Suppose a $100,000 T-Bond futures contract whose underlying's duration is 9 years and has a current market price of $98,750.Market interest rates are 6 percent today but are expected to rise to 7.5 percent.What is the expected change in this futures contract's market price as a result of this change in interest rates?

Question

Quizplus · Accepted Answer

To calculate the expected change in the futures contract's price, we need to use the modified duration formula:

Modified Duration = Macaulay Duration / (1 + Yield)

The Macaulay duration for this bond is 9 years. Using the current yield of 6%, we can calculate the modified duration:

Modified Duration = 9 / (1 + 0.06) = 8.49

Now we can estimate the expected change in the futures contract's price using the following formula:

Expected % Change in Futures Price = -Modified Duration × Δ Yield

where Δ Yield is the change in yield as a decimal (7.5% - 6% = 0.015).

Expected % Change in Futures Price = -8.49 × 0.015 = -0.1274

So the expected change in the futures contract's market price is:

Expected Change in Futures Price = $98,750 × -0.1274 = -$12,576.75

Therefore, the answer is B.

Suppose a $100,000 T-Bond Futures Contract Whose Underlying's Duration Is