Tree Row Bank has assets of $150 million, liabilities of $135 million, and equity of $15 million. The asset duration is six years and the duration of the liabilities is 4 years. Market interest rates are 10 percent. Tree Row Bank wishes to hedge the balance sheet with treasury bond futures contracts, which currently have a price quote of $95 per $100 face value for the benchmark 20-year, 8 percent coupon bond underlying the contract, a market yield of 8.5295 percent, and a duration of 10.3725 years.
c) Verify that the change in the futures position will offset the change in the cash balance sheet position for a change in market interest rates of plus 100 basis points and minus 50 basis points
d) If the bank had hedged with Treasury bill futures contracts that had a market value of $98 per $100 of face value and a duration of 0.25 years, how many futures contracts would have been necessary to fully hedge the balance sheet?