Behavioral Finance: Prospect Theory, Bias, and Strategy

Prospect Theory and Utility Theory

Prospect theory is a form of behavioral finance and economics that posits that people make decisions based on expected gains rather than expected losses. At the heart of behavioral finance is the idea that economic decision-making is not necessarily based on purely rational choices. One of the baseline assumptions of finance is that actors possess pure economic rationality. This assumption is made in order to help isolate other variables when studying financial decision-making, but it was never really intended to hold true in real life. In real life, emotions and biases enter into economic decision-making constantly, and behavioral finance is the field in which such decision-making is studied.

Economic actors are broken into three categories based on their decision-making heuristics. Some are viewed as being purely rational, but most fall into either the risk-averse or the risk-taking category, based on their observed behavior. When prospect theory was first described, it was grounded in the idea that people make decisions based on perceived gains rather than perceived losses (Kahnemann & Tversky, 1979). Their starting point was the finding that there are some decisions in which strict rationality has not been observed, and the authors sought to explain this pattern of irrational decision-making.

One example they used was a choice between a 50% chance of receiving 1,000 shekels or 0 shekels, versus 450 shekels guaranteed. In this scenario, the first option has an expected value of 500 shekels. The issue, of course, is that this expected value is an average across many runs of the simulation, and no single individual is actually faced with the option to receive exactly 500 shekels. The real choice is between remaining in one's current position and taking a shot at 1,000 shekels — in effect, gambling with house money. If subjects were already starting with 450 shekels, they would likely make a different choice. The claim that this represents irrational decision-making is therefore somewhat loaded; it does not constitute an equivalent scenario to situations involving genuine loss. In fact, while Kahnemann and Tversky frame the decision as one made under risk, there is literally no risk to the people answering the question because none of their own money is at stake.

Utility theory contrasts with prospect theory in that it focuses on decision-making through perfectly rational evaluation. Under utility theory, an option offering 1,000 with 50% probability has an expected utility of 500, which exceeds the certain value of 450. Expected utility theory holds that "under uncertainty, the weighted average of all possible levels of utility will best represent the utility at any given time" (Kahnemann & Tversky, 1979).

For a genuine violation of expected utility theory to occur, one would have to regularly choose an option with higher upside even when the expected utility is the same as a certain outcome. A more apt variation is a scenario in which the certain outcome is 500 and the alternative is a 50% chance at 1,000 or a 50% chance at zero. Both have an expected value of 500, yet more subjects choose the option with the 1,000 upside. Again, this relates to the structure of the question — gambling on upside with house money is psychologically different from a double-or-nothing wager on one's own funds, which makes the high-upside option psychologically easier to pursue.

Tversky and Kahnemann (1992) followed up their original paper with a revised version of the theory. This update "employs cumulative rather than separable decision weights" (p. 297). Central to this work is the finding that people's decision-making "overweights small probabilities and underweights medium to high probabilities" (p. 298). Nonlinear preferences are said to be particularly in play under prospect theory. While Tversky and Kahnemann cite Allais (1953), who found that the perceived difference between probabilities of .99 and 1.00 differs from that between .10 and .11, that example rests on a meaningful asymmetry: 1.00 represents certainty of outcome, while none of the others do — so it is naturally perceived differently because it genuinely is different.

Risk-seeking is another key concept in prospect theory, one that leads to the overweighting of small odds attached to large outcomes. This is the domain in which lotteries operate. A rational actor can often calculate the expected value of a lottery ticket, and that value is always far lower than the actual cost of the ticket — hence the characterization of lotteries as a tax on those who are mathematically challenged. Those who purchase lottery tickets are overweighting the jackpot, or they are incorporating the utility of daydreaming into their calculation. In either case, lotteries are an example where relatively low stakes, unlikely but massive rewards, and broad popular appeal combine to violate the principles of utility and rational decision-making.

The 1992 update to the theory also specifies that framing matters — as illustrated above in the distinction between playing with house money and playing with one's own. Dollar values for outcomes may be identical, but they are not perceived that way when the money was never actually earned. This applies to lottery tickets as well: people regard the cost of a ticket as negligible relative to their monthly budget, while the possible outcomes, however unrealistic, appear life-changing. Framing therefore plays a central role in prospect theory.

Another element of the revised model is cumulative prospect theory, which holds that the carriers of value are gains, and that "the value of each outcome is multiplied by a decision weight, not an additive probability" (Tversky & Kahnemann, 1992, p. 299). These elements collectively seek to explain both why people behave irrationally and how prospect theory diverges from utility theory.

The efficient market hypothesis is rooted in utility theory and therefore does not account for the behavior of actors who employ anything other than expected utility in their decision-making heuristic. It has long been recognized that investors are not rational actors, but the variety of irrational behaviors makes them difficult to systematically characterize.

Prospect theory can be used, for example, to explain the dot-com bubble of 1999, in which prices became disconnected from actual valuations. This occurred because investors believed that any random dot-com company could become the next Amazon, without accounting for the particular and unique set of fundamental business attributes that made Amazon what it was. Such irrational behavior can also be observed in daily market movements, where one company's announcement of lower-than-expected earnings sometimes depresses the stock prices of other companies on the assumption that the two are related — when the underperformance may in fact be entirely firm-specific.

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