What is common between choosing a portfolio of assets, and deciding whether to buy a lottery ticket? Or, between waiting for an oncoming car before making a turn, and studying an extra hour for a particular exam?
All these are instances of decisions under uncertainty, where one must choose among actions whose consequences are to some extent unpredictable, says T. W. Epps in ‘ Quantitative Finance: Its development, mathematical foundations, and current scope’ (www.landmarkonthenet.com).
He finds that writers draw a sharp line between the terms ‘uncertainty’ and ‘risk’ – the former used when the probabilities of different consequences of an action are considered to be unknown, and the latter, when probabilities are objectively given.
“With this distinction, money bet in a game of roulette would be considered at risk, while an investment in a portfolio would be considered to have uncertain future value. Most economists nowadays proceed as if people form subjective probabilities in the uncertain situation and then act on them as if they were objectively given, thus eliminating the need to distinguish the two concepts.”
Among the studies cited in the book on this topic is the Ellsberg paradox. “There are two urns. A subject is told that urn A contains a 50-50 mix of red and blue balls and that urn B contains only red and/or blue balls – but in unknown proportion; that is, urn B could have all red, all blue, or any mix in between,” runs the description. There is a reward for drawing a red ball, and the person gets just one draw and must choose from which urn to draw.
How would you behave in such a situation? Go for urn A or B? Daniel Ellsberg (1961), who performed the study, found that those confronted with such a choice almost uniformly chose to draw from urn A, suggesting that people find choices with unknown probabilities to be inherently riskier.
In effect, the probability of drawing red from A is known objectively to be ½, so that whether one gets red or blue from urn A is a ‘toss-up,’ explains Epps. “But since there is no reason to think that urn B has more of one colour than the other, the same should be true there as well. In other words, from considerations of symmetry the subjective probability of red from urn B should be ½ also, so it would seem that a rational individual would be indifferent as to the choice of urn.”
Raising the issue whether financial models should be based on expected-utility theory, along with a long chain of assumptions (such as frictionless markets and rational expectations), the author observes that the modelling of decision making under uncertainty has not been left to economists alone.
“This has been for many years an active field in psychology, and psychologists have carried out carefully controlled experiments to judge the adequacy of the expected-utility (EU) theory and some competing ones. More recently, experimental economists have made valuable contributions as well.”
For instance, as if to challenge even the basic ordinal utility theory that underlies models of consumers’ behaviour, there is now a substantial body of experimental evidence that does indicate that people – even smart people – systematically make intransitive choices, Epps reports.
He describes an experiment conducted in a Las Vegas casino, as captured in ‘a fascinating paper by psychologists Sarah Lichtenstein and Paul Slovic (1973).’ A space was made available for them to offer real P and $ bets to people who had come to the casino to gamble, Epps writes. “Presumably, these were individuals who were used to thinking probabilistically and to putting their own cash at risk.”
(For starters, as the book informs, the ‘$ bet’ offers relatively low probability of the large gain and a high probability of the small loss. The second prospect, ‘P bet,’ offers a higher probability of the moderate gain and low probability of the loss, with no chance at the best prize. Whether it is P or $, the subject is told that he ‘owns’ it, that is, he will get to play the game and take whatever is won or lost. Alternatively, the subject can choose to sell the bet for some amount of money instead of playing it.)
“In fact, interviews with those who chose to participate showed that most were better educated than the run-of-the-mill gambling crowd, having careers as engineers, lawyers, airline pilots, and so forth. Nevertheless, many of these experienced people made the ‘mistake’ of choosing P bets over $ bets while selling P bets for less.”
Instructive study.
