# Effective Annual Yield

Effective annual yield is a measure of annual return on investment that takes the compounding of interest into account. It is calculated by compounding and annualizing the holding period return.

The holding period return itself is not an annual rate so two investments can’t be compared directly using the holding period return. Effective annual yield makes holding period return comparable by standardizing it to annual basis and adjusting it for the effect of compound interest.

## Formula

Effective annual yield can be calculated using the following formula:

$$EAY={(1+HPR)}^\frac{365}{t}-1$$

Where EAY is the effective annual yield, HPR is the holding period return and t is the number of days for which holding period return is calculated.

## Example

You invested $10,000 on 1 January 2017 in stocks which paid dividends on$500 on 30 May 2017 and you sold the shares for \$10,300 on 31 July 2017.

We first to work out the holding period return:

$$HPR=\frac{10,300+500-10,000}{10,000}=8\%$$

We also need to know the time duration of the holding period return, which is 211 (i.e. the number of days between 1 January 2017 and 31 July 2017).

The effective annual yield is as follows:

$$EAY={(1+8\%)}^\frac{365}{211}-1=14.24\%$$

Effective annual yield is the effective rate of return because it accommodates the interest-on-interest that results in a compound interest. EAY calculated above is higher than simple annualization of holding period return which equals 13.83% (=8%×365/221)

Written by Obaidullah Jan