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.

The Motley Fool has a disclosure policy.

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  • Report this Comment On March 06, 2013, at 5:38 PM, Darwood11 wrote:

    Good article.

    I've never been enthralled with the idea of "black swans."

    However, I think that the point of the article is if one listens to the "generalists" then one is susceptible to the consequences of outlier events.

    Ok, I can accept that. But unless one can predict the future, then those "outlier" events will not only occur, but they will in "probability" have an impact on my financial planning and future.

    It's a sad fact, but a 90% loss is not restored by a 90% gain. In fact, in such an event, one will be left with less than 20% of their original investment. So an "outlier" will have a disproportionate effect.

    In other words, invest prudently for 6% annual gains, and one "market panic" may result in a 40% loss which will return me to 9 years ago. With only 40 years to save and invest, it's clear to me that the way to get ahead is to be a stockbroker.

    So I am more concerned with negative consequences than with the positives. I suspect I am not alone in this. And the pundits wonder why people fled to the safety of bonds?

  • Report this Comment On March 07, 2013, at 1:27 PM, Chuck2010 wrote:

    Avoiding losses is the premise of book, Winning The Losers Game by Ellis. He seems to rely on indexes and don't worry, based on the wisdom that no one can consistently stock pick and beat the market long term which needs to be at least a 15 year horizon (given our current experience over the last 10-12 years).

    Taleb's black swan thesis and suggestions for investing seem problematic (something like 90% safety with 10% in a basket of startups). Access to the truly dramatic growth in a startup is generally restricted to insiders, so it isn't clear to me how that would work for the rest of us.

    Ultimately, if you can't afford to lose it, seems best to stay out of the stock market.

  • Report this Comment On March 08, 2013, at 11:51 AM, BiotechMarc wrote:

    A 'fat tail' does not refer to an outlier or a black swan event. It refers to the shape of the distribution moving from the mean, specifically when it does not follow a normal distribution and instead follows a power law distribution. That means that the number of outlier events or black swans does not diminish as expected (in a normal distribution) as you get further from the mean and they tend to occur more frequently. I'm not meaning to be persnickety, as the article is otherwise factually correct.

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