ANSWER IS NOT $7111$

Yields on short$-$term bonds tend to be more volatile than yields on long$-$term bonds. Suppose that

you have estimated that the yield on $20-$year bonds changes by $8$ basis points for every $20\mathrm{.}25-$

basis$-$point move in the yield on $5-$year bonds. You hold a $$1\mathrm{.}2$ million portfolio of $5-$year maturity

bonds with modified duration $4$ years and desire to hedge your interest rate exposure with T$-$bond

futures, which currently have modified duration $9$ years and sell at $.$ How many futures

contracts should you sell?

Note: Do not round intermediate calculations. Round your final answer to the nearest whole

number.

Answer is complete but not entirely correct.