EAY vs EAR – what’s the difference?

The concept of both is the same thing – calculating the annualized return rate of a security.

Effective annual yield (EAY) usually calculates the annualized holding period yield (HPY) or yield to maturity (YTM), which is the return earned when a security is held until maturity. Remember that EAY:

• (Usually) assumes 365 days in a year
• Incorporates compounding

Formula:

$EAY={\left(1+HPY\right)}^{\frac{365}{t}}–1$

where HPY = holding period yield (or YTM)

Effective annualized rate (EAR) is usually converting a % rate (e.g. nominal 8% paid quarterly) to a rate that indicates the actual interest paid when compounding is taken into account. EAR tends to ‘scale up’ or ‘scale down’ payment periods such as semi-annually, quarterly, etc.

So for a nominal 8% rate paid quarterly:

Formula:

$$\begin{gathered} EAR={\left(1–\frac{annual nominal rate}{\# payments a year}\right)}^{\# payments a year} \\ ={\left(1–\frac{0.08}{4}\right)}^4 \\ =8.24\% \end{gathered}$$