# solution

Dudley Hill Bank has the following balance sheet:

The bank manager receives information from an economic forecasting unit that interest rates are expected to rise from 8 to 9 percent over the next six months.

a. Calculate the potential loss to Dudley Hillâ€™s net worth (E) if the forecast of rising rates proves to be true.

b. Suppose the manager of Dudley Hill Bank wants to hedge this interest rate risk with T-bond futures contracts. The current future price quote is 122.03125Â per 100 of face value for the benchmark 20-year, and the minimum contract size is 100,000,Â so Â  Â Â  equals 122,031.25. The duration of the deliverable bond is 14.5 years. That is, Â Â  Â Â 14.5 years. How many futures contracts will be needed? Should the manager buy or sell these contracts? Assume no basis risk.

c. Verify that selling T-bond futures contracts will indeed hedge the FI against a sudden increase in interest rates from 8 to 9 percent, a 1 percent interest rate shock.

d. If the bank had hedged with Eurodollar futures contracts that had a market value of \$98Â  per Â \$100 of face value, how many futures contracts would have been necessary to hedge fully the balance sheet?

e. How would your answer for part (b) change if the relationship of the price sensitivity of futures contracts to the price sensitivity of underlying bonds were Â Â  Â Â 1.15?

f. Verify that selling T-bond futures contracts will indeed hedge the FI against a sudden increase in interest rates from 8 to 9 percent, a 1 percent interest rate shock. Assume the yield on the T-bond underlying the futures contract is 8.45 percent as the bank enters the hedge, and rates rise by 1.154792 percent

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