Average yearly return -- there is a trick to calculating it: finding the "geometric mean," which is not properly calculated by merely summing up the yearly positive and negative percentages and dividing the sum by the number of years, as the novice supposes. For example, suppose a mutual fund company has told you its fund has gained 40% one year and only lost 30% the next. Have they earned 5% on average? Only if you erroneously figure the mean like this: 40%-30 = 10; 10/2 = 5%. In reality, your $100 rose to $140 after one year then fell by 30% the next: 140(.7)= $98. So, in fact, you lost two dollars overall.
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.
