Against the Gods: The Remarkable Story of Risk (53 page)

Kahneman realized that this pattern was exactly what Francis
Galton would have predicted. Just as large sweetpeas give birth to
smaller sweetpeas, and vice versa, performance in any area is unlikely
to go on improving or growing worse indefinitely. We swing back
and forth in everything we do, continuously regressing toward what
will turn out to be our average performance. The chances are that the
quality of a student's next landing will have nothing to do with
whether or not someone has told him that his last landing was good
or bad.

"Once you become sensitized to it, you see regression everywhere,"
Kahneman pointed out to Tversky.3 Whether your children do what
they are told to do, whether a basketball player has a hot hand in tonight's
game, or whether an investment manager's performance slips during this
calendar quarter, their future performance is most likely to reflect regression to the mean regardless of whether they will be punished or rewarded
for past performance.

Soon the two men were speculating on the possibility that ignoring
regression to the mean was not the only way that people err in forecasting future performance from the facts of the past. A fruitful collaboration
developed between them as they proceeded to conduct a series of clever
experiments designed to reveal how people make choices when faced
with uncertain outcomes.

Prospect Theory discovered behavior patterns that had never been
recognized by proponents of rational decision-making. Kahneman and
Tversky ascribe these patterns to two human shortcomings. First, emotion often destroys the self-control that is essential to rational decisionmaking. Second, people are often unable to understand fully what they
are dealing with. They experience what psychologists call cognitive
difficulties.

The heart of our difficulty is in sampling. As Leibniz reminded Jacob
Bernoulli, nature is so varied and so complex that we have a hard time
drawing valid generalizations from what we observe. We use shortcuts
that lead us to erroneous perceptions, or we interpret small samples as
representative of what larger samples would show.

Consequently, we tend to resort to more subjective kinds of measurement: Keynes's "degrees of belief' figure more often in our decision-making than Pascal's Triangle, and gut rules even when we think
we are using measurement. Seven million people and one elephant!

We display risk-aversion when we are offered a choice in one setting and then turn into risk-seekers when we are offered the same choice
in a different setting. We tend to ignore the common components of a
problem and concentrate on each part in isolation-one reason why
Markowitz's prescription for portfolio-building was so slow to find
acceptance. We have trouble recognizing how much information is
enough and how much is too much. We pay excessive attention to
low-probability events accompanied by high drama and overlook events
that happen in routine fashion. We treat costs and uncompensated losses
differently, even though their impact on wealth is identical. We start out
with a purely rational decision about how to manage our risks and then
extrapolate from what may be only a run of good luck. As a result, we
forget about regression to the mean, overstay our positions, and end up
in trouble.

Here is a question that Kahneman and Tversky use to show how
intuitive perceptions mislead us. Ask yourself whether the letter K
appears more often as the first or as the third letter of English words.
You will probably answer that it appears more often as the first letter.
Actually, K appears as the third letter twice as often. Why the error?
We find it easier to recall words with a certain letter at the beginning
than words with that same letter somewhere else.

The asymmetry between the way we make decisions involving
gains and decisions involving losses is one of the most striking findings
of Prospect Theory. It is also one of the most useful.

Where significant sums are involved, most people will reject a fair
gamble in favor of a certain gain-$100,000 certain is preferable to a 5050 possibility of $200,000 or nothing. We are risk-averse, in other words.

But what about losses? Kahneman and Tversky's first paper on
Prospect Theory, which appeared in 1979, describes an experiment
showing that our choices between negative outcomes are mirror images
of our choices between positive outcomes.' In one of their experiments they first asked the subjects to choose between an 80% chance of
winning $4,000 and a 20% chance of winning nothing versus a 100%
chance of receiving $3,000. Even though the risky choice has a higher
mathematical expectation-$3,200-80% of the subjects chose the $3,000 certain. These people were risk-averse, just as Bernoulli would
have predicted.

Then Kahneman and Tversky offered a choice between taking the
risk of an 80% chance of losing $4,000 and a 20% chance of breaking
even versus a 100% chance of losing $3,000. Now 92% of the respondents chose the gamble, even though its mathematical expectation of a
loss of $3,200 was once again larger than the certain loss of $3,000.
When the choice involves losses, we are risk-seekers, not risk-averse.

Kahneman and Tversky and many of their colleagues have found
that this asymmetrical pattern appears consistently in a wide variety of
experiments. On a later occasion, for example, Kahneman and Tversky
proposed the following problem.' Imagine that a rare disease is breaking out in some community and is expected to kill 600 people. Two
different programs are available to deal with the threat. If Program A is
adopted, 200 people will be saved; if Program B is adopted, there is a
33% probability that everyone will be saved and a 67% probability that
no one will be saved.

Which program would you choose? If most of us are risk-averse,
rational people will prefer Plan A's certainty of saving 200 lives over Plan
B's gamble, which has the same mathematical expectancy but involves
taking the risk of a 67% chance that everyone will die. In the experiment,
72% of the subjects chose the risk-averse response represented by
Program A.

