# Annualized Returns

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## Definition

Annualized returns are period returns re-scaled to a period of 1 year. This allows investors to compare returns of different assets that they have owned for different lengths of time.

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.

## Formula

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

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