Question $1(20$ marks$)$ Tree Row Bank has assets of $$150$ million, liabilities of $$135$ million, and equity of $$15$ million. The asset duration is six years and the duration of the liabilities is four years. Market interest rates are $10$ percent. Tree Row Bank wishes to hedge the balance sheet with Eurodollar futures contracts, which currently have a price quote of $$96$ per $$100$ face value for the benchmark three$-$month Eurodollar CD underlying the contract. The current rate on three$-$month Eurodollar CDs is $4\mathrm{.}0$ percent and the duration of these contracts is $0\mathrm{.}25$ years. Required: a$)$ Should the bank go short or long on the futures contracts to establish the correct macro$-$ hedge? $(4$ marks$)$ b$)$ Assuming no basis risk, how many contracts are necessary to fully hedge the bank? $(5$ marks$)$ c$)$ Verify that the change in the futures position will offset the change in the cash balance sheet position for a change in market interest rates of plus $100$ basis points and minus $50$ basis points. $(8$ marks$)$ d$)$ If the bank had hedged with Treasury bond futures contracts that had a market value of $$95$ per $$100$ of face value, a yield of $8\mathrm{.}5295$ percent, and a duration of $10\mathrm{.}3725$ years, how many futures contracts would have been necessary to fully hedge the balance sheet? Assume no basis risk. $(3$ marks$)$ Please give me the detailed process of solving the problem