IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0248904.html
   My bibliography  Save this article

Prospect theory, constant relative risk aversion, and the investment horizon

Author

Listed:
  • Haim Levy
  • Moshe Levy

Abstract

Prospect Theory (PT) and Constant-Relative-Risk-Aversion (CRRA) preferences have clear-cut and very different implications for the optimal asset allocation between a riskless asset and a risky stock as a function of the investment horizon. While CRRA implies that the optimal allocation is independent of the horizon, we show that PT implies a dramatic and discontinuous “jump” in the optimal allocation as the horizon increases. We experimentally test these predictions at the individual level. We find rather strong support for CRRA, but very little support for PT.

Suggested Citation

  • Haim Levy & Moshe Levy, 2021. "Prospect theory, constant relative risk aversion, and the investment horizon," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-21, April.
    • Handle: RePEc:plo:pone00:0248904
    DOI: 10.1371/journal.pone.0248904
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0248904
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0248904&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0248904?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Haim Levy & Enrico G. De Giorgi & Thorsten Hens, 2012. "Two Paradigms and Nobel Prizes in Economics: a Contradiction or Coexistence?," European Financial Management, European Financial Management Association, vol. 18(2), pages 163-182, March.
    2. Richard H. Thaler & Amos Tversky & Daniel Kahneman & Alan Schwartz, 1997. "The Effect of Myopia and Loss Aversion on Risk Taking: An Experimental Test," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 647-661.
    3. Merton, Robert C. & Samuelson, Paul A., 1974. "Fallacy of the log-normal approximation to optimal portfolio decision-making over many periods," Journal of Financial Economics, Elsevier, vol. 1(1), pages 67-94, May.
    4. Michael S. Haigh & John A. List, 2005. "Do Professional Traders Exhibit Myopic Loss Aversion? An Experimental Analysis," Journal of Finance, American Finance Association, vol. 60(1), pages 523-534, February.
    5. Jules van Binsbergen & Michael Brandt & Ralph Koijen, 2012. "On the Timing and Pricing of Dividends," American Economic Review, American Economic Association, vol. 102(4), pages 1596-1618, June.
    6. Botond Kőszegi & Matthew Rabin, 2006. "A Model of Reference-Dependent Preferences," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 121(4), pages 1133-1165.
    7. 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.
    8. Gerlinde Fellner & Matthias Sutter, 2009. "Causes, Consequences, and Cures of Myopic Loss Aversion – An Experimental Investigation," Economic Journal, Royal Economic Society, vol. 119(537), pages 900-916, April.
    9. Amos Tversky & Daniel Kahneman, 1991. "Loss Aversion in Riskless Choice: A Reference-Dependent Model," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(4), pages 1039-1061.
    10. Arjan B. Berkelaar & Roy Kouwenberg & Thierry Post, 2004. "Optimal Portfolio Choice under Loss Aversion," The Review of Economics and Statistics, MIT Press, vol. 86(4), pages 973-987, November.
    11. Moshe Levy & Haim Levy, 2013. "Prospect Theory: Much Ado About Nothing?," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 7, pages 129-144, World Scientific Publishing Co. Pte. Ltd..
    12. Shlomo Benartzi & Richard H. Thaler, 1999. "Risk Aversion or Myopia? Choices in Repeated Gambles and Retirement Investments," Management Science, INFORMS, vol. 45(3), pages 364-381, March.
    13. Uri Gneezy & Arie Kapteyn & Jan Potters, 2003. "Evaluation Periods and Asset Prices in a Market Experiment," Journal of Finance, American Finance Association, vol. 58(2), pages 821-837, April.
    14. Eisenbach, Thomas M. & Schmalz, Martin C., 2016. "Anxiety in the face of risk," Journal of Financial Economics, Elsevier, vol. 121(2), pages 414-426.
    15. Langer, Thomas & Weber, Martin, 2008. "Does commitment or feedback influence myopic loss aversion?: An experimental analysis," Journal of Economic Behavior & Organization, Elsevier, vol. 67(3-4), pages 810-819, September.
    16. Haim Levy & Enrico De Giorgi & Thorsten Hens, "undated". "Two Paradigms and Nobel Prizes in Economics: A Contradiction or Coexistence?," IEW - Working Papers 161, Institute for Empirical Research in Economics - University of Zurich.
    17. 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.
    18. Gordon, Myron J & Paradis, G E & Rorke, C H, 1972. "Experimental Evidence on Alternative Portfolio Decision Rules," American Economic Review, American Economic Association, vol. 62(1), pages 107-118, March.
