)
b. Calculate the insurance company’s profit spread and dollar value of profit at the end of Year 2 if
the insurance company must issue short-term notes on which it must pay that 7.1% annual
interest. (5 points)
c. What type of interest rate risk is the insurance company facing due to the different maturities
on its assets and liabilities? Why is this a concern to the insurance company? (3 points)
2. A bank has the following balance sheet. The loans have a 3-year maturity and earn 7.9% annually.
The interest is paid once a year and the principal will not be repaid until maturity. The securities do
not earn interest. The certificates of deposit (CDs) have a 1-year maturity. The bank must pay 5.4%
on the CDs.
Assets Liabilities & Equity
Cash $480,000 Demand deposits $750,000
Loans 2,960,000 Certificates of deposit 2,960,000
Securities 1,300,000 Equity 1,030,000
Total Assets $4,740,000 Total Liabilities & Equity $4,740,000
a. What is the net interest income (NII) for the bank at the end of the first year? (4 points)
b. Suppose that interest rates are expected to increase by 50 basis points (0.5%) at the end of the
first year. What will the NII be at the end of the second year? (4 points)
c. If interest rates change as expected, the value of the bank’s loans will decrease in value to
$2,933,752. What will happen to the market value of the bank’s equity? Why? (3 points)
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3. Given the following balance sheet, analyze the bank’s interest rate risk by answering the questions
below. Dollars are in millions.
Assets Liabilities and Equity
Cash $ 6.57 Demand deposits $ 34.77
1-month T-bills (5.55%) 25.88 6-month CDs (3.92%) 35.87
6-month T-bills (5.24%) 15.90 1-year CDs (4.5%) 38.76
10-year T-bonds (3.95%) 49.42 2-year CDs (2.95%) 21.43
5-year business loans (7.44%) 104.86 5-years CDs (3.00%) 56.87
7-year business loans (6.95%) 75.33 Long-term debt (5.15% fixed rate) 144.55 20-year mortgages, floating rate
(6.12%, reset every 6 months) 112.65 Equity 68.76
Premises 10.40
Total Assets $ 401.01 Total Liabilities and Equity $ 401.01
a. Calculate the bank’s net interest income (NII). (8 points)
b. Calculate (i) the one-year repricing gap (CGAP) and (ii) the gap ratio for the bank. (6 points)
c. Use the repricing gap model to estimate the change in net interest income (ΔNII) if interest rates
are expected to decrease by 125 basis points next year. Assume that the spread between rates
on assets and liabilities remains constant. (3 points)
d. Estimate ΔNII if interest rates on rate-sensitive assets decrease by 110 basis points and interest
rates on rate-sensitive liabilities decrease 140 basis points. (4 points)
e. Why are the answers in c. and d. different? How do these estimates represent the CGAP effect
and the spread effect? Explain. (3 points)
4. Suppose a bank has financed a $11,000,000 10-year loan with an annual coupon rate of 8.34% with
a 15-year $11,000,000 bond with a semiannual coupon rate of 6.76%. The yield on the loan is 8.55%
and the yield on the bond is 6.32%.
a. Calculate the (i) duration and (ii) modified duration for the loan. (7 points)
b. Calculate the (i) duration and (ii) modified duration for the bond. (7 points)
c. If market interest rates decrease 150 basis points, estimate the effect on the market value of the
bank’s equity from this arrangement. (6 points)
5. An insurance company owns a 30-year Treasury bond with a 4.75% coupon rate. The bond has a
$100,000 face value and pays its coupon semiannually. Its duration is 16.7891, current market price
is $107,700 and its current yield to maturity is 4.29%. The insurance company is concerned that
interest rates may increase by 82 basis points. Treasury bond futures on the same bond are
currently available with a price of 119.56.
a. If interest rates rise by 82 basis points, what will be the impact on the insurance company’s
Treasury bond value? Will it increase or decrease in value? By how much? Support your answer
with appropriate calculations. (4 points)
b. If the insurance company hedges its position in the Treasury bond with a Treasury future, what
position should it take in the future? Why? (3 points)
3
c. Suppose interest rates rise by the expected 82 basis points and the insurance company has
hedged its position as you recommend in b. Calculate the net value of the hedge after the
increase in interest rates. (6 points)
6. A financial institution currently uses a base rate of 6.5%, charges an origination fee of 0.88% and
requires a compensating balance of 15%. The Federal Reserve imposes a 10% reserve requirement
on the bank’s demand deposits. For a customer with a 4.9% risk premium, calculate the bank’s ROA
on the loan. (6 points)
7. A bank is considering a loan applicant for a $13,500,000 6-year loan. The servicing fee is expected to
be 110 basis points and the bank’s cost of funds, its RAROC benchmark, is 11.5%. The estimated
maximum change in the borrower’s risk premium is 3.7%. The loan’s duration is 4.5743 years and
current market interest rates for similar loans is 14.0%. Based on the RAROC model, should the bank
make the loan? Why or why not? (10 points)
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