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. $\begin{array}{llr}\text { Consumer loans } & \$ 50 \text { million Deposits } & \$ 235 \text { million } \\\text { Commercial Loans } & \$ 200 \text { million Equity } & \$ 15 \text { million } \\\text { Total Assets } & \$ 250 \text { million Total Liabilities \& Equity } & \$ 250 \text { million }\end{array}$ 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. , $\Delta$ R/(1 + R) = 0.01,the implied rate on the deliverable bonds in the futures market increases by 1.1 percent,i.e. , $\Delta$ R_f/(1 + R_f) = 0.011?

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