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Portfolio selection with consumption ratcheting

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  • Jeon, Junkee
  • Koo, Hyeng Keun
  • Shin, Yong Hyun

Abstract

In this paper we study the portfolio selection problem of a finite-lived agent who does not tolerate a decline in standard of living. The preference can be regarded as exhibiting extreme-form of habit formation and also related to loss aversion in the prospect theory. We show that the agent’s optimal portfolio exhibits a trend chasing behavior and the portfolio share of the risky asset fluctuates between 0 and the value of an unconstrained individual; the fluctuations do not attenuate as time gets near the end of the planning horizon. We also explore implications of the model for asset pricing and show that the model has a potential to match better the recent US data than traditional habit models. We provide a complete solution to the problem by considering a transformed problem, which is similar in its formal structure to an irreversible incremental investment problem and equivalent to an infinite series of optimal stopping problems.

Suggested Citation

  • Jeon, Junkee & Koo, Hyeng Keun & Shin, Yong Hyun, 2018. "Portfolio selection with consumption ratcheting," Journal of Economic Dynamics and Control, Elsevier, vol. 92(C), pages 153-182.
    • Handle: RePEc:eee:dyncon:v:92:y:2018:i:c:p:153-182
    DOI: 10.1016/j.jedc.2018.05.003
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    as
    1. Fortin, Ines & Hlouskova, Jaroslava, 2011. "Optimal asset allocation under linear loss aversion," Journal of Banking & Finance, Elsevier, vol. 35(11), pages 2974-2990, November.
    2. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
    3. Otrok, Christopher & Ravikumar, B. & Whiteman, Charles H., 2002. "Habit formation: a resolution of the equity premium puzzle?," Journal of Monetary Economics, Elsevier, vol. 49(6), pages 1261-1288, September.
    4. Philip H. Dybvig, 1995. "Dusenberry's Ratcheting of Consumption: Optimal Dynamic Consumption and Investment Given Intolerance for any Decline in Standard of Living," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(2), pages 287-313.
    5. Jing-Zhi Huang & Marti G. Subrahmanyam & G. George Yu, 1999. "Pricing And Hedging American Options: A Recursive Integration Method," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar, chapter 8, pages 219-239, World Scientific Publishing Co. Pte. Ltd..
    6. Frank Riedel & Xia Su, 2011. "On irreversible investment," Finance and Stochastics, Springer, vol. 15(4), pages 607-633, December.
    7. Ravi Jagannathan & Narayana R. Kocherlakota, 1996. "Why should older people invest less in stock than younger people?," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 20(Sum), pages 11-23.
    8. 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.
    9. Christopher Otrok & B. Ravikumar & Charles H. Whiteman, 2002. "Evaluating asset-pricing models using the Hansen-Jagannathan bound: a Monte Carlo investigation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(2), pages 149-174.
    10. Luigi Guiso & Monica Paiella, 2008. "Risk Aversion, Wealth, and Background Risk," Journal of the European Economic Association, MIT Press, vol. 6(6), pages 1109-1150, December.
    11. Guiso, Luigi & Jappelli, Tullio & Terlizzese, Daniele, 1996. "Income Risk, Borrowing Constraints, and Portfolio Choice," American Economic Review, American Economic Association, vol. 86(1), pages 158-172, March.
    12. David A. Marshall & Nayan G. Parekh, 1999. "Can Costs of Consumption Adjustment Explain Asset Pricing Puzzles?," Journal of Finance, American Finance Association, vol. 54(2), pages 623-654, April.
    13. Munk, Claus, 2008. "Portfolio and consumption choice with stochastic investment opportunities and habit formation in preferences," Journal of Economic Dynamics and Control, Elsevier, vol. 32(11), pages 3560-3589, November.
    14. Glenn W. Harrison & Morten I. Lau & E. Elisabet Rutström, 2007. "Estimating Risk Attitudes in Denmark: A Field Experiment," Scandinavian Journal of Economics, Wiley Blackwell, vol. 109(2), pages 341-368, June.
    15. 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.
    16. Hansen, Lars Peter & Jagannathan, Ravi, 1991. "Implications of Security Market Data for Models of Dynamic Economies," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 225-262, April.
    17. 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.
    18. John Y. Campbell & John Cochrane, 1999. "Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior," Journal of Political Economy, University of Chicago Press, vol. 107(2), pages 205-251, April.
    19. Charles N. Noussair & Stefan T. Trautmann & Gijs van de Kuilen, 2014. "Higher Order Risk Attitudes, Demographics, and Financial Decisions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(1), pages 325-355.
