Estimating Yield on a Premium Floating-Rate Note from Forward Rates
Summary
The document explains how to estimate the yield of a floating-rate note issued above par. Its example describes a multi-year note paying LIBOR plus a fixed spread and asks how the investor’s yield compares with that coupon margin. The proposed approach uses market-observed rates to estimate future coupon cash flows rather than treating future LIBOR fixings as arbitrary guesses.
First, derive expected floating coupons from the relevant LIBOR zero curve at each payment tenor, adding the note’s contractual spread. Then discount the resulting projected cash flows using a trial yield and solve for the yield that matches the issue price. This separates the curve’s role in projecting coupons from the yield’s role in pricing the note. The answer assumes semiannual payments and discrete compounding, and gives a general pricing equation rather than a worked numerical yield. It does not discuss alternative conventions, credit risk, or how the curve is built, so the method depends on having appropriate market rates and cash-flow dates.
Key ideas
- Project floating coupons using market-implied rates for the corresponding future tenors.
- Add the contractual spread to each projected reference-rate coupon.
- Discount the projected cash flows at a trial yield and solve for the yield consistent with the issue price.
- The stated pricing setup assumes semiannual coupons and discrete compounding.
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# What is the yield when a floating-rate note is issued above/below par?
# What is the yield when a floating-rate note is issued above/below par?
I am new in this area so all help is much appreciated!
Let's say a 3-year floating rate note pays a coupon of LIBOR+100 bps, and is issued at a premium with price = 100.5.
I understand that this must mean that the total yield for the investor is lower than LIBOR+100 bps. But how would you calculate what the yield is? I assume you must make guesses about the future LIBOR fixings?
## Answer by dmanuge (score 1, accepted)
https://quant.stackexchange.com/a/22086
Yes, you would make "guesses", but fortunately these guesses are derived from market-observed rates.
Assuming a semi-annual coupon rate and discrete compounding, the price of a bond ($P$) is given by:
$$ P=\sum_{i=1}^{2T} \frac{CF_i}{(1+\frac{Y}{2})^i} $$
where $CF_i$ is the cashflow at time $i$, $Y$ is the annual yield, and $T$ is the number of years. The cashflows are linked to LIBOR such that for all cashflows (except maturity):
$$CF_i = N(LIBOR_i +0.01)$$
where $N$ is the notional of the bond, and $LIBOR_i$ is the zero-coupon LIBOR rate at tenor $i$. Recall that LIBOR is a combination of rates that generate a curve at a variety of tenors. In order to determine the yield ($Y$), we must first determine the coupon payments that are based off of this curve. For example, a cashflow payment 1.5 years from now will be determined by the LIBOR zero-curve for the 1.5 year tenor. Once we solve for all of the cashflows ($CF_i$), the only remaining variable is $Y$.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.