Effective annual yield versus bond equivalent yield
There are lots of different kinds of bonds, many that don't pay interest periodically. These bonds, known as zero-coupon bonds, are instead discounted significantly and pay their interest at maturity.
Since there's no interest paid periodically, there's no effective annual yield. Instead, the return on these bonds is estimated using the bond equivalent yield. Since they're typically very short-term bonds, this is a way to approximate their annual yield if they lasted that long, allowing you to compare them to longer-term bonds.
The bond equivalent yield, then, is only a measure of the initial interest returned to the investor from the bond; the effective annual yield approximates the additional interest the interest coming from the bond could yield, if it were reinvested. Although the two sound similar, there's a world of difference.
Calculating effective annual yield
You can estimate the effective annual yield with a relatively simple formula.
Effective annual yield = [1 + (r/n)]^n - 1
In the formula:
r = nominal rate (the interest rate the bond itself is producing)
n = number of payments per year
If you have a bond that pays a 5% coupon twice yearly, you'd calculate the effective annual yield like this:
EAY = [1 + (0.05/2)]^2 - 1
EAY = [1 + (0.025)]^2 -1
EAY = (1.025)^2 -1
EAY = 1.0506 - 1
EAY = 0.0506 or 5.06%