Average Isn't Normal


Much of the traditional wisdom that we follow when making investment decisions is rooted in models referred to as modern portfolio theory. One of the theory's basic assumptions is that stock market returns are normally distributed. In other words, when graphed, the returns will form a traditional, bell-shaped curve.

The idea is that you can expect an average return to be your average experience. Returns either greater or less than the average are less and less likely as you move further and further from the average. At extreme tips of this nice little bell are positive or negative returns that are so unlikely to happen that they are thought to be almost statistically impossible.

We have heard a lot about these little guys. They're called black swans, fat tails and, most often, outliers. In theory, an outlier is something that is so unlikely that it is thought to be unrepresentative of the rest of the sample. In this case, these outliers generate returns that, according to the theory, we're almost never supposed to see.

When something is never supposed to happen, we don't spend much time thinking about it. Instead we focus on the average. This is certainly true when it comes to investing: We focus on the stock market average over time.

It's the average that we plug into our calculators when we project into the future. It's the average that we talk about. The problem is that average is not normal and focusing on it leads us to greatly underestimate the impact that these outliers can have when they do show up.

The reality is that they have such a huge impact that they actually obscure the importance of the average. In 2009, The Wall Street Journal discussed a study that shows the significant impact that outliers have had in history.

If you take the daily returns of the Dow from 1900 to 2008 and you subtract the 10 best days, you end up with about 60% less money than if you had stayed invested the entire time. I know that story has been told by the buy-and-hold crowd for years, but what you don't hear very often is what happens if you were to miss the worst 10 days. Keep in mind that we are talking about 10 days out of 29,694. If you remove the worst 10 days from history, you would have ended up with three times more money.

To be clear, this is not a suggestion to try to time the market, but an attempt to make a simple and narrow point: Outliers matter. In fact, they matter so much that they almost make the average meaningless. Because most of our lifetime return is determined by how many of these outliers we experience, it's time we stop ignoring them.

A version of this post appeared previously at The New York Times.

Carl Richards is a financial planner and the director of investor education for the BAM ALLIANCE, a community of more than 130 independent wealth management firms throughout the United States. Visit Behavior Gap for more of Carl's sketches and writings.

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