All About Annualized Returns
If you want to figure out how much you are making year over year, you have to calculate your annualized returns. Annualized returns converts an investment that has a rate of return in a manner different than one year into a format with which you can tell how much you are earning per year. Calculating annualized returns is exceedingly important for determining the success of equities on a yearly basis.
Annual vs. Annualized Returns
It is important not to confuse annual with annualized returns. An annual rate of return is the return on an investment over a one-year period, such as November 1 through October 31. An annualized rate of return is the return on an investment over a period that is not one year (such as a month, or two years), which is then multiplied or divided to give a comparable one-year return.
Example Formula
There is a simple formula to calculate annualized returns on an investment. Let's say you have an investment that starts at $100 and over 39 months has reached $150. There is a simple formula to calculate annualized returns on an investment. First you need to calculate the gain factor over those 39 months to find the annualized return. The gain factor would be 150/100, or 1.5. That's a gain factor of 50%. But that gain factor is for months, not years!
We must use the formula below to find annualized gains, which is represented by the letter A. The gain factor is 1.5 (as calculated above), while the number 39 (in superscript) represents the number of months for which our investment has been active and 12 is, of course, the number of months in a year.
(1+A)39/12 = 1.5
If you rearrange the formula you get: A = 1.512/39 – 1. A equals 13.29%. Thus, 13.29% is the rate of annualized returns. The general formula is as follows: Annualized Gain Factor = (1 + M-day-Gain)12/M, where M stands for the duration of your investment in months.
More Accurate Method
If you want a more accurate computation of annualized returns in terms of the example above, you would use 365.25 days per year, since not every month has an equivalent number of days. To use days in the formula above, you would simply have to figure out the number of days within that total 39 month period.
Calculating annualized returns gets more complicated as more variables become involved, such as if you have losses, taxes or varying rates of return that you would like to factor into your calculation of annualized return. There are arithmetic, known as the average annual return, and geometric, known as the compound return, methods of calculating rates of return. Average annual return is expressed like this: (Rate of Return for Year 1 + Rate of Return for Year 2) / 2. Compound return is expressed like this: (capital / return) ^ (1 / n) - 1 where n = number of years.
