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. The duration of the T$-$bond is $10\mathrm{.}3725$ AND THE YIELD TO MATURITY IS $8\mathrm{.}5295$ percent

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 Eurodollar futures contracts that had a market value of $$98$ per $$100$ of face value, how many futures contracts would have been necessary to hedge fully the balance sheet?

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