why is the duration of pay fixed swap negative

CFA Level III
#1

can someone explain why the duration of a pay fixed swap negative. I always get confused.

Thanks in advance

#2

Answering in bullet points:

Investment in bonds -> positive duration -> receive fixed amount

Issue bonds -> negative duration -> pay fixed amount

Pay fixed is like issuing bonds with fixed payment

Receive floating is like investing in bonds with floating payment

Fixed has higher absolute duration than floating payment (rates are reset periodically)

Pay fixed (negative duration) plus receive fixed (positve duration)

Overall: Negative Duration

#3

Two legs to pay fixed swap

  1. pay fixed: Look at it as shorting a bullet bond. If a bullet bond that receives fixed coupon payments is gives positive duration, a pay fixed will be negative.

Summary: Fixed payment asset = +ve duration, Fixed payment liability = -ve duration

  1. receive floating: close to zero. Duration = 1/2 * 1/n, where n is number of n periods in a year.

Overall: -ve duration

#4

Put very simply, if holding a bond provides positive duration then paying a fixed liability will provide negative duration. Opposites bro…

#5

When asking if a pay fixed swap will reduce CF risk and interest rate risk (duration) of a portfolio, consisting of a short floating rate bond…

The CF risk is reduced because your payments are now fixed (more certainty, less risk).

What happens to interest rate risk of the ENTIRE position?

I understand that duration is negative for the swap, AND, the duration of of the position is also negative.

However; the absolute value of duration is still nonzero…

Does this imply that interest rate risk is reduced or increased?

#6

You are long a floating rate note. You are short a fixed rate note. Fixed rate duration is generally larger than floating rate duration therefore the net effect is being short duration (you gain when interest rates rise).