Question: A portfolio manager would like to replicate the dollar duration of a portfolio composed of $20 million par value of 5-year bonds, by using a

A portfolio manager would like to replicate the dollar duration of a portfolio composed of $20 million par value of 5-year bonds, by using a combination of 10 year bonds and cash.

The following information pertains to the bonds under consideration:

Bond Coupon (%) Maturity (y) Price ($ per 100) Duration
1 5% 5 102.43 4.11
2 6% 10 106.4 8.38

What is the par value of the 10 year bonds that must be acquired for the cash+bond portfolio, in order to match the dollar duration of the original portfolio?

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