# pay fixed, receive floating swap calculation

last year’s exam had a question about this topic, yetI didn’t find in the CFA books specific calculation example. I understand how the receive/pay fixed swap duration is calculated but need to confirm whether the floating swap duration is equivalent to following example: (1/2 / 2) - 0.75 (2) = 0.25 - 1.5 = -1.25 [two year pay fixed, receive floating swap with semi-annual payments]. I didn’t recall coming across this in the book regarding how the “(1/2 / 2)” floating duration was calculated. why would it be divided by 2 whereas the pay fixed would be multiplied by 2…i thought the receive floating would be multiplied by 2 as well. Just making sure it’s the way it is done/calculated.

Pay fixed side is usually given, but if not, multiply (.75 x maturity of swap) for an approximation. Pay floating is half the time between payments (annual pay is .5 duration, semi-annual is .25, etc.).

You are estimating the duration on both fixed and floating legs… Floating usually has a very short maturity (3 months, 6 months…) Hence, to estimate the average duration, CFAI suggests to take the duration of semiannual payments (0.5) and divide it by two… which is why your floating leg has a formula (1/number of payments a year)/2 Now for the fixed side. CFAI simply suggest to take 75% of the maturity of the fixed bond. In this case, it says 2 years. So the duration of the fixed leg would be 2 years *75%. And if you are paying floating and receiving fixed, your net duration will be 75%*2 - 1/4

So whatever you are doing (like in the example above where you are paying floating) goes on the back-half of the equation? Fixed - Floating