Against the Gods: The Remarkable Story of Risk (30 page)

So the stock-market record has produced some kind of resemblance
to a random walk, at least on the basis of these 840 monthly observations, because data would not appear to be distributed in this manner
around the mean if stock-price changes were not independent of one
another-like throws of the dice. After correction for the upward drift,
changes were about as likely to be downward as upward; sequential
changes of more than a month or so at a time were rare; the volatility
ratios across time came remarkably close to what theory stipulates they
should have been.

Assuming that we can employ Jacob Bernoulli's constraint that the
future will look like the past, we can use this information to calculate
the risk that stock prices will move by some stated amount in any one
month. The mean monthly price change in the S&P table was 0.6%
with a standard deviation of 5.8%. If price changes are randomly distributed, there is a 68% chance that prices in any one month will
change by no less than -5.2% or by no more than +6.4%. Suppose we
want to know the probability that prices will decline in any one month.
The answer works out to 45%-or a little less than half the time. But a
decline of more than 10% in any one month has a probability of only
3.5%, which means that it is likely to happen only about once every
thirty months; moves of 10% in either direction will show up about
once in every fifteen months.

As it happens, 33 of the 840 monthly observations, or about 4% of
the total, were more than two standard deviations away from the
monthly average of +0.6%-that is, worse than -11% and greater than
12.2%. Although 33 superswings are fewer than we might expect in a perfectly random series of observations, 21 of them were on the downside; chance would put that number at 16 or 17. A market with a builtin long-term upward trend should have even fewer disasters than 16 or
17 over 816 months.

At the extremes, the market is not a random walk. At the extremes,
the market is more likely to destroy fortunes than to create them. The
stock market is a risky place.

Up to this point, our story has been pretty much about numbers.
Mathematicians have held center stage as we studied the innovations of
ancient Hindus, Arabs, and Greeks all the way up to Gauss and Laplace
in the nineteenth century. Probability rather than uncertainty has been
our main theme.

Now the scene is about to shift. Real life is not like Paccioli's game
of balla, a sequence of independent or unrelated events. The stock market looks a lot like a random walk, but the resemblance is less than perfect. Averages are useful guides on some occasions but misleading on
many others. On still other occasions numbers are no help at all and we
are obliged to creep into the future guided only by guesses.

This does not mean that numbers are useless in real life. The trick
is to develop a sense of when they are relevant and when they are not.
So we now have a whole new set of questions to answer.

For instance, which defines the risk of being hit by a bomb, seven
million people or one elephant? Which of the following averages should
we use to define the stock market's normal performance: the average
monthly price change of +0.6% from 1926 to 1995, the piddling average of only +0.1% a month from 1930 to 1940, or the enticing average
of +1.0% a month from 1954 to 1964?

In other words, what do we mean by "normal"? How well does any
particular average describe normal? How stable, how powerful, is an
average as an indicator of behavior? When observations wander away
from the average of the past, how likely are they to regress to that average in the future? And if they do regress, do they stop at the average or
overshoot it?

What about those rare occasions when the stock market goes up five months in a row? Is it true that everything that goes up must come
down? Doth pride always goeth before a fall? What is the likelihood
that a company in trouble will bring its affairs into order? Will a manic
personality swing over to depression any time soon, and vice versa?
When is the drought going to end? Is prosperity just around the comer?

The answers to all these questions depend on the ability to distinguish between normal and abnormal. Much risk-taking rests on the
opportunities that develop from deviations from normal. When analysts
tell us that their favorite stock is "undervalued," they are saying that an
investor can profit by buying the stock now and waiting for its value to
return to normal. On the other hand, mental depressions or manic
states sometimes last a lifetime. And the economy in 1932 refused to
move itself around the corner, even though Mr. Hoover and his advisers were convinced that prodding by the government would only deter
it from finding its way back all by itself.

Nobody actually discovered the concept of "normal" any more
than anybody actually discovered the concept of "average." But Francis
Galton, an amateur scientist in Victorian England, took the foundation
that Gauss and his predecessors had created to support the concept of
average-the normal distribution-and raised a new structure to help
people distinguish between measurable risk and the kind of uncertainty
that obliges us to guess what the future will bring.

Galton was not a scientist in search of immutable truths. He was a
practical man, enthusiastic about science but still an amateur. Yet his
innovations and achievements have had a lasting impact on both mathematics and hands-on decision-making in the everyday world.

rancis Galton (1822-1911) was a social snob who never worked to
earn a living, except for a brief stint in a hospital during his early
twenties.' Yet he was one of the most charming and likable of the
many characters mentioned in this account. He was Charles Darwin's
first cousin, an occasional inventor, and an avid explorer of parts of
Africa where whites had never been seen. He made a seminal contribution to the theory of risk management, but he made that contribution in
stubborn pursuit of an evil concept.

Measurement was Galton's hobby-or, rather, obsession. "Wherever
you can, count," he would say.' He took note of the size of heads, noses,
arms, legs, heights, and weights, of the color of eyes, of the sterility of
heiresses, of the number of times people fidgeted as they listened to lectures, and of the degree of color change on the faces of spectators at the
Derby as they watched the horses run. He classified the degree of attractiveness of girls he passed on the street, pricking a hole in a left-pocket
card when a girl was comely and pricking a right-pocket card when she
was plain. In his "Beauty Map" of Britain, London girls scored highest;
Aberdeen girls scored lowest. He examined 10,000 judges' sentences
and observed that most of them occurred at regular intervals of 3, 6, 9,
12, 15, 18, and 24 years, while none appeared at 17 and only a few at 11
or 13. At a cattle exhibition, he tabulated the guesses of 800 visitors as to the weight of an ox and found that the "average vox populi was correct to within one percent of the real value."3

Galton's Anthropometric Laboratory, which he established in 1884,
measured and kept track of the range and character of every possible
measurement of the human body, including even finger prints. Finger
prints fascinated Galton because, unlike every other part of the body,
their configuration never changes as a person grows older. In 1893, he
published a 200-page book on the subject that soon led to the widespread use of finger printing by police.

Galton's compulsion to measure was evident even on a trip to Africa
in 1849 to hunt big game in what is now Namibia. When he arrived at
a village of Hottentots, he discovered "figures that would drive the
females of our land desperate-figures that could afford to scoff at
Crinoline."4 One woman in particular caught his attention.' As a scientific man, he reported, he was "exceedingly anxious to obtain accurate
measurements of her shape." Unable to speak Hottentot and uncertain
how to undertake this urgent piece of research, he still managed to
achieve his goal:

Of a sudden my eye fell upon my sextant; the bright thought struck
me, and I took a series of observations upon her figure in every direction.... [T]his being done, I boldly pulled out my measuring tape,
and measured the distance from where I was to the place where she
stood, and having thus obtained both base and angles, I worked out
the results by trigonometry and logarithms.

Galton was the personification of the Victorian Englishman who
strode the earth as though it were his private preserve. On another occasion during his hunting trip to Africa, he grew worried that the local
chieftain might attack his camp. Clad in his red hunting coat, cap, and
jackboots, he mounted an ox, charged up to the largest hut in the village,
and forced the ox's head into the hut. The camp was never attacked.

At another village, he committed a social gaffe by refusing to take
part in a ritual in which the host gargles and then spits the liquid into
the face of his guest. And when King Nangoro presented him with
Princess Chapange for an evening of pleasure, Galton was aghast when
she arrived for the occasion "raddled with ochre and butter." "I was
dressed in my one well-preserved suit of white linen, so I had her
ejected with scant ceremony."