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MathinTucson
04-20-2009, 08:08 PM
From page 351 in Managing Investment Portfolios:

"We have constructed a portfolio consisting of three bonds in equal par amounts of $1,000,000 each."

They give the following information
Bond Market Value Duration Dollar Duration
1 $1,065,613 5.025 53,548
2 $ 978,376 1.232 12,054
3 $1,034,693 4.479 46,343

They calculate the dollar duration of the portfolio as
.01 x (1,065,613x5.025 + 978,376x1.232 + 1,034,693x4.479)/3 = 37,315

This answer says that a 100bps change in interest rates would change the value of the portfolio by $37,315. But if the portfolio consists of the three bonds, why wouldn't the change in portfolio value equal the sum of the changes in the values of the three bonds making up the portfolio (i.e., the sum of the dollar durations)?

I can understand why the duration of a portfolio is a weighted average of the durations of the component parts, but dollar duration represents an absolute change in value, not a percentage change.

Any thoughts?