On January $4,2021,$ an $FI$ has the following balance sheet $($rates $=10$ percent$)$

Assets

A

$D_A=6$ years

Liabilities$/$Equity

$D_L=4$ years

Duration Gap $=[6-(\frac{170}{200})4]=2\mathrm{.}6$ years $>0$

The $FI$ manager thinks rates will increase by $0\mathrm{.}75$ percent in the next three months. If this

happens, the equity value will change by:

$E=-[6-\frac{170}{200}(4)]200m\frac{0\mathrm{.}0075}{1\mathrm{.}10}=-$$$3,545,455$

The $Fl$ manager will hedge this interest rate risk with either futures contracts or option

contracts.

If the Fl uses futures, it will select June T$-$bonds to hedge. The duration on the T$-$bonds

underlying the contract is $14\mathrm{.}5$ years, and the T$-$bonds are selling at a price of $$114\mathrm{.}34375$ per

$$100,$ or $$114,343\mathrm{.}75.$ T$-$bond futures rates, currently $9$ percent, are expected to increase by

$1\mathrm{.}25$ percent over the next three months.

If the $Fl$ uses options, it will buy puts on $15-$year T$-$bonds with a June maturity, an exercise price

of $113,$ and an option premium of $136\%$ percent. The spot price on the T$-$bond underlying the

option is $$135\mathrm{.}71875$ per $$100$ of face value. The duration on the T$-$bonds underlying the

options is $14\mathrm{.}5$ years, and the delta of the put options is $-0\mathrm{.}75.$ Managers expect these T$-$bond

rates to increase by $1\mathrm{.}24$ percent from $7\mathrm{.}875$ percent in the next three months.

If by April $4,2021,$ balance sheet rates actually fall by $0\mathrm{.}75$ percent, futures rates fall by $1\mathrm{.}05$

percent, and T$-$bond rates underlying the option contract fall by $1\mathrm{.}24$ percent, would the $FI$ have

been better off using the futures contract or the option contract as its hedge instrument? Why?