# Cumulative vs Annual Compound Rates of Return

Returns can be presented on a cumulative basis or as an annual compound rate. It is critical that investors understand the difference between these two methods of reporting.

### Cumulative Returns

Cumulative returns express the total percentage increase in the value of an investment from the time it was purchased.

Example: You purchased XYZ shares 10 years ago for \$10,000. Today XYZ shares are worth \$20,000. To calculate the cumulative investment return, you would first take the current value of your XYZ shares (\$20,000) and subtract the price at which you originally purchased the shares (\$10,000). This would give you your total dollar gain (\$10,000). Next divide your total dollar gain by the total cost of the shares (\$10,000 initial investment/ \$10,000 gain = 1, or as expressed as a percent: 100%). In this example, over a ten year period you have doubled your investment and your cumulative return is 100%.

Brokerage account statements generally report a cumulative return in the gain/loss section of their statements.

### Annual Compound Returns

Annual compound returns express the rate of return which, if compounded over the years covered by the performance history, would yield the cumulative gain or loss actually achieved during that period.

A simple way to think about annual compound returns is to consider its use in banking. If you were to go into a bank and ask the teller what their savings accounts were yielding, you would be given an annual compound rate (or something very similar).

Revisiting our previous example: In order to achieve a 100% cumulative rate of return over a ten year period, what annual compound rate of return must your XYZ shares achieve?

The answer is 7.2%. If your XYZ shares grow at a 7.2% annual compound rate for 10 years, you will have doubled your investment and achieved a 100% cumulative rate of return.

The math involved in this calculation is complex. If you would like dive into the details you can read more here:  Calculate a Compound Annual Rate of Return

### Why Should I Care About Annualizing Returns?

Returns expressed as an annual compound rate are useful because they give investors the opportunity to make direct comparisons. Annual compound rates of return are often quoted on a 1,3,5, and 10 year basis. This gives investors the ability to easily compare how different investments performed during the same periods of time.

To highlight the challenges involved with comparing two investment’s cumulative returns, consider the following:

Question: Did an investment with a five-year cumulative return of 93% do better or worse than one with a ten-year cumulative return of 271%?

Answer: Their annual compound rates of return were identical, 14%.

### Conclusion

When an advisor or fund manager provides you with a performance figure touting high returns, it is critical that you understand whether you are being quoted a cumulative rate of return or an annual compound rate. As you have hopefully learned by reading this article, the two methods of reporting express very different things.

The information in this post was compiled by S. Zachary Fineberg, Managing Member of Fineberg Wealth Management, LLC, a registered investment advisor. If you would like to schedule a consultation to discuss how Fineberg Wealth Management can help you reach your long-term financial goals, please contact us by email or call (734) 230-7900.