# Duration of short position in a fixed rate bond

In determining the duration of fixed paying swap, the calc is DUR Float - DUR Fixed. I get the calc for DUR Float, but if the DUR fixed isn’t given, I’m not sure how to calc it.

The CFAI text Reading 38 p384 gives an explanation in the second paragraph that I just couldn’t follow. Anyone have a grasp on this?

75% of lenght of swap?

e.g. 2 years * 0.75 =1.5 -> Duration

75% of term is the duration of the fixed in a swap by convention

75% is it by default? If so, great, why do they go through the calc in the book?

are you sure about the pg # ?

oops p484

484

Original Floating rate (Pay Floating, Quarterly) = -0.5 * .25 = -0.125

Now by converting to fixed since you feared rising interest rates

your duration of the Swap = -0.75 * Maturity (Pay Fixed) + 0.125 (receive fixed)

so your net duration changed to -0.75 * Maturity of Loan.

IF loan was a 1 year loan, your net duration increased 6 fold = (0.75/0.125)

that is all :!

Thanks, but my question was how to come up with the .75 for the Fixed. If it is just convention, I’m good with it.

it’s a convention, if it’s not given use .75.