Suppose you want to hedge a $500 million bond portfolio with a duration of 5.1 years using 10-year Treasury note futures with a duration of 6.7 years, a futures price of 102, and 3 months to...

Suppose you want to hedge a $500 million bond portfolio with a duration of 5.1 years using 10-year Treasury note futures with a duration of 6.7 years, a futures price of 102, and 3 months to expiration. The multiplier on Treasury note futures is $100,000. How many contracts do you buy or sell?