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Calculate the Rate of Return on Investments

 

To understand how to calculate the rate of return on your investments, please follow this investment scenario. Let's say you invest $10,000 in stock, which is called your capital. One year later, your investment yields $11,0000. 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,

(($11000 - $10000) / $10000) × 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.

Value of Investment Chart

You initially invest $10,000. One year later, your investment grows to $20,000 in value. The year after that, the investment drops back to $10,000. The rate of return after the first year is

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

(($20000 - $10000) / $10000) × 100% = 100%

The rate of return after the second year is

(($10000 - $20000) / $20000) × 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: (10000 / 10000) ^ .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.

 

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