13. Among the hedges described below for a bond portfolio, what is the best duration?based hedge using 3?month US Treasury bond futures contract? Assume that

?            your bond portfolio has a value of USD 1 million as of today.

?            the duration of your bond portfolio in 3 months is 8.5 years.

?            the 3?month futures contract is quoted USD 95.5.

?            the cheapest?to?deliver Treasury bond under the futures contract has a coupon of 5.75%, maturity in 11.8 years and a duration of 7.7 years in 3 months.

?            each futures contract requires the delivery of USD 100,000 face value of bonds.

A. Long 13 contracts

B. Short 13 contracts

C. Long 12 contracts

D. Short 12 contracts

Correct answer is Dfficeffice" />

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