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 $10$ basis points for every $26-$basis$-$point move in the yield on $5-$year bonds. You hold a $$1\mathrm{.}8$ 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 $F_0=$$$80.$ 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.