# Annualized Total Returns

Annualized Total returns are period returns re-scaled to show the compound annual growth rate of the security. This allows investors to compare returns of different assets that they have owned for different lengths of time. It also gives the investor an idea of the returns that they would have returned per year if they had been invested in the security during the time frame of the annualized metric.

For example, if a person bought Fund A 2 years ago at a price of $10 and it is currently at $14 and paid $1 in distributions within that time, it's period return is (($14 + $1)-$10)/$10 = 50%. However, since one year is only 1/2 of the time of 2 years, it's annualized return is (($14+$1)/$10)^(1/2) - 1 = 22.47%.

And if they also bought Fund B 6 months ago at a price of $10 and it is currently a price of $11 and paid $1 in distributions over that time, its period return is (($11+$1)-$10)/$10 = 20%. However, since there are 2 six month periods in one year, it's annualized return is ($12/$10)^2 - 1 = 44%.

The investor can therefore compare how quickly Fund A's price is increasing compared to Fund B's better than they could with a period return, since the holding period is now comparable.

The general formula is below, where t is the holding period time in years.

Annualized Total Returns = (Period Ending Price + Dividends and Distributions paid over time period / Period Starting price) ^ (1/t) - 1