How do I convert between bond equivalent yield and effective annual yield, and when does it matter?
In my CFA Level I studies, I keep seeing BEY (bond equivalent yield) quoted as semiannual rates. But when comparing investments with different compounding frequencies, I need EAY (effective annual yield). How do I convert and when is each appropriate?
Bond equivalent yield (BEY) and effective annual yield (EAY) serve different purposes, and knowing when to use each is critical for CFA Level I Fixed Income.
BEY (Bond Equivalent Yield): The annualized yield using semiannual compounding, which is the convention for most US bond markets. It's simply 2x the semiannual yield.
BEY = 2 x semiannual yield
EAY (Effective Annual Yield): The true annualized return accounting for compounding. This is the apples-to-apples comparison rate.
EAY = (1 + semiannual yield)^2 - 1
Conversion Example: Fairmont Industries issues a bond with a semiannual yield of 3.25%:
- BEY = 2 x 3.25% = 6.50%
- EAY = (1.0325)^2 - 1 = 1.06606 - 1 = 6.606%
The EAY is higher because it accounts for the compounding effect of reinvesting the first semiannual coupon.
Going the Other Way — EAY to BEY: Semiannual yield = (1 + EAY)^0.5 - 1 BEY = 2 x [(1 + EAY)^0.5 - 1]
If EAY = 7.00%: Semiannual yield = (1.07)^0.5 - 1 = 1.03441 - 1 = 3.441% BEY = 2 x 3.441% = 6.882%
When to Use Each:
| Situation | Use |
|---|---|
| Comparing US bonds to each other | BEY (market convention) |
| Comparing bond yield to a quarterly-compounding CD | EAY (common basis needed) |
| Yield quoted on a money market instrument | Convert to BEY or EAY for comparison |
| Exam says "effective annual rate" | EAY |
| Exam says "yield" with no qualifier | Likely BEY |
Multi-Compounding Comparison: Suppose you're comparing:
- Bond A: BEY = 6.50% (semiannual compounding)
- Bank CD: 6.40% compounded quarterly
- Money market fund: 6.30% compounded daily
Convert all to EAY:
- Bond A: (1 + 0.065/2)^2 - 1 = 6.606%
- Bank CD: (1 + 0.064/4)^4 - 1 = 6.555%
- Money market: (1 + 0.063/365)^365 - 1 = 6.503%
Bond A offers the best effective return despite not having the most frequent compounding.
Exam Tip: The exam loves to test whether you can convert between yield conventions to make a valid comparison. If two instruments have different compounding frequencies, always convert to EAY before comparing. If both are semiannual US bonds, BEY is fine.
More yield conversion practice in our CFA Level I Fixed Income materials.
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