Swap Durations

CFA Level III Derivatives
#1

Pls help - I’m confused :frowning_face:here is my (mistaken?) understanding;

Company A takes out a pay floating swap. Since, pay floating swaps have positive duration, company now has a higher duration (conclusion 1) .

Company A has fixed rate debt, and through a pay floating swap effectively ends up with a net floating rate liability. Thus, the firm’s equity is now sensitive to interest rate changes. In effect, the company has a net liability with a lower duration than before the swap (conclusion 2), as A is left with floating rather than fixed debt.

But my conclusions 1 & 2 are contradicting one another! :sob: Can someone please enlighten me (this is driving me to grumpiness). Thank you in advance.

#2

Okay so ill spell it out like this:

  1. company A has a pay fixed liability originally from what you say above

  2. company enters into a received fixed, pay floating swap, as yu state above.

  3. the swap has a higher duration since youre receiving fixed.

  4. now the fixed liability is cancelled out, paying and receiving it. You’re left with a pay floating which has a duration of half its reset period. (Lower)

#3

thanks googs 1484. i follow that, but the duration maths does not seem intuitive… :frowning_face:

  1. company A has a pay fixed liability originally from what you say above Say Duration is 5.0

  2. company enters into a received fixed, pay floating swap, as yu state above. Say Duration of swap is 4.0

  3. the swap has a higher duration since youre receiving fixed.

  4. now the fixed liability is cancelled out, paying and receiving it. You’re left with a pay floating which has a duration of half its reset period. (Lower) Understood, but if you add Duarations from step 1) 5.0 + step 2) 4.0 = 9.0 i.e. higher not lower duration ?

#4

Company has to pay a fixed liability - Duration = 5 originally.

You enter into a Pay Floating, Received Fix Swap. Say 1/2 year Float, 5 year Fixed => Duration of Swap = 0.5*0.5 - 5*0.75 = -3.5

Net Duration including the Swap = -5 - (-3.5) = -=1.5

===================

You entered into Pay Floating because you expected your interest rates to fall. But if they rose instead - you are up against it. You are going to pay something to the tune of the (1.5 Duration Level) on the fixed liability + additional on the Floating side as well (because of the higher interest rates you pay on the floating side).

also your market value of your liability will RISE - because it is a falling interest rate environment.

#5

thank you, cpk 123. The arithmetic now makes sense, using the negative duration for the original fixed liability i.e. -5 rather than the +5 which I had.

#6

You sure your math is right cpk? The pay fixed side is .75 of its maturity I believe, not .75 of its duration. The duration is what we are after.

#7

Based on mr-stress example I’d say our overall exposure is -5 duration on pay fixed liability, +4 net duration on receive fixed pay floating swap, for a total of 4-5=-1 net duration.

#8

agree googs1484 net duration = -4- (-5) = +1

i think cpk was assuming 5 year floating bond rather than duration

#9

-1 net duration Mr stress. Paying a duration of -5…receiving a duration of 4…4-5=-1