    19. Levy, Haim, 1994. "Absolute and Relative Risk Aversion: An Experimental Study," Journal of Risk and Uncertainty, Springer, vol. 8(3), pages 289-307, May.
    20. 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.
    21. Alan Kirman, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(1), pages 137-156.
    22. Paul A. Samuelson, 2011. "Lifetime Portfolio Selection by Dynamic Stochastic Programming," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 31, pages 465-472, World Scientific Publishing Co. Pte. Ltd..
    23. Levy, Moshe & Levy, Haim & Solomon, Sorin, 1994. "A microscopic model of the stock market : Cycles, booms, and crashes," Economics Letters, Elsevier, vol. 45(1), pages 103-111, May.
    24. Kahneman, Daniel & Knetsch, Jack L & Thaler, Richard H, 1990. "Experimental Tests of the Endowment Effect and the Coase Theorem," Journal of Political Economy, University of Chicago Press, vol. 98(6), pages 1325-1348, December.
    25. Brown, Alexander L. & Imai, Taisuke & Vieider, Ferdinand & Camerer, Colin, 2020. "Meta-Analysis of Empirical Estimates of Loss-Aversion," MetaArXiv hnefr, Center for Open Science.
    26. Uri Gneezy & Jan Potters, 1997. "An Experiment on Risk Taking and Evaluation Periods," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 631-645.
    27. Campbell, John Y. & Viceira, Luis M., 2002. "Strategic Asset Allocation: Portfolio Choice for Long-Term Investors," OUP Catalogue, Oxford University Press, number 9780198296942.
    28. Bali, Turan G. & Demirtas, K. Ozgur & Levy, Haim & Wolf, Avner, 2009. "Bonds versus stocks: Investors' age and risk taking," Journal of Monetary Economics, Elsevier, vol. 56(6), pages 817-830, September.
    29. Matthew Rabin, 2000. "Risk Aversion and Expected-Utility Theory: A Calibration Theorem," Econometrica, Econometric Society, vol. 68(5), pages 1281-1292, September.
    30. Joost M. E. Pennings & Ale Smidts, 2003. "The Shape of Utility Functions and Organizational Behavior," Management Science, INFORMS, vol. 49(9), pages 1251-1263, September.
    31. Shlomo Benartzi & Richard H. Thaler, 1995. "Myopic Loss Aversion and the Equity Premium Puzzle," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 110(1), pages 73-92.
    32. M. Levy, 2010. "Loss aversion and the price of risk," Quantitative Finance, Taylor & Francis Journals, vol. 10(9), pages 1009-1022.
    33. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
    34. Mehra, Rajnish & Prescott, Edward C., 2003. "The equity premium in retrospect," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 14, pages 889-938, Elsevier.
    35. Enrico Diecidue & Moshe Levy & Jeroen Ven, 2015. "No aspiration to win? An experimental test of the aspiration level model," Journal of Risk and Uncertainty, Springer, vol. 51(3), pages 245-266, December.
    36. Fraser-Mackenzie, P. & Sung, M. & Johnson, J.E.V., 2015. "The prospect of a perfect ending: Loss aversion and the round-number bias," Organizational Behavior and Human Decision Processes, Elsevier, vol. 131(C), pages 67-80.
    37. Kroll, Yoram & Levy, Haim & Rapoport, Amnon, 1988. "Experimental tests of the mean-variance model for portfolio selection," Organizational Behavior and Human Decision Processes, Elsevier, vol. 42(3), pages 388-410, December.
    38. Bilgin, Baler, 2012. "Losses loom more likely than gains: Propensity to imagine losses increases their subjective probability," Organizational Behavior and Human Decision Processes, Elsevier, vol. 118(2), pages 203-215.
    39. Alan P. Kirman, 1992. "Whom or What Does the Representative Individual Represent?," Journal of Economic Perspectives, American Economic Association, vol. 6(2), pages 117-136, Spring.
    40. George Wu & Richard Gonzalez, 1996. "Curvature of the Probability Weighting Function," Management Science, INFORMS, vol. 42(12), pages 1676-1690, December.
    41. Alexander Klos & Elke U. Weber & Martin Weber, 2005. "Investment Decisions and Time Horizon: Risk Perception and Risk Behavior in Repeated Gambles," Management Science, INFORMS, vol. 51(12), pages 1777-1790, December.
    42. Francisco J. Gomes, 2005. "Portfolio Choice and Trading Volume with Loss-Averse Investors," The Journal of Business, University of Chicago Press, vol. 78(2), pages 675-706, March.
    43. Friend, Irwin & Blume, Marshall E, 1975. "The Demand for Risky Assets," American Economic Review, American Economic Association, vol. 65(5), pages 900-922, December.
    44. Lucas, Robert Jr, 1976. "Econometric policy evaluation: A critique," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 1(1), pages 19-46, January.
    45. MOSSIN, Jan, 1968. "Optimal multiperiod portfolio policies," LIDAM Reprints CORE 19, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    46. Douglas W. Blackburn & Andrey D. Ukhov, 2013. "Individual vs. Aggregate Preferences: The Case of a Small Fish in a Big Pond," Management Science, INFORMS, vol. 59(2), pages 470-484, August.
