Question

A bank wishes to hedge its $30 million face value bond portfolio (currently priced at 99 percent of par). The bond portfolio has a duration of 9.75 years. It will hedge with T-bond futures ($100,000 face) priced at 98 percent of par. The duration of the T-bonds to be delivered is nine years. How many contracts are needed to hedge? Should the contracts be bought or sold? Ignore basis risk.

Answer 1

The wishes to hedge against a fall in the value of the bond portfolio. The value of the bond portfolio would fall if interest rates rise. Therefore, T-bond futures should be sold because T-bond futures gain in value if interest rates rise.

Number of contracts to sell = (market value of bond portfolio * duration of bond portfolio) / (price of T-bond futures * duration of T-bond futures)

Number of contracts to sell = (($30,000,000 * 99%) * 9.75) / (($100,000 * 98%) * 9)

Number of contracts to sell = 328.32

As fractional contracts cannot be sold, this is rounded off to 328

Number of contracts to sell = 328