How to Calculate Cumulative Returns

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Investments give returns; otherwise, why would anyone take the risk? There are many ways to examine returns, as well. Cumulative and annual returns are two key parameters, but return percentages can splinter off into several meaningful financial ratios to examine an investment's value and potential. Calculation complications arise in cases where interest is compounded, i.e., new interest calculations are based not only on the principal amount of an investment but the principal plus previous interest that has accumulated.


What Is Cumulative Return?

Per the writers at Fineberg Wealth, cumulative returns look at an investment's return over a longer period of time, comparing the end value of the investment against the principal value. It's primarily a way to look at the overall performance of an investment over time. For example, let's say you purchased ​100 shares of Stock A five years ago for $10,000​. At the end of ​five years​, your shares of stock are now worth ​$14,000​, giving you a ​$4,000​ gain over that time period. To calculate cumulative return: ​($4,000 gain) / ($10,000 initial investment) = 0.4 —> 40 percent​.


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Over these ​five years​, your investment has seen a cumulative return of ​40 percent​. You could compare this number with cumulative returns on other investments over five-year stretches, to see which ones outperform the others. However, you can't just take this value and divide by five to get an annual compound return of ​(0.4 / 5) = 0.08, or 8 percent​, unless you have a simple loan that doesn't compound interest. Since most viable investment options today do compound, you'll need to look at how to calculate annual returns if you want to evaluate investments by year.


Compounded Interest and Annual Returns

The concept of compounding interest is that after some period of time (usually either quarterly or annually), the interest collected on a principal investment is then deposited back into that investment, changing the value of the investment. The next year, interest is calculated using the higher amount that includes the previous year's interest.

The equation is a bit complicated but is represented as: A = P * [1 + (r/n) ] ^ (nt), where A = final amount; P = the initial value of the principal; r = interest rate; n= number of times the interest rate is applied per time period; and t = number of time periods elapsed between P and A.


Cumulative Rate of Return

Adding the cumulative rate of return to this equation, it can be rearranged as: (1 + RA) ^ n = 1 + RC. Where RA is the annualized rate of return, RC is the cumulative rate of return (calculated above) and n is the number of years considered in the calculation of RC.

Using the example given above, we know n = 5 and RC = 0.4. Manipulating the equation yields RA = [ (1 + RC) ^ (1/n) ] -1. You can find calculators online to do these math problems; for this particular example, the annual rate of return is 0.6961, or 6.96 percent. This is less than the erroneous 8 percent you would have calculated using simple arithmetic.


Using the cumulative return to calculate the annual compounded return gives you multiple points of comparison with other potential investments. This can help you decide whether to keep your money where it is currently invested or move it to a place with potentially higher returns.

Consider also:What Is Total Cumulative Shareholder Return?