# How to quantify the coupon effect?

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

• What he proposes to do is to estimate a linear regression, to find the coefficients c and d. Then to identify bonds that have a yield higher than implied by the regression line (i.e. bonds that are attractive even after considering the coupon effect). Are you familiar with regression as a statistical technique? Apr 8, 2019 at 16:48
• Hi Alex C. Thanks, but that's not my issue. What I don't understand is the intuition involved behind (1.2), where the equation itself is derived from. And even when it's simplified to (1.3) is it not the wrong way around. Naively had I not seen this then to express as a linear function I would have written something like: Bond Yield - Par = (Bond Coupon - Par) * coefficient + constant. But even that seems a leap.
– BG25
Apr 8, 2019 at 19:06
• I agree with you that this equation does not have a firm theoretical basis. It is an ad-hoc, empirical approach. A sounder method would be based on an estimated yield curve IMO. Apr 8, 2019 at 20:38
• @VanillaCall - does that imply that the spread in z-spreads of two bonds of similar maturity should roughly equal the coupon effect? Sorry this should be a question/comment as opposed to an answer. Aug 6 at 11:24