Prospect theory and the “forgotten” fourfold pattern of risk preferences
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Markowitz (Journal of Political Economy 60:151–158, 1952) identified a fourfold pattern of risk preferences in outcome magnitude: When outcomes are large, people are risk averse in gains and risk seeking in losses, but risk preferences reverse when the outcomes are small, with people exhibiting risk seeking in gains and risk aversion in losses. This fourfold pattern was not addressed by either version of prospect theory (Kahneman and Tversky Econometrica 47:363–391, 1979; Tversky and Kahneman Journal of Risk and Uncertainty 5:297–323, 1992). We show how prospect theory can accommodate the pattern by combining an overweighting of low probabilities with a decreasingly elastic value function. We then examine the performance of prospect theory with two decreasingly elastic value functions: Prospect theory performs better, both quantitatively and qualitatively, with a normalized logarithmic value function than with a normalized exponential value function. We discuss several issues, and speculate about why Tversky and Kahneman did not address Markowitz’s fourfold pattern.
KeywordsRisk aversion Risk seeking Gains Losses Fourfold patterns of risk preferences Markowitz Prospect theory
JEL ClassificationsC51 C52 C91 D03 D90
This work was supported by the Fundação para a Ciência e Tecnologia [project POCI 2010; grant numbers PTDC/PSI-PCO/101447/2008, PTDC/MHC-PCN/3805/2012], by the Economic and Social Research Council [grant number ES/K002201/1], and by the Leverhulme Trust [grant number RP2012-V-022]. Our article has greatly benefited from comments given by Peter Wakker.
- Bernoulli, D. (1738). Specimen theoriae novae de mensura sortis. Commentarii academiae scientiarum imperialis petropolitanae. Translated, Bernoulli, D. (1954). Exposition of a new theory on the measurement of risk. Econometrica, 22, 23–36.Google Scholar
- Camerer, C. F., & Ho, T.–H. (1994). Violations of the betweenness axiom and nonlinearity in probability. Journal of Risk and Uncertainty, 8, 167–196.Google Scholar
- Hayden, B. Y., & Platt, M. L. (2009). The mean, the median, and the St. Petersburg Paradox. Judgment and Decision Making, 4, 256–273.Google Scholar
- Kahneman, D., & Tversky, A. (1982). The psychology of preferences. Scientific American, 248, 163–169.Google Scholar
- Kirby, K. N. (2011). An empirical assessment of the form of utility functions. Journal of Experimental Psychology: Learning, Memory, and Cognition, 37, 461–476.Google Scholar
- Luce, R. D. (1959). Individual choice behavior: A theoretical analysis. New York, NY: Wiley.Google Scholar
- Samuelson, P. A. (1977). St. Petersburg Paradoxes: Defanged, dissected and historically described. Journal of Economic Literature, 15, 24–55.Google Scholar
- Schoemaker, P. J. H. (1982). The expected utility model: Its variants, purposes, evidence, and limitations. Journal of Economic Literature, 20, 529–563.Google Scholar
- Scholten, M., Read, D., & Sanborn, A. (2014). Weighing outcomes by time or against time? Evaluation rules in intertemporal choice. Cognitive Science. doi: 10.1111/cogs.12104.
- StatSoft. (2003). Statistica (Version 6) [Computer software]. Tulsa, OK.Google Scholar