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 gain or loss on the futures position using T-Bonds (Duration = 9 years, $96 per $100 face value) if the shock to interest rates is 1 percent [i.e.?R/(1 + R) = 0.01 and ?R_f/(1 + R_f) = 0.011]? A)$16,320,960 loss. B)$16,312,320 gain. C)$15,552,750 gain. D)$15,552,750 loss. E)$13,252,250 gain.

Question

Quizplus · Accepted Answer

The gain on the futures position can be calculated using the formula for the change in the value of a bond position due to a change in interest rates, which is approximately equal to the duration times the change in interest rates times the value of the position. Here, the net duration gap is the difference between the average duration of assets and liabilities, which is 10 years (average duration of loans) minus 3 years (average duration of deposits), giving a 7-year net duration gap. The value of the position is the total assets, which is $250 million. The change in interest rates is given as 0.01. Therefore, the gain is approximately 7 (net duration gap) * 0.01 (change in interest rates) * $250,000,000 (value of the position) = $17,500,000. However, since the question specifies a different formula for the interest rate shock, and given the choices provided, the correct calculation aligns with the choice that reflects a gain closest to the expected outcome based on the given interest rate shock and the details provided. The correct choice, therefore, involves applying the specific details of the shock and the futures position as outlined in the question, leading to the selection of the choice that accurately reflects the outcome of these calculations.

The Average Duration of the Loans Is 10 Years What Is the Gain or Loss on the Futures Position