# Average annual return

## Average yearly return

• As investors use the term, the return an investment provides over a period of time, expressed as a time-weighted annual percentage. Sources of returns can include dividends, returns of capital and capital appreciation. The rate of annual return is measured against the principal amount of the investment and represents a geometric mean rather than a simple arithmetic mean.
• Annual return is the de facto method for comparing the performance of investments with liquidity, which includes stocks, bonds, funds, commodities, and some types of derivatives.

Sumflow 21:06, October 19, 2010 (PDT)

The formula for the average yearly return as a geometric mean: AYR = (1 + first year's % return)(1 + second year's % return)(1 + third year's % return)and so on = X. Then take the square root of X for two years of returns, the cube root of X for three years of returns, and so on = Y. Then Y - 1 = AYR. In the above example: AYR = (1.4)(.7) = .98; the square root of .98 = .9899 - 1 = -1%. Thus, instead of gaining 5% per year on average, the fund lost 1% per year on average. A shortcut: avoid the last two steps by just looking at X, say, .98, and seeing what portion of your original investment would be left, which is often all you really need to know to get a sense of the true outcome of the yearly returns over the given period.