Prospect Theory and Utility Theory: Temporary Versus Permanent Attitude towards Risk

Haim Levy, Zvi Wiener
2013 Social Science Research Network  
Prospect Theory (PT), which relies on subjects' behavior as observed in laboratory experiments contradicts the behavior predicted by the Expected Utility (EU) paradigm. In this study, we introduce the concept of Temporary Attitude Towards Risk (TATR) and Permanent Attitude Towards Risk (PATR). Using these concepts, we build a model that merges both the PT and the EU paradigms. The TATR and PATR concepts explain recent experimental findings and the observed stock price overreaction. We relate
more » ... properties of PT to some well-known financial and economic results. We show that a positive risk premium with decreasing absolute risk aversion (DARA) can be consistent with the S-shaped value function used in PT. Finally, we introduce the Prospect Stochastic Dominance (PSD) rule for partial ordering of uncertain prospects for all S-shaped value functions. JEL Classification Codes: D81, G0 Theories of decision making under uncertainty and, in particular, portfolio selection, assume (explicitly or implicitly) expected utility (EU) maximization. Yet, EU is criticized on several grounds. Probably the most well known criticism was made by the French economist, Maurice Allais (1953, 1988, 1990), who showed that preferences are non-linear. According to Allais, an increase in the probability of receiving an amount w from .99 to 1.00 has more impact on individuals than an increase in the probability of receiving w from .10 to .11. This contradicts the expected utility theory that predicts an equal increase, of 0.01U(w) in both cases, U being the utility function. Markowitz (1952) also pointed out possible contradictions to the expected utility theory as early as 1952. Markowitz proposes a utility function that explains gambling and insurance which differs significantly from Friedman and Savage's (1948) utility function. To the best of our knowledge, Markowitz was the first to raise a few important issues, later on confirmed by experimental studies. First, he claims that not only total wealth but also change of wealth may be a factor in the decision making process, and second, that "temporary" changes in the utility function might take place and therefore a distinction should be made between "customary" wealth and present wealth. Moreover, he also suggested that the inflection point temporarily "travels" along the utility function: "So far I have assumed that the second inflection corresponds to present wealth. There are reasons for believing that this is not always the case. For example, suppose that our hypothetical stranger, rather than offering to give you $X or a chance of $Y, had instead first given you the $X and then had offered you a fair bet which if lost would cost you -$X and if won
doi:10.2139/ssrn.2197750 fatcat:qt33pofogfactbdvkn5fckeyoa