Pricing Floaters with Projected Coupons and Discount Margins
Summary
The document explains a common way to calculate a floating-rate bond's yield. Rather than constructing a synthetic fixed-rate bond, the analyst projects each unset coupon from the relevant reference-rate curve and adds the bond's quoted margin. The projected coupons, known coupons, and principal repayments form cash flows whose internal rate of return is solved using the bond's dirty price. The same projected cash flows can support spread measures such as Z-spread or discount margin.
A floater's yield changes when either projected rates or its price changes, which is why such bonds are generally quoted by price or discount margin instead of yield. A change in discount margin can be used to derive a new price, from which yield and other spreads can be recalculated; the result depends on projection-curve assumptions. For risk scenarios, the answer distinguishes the curve used to forecast coupons from the curve used to discount cash flows and notes they may move together. Flat-yield conventions that hold the current index rate constant are also mentioned as a simplifying alternative.
Key ideas
- Project unset coupons from the reference-rate curve and add the quoted margin.
- Calculate yield by solving for the internal rate of return of projected cash flows against dirty price.
- Discount margin and other spread measures can be applied to floater cash flows.
- Floater yields vary with both coupon projections and price, so floaters are commonly quoted by price or discount margin.
- Keep the projection curve and discount curve conceptually distinct in risk scenarios.
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Full text
# How does the yield of a floater change when the discount/required margin changes?
# How does the yield of a floater change when the discount/required margin changes?
On this site: https://ebrary.net/14293/economics/actual_floater, it says that the yield of a floater is deteremined like this:
> That yield is determined by assuming the coupon rate on the floater is swapped to a synthetic fixed rate and then solving for the internal rate of return.
But how is actually the synthetic bond created? Lets say that the disount/required margin of a floater increases by on basis point. Then the price of the floater decreases. How would one then find an equivalent fixed rate security?
I assume that market value must be the same for the synthetic bond and the floater. So in the synthetic security we can either increase the yield, or the yield can stay the same and we can decrease the coupon payments, or a comination?
Is there any rule to how the yield of a floater changes when the discount margin changes?
## Answer by Dimitri Vulis (score 1)
https://quant.stackexchange.com/a/60181
This is not how most people calculate the yield of a floater.
The way most people calculate the yield of a floater is:
1 for each remaining unset coupon, project the values of the index that will be used (such as 3Mo LIBOR, daily SOFR, SONIA, ESTR, etc - see Forecast 3m LIBOR USD. Budget purpose for example); and project the coupons. For example, if a floater has a coupon that in 1 year is reset from 3 months LIBOR plus 100 basis points ("quoted margin"), and if the projection curve predicts that 3 months LIBOR will be 30 basis points when this coupon is reset, then you project that the coupon will be 30+100 = 130 basis points.
2 Just as you would for a fixed-coupon instrument, solve for the internal rate of return (IRR) of the cash flows where you pay the dirty price on setlement date and receiver the set coupon(s), the unset coupons projected in step 1, and principal repayments.
Various spreads that make sense for fixed-coupon bonds (Z-spread, OAS, etc) work just as well for floaters, discounting the future cash flows by your bond funding cost. You can also calculate the discount margin (DM), which is similar to these spreads.
(Sometimes people calculate "flat yield" and "flat discount margin" by taking the current value of the index and assuming that it will remain constant, so you don't need to project it from the curve in step 1. This is the default behavior of the Bloomberg Terminal - a setting which you may want to change.)
The yield of a floater changes every time the projection curve changes, so, unlike fixed-coupon bonds, floaters are almost never quoted on yield. Floaters are usually quoted on price or on DM. Backing out price from DM (the inverse of the price to DM calculation) is depends somewhat on the projection curve assumptions.
If you want to reprice the bond under various risk scenarios, then you should not assume that your discount curve (funding) and the projection curve (used to predict unset coupons) are the same. But the two curves will be correlated. In particular, for a dv01 scenario, you may want to perturb both discount and projection curves by the same 1 basis point up and down.
If the DM moves (e.g. because the bond issuer's credit changes), then you back out the new bond price (the inverse of the price to DM calculation), and use the new price to calculate the new yield, Z-spread, and other spreads, which will all change by about the same amount as the perturbed DM.
As you see, there's no synthetic fixed-coupon bond in this picture. You could make one up, but I don't see how that would benefit anyone in understanding the value of the floater.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.