    47. Mohammed Abdellaoui, 2000. "Parameter-Free Elicitation of Utility and Probability Weighting Functions," Management Science, INFORMS, vol. 46(11), pages 1497-1512, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Butt, Adam & Khemka, Gaurav & Warren, Geoffrey J., 2022. "Heterogeneity in optimal investment and drawdown strategies in retirement," Pacific-Basin Finance Journal, Elsevier, vol. 74(C).
    2. Moshe Levy, 2022. "An evolutionary explanation of the Allais paradox," Journal of Evolutionary Economics, Springer, vol. 32(5), pages 1545-1574, November.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jakusch, Sven Thorsten, 2017. "On the applicability of maximum likelihood methods: From experimental to financial data," SAFE Working Paper Series 148, Leibniz Institute for Financial Research SAFE, revised 2017.
    2. M. Levy, 2010. "Loss aversion and the price of risk," Quantitative Finance, Taylor & Francis Journals, vol. 10(9), pages 1009-1022.
    3. Horst Zank, 2010. "On probabilities and loss aversion," Theory and Decision, Springer, vol. 68(3), pages 243-261, March.
    4. Mohammed Abdellaoui & Han Bleichrodt & Corina Paraschiv, 2007. "Loss Aversion Under Prospect Theory: A Parameter-Free Measurement," Management Science, INFORMS, vol. 53(10), pages 1659-1674, October.
    5. Hueber, Laura & Schwaiger, Rene, 2022. "Debiasing through experience sampling: The case of myopic loss aversion," Journal of Economic Behavior & Organization, Elsevier, vol. 198(C), pages 87-138.
    6. Rene Schwaiger & Laura Hueber, 2021. "Do MTurkers Exhibit Myopic Loss Aversion?," Working Papers 2021-12, Faculty of Economics and Statistics, Universität Innsbruck.
    7. John Beshears & James J. Choi & David Laibson & Brigitte C. Madrian, 2017. "Does Aggregated Returns Disclosure Increase Portfolio Risk Taking?," The Review of Financial Studies, Society for Financial Studies, vol. 30(6), pages 1971-2005.
    8. Jakusch, Sven Thorsten & Meyer, Steffen & Hackethal, Andreas, 2019. "Taming models of prospect theory in the wild? Estimation of Vlcek and Hens (2011)," SAFE Working Paper Series 146, Leibniz Institute for Financial Research SAFE, revised 2019.
    9. Simon Gächter & Eric J. Johnson & Andreas Herrmann, 2022. "Individual-level loss aversion in riskless and risky choices," Theory and Decision, Springer, vol. 92(3), pages 599-624, April.
    10. Lucks, Konstantin, 2016. "The Impact of Self-Control on Investment Decisions," MPRA Paper 73099, University Library of Munich, Germany.
    11. Alex Markle & George Wu & Rebecca White & Aaron Sackett, 2018. "Goals as reference points in marathon running: A novel test of reference dependence," Journal of Risk and Uncertainty, Springer, vol. 56(1), pages 19-50, February.
    12. Glätzle-Rützler, Daniela & Sutter, Matthias & Zeileis, Achim, 2015. "No myopic loss aversion in adolescents? – An experimental note," Journal of Economic Behavior & Organization, Elsevier, vol. 111(C), pages 169-176.
    13. Anderson, Anders E. S., 2004. "One for the Gain, Three for the Loss," SIFR Research Report Series 20, Institute for Financial Research.
    14. Xie, Yuxin & Hwang, Soosung & Pantelous, Athanasios A., 2018. "Loss aversion around the world: Empirical evidence from pension funds," Journal of Banking & Finance, Elsevier, vol. 88(C), pages 52-62.
    15. Neszveda, G., 2019. "Essays on behavioral finance," Other publications TiSEM 05059039-5236-42a3-be1b-3, Tilburg University, School of Economics and Management.
    16. Stefan Zeisberger & Thomas Langer & Martin Weber, 2012. "Why does myopia decrease the willingness to invest? Is it myopic loss aversion or myopic loss probability aversion?," Theory and Decision, Springer, vol. 72(1), pages 35-50, January.
    17. Lee, Boram & Veld-Merkoulova, Yulia, 2016. "Myopic loss aversion and stock investments: An empirical study of private investors," Journal of Banking & Finance, Elsevier, vol. 70(C), pages 235-246.
    18. Peter Brooks & Horst Zank, 2005. "Loss Averse Behavior," Journal of Risk and Uncertainty, Springer, vol. 31(3), pages 301-325, December.
    19. Veld, Chris & Veld-Merkoulova, Yulia V., 2008. "The risk perceptions of individual investors," Journal of Economic Psychology, Elsevier, vol. 29(2), pages 226-252, April.
    20. Epper, Thomas & Fehr-Duda, Helga, 2017. "A Tale of Two Tails: On the Coexistence of Overweighting and Underweighting of Rare Extreme Events," Economics Working Paper Series 1705, University of St. Gallen, School of Economics and Political Science.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:plo:pone00:0248904. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.