# Average Return – Definition

### Average Return Definition

The average return is the amount the average amount that an asset returns to the holder over a specified period of time. The average return can be calculated as the “arithmetic mean” or “geometric mean”.

Arithmetic means is the sum of all returns of a defined period of time divided by that period of time.

Average return (Arithmetic mean) = sum of returns/number of return

This is useful when you receive the return on your asset or investment and do not invest it back into the asset.

Geometric mean is similar but takes into account compounding of the return. That is, it takes into account when the return is added into the principal invested into the asset.

Geometric mean is calculated as  ([(1+R1​)(1+R2​)…(1+Rn​)]^1/n) − 1

Or

The nth root of R1 x R2 x R3

where:∙R1​…Rn​ are the returns of an asset (or other observations for averaging).​

So, if you invest \$100 and earn \$10 (10%). Now you have \$110. Next year, you receive \$11 (10% of \$110). Next year, you receive \$12.1 (10% of \$121). You have received \$33.1.

Arithmetic average return would be 33.1 / 3 = 11.03%

Geormetric average return would be 10%, as the 3rd root of (1.1 x 1.1 x 1.1) = 1.1 or 10%

### A Little More on What is Average Return

The average return is generally used to define what are the historical returns on a single security (such as stock) or portfolio of securities.

The geometric mean is a more precise calculation. It eliminates the distorting effects on growth rates created by various inflows and outflows of money into an account over time. It will always be lower than the arithmetic mean. Also, a major advantage is that that the original amount invested is not necessary. You simply need to know the rates of return for each year.

This makes the geometric mean a better method of comparing separate securities.

when looking at two or more investments’ performance over more various time periods.

### Reference for “Average Return”

https://www.investopedia.com/terms/a/averagereturn.asp

https://www.calculator.net/average-return-calculator.html

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