Suppose you want to hedge a $$420$ million bond portfolio with a duration of $7\mathrm{.}8$ years using $10-$year Treasury note futures with a duration of $4\mathrm{.}8$ years, a futures price of $103,$ and $102$ days to expiration. The multiplier on Treasury note futures is $$100,000.$ How many contracts do you buy or sell? $($Round your answer to the nearest whole number.$)$

Contracts

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