    20. Nicole El Karoui & Monique Jeanblanc-Picqué, 1998. "Optimization of consumption with labor income," Finance and Stochastics, Springer, vol. 2(4), pages 409-440.
    21. Koo, Byung Lim & Koo, Hyeng Keun & Koo, Jung Lim & Hyun, ChongSeok, 2012. "A generalization of Dybvig’s result on portfolio selection with intolerance for decline in consumption," Economics Letters, Elsevier, vol. 117(3), pages 646-649.
    22. Riedel, Frank, 2009. "Optimal consumption choice with intolerance for declining standard of living," Journal of Mathematical Economics, Elsevier, vol. 45(7-8), pages 449-464, July.
    23. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    24. Hanqing Jin & Xun Yu Zhou, 2008. "Behavioral Portfolio Selection In Continuous Time," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 385-426, July.
    25. Miao, Jianjun & Zhang, Yuzhe, 2015. "A duality approach to continuous-time contracting problems with limited commitment," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 929-988.
    26. Constantinides, George M, 1990. "Habit Formation: A Resolution of the Equity Premium Puzzle," Journal of Political Economy, University of Chicago Press, vol. 98(3), pages 519-543, June.
    27. Pindyck, Robert S, 1988. "Irreversible Investment, Capacity Choice, and the Value of the Firm," American Economic Review, American Economic Association, vol. 78(5), pages 969-985, December.
    28. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    29. Luis M. Viceira, 2001. "Optimal Portfolio Choice for Long‐Horizon Investors with Nontradable Labor Income," Journal of Finance, American Finance Association, vol. 56(2), pages 433-470, April.
    30. Bauer, Daniel & Kling, Alexander & Russ, Jochen, 2008. "A Universal Pricing Framework for Guaranteed Minimum Benefits in Variable Annuities 1," ASTIN Bulletin, Cambridge University Press, vol. 38(2), pages 621-651, November.
    31. Grochulski, Borys & Zhang, Yuzhe, 2011. "Optimal risk sharing and borrowing constraints in a continuous-time model with limited commitment," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2356-2388.
    32. Sundaresan, Suresh M, 1989. "Intertemporally Dependent Preferences and the Volatility of Consumption and Wealth," The Review of Financial Studies, Society for Financial Studies, vol. 2(1), pages 73-89.
    33. Xue Dong He & Xun Yu Zhou, 2011. "Portfolio Choice Under Cumulative Prospect Theory: An Analytical Treatment," Management Science, INFORMS, vol. 57(2), pages 315-331, February.
    34. Barone-Adesi, Giovanni & Whaley, Robert E, 1987. "Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-320, June.
    35. Kim, In Joon, 1990. "The Analytic Valuation of American Options," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 547-572.
    36. Robert B. Barsky & F. Thomas Juster & Miles S. Kimball & Matthew D. Shapiro, 1997. "Preference Parameters and Behavioral Heterogeneity: An Experimental Approach in the Health and Retirement Study," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 537-579.
    37. Antoine Bommier & Jean-Charles Rochet, 2006. "Risk Aversion and Planning Horizons," Journal of the European Economic Association, MIT Press, vol. 4(4), pages 708-734, June.
    38. Peter Carr & Robert Jarrow & Ravi Myneni, 2008. "Alternative Characterizations Of American Put Options," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 5, pages 85-103, World Scientific Publishing Co. Pte. Ltd..
    39. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
    40. 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.
    41. Basak, Suleyman, 2002. "A comparative study of portfolio insurance," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1217-1241, July.
    42. Nicholas Barberis & Ming Huang & Tano Santos, 2001. "Prospect Theory and Asset Prices," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 116(1), pages 1-53.
    43. Fulga, Cristinca, 2016. "Portfolio optimization under loss aversion," European Journal of Operational Research, Elsevier, vol. 251(1), pages 310-322.
    44. Goran Peskir, 2005. "On The American Option Problem," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 169-181, January.
    45. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14, April.
    46. Watson, John G. & Scott, Jason S., 2014. "Ratchet consumption over finite and infinite planning horizons," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 84-96.
    47. Basak, Suleyman, 1995. "A General Equilibrium Model of Portfolio Insurance," The Review of Financial Studies, Society for Financial Studies, vol. 8(4), pages 1059-1090.
    48. Kyoung Jin Choi & Gyoocheol Shim & Yong Hyun Shin, 2008. "Optimal Portfolio, Consumption‐Leisure And Retirement Choice Problem With Ces Utility," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 445-472, July.
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    Cited by:

