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…