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Prospect theory and the “forgotten” fourfold pattern of risk preferences

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  • Marc Scholten
  • Daniel Read

Abstract

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. Copyright Springer Science+Business Media New York 2014

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  • Marc Scholten & Daniel Read, 2014. "Prospect theory and the “forgotten” fourfold pattern of risk preferences," Journal of Risk and Uncertainty, Springer, vol. 48(1), pages 67-83, February.
  • Handle: RePEc:kap:jrisku:v:48:y:2014:i:1:p:67-83
    DOI: 10.1007/s11166-014-9183-2
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    as
    1. Drazen Prelec & George Loewenstein, 1991. "Decision Making Over Time and Under Uncertainty: A Common Approach," Management Science, INFORMS, vol. 37(7), pages 770-786, July.
    2. Robin M. Hogarth & Hillel J. Einhorn, 1990. "Venture Theory: A Model of Decision Weights," Management Science, INFORMS, vol. 36(7), pages 780-803, July.
    3. Mohammed Abdellaoui & Han Bleichrodt & Olivier L’Haridon, 2008. "A tractable method to measure utility and loss aversion under prospect theory," Journal of Risk and Uncertainty, Springer, vol. 36(3), pages 245-266, June.
    4. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    5. Han Bleichrodt & Jose Luis Pinto, 2000. "A Parameter-Free Elicitation of the Probability Weighting Function in Medical Decision Analysis," Management Science, INFORMS, vol. 46(11), pages 1485-1496, November.
    6. Harry Markowitz, 1952. "The Utility of Wealth," Journal of Political Economy, University of Chicago Press, vol. 60, pages 151-151.
    7. Samuelson, Paul A, 1977. "St. Petersburg Paradoxes: Defanged, Dissected, and Historically Described," Journal of Economic Literature, American Economic Association, vol. 15(1), pages 24-55, March.
    8. Charles A. Holt & Susan K. Laury, 2002. "Risk Aversion and Incentive Effects," American Economic Review, American Economic Association, vol. 92(5), pages 1644-1655, December.
    9. Helga Fehr-Duda & Adrian Bruhin & Thomas Epper & Renate Schubert, 2010. "Rationality on the rise: Why relative risk aversion increases with stake size," Journal of Risk and Uncertainty, Springer, vol. 40(2), pages 147-180, April.
    10. Camerer, Colin F & Ho, Teck-Hua, 1994. "Violations of the Betweenness Axiom and Nonlinearity in Probability," Journal of Risk and Uncertainty, Springer, vol. 8(2), pages 167-196, March.
    11. Fennema, Hein & van Assen, Marcel, 1998. "Measuring the Utility of Losses by Means of the Tradeoff Method," Journal of Risk and Uncertainty, Springer, vol. 17(3), pages 277-295, December.
    12. Andersen, Steffen & Harrison, Glenn W. & Lau, Morten Igel & Rutström, Elisabet E., 2010. "Behavioral econometrics for psychologists," Journal of Economic Psychology, Elsevier, vol. 31(4), pages 553-576, August.
    13. Mohammed Abdellaoui & Frank Vossmann & Martin Weber, 2005. "Choice-Based Elicitation and Decomposition of Decision Weights for Gains and Losses Under Uncertainty," Management Science, INFORMS, vol. 51(9), pages 1384-1399, September.
    14. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
    15. George Loewenstein & Drazen Prelec, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, Oxford University Press, vol. 107(2), pages 573-597.
    16. al-Nowaihi, Ali & Dhami, Sanjit, 2009. "A value function that explains the magnitude and sign effects," Economics Letters, Elsevier, vol. 105(3), pages 224-229, December.
    17. repec:cup:judgdm:v:4:y:2009:i:4:p:256-272 is not listed on IDEAS
    18. Paul J. H. Schoemaker, 1990. "Are Risk-Attitudes Related Across Domains and Response Modes?," Management Science, INFORMS, vol. 36(12), pages 1451-1463, December.
    19. Marc Rieger & Mei Wang, 2006. "Cumulative prospect theory and the St. Petersburg paradox," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(3), pages 665-679, August.
    20. Donkers, Bas & Melenberg, Bertrand & Van Soest, Arthur, 2001. "Estimating Risk Attitudes Using Lotteries: A Large Sample Approach," Journal of Risk and Uncertainty, Springer, vol. 22(2), pages 165-195, March.
