# Duration of Fixed Rate Swap - Assume 0.75 x N?

I understand the concept behind duration of fixed and floating rate swaps, but most of the problems I’ve seen give you the fixed rate duration. However, in one of my recent practice questions, they did not provide the number and the answer guide said I should assume 0.75 x # of years, is that a general rule of thumb? I don’t recall reading 0.75… thanks in advance.

No. Floating rate side should always between 0 and 1, regardless of number of years. I woul say rule of thumb is to assume its 0.5.

Read my question over again, I’m asking how to calculate the duration of fixed rate of the swap. I know that floating is 0.5x the next reset period, but how does one calculate the fixed rate if not given? If I enter a 2 year swap, with 6m resets, then floating = 0.5 x 0.5 (half year) = 0.25. However, for fixed do I assume 0.75 x 2 (# of years for swap) = 1.5?

The swap (in this case) is a combination of a short hypothetical fixed rate bond and a long hypothetical floating rate bond -> therefore you can assume that the hypothetical bond has the same maturity as the swap, always (for the purpose of calculating swap duration).

For the 1 year Swap: FRN Duration is 0.0417 and Fixed Rate Duration is -0.75 (75% of a year). Swap Duration is -0.7083.

For the 2 year Swap: FRN Duration is 0.25 and Fixed Rate Duration is -1.5 (75% of two years). Swap Duration is -1.25.

Interested to know as well…

A pay fixed receive floating swap is just a portfolio of a long floater and short fixed rate bond so these two constituent securities must have the same maturity as the swap they replicate.

As for 0.75 -> that number was picked out of the blue, it could be anything. They use 0.75 x No. of Years as a rough estimate of the ‘average or typical’ bond’s duration - they would give this to us on the exam.

I UNDERSTAND that a plain vanilla swap can be thought of issuing fixed, investing floating. My question is even simpler however, as you demonstrated above… how/why do we always assume the duration of a fixed rate bond (or the fixed leg of a swap) is 0.75 x maturity.

Where does the 0.75 come from? I know in general, the majority of cash flows will be weighted towards the end of the bond given it’s bullet structure but it still doesn’t explain to me at least, why 0.75 as opposed to 0.8 or 0.82? Is 0.75 an easy number to remember, and in general is “close enough”?

0.75 is a rough estimate to go by, calculating the bond’s actual duration would be too time consuming as that depends on coupon, maturity, ytm etc. etc.

Many thanks!

Unfortunately the practice question I did not disclose to use 0.75 in the vignette. I guess I will use 0.75 going forward as my assumption as that’s what the answer guide stated to use.

Which vignette is this?

This part is incorrect.

For floating side, it is half of the repricing frequency…

Ex) semi anual payments/repricing: .5 x .5 = .25 duration

quarterly payments/repricing = .5 x .25 = .125 duration

For fixed side: assume duration is .75 of n (if a duration is not given)

I stumbled on this question as well, having never heard of the 75% of maturity rule. This was on a CFAI mock so it’s defnitiely fair game. I did read through the curriculum and found the explanation of 75%, although it is not emphasized much. If not given the fixed side duration, assume it is 75% of maturity.

Mock 2012, question 40

I got the same doubt and confirmed that the Schweser does not mention it.

The curriculum however does mention to use 0.75 as a suggestion (book 5, page 451).

However I find it to be VERY STUPID, and even more to fail do mention it in the stem. In times of low interest rates and consequently low coupons, medium duration is probably closer to 1 than it is to 0.75.

Yeah, i saw this question this morning and said WTF?