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.

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Quizplus · Accepted Answer

The correct answer is B because the number of T-bond futures contracts necessary to hedge the balance sheet is 1,888 contracts. This is calculated by taking the total duration of the assets (10 years * $50 million + 10 years * $200 million = $2,500 million-years) and subtracting the total duration of the liabilities (3 years * $235 million = $705 million-years), which gives a net duration of $1,795 million-years. Dividing this by the duration of the deliverable bonds (9 years) gives the number of contracts needed (1,888 contracts).

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