What Mutual Fund Investors Should Learn from Benoit Mandelbrot

Mathematician Benoit Mandelbrot died last week at the age of 85. He is most well known as the father of fractal geometry, which deals with irregularly shaped objects, the likes of which are often found in nature. (For example, he said that his work in this field was inspired by his attempts to measure the length of Britain's coast. He found that the answer depended on how closely you looked. From a distance, one doesn't notice the many jagged edges that are apparent upon close examination.)

But beyond his contributions to mathematics and physics, Mandelbrot's curiosity also led him to examine the financial markets. And his work there carries implications for all investors.

Much of modern finance is based upon the assumption that stock markets are "normal"; that is, the range of returns they provide will follow a traditional bell-shaped curve, as seen below. Bell curves depict what is known as a "normal distribution," in which the vast majority of observations cluster around the group's average, with a decreasing number of outliers falling further away on each end of the scale.

Many of the things we can measure -- such as IQs or life spans -- follow a normal distribution.

But, as Mandelbrot pointed out in an article he co-wrote with Nassim Taleb for Fortune magazine in 2005, while we "can disregard the odds of a person's being miles tall or tons heavy ... similarly excessive observations can never be ruled out in economic life."
The 1987 stock market crash, for instance -- in which the Dow lost nearly 23 percent in a single day -- was a 22 standard deviation event. It was so far from the average daily market return that the odds of such an extreme decline occurring, if market returns were normally distributed, were one in 100 quindecillion (that's 100 followed by 48 zeros), or something, as Mandelbrot and Taleb wrote, we should see "only once in several billion billion years."

But as Mandelbrot pointed out, such volatility in the financial markets is far from rare. Huge swings in value occur with much greater frequency than traditional financial models would predict. Mandelbrot had little patience for such models. In his 2004 book The (Mis)Behavior of Markets, he wrote "I believe the conventional models ... are not merely wrong; they are dangerously wrong. They are like a shipbuilder who assumes that gales are rare and hurricanes myth; so he builds his vessel for speed, capacity and comfort -- giving little thought to stability and strength."

As you might imagine, Mandelbrot's opinions didn't endear him to many of his peers (although they gained more regard in recent years, particularly after his criticisms were borne out in the recent financial crisis, with its roots in the inability of Wall Street's models to anticipate a widespread housing bust and its effects). In The Myth of the Rational Market, Justin Fox quoted physicist M.F.M. Osborne telling a group of finance students why they could ignore Mandelbrot's work:

You ask what is probable and what is improbable, but definitely not impossible. For rainfall, you take 99% of occasions when you average less than two inches of rain ... That kind of information is significant for grazing or agriculture ... The improbable situation, which may give much more than 1% of the total rain which may fall, is really concerned with a different caliber of problems. Are roads going to be washed away, is it safe to build a house in certain locations if you want to live there for twenty or thirty years?

To do so, Mandelbrot offered investors some advice:

1. First, recognize that, as my Moneywatch colleague Larry Swedroe wrote recently, a tiny majority of days are responsible for the lion's share of the market's total return. Miss them, and your return is likely to be a fraction of what it might have been.
2. Second, as he wrote in his 2004 book, "If you can find some market properties that remain consistent over time or place, you can ... make sounder financial decisions." Fortunately, we have one such property that all investors should take into account: low costs produce higher net returns than high costs.
3. Finally, as Mandelbrot wrote in his Fortune article, "diversify as broadly as you can ... [and remember that] passive indexing is far more effective than active selection."

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