A portfolio manager plans to use a Treasury bond futures contract to hedge a bond portfolio over the next three months(until June 30). The portfolio is worth $100 million and consists of identical bonds with maturity of 3.25 years. The coupon rate is 8% (paid semiannually with the next payment in 3 months) and yield to maturity 10% continuously compounded. The yield curve is flat and assumed to remain flat. The futures price is 95-5, and each futures contract is on $100,000 of bonds. The T-bond that is expected to be cheapest to deliver has the coupon rate of 10%, YTM 9% and maturity on June 30, 2031.

1. What will be the duration of managers bond portfolio on June 30?
2. What will be the duration of the cheapest T-bond on June 30?
3. What position in futures contracts is required?