Bond Equivalent Yield, Effective Annual Yield, and Yield Comparisons
Summary
The document compares a simple annualized return calculation for short-term discount instruments with an effective annual yield that assumes proceeds can be reinvested at the same rate. The distinction is compounding: a noncompounded annualization scales the holding-period return by time, while an effective annual yield compounds it across repeated periods. They therefore answer different questions about return.
The response also describes a common industry use of bond equivalent yield: converting yields with different compounding conventions to a semiannual basis, reflecting the quoting convention of many government bonds. This provides a common comparison format across instruments with different payment schedules, even though a computer can calculate conversions directly. The answer cautions that the example's use of the term may differ from industry convention, and presents historical convenience as a possible reason for the convention. It does not establish that the displayed yield measure is universally defined or suitable for every instrument.
Key ideas
- Simple annualization does not assume reinvestment or compounding of the holding-period return.
- Effective annual yield compounds returns across periods and assumes reinvestment at the same rate.
- Bond equivalent yield can standardize quotations to a semiannual compounding convention.
- A common quoting basis helps compare instruments with different compounding schedules.
- The term's application may differ by context, so the yield convention should be checked.
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Full text
# What is the purpose of Bond Equivalent Yield?
# What is the purpose of Bond Equivalent Yield?
In this example here (https://www.canararobeco.com/smartomorrows/intermediate-articles/intermediate_detail/what-is-bond-equivalent-yield) BEY is defined as follows
$$BEY=\frac{ParValue-PurchasePrice}{PurchasePrice}\times \frac{365}{d}$$
it then says the difference in BEY between the two example instruments is 0.43% (16.44% vs 16.01%).
When I calculate the annualized rate of return (or Equivalent Annual Yield) of the two instruments by the formula $$EAY=(\frac{ParValue}{PurchasePrice})^{\frac{365}{d}}-1$$ I get 17.13% for the 925 FV bond maturing in 180 days and 16.89% for the 950 FV bond maturing in 120 days.
Is BEY just an approximation for return from a time when calculating negative powers was a significant inconvenience? Why use it now rather than calculate the actual rate of return?
## Answer by D Stanley (score 2)
https://quant.stackexchange.com/a/81831
They seem to be applying "Bond Equivalent Yield" to securities that mature in less than one year by just extrapolating out the periodic yield to a full year with no compounding. If you instead continuously reinvest the returns into new products with the same return, then your second formula would be more appropriate.
I would also argue that their application of "Bond Equivalent Yield" in that case is different than industry standard, since the industry standard is to convert the APR from an instrument of any compounding rate into a semi-annually compounded rate, since most US (and other) government bonds pay coupon semiannually (and are quoted as such), so that the yields are comparable.
> what is the point when I can use `((1+IRR_semi_annual)^2)-1` for a semi-annually paying instrument to compare to an annually paying instrument
Sure, you can do that, but what about bonds that compound quarterly? Loans that are paid monthly? The math isn't hard for a computer, but not simple to do by hand. I suspect that BEY is partly a holdover from times before computers were prevalent to provide a comparable yield across different investment types (using US/UK government bonds as the standard) without forcing anyone to change their quoting convention.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.