FINANCI pter 14 Question 8 (of 8) 10.00 points Suppose you want to hedge a $420

Question

FINANCI pter 14 Question 8 (of 8) 10.00 points Suppose you want to hedge a $420 million bond portfolio with a duration of 3.6 years using 10-year Treasury note futures with a duration of 5.1 years, a futures price of 102, and 9 months to expiration. The multiplier on Treasury note futures is $100,000. How many contracts do you buy or sell? (Round your answer to the nearest whole number.) (Click to select) to sell to buy References eBook & Resources Worksheet Learning Objective: 14-04 How futures contracts can be used to transfer price risk Difficulty: Core Section: 14.5 Stock Index Futures MacBook Air 2 3 4 6 G H

Explanation / Answer

Number of contracts to be purchased/ sold is given by the formula :  
(Portfolio Value * Duration of the portfolio) / (Future Contract Price * Multiplier * Duration of futures contract)

Putting the values, No of contracts required = (420,000 * 3.6)/(102* 100,000* 5.1) = 29 (rounded to nearest integer)

As we are long on the bond, we would need to take short position in futures contract or sell the futures contract.
This long bond/short futures contract would give the intended hedge against the price fluctuations.
For ex- if the interest rates increase, bond values will reduce but the loss in the long portfolio position would be covered up by gain in the short futures position and vice versa.

This price senstivity hedge works well for small changes in interest rates but does not work well for large changes as the ratio changes continuosly.

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