# Annualized Price Return

Annualized 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 Stock A 2 years ago for $10 and it is currently selling at $15, it's period return is ($15-$10)/$10 = 50%. However, since one year is only 1/2 of the time of 2 years, it's annualized return is ($15/$10)^(1/2) - 1 = 22.47%.

And if they also bought Stock B 6 months ago for $10 and it is currently selling for $12, its period return is ($12-$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 Stock A's price is increasing compared to Stock B's better than he or she 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.

(Period Ending Price/Period Beginning Price)^(1/t) - 1