    21. Pavlo R. Blavatskyy, 2005. "Back to the St. Petersburg Paradox?," Management Science, INFORMS, vol. 51(4), pages 677-678, April.
    22. Henry Stott, 2006. "Cumulative prospect theory's functional menagerie," Journal of Risk and Uncertainty, Springer, vol. 32(2), pages 101-130, March.
    23. Kontek, Krzysztof, 2009. "On Mental Transformations," MPRA Paper 16516, University Library of Munich, Germany.
    24. Schoemaker, Paul J H, 1982. "The Expected Utility Model: Its Variants, Purposes, Evidence and Limitations," Journal of Economic Literature, American Economic Association, vol. 20(2), pages 529-563, June.
    25. Mullet, Etienne, 1992. "The probability + utility rule in attractiveness judgments of positive gambles," Organizational Behavior and Human Decision Processes, Elsevier, vol. 52(2), pages 246-255, July.
    26. George Wu & Richard Gonzalez, 1996. "Curvature of the Probability Weighting Function," Management Science, INFORMS, vol. 42(12), pages 1676-1690, December.
    27. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    28. Kobberling, Veronika & Wakker, Peter P., 2005. "An index of loss aversion," Journal of Economic Theory, Elsevier, vol. 122(1), pages 119-131, May.
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    6. Mel Win Khaw & Ziang Li & Michael Woodford, 2022. "Cognitive Imprecision and Stake-Dependent Risk Attitudes," CESifo Working Paper Series 9923, CESifo.
    7. Ranoua Bouchouicha & Peter Martinsson & Haileselassie Medhin & Ferdinand M. Vieider, 2017. "Stake effects on ambiguity attitudes for gains and losses," Theory and Decision, Springer, vol. 83(1), pages 19-35, June.
    8. Julius Pahlke & Sebastian Strasser & Ferdinand Vieider, 2015. "Responsibility effects in decision making under risk," Journal of Risk and Uncertainty, Springer, vol. 51(2), pages 125-146, October.
    9. Ranoua Bouchouicha & Ferdinand M. Vieider, 2017. "Accommodating stake effects under prospect theory," Journal of Risk and Uncertainty, Springer, vol. 55(1), pages 1-28, August.
    10. Xiaodong Du & Hongli Feng & David A. Hennessy, 2017. "Rationality of Choices in Subsidized Crop Insurance Markets," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 99(3), pages 732-756.
    11. Oliver, Adam, 2018. "Your money and your life: risk attitudes over gains and losses," LSE Research Online Documents on Economics 88583, London School of Economics and Political Science, LSE Library.
    12. David Alan Peel & David Law, 2017. "Loss Aversion And Ruinous Optimal Wagers In Cumulative Prospect Theory," Economics Bulletin, AccessEcon, vol. 37(1), pages 352-360.
    13. Géraldine Bocquého & Julien Jacob & Marielle Brunette, 2020. "Prospect theory in experiments : behaviour in loss domain and framing effects," Working Papers hal-02987294, HAL.
    14. Georgalos, Konstantinos & Paya, Ivan & Peel, David A., 2021. "On the contribution of the Markowitz model of utility to explain risky choice in experimental research," Journal of Economic Behavior & Organization, Elsevier, vol. 182(C), pages 527-543.
    15. Leoneti, Alexandre Bevilacqua & Gomes, Luiz Flavio Autran Monteiro, 2021. "A novel version of the TODIM method based on the exponential model of prospect theory: The ExpTODIM method," European Journal of Operational Research, Elsevier, vol. 295(3), pages 1042-1055.
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    17. Ivan Paya & David Peel & Konstantinos Georgalos, 2020. "On the Predictions of Cumulative Prospect Theory for Third and Fourth Order Preferences," Working Papers 293574809, Lancaster University Management School, Economics Department.
    18. Glenn W. Harrison & J. Todd Swarthout, 2016. "Cumulative Prospect Theory in the Laboratory: A Reconsideration," Experimental Economics Center Working Paper Series 2016-04, Experimental Economics Center, Andrew Young School of Policy Studies, Georgia State University.
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    More about this item

    Keywords

    Risk aversion; Risk seeking; Gains; Losses; Fourfold patterns of risk preferences; Markowitz; Prospect theory; C51; C52; C91; D03; D90;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General

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