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Question: suppose you manage a bond portfolio with a current value...

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Suppose you manage a bond portfolio with a current value of $150,000,000 and a duration of 7.32. You need to hedge the interest rate risk of this portfolio for some reason. Today's date is Monday, December 10th, 2018 so the settlement price for a treasury bond is the 11th. You decide to use the 10-year T-note futures to hege. The cheapest to deliver bond is the 3% coupon bond with maturity date September 30, 2025 which is currently selling for a yield of 2.766% (price of 101.4766 or 1.014766 per 1$ of face value)

What is the duration of the CTD bond?

How many futures contracts do you enter into?

Do you go long or short these contracts?

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