What if an investment returned 5%, 20%, and 50% over three years?

Year 1: $100 * .05 = $105

Year 2: $105 * .20 = $126

Year 3: $126 * .50 = $189

What was the annual return? Can you just average the percentages?

Let’s try it. The average of 5%, 20%, and 50% is 25%

Did you average 25% a year?

Year 1: $100 * .25 = $125

Year 2: $125 * .25 = $156.25

Year 3: $156.25 * .25 = $195.31

No, 25% for 3 years gets you a different amount!

You calculate the average annual return via the geometric mean (not the arithmetic mean)

\(\sqrt[3]{1.05 * 1.20 * 1.50} -1 = .236 \)

Your annual return was actually 23.6%

Year 1: $100 * .236 = $123.6

Year 2: $123.6 * .236 = $152.77

Year 3: $152.77 * .236 = $188.82 …