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 four 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 $8\mathrm{.}5295$ percent, and a duration of $10\mathrm{.}3725$ years. $(LG24-2,LG24-3)$

a$.$ Should the bank go short or long on the futures contracts to establish the correct macrohedge?

b$.$ How many contracts are necessary to fully hedge the bank?

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 $0\mathrm{.}25$ year, how many futures contracts would have been necessary to fully hedge the balance sheet?

e$.$ What additional issues should be considered by the bank in choosing between $T-$bond or $T-$bill futures contracts?