Now consider the identical problem posed differently. If Program
C is adopted, 400 of the 600 people will die, while Program D entails
a 33% probability that nobody will die and a 67% probability that 600
people will die. Note that the first of the two choices is now expressed
in terms of 400 deaths rather than 200 survivors, while the second program offers a 33% chance that no one will die. Kahneman and Tversky
report that 78% of their subjects were risk-seekers and opted for the
gamble: they could not tolerate the prospect of the sure loss of 400
lives.

This behavior, although understandable, is inconsistent with the
assumptions of rational behavior. The answer to a question should be
the same regardless of the setting in which it is posed. Kahneman and
Tversky interpret the evidence produced by these experiments as a
demonstration that people are not risk-averse: they are perfectly willing
to choose a gamble when they consider it appropriate. But if they are not risk-averse, what are they? "The major driving force is loss aversion," writes Tversky (italics added). "It is not so much that people hate
uncertainty-but rather, they hate losing."6 Losses will always loom
larger than gains. Indeed, losses that go unresolved-such as the loss of
a child or a large insurance claim that never gets settled-are likely to
provoke intense, irrational, and abiding risk-aversion.?

Tversky offers an interesting speculation on this curious behavior:

Probably the most significant and pervasive characteristic of the
human pleasure machine is that people are much more sensitive to
negative than to positive stimuli.... [T]hink about how well you feel
today, and then try to imagine how much better you could feel....
[T]here are a few things that would make you feel better, but the
number of things that would make you feel worse is unbounded.8

One of the insights to emerge from this research is that Bernoulli had
it wrong when he declared, "[The] utility resulting from any small
increase in wealth will be inversely proportionate to the quantity of
goods previously possessed." Bernoulli believed that it is the pre-existing
level of wealth that determines the value of a risky opportunity to
become richer. Kahneman and Tversky found that the valuation of a
risky opportunity appears to depend far more on the reference point
from which the possible gain or loss will occur than on the final value of
the assets that would result. It is not how rich you are that motivates your
decision, but whether that decision will make you richer or poorer. As a
consequence, Tversky warns, "our preferences ... can be manipulated
by changes in the reference points."9

He cites a survey in which respondents were asked to choose
between a policy of high employment and high inflation and a policy of
lower employment and lower inflation. When the issue was framed in
terms of an unemployment rate of 10% or 5%, the vote was heavily in
favor of accepting more inflation to get the unemployment rate down.
When the respondents were asked to choose between a labor force that
was 90% employed and a labor force that was 95% employed, low inflation appeared to be more important than raising the percentage employed by five points.

Richard Thaler has described an experiment that uses starting
wealth to illustrate Tversky's warning.10 Thaler proposed to a class of
students that they had just won $30 and were now offered the follow ing choice: a coin flip where the individual wins $9 on heads and loses
$9 on tails versus no coin flip. Seventy percent of the subjects selected
the coin flip. Thaler offered his next class the following options: starting wealth of zero and then a coin flip where the individual wins $39
on heads and wins $21 on tails versus $30 for certain. Only 43 percent
selected the coin flip.

Thaler describes this result as the "house money" effect. Although
the choice of payoffs offered to both classes is identical-regardless of the
amount of the starting wealth, the individual will end up with either $39
or $21 versus $30 for sure-people who start out with money in their
pockets will choose the gamble, while people who start out with empty
pockets will reject the gamble. Bernoulli would have predicted that the
decision would be determined by the amounts $39, $30, or $21 whereas
the students based their decisions on the reference point, which was $30
in the first case and zero in the second.

Edward Miller, an economics professor with an interest in behavioral matters, reports a variation on these themes. Although Bernoulli
uses the expression "any small increase in wealth," he implies that
what he has to say is independent of the size of the increase." Miller
cites various psychological studies that show significant differences in
response, depending on whether the gain is a big one or a small one.
Occasional large gains seem to sustain the interest of investors and
gamblers for longer periods of time than consistent small winnings.
That response is typical of investors who look on investing as a game
and who fail to diversify; diversification is boring. Well-informed
investors diversify because they do not believe that investing is a form
of entertainment.

Kahneman and Tversky use the expression "failure of invariance"
to describe inconsistent (not necessarily incorrect) choices when the
same problem appears in different frames. Invariance means that if A is
preferred to B and B is preferred to C, then rational people will prefer
A to C; this feature is the core of von Neumann and Morgenstern's
approach to utility. Or, in the case above, if 200 lives saved for certain
is the rational decision in the first set, saving 200 lives for certain should
be the rational decision in the second set as well.

But research suggests otherwise:

The failure of invariance is both pervasive and robust. It is as common among sophisticated respondents as among naive ones....
Respondents confronted with their conflicting answers are typically
puzzled. Even after rereading the problems, they still wish to be risk
averse in the "lives saved" version; they will be risk seeking in the
"lives lost" version; and they also wish to obey invariance and give
consistent answers to the two versions....