Measuring the Coupon Effect on Bond Yields with Curve-Discounted Cash Flows
Summary
The document explores the coupon effect: for bonds with comparable duration and credit risk, coupon differences can affect yield comparisons, particularly when the yield curve slopes upward. It presents a piecewise linear relationship from a fixed-income text, in which the yield difference from a similar-duration par bond depends on whether the bond’s coupon is above or below the par bond’s yield. The coefficients are not explained or estimated in the document.
The response offers a direct way to quantify the effect: discount each bond’s cash flows using zero-coupon rates, derive each bond’s price, and calculate its yield. The difference between the resulting yields is the coupon effect. This approach makes the yield comparison explicit, but the document provides no worked example or market evidence, and the result depends on the chosen zero-coupon curve and assumptions about matching credit risk and maturity.
Key ideas
- Coupon differences can influence yield comparisons between bonds of similar duration and credit risk.
- The cited relationship models yield deviations from a similar-duration par bond using coupon spread and piecewise coefficients.
- A practical measurement discounts each bond’s cash flows at zero-coupon rates, then derives its yield.
- The difference between the yields calculated from the two cash-flow profiles measures the coupon effect.
- The method depends on the discount curve and on comparing bonds with suitably similar risk and maturity.
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Full text
# How to quantify the coupon effect?
# How to quantify the coupon effect?
I'm reading Moorad Choudhry's book "Advanced Fixed Income Analysis"
The first chapter briefly touches on the coupon effect which I understand from other sources is the effect of pricing an annuity (the coupons) and a zero-coupon bond (the repayment of the notional), and so in an upward sloping curve the higher coupon bond will have a lower yield. But I'm not sure I understand the below (from section 1.2.3), and I can't find other sources for this type of analysis.
> One method used to identify relative value is to quantify the coupon effect on the yields of bonds. The relationship between yield and coupon is given by (1.2): $ rm = rm_P + c \cdotp max(C_{PD} - rm_P,0) + d \cdotp min(C_{PD} - rm_P,0) $ (1.2) where $ rm $ is the yield on the bond being analysed $ rm_P $ is the yield on the par bond of specified duration $ C_{PD} $ is the coupon on an arbitrary bond of similar duration to the part [sic] bond and $ c $ and $d$ are coefficients. The coefficient $c$ reflects the effect of a high coupon on the yield of a bond. If we consider a case where the coupon rate exceeds the yield on the similar-duration par bond ($C_{PD} > rm_P$), (1.2) reduces to (1.3): $ rm = rm_P + c \cdotp (C_{PD} - rm_P) $. (1.3) Equation (1.3) specifies the spread between the yield on a high coupon bond and the yield on a par bond as linear function of the spread between the first bond's coupon and the yield and coupon of the part bond.
Is anyone better able to explain what I am looking at? Or provide a better source?
Thanks
## Answer by VanillaCall (score 4)
https://quant.stackexchange.com/a/45113
Equations don't look intuitive. To quantify coupon effect for the same credit risk and maturity, discount the cash flows of a bond to get the price and then yield. Then discount the second set of cash flows to get the price and then yield. The difference between the yields is your coupon effect.
Use zero coupon rates to discount the cash flows.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.