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	102.85	4.06
2	6%	10	106.53	8.05

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?

Correct Answer

9,738,510.07 margin of error +/- 1%

First, find the dollar duration of the existing portfolio.

Then find the value of the new portfolio that would have the same dollar duration.

Keep in mind that duration of cash is 0.

Keep in mind also the difference between market value of par value! You are given portfolio par value and are asked for par value, but dollar duration is based on market price.