A question on Interest Rate Swap Fixed Leg Duration

CFA Level III Derivatives
#1

Hi guys, a quick question about the fixed leg duration in interest rate swap -

if it is not given in the case, can we assume that the " duration of the fixed leg is 75% of is maturity"?

Thanks!

#2

They’ll give it to you.

#3

Thanks S2000Magician!

I was just reviewing the 2014 real exam, Question 9, B where this is not given in the case but the answer was using 0.75 by default. So i was wondering if this can be used by default.

#4

Yes

#5

text does mention it as a default value that fixed rate swap’s duration is 75% of maturity.

Also in questions - I have not seen it mentioned at all, but used in the answer.

#6

Can someone please explain the example from the Lehigh topic test? In Q2 why is the duration of the swap -3.625? Why do we choose swap C? Thanks!

#7

Hi CPK, could you please advise me where can we find the default rate of 75% for fixed leg? Thanks

#8

we choose swap C because the higher Duration makes it a Lower Swap Notional Amount.

If it were a quarter year swap with 5 year duration

Fixed side = -5 *.75 = -.375

add in 0.125 for the floating side -> -3.75 + 0.125 = -3.625

#9

hi Medusa, i havent checked the topic you mentioned, but i think it should be same as the one in 2014 AM setion. First you calculate the Duration of all the swaps based on the rule (75% for fixed leg and 50% for floating leg). And then the case might or might not mention the low notional requirement for the Swap they purchase. Based on the NPswap = (Dtarget - Dportfolio)/Dswap * Portfolio notional, you will then choose accordingly.

#10

Thanks cpk123! So we’re just assuming a quarterly pay floating? Because the question doesn’t mention anything like that, if I’m not mistaken?

#11

medusa, i do not have access to the question you are referring to

#12

from the book - this para - and the highlighted text in BOLD

“Now let us discuss the duration of a swap. Remember that entering a pay-fixed, receive-floating swap is similar to issuing a fixed-rate bond and using the proceeds to buy a floating-rate bond. The duration of a swap is thus equivalent to the duration of a long position in a floating-rate bond and a short position in a fixed-rate bond. The duration of the long position in the floating-rate bond would, again, be about 0.125. What would be the duration of the short position in the fixed-rate bond? A one-year fixed-rate bond with quarterly payments would probably have a duration of between 0.6 and 1.0. Let us assume this duration is about 0.75 (nine months) or 75 percent of the maturity, an assumption we shall make from here out. So the duration of the swap would be roughly 0.125 – 0.75 = –0.625.”