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?

Question

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?

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The Answer of 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.

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