    1. Hansjoerg Albrecher & Pablo Azcue & Nora Muler, 2020. "Optimal ratcheting of dividends in a Brownian risk model," Papers 2012.10632, arXiv.org.
    2. Kyoung Jin Choi & Junkee Jeon & Hyeng Keun Koo, 2018. "Duesenberry's Theory of Consumption: Habit, Learning, and Ratcheting," Papers 1812.10038, arXiv.org.
    3. Hyun Jin Jang & Zuo Quan Xu & Harry Zheng, 2020. "Optimal Investment, Heterogeneous Consumption and Best Time for Retirement," Papers 2008.00392, arXiv.org, revised Jun 2022.
    4. Ferrari, Giorgio & Zhu, Shihao, 2023. "Optimal Retirement Choice under Age-dependent Force of Mortality," Center for Mathematical Economics Working Papers 683, Center for Mathematical Economics, Bielefeld University.
    5. Geonwoo Kim & Junkee Jeon, 2024. "Dynamic Asset Allocation and Retirement Decision with Consumption Ratcheting and Effort Choice," Mathematics, MDPI, vol. 12(23), pages 1-18, December.
    6. Giorgio Ferrari & Shihao Zhu, 2023. "Optimal Retirement Choice under Age-dependent Force of Mortality," Papers 2311.12169, arXiv.org.
    7. Chen, Guodong & Lee, Minjoon & Nam, Tong-yob, 2020. "Forced retirement risk and portfolio choice," Journal of Empirical Finance, Elsevier, vol. 58(C), pages 293-315.
    8. Jeon, Junkee & Koo, Hyeng Keun & Park, Kyunghyun, 2021. "Finite horizon portfolio selection with durable goods," Mathematical Social Sciences, Elsevier, vol. 111(C), pages 55-67.
    9. Junkee Jeon & Hyeng Keun Koo & Kyunghyun Park, 2018. "Optimal Insurance with Limited Commitment in a Finite Horizon," Papers 1812.11669, arXiv.org, revised Jan 2019.
    10. Bahman Angoshtari & Erhan Bayraktar & Virginia R. Young, 2021. "Optimal Investment and Consumption under a Habit-Formation Constraint," Papers 2102.03414, arXiv.org, revised Nov 2021.
    11. Choi, Kyoung Jin & Jeon, Junkee & Koo, Hyeng Keun, 2022. "Intertemporal preference with loss aversion: Consumption and risk-attitude," Journal of Economic Theory, Elsevier, vol. 200(C).
    12. Jeon, Junkee & Park, Kyunghyun, 2020. "Dynamic asset allocation with consumption ratcheting post retirement," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    13. Junkee Jeon & Kyunghyun Park, 2021. "Portfolio selection with drawdown constraint on consumption: a generalization model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(2), pages 243-289, April.
    14. Chonghu Guan & Zuo Quan Xu, 2023. "Optimal ratcheting of dividend payout under Brownian motion surplus," Papers 2308.15048, arXiv.org, revised Jul 2024.

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    More about this item

    Keywords

    Portfolio selection; Intolerance for decline in consumption; Risk attitude; Asset pricing;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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