Swap - Fixed rate versus float rate duration

[GET_RID]

Hi guyz,

In a swap, being a fixed rate payer why do we multiply the maturity of the swap by 75% to get the duration of the fixed leg swap.

[sunseeker]

Because the fixed leg of the swap (which has longer duration) can be deemed as a fixed-rate bond and usually fixed-rate bonds have a duration equal to 75% of their life.

Hope it helps

[S2000magician]

@sunseeker

Because the fixed leg of the swap (which has longer duration) can be deemed as a fixed-rate bond and usually fixed-rate bonds have a duration equal to _ somewhere in the neighborhood of _ 75% of their life.

There.

That’s better.

[sunseeker]

much appreciated S2000magician.

[QuinnJ]

Thanks for the info. Is the concept mentioned anywhere in the book? Or it is more based on practical experiences.

[S2000magician]

I don’t recall if it’s mentioned in the curriculum or not.

A (very, very rough) rule of thumb.

[cpk123]

you need to read the white text well in the CFA Level III curriculum, definitely

“The terms of the swap will affect the need to renew it as well as its duration and the notional principal required. It would probably be best for the swap to have a maturity at least as long as the period during which the duration adjustment applies. Otherwise, the swap would expire before the bond matures, and QAM would have to initiate another swap. The maturity and payment frequency of the swap affect the duration. Continuing with the assumption (for convenience) that the duration of the fixed-rate bond is approximated as 75 percent of its maturity, we find, for example, that a one-year swap with semi-annual payments would have a duration of 0.25 – 0.75 = –0.50. A one-year swap with quarterly payments would have a duration of 0.125 – 0.75 = –0.625. A two-year swap with semiannual payments would have a duration of 0.25 – 1.50 = –1.25. A two-year swap with quarterly payments would have a duration of 0.125 – 1.50 = –1.375.”

[jahid_107]

@cpk123

you need to read the white text well in the CFA Lievel III curriculum, definitely

“The terms of the swap will affect the need to renew it as well as its duration and the notional principal required. It would probably be best for the swap to have a maturity at least as long as the period during which the duration adjustment applies. Otherwise, the swap would expire before the bond matures, and QAM would have to initiate another swap. The maturity and payment frequency of the swap affect the duration. Continuing with the assumption (for convenience) that the duration of the fixed-rate bond is approximated as 75 percent of its maturity, we find, for example, that a one-year swap with semi-annual payments would have a duration of 0.25 – 0.75 = –0.50. A one-year swap with quarterly payments would have a duration of 0.125 – 0.75 = –0.625. A two-year swap with semiannual payments would have a duration of 0.25 – 1.50 = –1.25. A two-year swap with quarterly payments would have a duration of 0.125 – 1.50 = –1.375.”

Hello cpk123!!!

I am perplexed with how curriculum calculates the duration of the float component and rationale behind the calculation. Would you please explain me.

[cpk123]

float = average of the time period the floating leg is due at.

E.g. a quarterly period float leg - has 0 duration at the start, and resets to the par value at the end of a quarter year. So average of 0 and 0.25 = 0.125 is the duration of the floating quarterly swap.

For a half year floating leg = (0 + 0.5)/2 = 0.25