Question

A $300 million bond portfolio currently has a modified duration of 12.5. The portfolio manager would like to reduce the modified duration of the bond portfolio to 8, by using a futures contract priced at $105,250. The futures contract has an implied modified duration of 9.25. The portfolio manager has estimated that the yield on the bond portfolio is about 8% more volatile than the implied yield on the futures contract. Should he enter a long or a short futures position? Calculate the number of contracts needed to change the duration of the bond portfolio

Answer 1

Number of contracts needed to change duration	=	{(target duration - current duration)* yield volatility * portfolio value } / {duration of future contract * contract price * contract yield volatility}
		=(8-12.5)*300000000*1.08/(105250*9.25)
		-1498
		contracts Since the answer is with negative sign, hence future contracts are to be shorted.