Your bond portfolio has a value of $10,600,000 with a duration of 2.2 years. How many 90-day US Treasury bill futures contracts do you need to hedge this exposure if the futures contract is priced at $995,000? Assume you are carrying out duration-based hedging.
A) 1.21
B) 5.86
C) 10.65
D) 93.75

Question

Quizplus · Accepted Answer

To hedge the exposure of the bond portfolio using duration-based hedging, you need to calculate the number of futures contracts required. The formula to calculate this is:$$ \text{Number of Contracts} = \frac{\text{Portfolio Value} \times \text{Portfolio Duration}}{\text{Futures Price} \times \text{Futures Duration}} $$Given that the portfolio value is $10,600,000, the portfolio duration is 2.2 years, and the futures contract is priced at $995,000, we need to adjust the duration for the 90-day (or approximately 0.25 year) US Treasury bill futures contract. Since the duration of a 90-day T-bill is approximately its time to maturity (because it's a short-term, discount instrument with no coupon payments), we use 0.25 years as the futures duration.$$ \text{Number of Contracts} = \frac{10,600,000 \times 2.2}{995,000 \times 0.25} $$$$ \text{Number of Contracts} = \frac{23,320,000}{248,750} $$$$ \text{Number of Contracts} = 93.75 $$Therefore, you would need 93.75 futures contracts to hedge the exposure. Since you cannot purchase a fraction of a contract, in practice, you would round to the nearest whole number of contracts.

Your Bond Portfolio Has a Value of $10,600,000 with a Duration