The periodic return from stocks calculates the stock's growth for a given period of time. This offers a metric of performance for the stock and may be calculated for several consecutive periods. Multiple period returns highlight stable, accelerated or diminished growth across time to offer a measure of consistency. Armed with multiple period returns, you may also calculate a cumulative return for all periods or calculate an average periodic return.
Periodic growth is the percent increase in stock value over a specific period of time. It is calculated by subtracting the stock's starting value from the ending value and dividing the result by the starting value. As an example, if stock ABC was valued at $20 on June 1st and grew to $25 by the end of the month, subtract $20 from $25 to get $5. Dividing $5 by $20 shows a 0.25, or 25 percent, periodic return.
Cumulative Periodic Return
A cumulative periodic return is just a periodic return comprised of several periods. It can be calculated in the exact same manner, but if you no longer have the original starting and ending values, you can calculate cumulative return using each period's return. To do so, add 1 to each periodic return, multiply each return and then subtract 1. In the previous example, if stock ABC dropped to $15 by the end of July and grew to $30 at the end of August, you could use the same periodic return method by subtracting $20 from $30 and then dividing by $20 to get a return of 0.50, or 50 percent. However, if you only knew each period's return was 0.25, -0.40 and 1.00, you would add 1 to each figure to get 1.25, 0.60 and 2.00. Multiplying these out gives you 1.50. Subtracting 1 leaves you with the same 0.50, or 50 percent, return.
Average Periodic Return
Although multiple periodic returns offer a hallmark of consistency, you might want to equalize all those period returns to derive a periodic average. Unfortunately, you can't use the typical averaging formula for this calculation because it would not consider compounding effects, but the calculation is still relatively easy. Just add 1 to the cumulative periodic return and take the nth-root of it, where "n" is the number of periods contained in the cumulative return, and subtract 1. In the previous example, 1 plus 0.50 gives you 1.50. Because there were three periods, you take the cube-root to get 1.145. Subtracting 1 derives the periodic average return of 0.145, or 14.5 percent.
Periodic returns don't allow a good comparison to investments that rely on differing time periods. The solution is the extrapolate the periodic return to an annualized return for easier comparison. To do this, just add 1 to the periodic return and raise the result to the nth power, where "n" is the number of periods in a year, and subtract 1. In the initial example, adding 1 to 0.25 gives you 1.25. Because there are 12 months in a year, raise 1.25 to the power of 12 to get 14.55. Subtracting 1 leaves you with an annualized return of 13.55, or a whopping 1,355 percent. As you can see, the massive one-month return extrapolates to an enormous annualized return. For this reason, it is often more reliable to use an average period return or a periodic return that spans a longer duration.
C. Taylor embarked on a professional writing career in 2009 and frequently writes about technology, science, business, finance, martial arts and the great outdoors. He writes for both online and offline publications, including the Journal of Asian Martial Arts, Samsung, Radio Shack, Motley Fool, Chron, Synonym and more. He received a Master of Science degree in wildlife biology from Clemson University and a Bachelor of Arts in biological sciences at College of Charleston. He also holds minors in statistics, physics and visual arts.