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A manager is holding a bond portfolio worth $12 million with a modified duration of 7 years. She would like to hedge the risk of

A manager is holding a bond portfolio worth $12 million with a modified duration of 7 years. She would like to hedge the risk of the portfolio by short-selling Treasury bonds. The modified duration of T-bonds is 8 years. How many dollars worth of T-bonds should she sell to minimize the variance of her position?

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