Suppose you manage a $67.8 million bond portfolio that has a weighted average duration of 4.15 years. Concerned about your interest rate risk...

Suppose you manage a $67.8 million bond portfolio that has a weighted average duration of 4.15 years. Concerned about your interest rate risk exposure, you decide to hedge your position. If futures contracts on 5-year Treasury notes settling in 3 months are currently priced at 100-222, how many futures contracts must you buy or sell to perfectly hedge away all interest rate risk? Assume that 5-year Treasury notes currently yield 2.32 and have a duration of 3.95 years.