Question 721.2. It is August and Sally is a fund manager with $50.0 million invested in government bonds who is worried that interest rates are expected to be volatile over the next quarter (note: this question is inspired by Hull’s EOC Problem 6.18). She decides to use the December Treasury bond ("T-bond") futures contract to hedge the value of the portfolio. The current futures price is 108-00 or $108.00. Because each contract is for the delivery of $100,000 face value of bonds, the futures contract price is therefore $108,000.00. Suppose the modified duration of the bond portfolio in three months will be 13.0 years. The cheapest-to-deliver (CTD) in the T-bond contract is anticipated to be an bond with 18.0 years to maturity that pays a 5.0% semi-annual coupon; at maturity, the duration of this CTD bond is expected to be about 12.0 years.

However, the manager does not want to completely neutralize duration. Rather, she wants to REDUCE the portfolio's duration by 7.0 years, from 13.0 years to 6.0 years. About how many T-bond futures contracts should she trade to achieve this reduction in duration of the net portfolio?