1. Use the following information about a hypothetical government security dealer named M.P. Jorgan. Market yields are in parenthesis, and amounts are in millions. All securities are selling at par equal to book value. (4 points)
Assets Liabilities and Equity
Cash $10 Overnight repos $250
1-month T-bills (7.05%) 85 Subordinated debt
3-month T-bills (7.25%) 100 7-year fixed rate (8.55%) 140
2-year T-notes (7.50%) 90
8-year T-notes (8.96%) 100
5-year munis (floating rate)
(8.20% reset every 6 months) 50 Equity 45
Total assets $435 Total liabilities & equity $435
a. What is the repricing gap if the planning period is 30 days? 3 months? 2 years? Recall that cash is a noninterest-earning asset.
b. What is the impact over the next 30 days on net interest income if interest rates increase 50 basis points on RSA and increase 70 basis points on RSL?
- The following one-year runoffs are expected: $10 million for two-year T-notes and $20 million for eight-year T-notes. What is the one-year repricing gap?
- If runoffs are considered, what is the effect on net interest income at year-end if interest rates rise 50 basis points for RSA and increase 80 basis points for RSL?
2. Gunnison Insurance has reported the following balance sheet (in thousands): (6 points)
Assets Liabilities and Equity
2-year Treasury note $175 1-year commercial paper $135
15-year munis $165 5-year note $160
Total Assets $340 Total Liabilities & Equity $340
All securities are selling at par equal to book value. The two-year notes are yielding 5 percent, and the 15-year munis are yielding 9 percent. The one-year commercial paper pays 4.5 percent, and the five-year notes pay 8 percent. All instruments pay interest annually. (5 points)
a. What is the weighted-average maturity of the assets for Gunnison?
b. What is the weighted-average maturity of the liabilities for Gunnison?
c. What is the maturity gap for Gunnison?
d. Calculate the values of all four securities of Gunnison Insurance’s balance sheet assuming that all interest rates increase 2 percent. What is the dollar change in the total asset and total liability values? What is the percentage change in these values?
e. What is the dollar impact on the market value of equity for Gunnison? What is the percentage change in the value of the equity?
1. You have discovered that the price of a bond rose from $975 to $995 when the yield to maturity fell from 9.75 percent to 9.25 percent. What is the duration of the bond? (1 point)
2. Calculate the duration of a two-year, $1,000 bond that pays an annual coupon of 10 percent and trades at a yield of 14 percent. What is the expected change in the price of the bond if interest rates decline by 0.50 percent? (2 points)
3. Suppose you purchase a six-year, 8 percent coupon bond (paid annually) that is priced to yield 9 percent. The face value of the bond is $1,000. (3 points)
a. Show that the duration of this bond is equal to five years.
b. Show that if interest rates rise to 10 percent within the next year and your investment horizon is five years from today, you will still earn a 9 percent yield on your investment.
c. Show that a 9 percent yield also will be earned if interest rates fall next year to 8 percent.
4. The following balance sheet information is available (amounts in thousands of dollars and duration in years) for a financial institution:
T-bills $90 0.50
T-notes 55 0.90
T-bonds 176 x
Loans 2,724 7.00
Deposits 2,092 1.00
Federal funds 238 0.01
Treasury bonds are five-year maturities paying 6 percent semiannually and selling at par. (5 points)
a. What is the duration of the T-bond portfolio?
b. What is the average duration of all the assets?
c. What is the average duration of all the liabilities?
d. What is the leverage adjusted duration gap? What is the interest rate risk exposure?
e. What is the forecasted impact on the market value of equity caused by a relative upward shift in the entire yield curve of 0.5 percent [i.e., DR/(1+R) = 0.0050]?
f. If the yield curve shifts downward by 0.25 percent [i.e., DR/(1+R) = -0.0025], what is the forecasted impact on the market value of equity?
g. What variables are available to the financial institution to immunize the balance sheet? How much would each variable need to change to get DGAP equal to 0?
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