How do I convert between bond equivalent yield and effective annual yield, and when does it matter?

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:

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.