Calculating the Rate of Return on Investments

Let's say you invest \$100 in stock, which is called your capital. One year later, your investment yields \$110. What is the rate of return of your investment? We calculate it by using the following formula:

((Return - Capital) / Capital) × 100% = Rate of Return

Therefore,

((\$110 - \$100) / \$100) × 100% = 10%

Your rate of return is 10%.

There are two ways to measure the rate of return on an investment.

Average annual rate of return (also known as average annual arithmetic return)
Compound rate of return (also called average annual geometric return)

A simple example below will show what these two yardsticks measure.

You initially invest \$100. One year later, your investment grows to \$200 in value. The year after that, the investment drops back to \$100. The rate of return after the first year is

((Return - Capital) / Capital) × 100% = Rate of Return

((\$200 - \$100) / \$100) × 100% = 100%

The rate of return after the second year is

((\$100 - \$200) / \$200) × 100% = -50%

By using the formulas for calculating the average annual rate of return, we get a percentage that measures gains accurately over only a short period. Whereas, the geometric or compound rate of return is a better yardstick to measure your investment over the long run. The arithmetic mean or average return should be used to calculate return on investment only in the short-term.

Average annual return (arithmetic mean) = (Rate of Return for Year 1 + Rate of Return for Year 2) / 2 = (100% + (-50%)) / 2 = 25% (Arithmetic return = 25%)
Compound return (geometric mean) = (capital / return) ^ (1 / n) - 1 where n = number of years. The formula is (100 / 100) ^ .5 - 1 = 0%. (Geometric return = 0%)

Note : Mutual fund managers report the average annual rate of return (arithmetic) on the investments they manage. As shown in the above example, the arithmetic return of the investment is 25%, even though the value of the investment is the same as it was two years ago. Thus, mutual fund reports are somewhat deceptive.