[ 2009 FRM Sample Exam ] Market risk measurement and management Q13

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It is generally assumed that the value of a bond portfolio to be hedged by the maturity of the futures contract will be the same as its today's value.  In this question, the portfolio value at the maturity of the futures will be $1 million.

The duration?based hedge ratio is

       N = (portfolio value * portfolio duration) / (futures contract value * futures duration)

N is the number of futures contract required to hedge the portfolio and it should be rounded to the nearest whole number.

A is incorrect because, to hedge the bond portfolio, we need to short bond futures.

B is incorrect because

N = (1,000,000 * 8.5) / ($100,000 * 0.955 * 7.7) = 11.56 ≈ 12 contracts

C is incorrect because, to hedge the bond portfolio, we need to short bond futures.

D is correct because

N = (1,000,000 * 8.5) / ($100,000 * 0.955 * 7.7) = 11.56 ≈ 12 contracts

Reference: John Hull, Options, Futures, and Other Derivatives, 5th ed. (ffice:smarttags" />New York: Prentice Hall, 2003), Chapter 5.

Type of Question: Market Risk