Question

Suppose you want to hedge a $260 million bond portfolio with a duration of 8.5 years using 10-year Treasury note futures with a duration of 6.4 years, a futures price of 102, and 92 days to expiration. The multiplier on Treasury note futures is $100,000. How many contracts do you buy or sell

Answer 1

To hedge a $260 million bond portfolio with a duration of 8.5 years using 10-year Treasury note futures with a duration of 6.4 years, approximately 34 contracts need to be bought or sold.

Step-by-step explanation:

To hedge the $260 million bond portfolio with a duration of 8.5 years, using 10-year Treasury note futures with a duration of 6.4 years, you need to calculate the number of contracts to buy or sell.

First, calculate the modified duration of the bond portfolio:

Modified Duration of Bond Portfolio = Duration of Bond Portfolio / Duration of Treasury note futures

Modified Duration of Bond Portfolio = 8.5 / 6.4

Modified Duration of Bond Portfolio = 1.328125

Next, calculate the number of contracts:

Number of Contracts = (Portfolio Value * Modified Duration of Bond Portfolio) / (Futures Price * Duration of Treasury note futures * Multiplier)

Number of Contracts = (260,000,000 * 1.328125 / (102 * 6.4 * 100,000)

Number of Contracts = 34.17968

Therefore, you would need to buy or sell approximately 34 futures contracts.

Answer 2

To hedge the $260 million bond portfolio with a duration of 8.5 years using 10-year Treasury note futures with a duration of 6.4 years, you would need to buy or sell approximately 3,414 contracts.

Step-by-step explanation:

To calculate the number of futures contracts needed to hedge the $260 million bond portfolio, we need to determine the hedge ratio. The hedge ratio is calculated as the duration of the bond portfolio divided by the duration of the futures contract. In this case, the hedge ratio is 8.5 years / 6.4 years = 1.3281.

Next, we need to calculate the notional value of each futures contract. The notional value is equal to the futures price multiplied by the multiplier. In this case, the notional value is $102,000.

Finally, we divide the notional value of the bond portfolio by the notional value of each futures contract, and multiply by the hedge ratio to determine the number of contracts to buy or sell. So, the number of contracts to buy or sell is $(260,000,000 / $102,000) * 1.3281 = 3,413.75. Since you can't have fractional contracts, you would need to round this up or down to the nearest whole number depending on your risk tolerance and market conditions.