Against the Gods: The Remarkable Story of Risk (34 page)

Karl Pearson, Galton's principal biographer and an outstanding
mathematician himself, observed that Galton had created "a revolution
in our scientific ideas [that] has modified our philosophy of science and
even of life itself. "40 Pearson did not exaggerate: regression to the mean
is dynamite. Galton transformed the notion of probability from a static
concept based on randomness and the Law of Large Numbers into a
dynamic process in which the successors to the outliers are predestined
to join the crowd at the center. Change and motion from the outer
limits toward the center are constant, inevitable, foreseeable. Given the
imperatives of this process, no outcome other than the normal distribution is conceivable. The driving force is always toward the average,
toward the restoration of normality, toward Quetelet's homme moyen.

Regression to the mean motivates almost every variety of risk-taking and forecasting. It is at the root of homilies like "What goes up must
come down," "Pride goeth before a fall," and "From shirtsleeves to
shirtsleeves in three generations." Joseph had this preordained sequence
of events in mind when he predicted to Pharaoh that seven years of
famine would follow seven years of plenty. It is whatJ.P. Morgan meant
when he observed that "the market will fluctuate." It is the credo to
which so-called contrarian investors pay obeisance: when they say that
a certain stock is "overvalued" or "undervalued," they mean that fear or
greed has encouraged the crowd to drive the stock's price away from an
intrinsic value to which it is certain to return. It is what motivates the
gambler's dream that a long string of losses is bound to give way to a
long string of winnings. It is what my doctor means when he predicts
that "tincture of time" will cure my complaints. And it is what Herbert
Hoover thought was going to happen in 1931, when he promised that
prosperity was just around the corner-unhappily for him and for everyone else, the mean was not where he expected it to be.

Francis Galton was a proud man, but he never suffered a fall. His
many achievements were widely recognized. He ended a long, full life
as a widower traveling and writing in the company of a much younger female relative. He never allowed his fascination with numbers and facts
to blind him to the wonders of nature, and he delighted in diversity:

It is difficult to understand why statisticians commonly limit their
inquiries to Averages, and do not revel in more comprehensive views.
Their souls seem as dull to the charm of variety as that of the native of
one of our flat English counties, whose retrospect of Switzerland was
that, if its mountains could be thrown into its lakes, two nuisances
would be got rid of at once.41

egression to the mean provides many decision-making systems with their philosophical underpinnings. And for good
reason. There are few occasions in life when the large are
likely to become infinitely large or when the small are likely to become
infinitely small. Trees never reach the sky. When we are tempted-as
we so often are-to extrapolate past trends into the future, we should
remember Galton's peapods.

Yet if regression to the mean follows such a constant pattern, why
is forecasting such a frustrating activity? Why can't we all be as prescient
as Joseph in his dealings with Pharaoh? The simplest answer is that the
forces at work in nature are not the same as the forces at work in the
human psyche. The accuracy of most forecasts depends on decisions
being made by people rather than by Mother Nature. Mother Nature,
with all her vagaries, is a lot more dependable than a group of human
beings trying to make up their minds about something.

There are three reasons why regression to the mean can be such a
frustrating guide to decision-making. First, it sometimes proceeds at so
slow a pace that a shock will disrupt the process. Second, the regression
may be so strong that matters do not come to rest once they reach the
mean. Rather, they fluctuate around the mean, with repeated, irregular deviations on either side. Finally, the mean itself may be unstable, so
that yesterday's normality may be supplanted today by a new normality that we know nothing about. It is perilous in the extreme to assume that prosperity is just around the corner simply because it always has
been just around the corner.

Regression to the mean is most slavishly followed on the stock market. Wall Street folklore is full of such catch phrases as "Buy low and sell high," "You never get poor taking a profit," and "The bulls get something and the bears get something but the hogs get nothing." All are variations on a simple theme: if you bet that today's normality will extend indefinitely into the future, you will get rich sooner and face a smaller risk of going broke than if you run with the crowd. Yet many investors violate this advice every day because they are emotionally incapable of buying low or selling high. Impelled by greed and fear, they run with the crowd instead of thinking for themselves.

It is not all that easy to keep the peapods in mind. Since we never know exactly what is going to happen tomorrow, it is easier to assume that the future will resemble the present than to admit that it may bring some unknown change. A stock that has been going up for a while somehow seems a better buy than a stock that has been heading for the cellar. We assume that a rising price signifies that the company is flourishing and that a falling price signifies that the company is in trouble. Why stick your neck out?

Professionals are just as likely as amateurs to try to play it safe. For example, in December 1994, analysts at the brokerage firm of Sanford C. Bernstein & Co. found that professionals who tend to forecast a higherthan-average growth rate for a company consistently overestimate the actual results, while pessimists consistently underestimate them.*
"[O]n average," the analysts reported, "expectations are not met."'

The consequences are clear: stocks with rosy forecasts climb to unreal heights while stocks with dismal forecasts drop to unreal lows. Then regression to the mean takes over. The more realistic and stouthearted investors buy as others rush to sell, and sell as others rush to buy. The payoff comes when the actual earnings surprise those who followed the trend.

History tells us of many legendary investors who made fortunes by
betting on regression to the mean, by buying low and selling high.
Among them are Bernard Baruch, Benjamin Graham, and Warren
Buffett. That contrarian position is confirmed by a wealth of academic
research.

But the few who made it big by copping the bets of the crowd
receive all the attention. We hear little about those investors who tried
the same thing and failed, either because they acted too soon or not at
all, or because the mean to which they expected stock prices to regress
was not the mean to which they actually did regress.

Consider those investors who had the temerity to buy stocks in
early 1930, right after the Great Crash, when prices had fallen about
50% from their previous highs. Prices proceeded to fall another 80%
before they finally hit bottom in the fall of 1932. Or consider the cautious investors who sold out in early 1955, when the Dow Jones
Industrials had finally regained their old 1929 highs and had tripled over
the preceding six years. Just nine years later, prices were double both
their 1929 and their 1955 highs. In both cases, the anticipated return to
"normal" failed to take place: normal had shifted to a new location.

In discussing the issue of whether regression to the mean governs
the behavior of the stock market, we are really asking whether stock
prices are predictable, and if so under what conditions. No investor can
decide what risks to take before answering that question.

There is some evidence that the prices of certain stocks rise "too
high" and fall "too low." In 1985 at the annual meeting of the American
Finance Association, economists Richard Thaler and Werner DeBondt
presented a paper titled, "Does the Stock Market Overreact?"' To test
whether extreme movements of stock prices in one direction provoke
regression to the mean and are subsequently followed by extreme movements in the other direction, they studied the three-year returns of over
a thousand stocks from January 1926 to December 1982. They classified
the stocks that had gone up by more or had fallen by less than the market average in each three-year period as "winners," and the stocks that
had gone up by less or had fallen by more than the market average as "losers." They then calculated the average performance of each group
over the subsequent three years.