# Arithmetic Average Return

## Formula

The Arithmetic Average Return is a way of calculating an average return for an investment over multiple periods. It is simply the average of all the arithmetic returns for each period. To calculate it, you add up the individual Arithmetic Return values, r_(arith), for each period, then divide by the number of periods n as shown in the following formula:

bar(R) = 1/n*sum_(i=1)^nr_(arith,i) xx 100%

You multiply the value by 100% so that the result is a percentage.

## Example

Dean invests in a mutual fund. In the first year, the value of his investment goes up by 10%, in the second year the value goes down by 5% and in the third year the value goes up by 7%. The arithmetic average return is then:

R = 1/3*(0.1 -0.05 + 0.07)*100%

R = (0.12 / 3)*100%

R = 4%