# Swap Duration

Here’s a question from Schweser’s QBank:

A pay-floating counterparty in a plain-vanilla interest-rate swap also holds a long position in a fixed-rate bond. If the maturity of the bond and swap are both two years, the duration of the position will be:

_A) zero. B) greater than the duration of the bond alone. C)_less than the duration of the bond but greater than zero.

Your answer: C was incorrect. The correct answer was B) greater than the duration of the bond alone.

The duration of the position will increase with the addition of the pay-floating/receive-fixed position. Both of the remaining answers cannot be correct.

Why is C wrong? From my understanding:

The pay-floaiting side of a swap has an asset with a duration slightly less than the duration of the fixed payment structure. For example, for simplicity in this question, let’s say the reset was every 2 years. Then, ignoring prevent valuing, the floating payment would have the effect of -1 on the duration, and the fixed receipts would be +2 to the duration, so the duration of the swap asset alone would be about 1. So, when I look at option C above, the duration of the bond MUST be greater than the duration of the swap, right? Adding a bond position will increase the weighted average duration of the portfolio.

I mean the duration of the portofolio in the question is just:

Weighted Duration of Bond + Weighted Duration of Fixed Receipts - Weighted Duration of Floating Payments

Since the maturity of the bond and the swap are the same, mustn’t the duration of the swap be less than the bond?

This question/explanation is really confusing me. Duration of swaps seems really simple…

Hey this is more simple than you’re making it. Remember receiving fixed payments increases your portfolio duration and floating decreases.

Owning a bond = receiving fixed

Swap: Receiving fixed, pay floating.

So the swap is doubling the receive fixed exposure. If you wanted to decrease duration you’d buy a PAY fixed swap.

As SlaveII says, your duration is the duration of th bond plus the duration of the swap, and the duration of the swap is nearly the same as that of the bond.

If the bond’s duration is, say, 1½ years, the duration of this portfolio is about 3 years.