A bank has the following information:

Assets $($$M$)175$

Asset Duration $($Yrs$)5\mathrm{.}25$

Liabilities $($$M$)150$

Liability Duration $($Yrs$)3\mathrm{.}5$

Market yields $(\%)4\mathrm{.}00\%$

The bank wants to hedge with a Eurodollar futures contract with the following characteristics

Price $(\%$ of face value$)96$

Rate on Eurodollar CDs $(\%)2\%$

Duration of Eurodollar contracts $0\mathrm{.}75$

a$.$ What is the correct strategy for hedging futures to offset losses on the bank portfolio and why?

b$.$ Assuming spot and futures price move in a $1$ to $1$ manner, how many futures contracts are needed to fully hedge the bank portfolio?

c$.$ If rates were to rise or fall by $75$bps show that the hedge would leave the bank immunized

d$.$ If instead of using Eurodollar futures the bank used Treasury bond futures with the following characteristics

how many futures contracts would it need to fully immunize the balance sheet?

Treasury futures Price $(\%$ of face value$)$ $$97$

Yield $2\mathrm{.}50\%$

Duration $8$

e$.$ What considerations would help make the decision whether to go with Treasury or Eurodollar futures?