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 bond portfolio using duration-based hedging, you need to calculate the number of futures contracts required. The formula to calculate this is:$$ \text{Number of contracts} = \frac{\text{Value of Portfolio} \times \text{Duration of Portfolio}}{\text{Price of Futures Contract} \times \text{Duration of Futures Contract}} $$Given:- Value of Portfolio = $10,600,000- Duration of Portfolio = 2.2 years- Price of Futures Contract = $995,000- Duration of Futures Contract for a 90-day (or 0.25 year) T-bill is approximately 0.25 years, as the duration of a T-bill is roughly equal to its time to maturity.$$ \text{Number of contracts} = \frac{10,600,000 \times 2.2}{995,000 \times 0.25} = \frac{23,320,000}{248,750} = 93.75 $$Therefore, you would need 93.75 futures contracts to hedge the exposure. Since you cannot purchase a fraction of a contract, you would need to round this number to the nearest whole number depending on your hedging strategy.

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