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Why Floating-Rate Note Yields Depend on Projected Coupons

Article Quant Q&A · Author: NewInvestor
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Summary

The document explains that a floating-rate note’s yield to maturity is an internal rate of return based on its coupons and principal repayment. Because future coupon amounts have not yet been set, the calculated yield depends on the method used to project those payments; consequently, the yield can vary more than the discount margin.

It describes two common projection approaches in a Bloomberg terminal: holding the current index value constant or using the swap curve to project future index rates. To reconcile a yield quoted by another source, the answer recommends first matching the projected coupon cash flows, then checking whether the same cash flows produce the same IRR under the relevant conventions. The example’s yield discrepancy is not resolved, and the document notes that market data and calculation conventions may differ.

Key ideas

  • A floating-rate note’s yield is the IRR of its projected coupons and principal repayment.
  • Future coupon projections materially affect the calculated yield because those payments are not yet known.
  • Projection approaches can hold the current index rate constant or use a swap curve for future rates.
  • Yield comparisons should first reconcile projected cash flows, then reconcile IRR conventions.

Tags

Fixed incomeDerivatives pricingStatistics
Full text
# Calculating YTM for a floating rate bond


# Calculating YTM for a floating rate bond












I am trying to understand how YTM's are calculated for floating rate notes. I have had a go at calculating it and I am always a few bps off for every FRN I try to calculate. Does anyone have any ideas as to what I could be doing wrong?

*I am looking at a run sheet that I get from my advisory network.

Last price $101.25 Quoted margin 0.89% + 2.8% = 3.69% Quarterly payments

PMT = 3.69/4 = 0.9225 FV = 100 PV = -101.21 n = 4

I get the answer 2.16%

But the run sheet says 2.38%. What would I be missing?

Many thanks

## Answer by Dimitri Vulis (score 1)

https://quant.stackexchange.com/a/51763

The yield is the internal rate of return of the coupons and the principal repayment. For a floater, the future unset coupons are not known, and the value of the yield depends a lot on how you project them, making the yield less stable than DM.

On Bloomberg terminal, for example, there is a setting for how to project a floater's coupons. The default is to use the same index value. The non-default behavior is to use the swap curve to project the libor rate on future coupon dates.

I suggest you separate the project of matching other people's yields into two parts.

First, see if you can get their projected coupons, and see whether you match those or understand why they don't match (could well be due to different market data).

Second, check that if you plug their cash flows into your IRR calculation, you get the same answer as them - aren't missing some obscure conventions.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.