A manager is holding a bond portfolio worth $$11$ million with a modified duration of $6$ years. She would like to hedge the risk of the

portfolio by short$-$selling Treasury bonds. The modified duration of T$-$bonds is $7$ years. How many dollars' worth of T$-$bonds should she

sell to minimize the variance of her position? $($Enter your answer in dollars not millions rounded to the nearest dollar value.$)$

Dollars' worth of T$-$bonds to be sold