Jackie manages a $620 million bond portfolio which has a duration of 4.05 years. She wants to hedge the portfolio with Treasury note futures that have a duration of 4.53 years and a futures price of 112. U.S. Treasury notes futures contracts are based on a par value of $100,000 and quoted as a percentage of par. How many contracts does she need to sell to complete this hedge?

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Quizplus · Accepted Answer

To hedge a bond portfolio using Treasury note futures, the number of contracts needed can be calculated using the formula:$$ \text{Number of Contracts} = \frac{\text{Portfolio Value} \times \text{Duration of Portfolio}}{\text{Futures Price} \times \text{Contract Size} \times \text{Duration of Futures}} $$Given:- Portfolio Value = $620,000,000- Duration of Portfolio = 4.05 years- Futures Price = 112 (since futures are quoted as a percentage of par, the actual price is 112% of $100,000 = $112,000)- Contract Size = $100,000- Duration of Futures = 4.53 years$$ \text{Number of Contracts} = \frac{620,000,000 \times 4.05}{112,000 \times 100,000 \times 4.53} $$$$ \text{Number of Contracts} = \frac{2,511,000,000}{508,360,000} $$$$ \text{Number of Contracts} \approx 4,949 $$Therefore, Jackie needs to sell approximately 4,949 contracts to hedge her bond portfolio.

Jackie Manages a $620 Million Bond Portfolio Which Has a Duration