$38.$ Radford Bank has a long position in $$275,000$ face value Treasury Bonds. The life of these bonds is $15$ years, but the duration is $12\mathrm{.}5$ years. These bonds generate $8\%$ yield. The current market value of these bonds is $97$:$25.$ The FI is taking position in the futures market in a similar asset that has face value of $$100,000$ per contract and currently selling for $97\%$ of face value. Duration of the futures contract is $6$ years and yield is $6\mathrm{.}5\%.$

How many contracts are needed to offset risk on the balance sheet?

a$.$ Long $3$

b$.$ Long $6$

c$.$ Short $6$

d$.$ Short $4$

$39.$ Radford Bank has a long position in $$275,000$ face value Treasury Bonds. The life of these bonds is $15$ years, but the duration is $12\mathrm{.}5$ years. These bonds generate $8\%$ yield. The current market value of these bonds is $97$:$25.$ The FI is taking position in the futures market in a similar asset that has face value of $$100,000$ per contract and currently selling for $97\%$ of face value. Duration of the futures contract is $6$ years and yield is $6\mathrm{.}5\%.$

What will be the net gain$/$loss from taking a position in the futures market if $$R is $1\%?$

a$.$ $$1050\mathrm{.}25$

b$.$ $$1233\mathrm{.}45$

c$.$ $$0$

d$.$ $$1666\mathrm{.}23$