$5.($Macrohedging with Futures$-$Step $3)$ 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 $($face value of the contract is $$1,000,000).$ The current rate on three$-$

month Eurodollar CDs is $4\mathrm{.}0$ percent and the duration of these contracts is $0\mathrm{.}25$ years.

a$.$ how many contracts are necessary to fully hedge the bank?

b$.$ 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.

$6.($Macrohedging with Futures$-$Step $3)$ 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.

If the bank had hedged with Treasury bond futures contracts that had a market value of $$95$ per

$$100$ of face value 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.