The Average Duration of the Loans Is 10 Years What Is the Number of T-Bond Futures Contracts Necessary to Duration

Multiple Choice

The average duration of the loans is 10 years.The average duration of the deposits is 3 years. $$\begin{array} { | l | r | l | r | } \hline \text { Consumer loans } & \$ 50 \text { million } & \text { Deposits } & \$ 235 \text { million } \\\hline \text { Commercial Loans } & \$ 200 \text { million } & \text { Equity } & \$ 15 \text { million } \\\hline \text { Total Assets } & \$ 250 \text { million } & \text { Total Liabilities \& Equity } & \$ 250 \text { million } \\\hline\end{array}$$ What is the number of T-bond futures contracts necessary to hedge the balance sheet if the duration of the deliverable bonds is 9 years and the current price of the futures contract is $96 per $100 face value and if basis risk shows that for every 1 percent shock to interest rates, i.e., ?R/(1 + R) = 0.01, the implied rate on the deliverable bonds in the futures market increases by 1.1 percent, i.e., ?R_f/(1 + R_f) = 0.011?

A) 1,500 contracts.
B) 1,888 contracts.
C) 2,100 contracts.
D) 2,408 contracts.
E) 3,100 contracts.