Effective Annual Yield
Effective Annual Yield
The annually compounded yield equivalent to a nominal yield compounded m times per year. A bond quoted at a 6% semi-annual yield actually earns 6.09% a year.
When to use: Use to compare bonds with different coupon frequencies, or a bond yield against an annually compounded return such as a bank rate.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| EAY | Effective Annual Yield | Annually compounded equivalent of the nominal yield | % |
| y | Yield | Annual yield as a decimal; periodic yield is y/m | % |
| m | Coupons per Year | Number of coupons paid per year (e.g. 2 for semi-annual) | integer |
Real-Life Examples
Example 1: Semi-Annual 6%
A bond quoted at a 6% yield with semi-annual coupons.
Given
Step-by-Step
The bond-equivalent yield of 6% is really 6.09% on an annual basis, because the first coupon earns a half-year of interest before year end.
Example 2: Monthly-Pay Bond
A monthly-pay bond quoted at 4.75%.
Given
Step-by-Step
Twelve compounding periods add about 10 basis points to the quoted rate.
Frequently Asked Questions
Mathematically yes; this is the EAR formula applied to a bond yield. Bond markets quote nominal yields by convention, so the conversion matters when comparing to annually compounded rates.