A hedge fund owns a $15 million bond portfolio with a modified duration of 11 years and needs to hedge risk but T-bond futures are only available with a modified duration of the deliverable instrument of 10 years.The futures are priced at $105,000.The proper hedge ratio to use is ______.

Question

Quizplus · Accepted Answer

Hedge ratio = Bond portfolio market value / (Futures price x Futures conversion factor x Futures modified duration)
Futures conversion factor = Bonds underlying futures contract / Bond price
Futures conversion factor for T-bonds is $100,000 par value / Bond price, which for a bond yielding 5% and maturing in 15 years is $128.11.
Hence, Hedge ratio = 15,000,000 / (105,000 x 128.11 x 10) = 157.12 (rounded to nearest whole number)
Therefore, the best choice is B) 157 as it is the closest to hedge ratio obtained.

A Hedge Fund Owns a $15 Million Bond Portfolio with a Modified