Why Bond Yields Alone Cannot Determine Total Returns
Summary
The document asks whether daily total returns for a fixed-rate bond can be recovered from a historical yield series when coupon information is unavailable, as may occur with generic constant-maturity government yields. The response explains that yield does not uniquely determine a bond’s coupon or price. Bonds sharing the same yield can trade at different prices relative to par and have different coupon rates, so their interest accrual and total returns can differ.
Converting an annual yield into a daily rate under a chosen compounding convention can provide a daily yield equivalent, but it does not recover the coupon income or the change in value caused by time passing. Total return combines coupon accrual with price appreciation or accretion, and the missing bond characteristics prevent an exact calculation from yields alone. The answer is qualitative and does not supply an estimation method for interpolated yields or address assumptions that could make a proxy return series useful.
Key ideas
- A yield series alone does not identify a bond’s coupon rate or price relative to par.
- Bonds with the same yield can have different coupon income and total returns.
- Converting annual yield to a daily rate does not determine coupon accrual.
- Exact total return calculation needs information about both coupon income and bond price evolution.
Tags
Full text
# Can one compute the total return of a fixed-rate bond without having the coupon? # Can one compute the total return of a fixed-rate bond without having the coupon? Say that I have a historical series of yields and no coupon data because these yields come from a generic government bond, hence an constant maturity interpolation. How would I go about computing the daily returns of the bond, without having information on the coupon? ## Answer by D Stanley (score 0, accepted) https://quant.stackexchange.com/a/74728 No - a bond with a 10% yield valued at par and a bond with a 10% yield valued at 80% of par will have very different coupon rates. You could get a daily yield by just converting the annual yield to a daily yield (i.e. `(1+y)^(1/365) - 1` if you assume a 365-day year and daily compounding), but it would not tell you the exact amount of interest that accrues. It would be a combination of interest from the coupon and accretion of the bonds value based on the passage of time.
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.