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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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    2. 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.
    3. 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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    7. Stefan Schiller, 2017. "The Quest for Rationality: Chief Financial Officers’ and Accounting Master’s Students’ Perception of Economic Rationality," SAGE Open, , vol. 7(2), pages 21582440177, April.
    8. Konstantinos Georgalos & Ivan Paya & David Peel, 2023. "Higher order risk attitudes: new model insights and heterogeneity of preferences," Experimental Economics, Springer;Economic Science Association, vol. 26(1), pages 145-192, March.
    9. Adam Oliver, 2018. "Your money and your life: Risk attitudes over gains and losses," Journal of Risk and Uncertainty, Springer, vol. 57(1), pages 29-50, August.
    10. Mel Win Khaw & Ziang Li & Michael Woodford, 2022. "Cognitive Imprecision and Stake-Dependent Risk Attitudes," CESifo Working Paper Series 9923, CESifo.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
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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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