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…