The Handbook of Risk

By Ben Warwick

John Wiley & Sons

ISBN: 0-471-06412-2

Chapter One

The Failure of Invariance Peter L. Bernstein

Can everyone be "above average"? According to the author, there are significant differences between how people should make decisions and the way decisions are actually made. From ignoring nature's tendency to regress toward the mean to placing too much emphasis on current events in shaping our view of the world, Bernstein presents a lively and interesting view of behavioral finance and risk aversion.

All of us think of ourselves as rational beings even in times of crisis, applying the laws of probability in cool and calculated fashion to the choices that confront us. We like to believe we are above average in skills, intelligence, farsightedness, experience, refinement, and leadership. Who admits to being an incompetent driver, a feckless debater, a stupid investor, or a person with an inferior taste in clothes? Yet how realistic are such images? Not everyone can be above average. Furthermore, the most important decisions we make usually occur under complex, confusing, indistinct, or frightening conditions. Not much time is available to consult the laws of probability. Life is not a game of balla. It often comes trailing Kenneth Arrow's clouds of vagueness.

And yet most humans are not utterly irrational beings who take risks without forethought or who hide in a closet when anxiety strikes. As we shall see, the evidence suggests that we reach decisions in accord with an underlying structure that enables us to function predictably and, in most instances, systematically. The issue, rather, is the degree to which the reality in which we make our decisions deviates from the rational decision models of the Bernoullis, Jevons, and von Neumann. Psychologists have spawned a cottage industry to explore the nature and causes of these deviations.

The classical models of rationality-the model on which game theory and most of Markowitz's concepts are based-specifies how people should make decisions in the face of risk and what the world would be like if people did in fact behave as specified. Extensive research and experimentation, however, reveal that departures from that model occur more frequently than most of us admit. You will discover yourself in many of the examples that follow.

The most influential research into how people manage risk and uncertainty has been conducted by two Israeli psychologists, Daniel Kahneman and Amos Tversky. Although they now live in the United States, one at Princeton and the other at Stanford, both served in the Israeli armed forces during the 1950s. Kahneman developed a psychological screening system for evaluating Israeli army recruits that is still in use. Tversky served as a paratroop captain and earned a citation for bravery. The two have been collaborating for nearly thirty years and now command an enthusiastic following among both scholars and practitioners in the field of finance and investing, where uncertainty influences every decision.

Kahneman and Tversky call their concept Prospect Theory. After reading about Prospect Theory and discussing it in person with both Kahneman and Tversky, I began to wonder why its name bore no resemblance to its subject matter. I asked Kahneman where the name had come from. "We just wanted a name that people would notice and remember," he said. Their association began in the mid-1960s when both were junior professors at Hebrew University in Jerusalem. At one of their first meetings, Kahneman told Tversky about an experience he had had while instructing flight instructors on the psychology of training. Referring to studies of pigeon behavior, he was trying to make the point that reward is a more effective teaching tool than punishment. Suddenly one of his students shouted, "With respect, Sir, what you're saying is literally for the birds ... My experience contradicts it." The student explained that the trainees he praised for excellent perfomance almost always did worse on their next flight, while the ones he criticized for poor performance almost always improved.

Kahneman realized that this pattern was exactly what Francis Galton would have predicted. Just as large sweet peas give birth to smaller sweet peas, 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. 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 decision making. 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 50-50 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 and 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 Program A's certainty of saving 200 lives over Program 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." 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."

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."

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. Thaler proposed to a class of students that they had just won $30 and were now offered the following 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 on heads and wins $21 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 chose the gamble, while people who start with empty pockets will reject the gramble. 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 in the second.

Edward Miller, an economics professor with an interest in behavioral matters, reports a variation on these themes.


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