“The stock market returns an average of 10% per year.” How often have you heard that saying? Do you really understand what it means? Just why is Queen Latifah famous, anyway? Sorry…I got distracted.

Please carefully review the following numeric series: -20%, +20%, -20%, +20%, -20%, +20%. If those were your yearly investment results for the past six years, what was your average yearly rate of return? If you said “-2.02% per year”, you are correct. If you said “0% per year”, you have mistaken arithmetic return for geometric return. If you said “yellow”, you may have attended a public school in South Carolina, and for that I am truly sorry.

Let’s back up and assume that you invested $100,000 and earned those aforementioned returns. After one year, you would have $80,000$100,000 minus 20%. After two years, you would be worth $96,000The first year’s $80,000 plus 20%. Notice a pattern here? Even though your first two returns (-20% and +20%) averaged out to zero, you still lost money overall. Follow that trend for six years and you’d be left with just shy of $88,474, or barely enough to buy Apple’s newest iFad.

A frequent investing mistake when calculating yearly returns is to add the returns for each year, and divide by the number of years. While this is the common definition of “average”, this actually denotes an arithmetic average, which provides incorrect results when reviewing financial data.

In fact, the correct method is to convert to a decimal and multiply by your starting capital. In the case above, $100,000 x 1.2 x 0.8 x 1.2 x 0.8 x 1.2 x 0.8 = $88,473.60. And ($88,473 / $100,000) raised to .1666661 / number of years, which is six equals 0.979796, or a loss of about 2.02% per year. Let’s try it again with a zero “average” return but larger deviations: $100,000 x 1.4 x 0.6 x 1.4 x 0.6 x 1.4 x 0.6 = $59,270.40, or -8.35% per year. Oh no!

^ Not relevant to this topic, but a good Brad Pitt “Oh No” pic

The overriding lesson here is that the geometric return is always less than or equal to the arithmetic return, and will be drastically lower in times of high volatility. Consider if your financial adviser handed you the following results for four years of investing: +100%, +100%, +100%, -100%. Arithmetic average: 50% per year. Geometric (real) average: 0%. You lost all your money. Go back to the starting line. Do not pass Go. Do not collect $200. Do not adopt a Cambodian baby with Angelina Jolie.

To follow up with my starting paragraph, historically the United States stock market has returned approximately 10%equity appreciation plus dividends each year. This is a compound (geometric) return, which is tantamount to multiplying your money by 1.1 per annum. By now you should realize that this means the arithmetic average was well over 10% per year, and this also means the next time you hear your pretentious neighbor brag about last year’s 60% return on his volatile hedge fund after a rough starting stretch, you can rest easy knowing that the law of geometric averages is a high barrier to hurdle.

I’m just kidding, you should let your dog out to go pee in his yard.