How to calculate the bond equivalent yield and effective annual yield
About this lesson
In this video, I will discuss the difference between bond equivalent yield and effective annual yield and their calculations.
Two ways to annualize a yield
Most bonds pay coupons every six months, so their yield is first calculated per half-year. There are two ways to turn it into a yearly figure:
- Bond equivalent yield (BEY): multiply the six-month yield by 2. This is how bond yields are usually quoted. It ignores compounding.
- Effective annual yield (EAY): compound the six-month yield over the year.
The formulas
With r as the six-month yield:
BEY = 2 × r
EAY = (1 + r)2 − 1
Example
A bond’s yield is 4% per six months.
- BEY = 2 × 4% = 8.00%
- EAY = 1.042 − 1 = 8.16%
The EAY is higher because the coupon received after six months earns interest for the rest of the year.
Converting between them
- From BEY to EAY: EAY = (1 + BEY ÷ 2)2 − 1
- From EAY to BEY: BEY = 2 × [(1 + EAY)1/2 − 1]
Why it matters
When you compare a bond (quoted as a BEY) with an investment quoted as an effective annual rate, convert them to the same basis first. Otherwise, the bond will look slightly worse than it really is. See also the effective annual interest rate.
Next chapter: Macaulay duration.