# Why does the coupon effect mean that higher yields do not necessarily mean that a bond is more attractive?

In Tuckman, it says "The fact that fairly priced bonds of the same maturity but different coupons have different yields-to-maturity is called the coupon effect. The implication of this effect is that yield is not a reliable measure of relative value. Just because one fixed income security has a higher yield than another does not necessarily mean that it is a better investment. Any such difference may very well be due to the relationship between the time pattern of the security's cash flows and the term structure of spot rates."

Surely higher yields still mean that the investment is better? I am not sure what it is saying here.

• You can't just look at maturity. The yield of a 5% 2025 bond and a 1% 2025 bonds are not directly comparable. Sure the 2 bonds have same maturity, but with the 5% bond you get your cash flows sooner (technically: shorter duration). So in a rising Term Structure the 5% has lower yield than the 1%. Effectively you are lending money for a longer period of time with the 1%. (Only for ZCB is maturity and duration identical). – noob2 Dec 8 '20 at 17:25
• @noob2 Thank you - what, for example, would make an appropriate comparison of yields? – junior_pm Dec 8 '20 at 17:35
• "what, for example, would make an appropriate comparison of yields" - would guess something like OAS or ASW spread. – user42108 Dec 8 '20 at 18:12
• Tuckman is a very good writer. Having convinced you early on that yield comparison is not sufficient for relative value, he has motivated you to read the remaining several hundred pages where he discusses this issue, which is basically what modern quant finance is all about. :) – noob2 Dec 8 '20 at 18:13

## 3 Answers

Try to think of yield as a mathematical construct for convenience. The procedure is as follows

1. Find the fair bond price by discounting the cashflows using the current market discount rates.
2. Find the yield $$y$$ such the discounted cashflows using this "single constant rate" equals the bond price. So think of the yield as an average interest rate that would apply for all the cashflows. As a first order approximation, the yield is the "cashflow-time"-weighted average interest rate.

So, whatever the bond coupon, if the bond is valued fairly using the correct discount rates, then the average rate or yield will be just fair, by definition.

However, if you compare two bonds where one bond has substantial credit-risk, then the discount rates for the risky bond will be higher, and thus also the yield. However, as long as the discount rates are correct, this junk bond is still fairly priced given the risk.

So some reasons one bond would be more attractive would be if there is a mis-pricing in the bond, e.g. the market wrongly prices the risk (u have insider info that the issuer will have credit problems), or if you as an investor have atypical preferences for certain bond characteristics e.g. due to hedging or cashflow liabilities and/or risk-preferences.

There are a number of measures that you can look at to asses the relative value of two bonds of the same credit but different maturities and coupons (Treasuries). For one, you can discount each bond using libor or ois swap discount rates (ASW), which is basically a swap spread. You can run oas to the swap curve or to a treasury curve spline model. You can plot yields versus a treasury spline versus maturity. To correct for bonds with the same maturity but different coupons you can plot yields versus duration. You can run 3 month and 12 month total returns including yield and roll down. You can divide these dollar returns by duration. You can use a constant oas model to roll the bonds down the curve or you can roll them yourself to the next shortest bond (3m, 12m). For treasuries specifically we can roll a note to a shorter maturity notes yield and adjust the treasuries coupon to match the coupon of the note that we are analyzing. This can be done by using the principal and coupon strips related to that treasury.

The coupon effect has nothing to do with credit risk - it has to do with a non-flat interest rate curve.

The calculation for YTM assumes that all coupons are reinvested at a single rate (the YTM) over time. But in reality, the forward curve of interest rates generally has a upward slope, so early coupons will (if the forward curve holds true) be reinvested at a lower rate than the average rate for a longer period of time, bringing the actual overall yield down.

The larger the coupon, the larger this effect. For a bond with small (or no) coupons, the effect of reinvestment risk is smaller since the overall yield of the bond is determined less by the reinvested coupons and more by the initial price paid for the bond.

Surely higher yields still mean that the investment is better?

If all other factors (duration, coupon, credit risk etc.) are equal then yes, a higher yield is a better investment. How I interpret what Tuckman is saying is that you can't take one measure (like yield) in a vacuum. You must also look at the coupon rate to see if there's some additional risk that's not captured in the YTM. In addition (not inferred from the quote), one must look at measures like duration (a measure of interest rate risk), OAS, credit risk, etc. to determine if one high-yield investment is "better" than another.