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Time consistent vs. time inconsistent dynamic asset allocation: Some utility cost calculations for mean variance preferences

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  • Lioui, Abraham

Abstract

We solve for the time consistent dynamic asset allocation of an investor with a mean variance objective function in a multiple assets affine setting. We use as a benchmark the pre-commitment strategy widely used in the literature and assess the potential welfare gains from pre-commitment by comparing the time consistent strategy to the pre-commitment, time inconsistent, strategy. The gains from pre-commitment are simply considerable since, in some cases, at the 5 years horizon the yearly certainty equivalent of the pre-commitment strategy is 48% compared with 9% for the time consistent strategy. However, these welfare gains result from huge and unrealistic positions in the risky assets; in some cases, the pre-commitment strategy is more than 60 times the time consistent strategy. We thus looked for alternative time inconsistent strategies that improve relative to the time consistent strategy while still involving reasonable risky asset positions. To identify these strategies, we explore an original aspect of the time consistent mean variance strategy: the presence of intertemporal hedging in such a strategy reflects welfare degradation. Therefore, a natural candidate is the time consistent strategy without the intertemporal hedging component. The second component of the time consistent strategy is the traditional myopic component discounted. We show that this component could be seen as a standard myopic strategy which is marked to market and the discount factor acts as a tailing factor. This marked to market myopic (MMM) strategy is shown to yield reasonable risky assets positions and substantial welfare gains at long horizons relative to the time consistent strategy. We also show that it dominates the standard myopic strategy as well as the equally weighted strategy.

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  • Lioui, Abraham, 2013. "Time consistent vs. time inconsistent dynamic asset allocation: Some utility cost calculations for mean variance preferences," Journal of Economic Dynamics and Control, Elsevier, vol. 37(5), pages 1066-1096.
  • Handle: RePEc:eee:dyncon:v:37:y:2013:i:5:p:1066-1096
    DOI: 10.1016/j.jedc.2013.01.007
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    as
    1. John Y. Campbell & Luis M. Viceira, 1999. "Consumption and Portfolio Decisions when Expected Returns are Time Varying," The Quarterly Journal of Economics, Oxford University Press, vol. 114(2), pages 433-495.
    2. Amihud, Yakov & Hurvich, Clifford M., 2004. "Predictive Regressions: A Reduced-Bias Estimation Method," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 39(4), pages 813-841, December.
    3. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    4. John Y. Campbell & Karine Serfaty‐De Medeiros & Luis M. Viceira, 2010. "Global Currency Hedging," Journal of Finance, American Finance Association, vol. 65(1), pages 87-121, February.
    5. Jakub W. Jurek & Luis M. Viceira, 2011. "Optimal Value and Growth Tilts in Long-Horizon Portfolios," Review of Finance, European Finance Association, vol. 15(1), pages 29-74.
    6. Cvitanic, Jaksa & Lazrak, Ali & Wang, Tan, 2008. "Implications of the Sharpe ratio as a performance measure in multi-period settings," Journal of Economic Dynamics and Control, Elsevier, vol. 32(5), pages 1622-1649, May.
    7. Sørensen, Carsten, 1999. "Dynamic Asset Allocation and Fixed Income Management," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(4), pages 513-531, December.
    8. Abraham Lioui & Patrice Poncet, 2005. "Dynamic Asset Allocation with Forwards and Futures," Springer Books, Springer, number 978-0-387-24106-7, June.
    9. Wachter, Jessica A., 2002. "Portfolio and Consumption Decisions under Mean-Reverting Returns: An Exact Solution for Complete Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 37(1), pages 63-91, March.
    10. Victor DeMiguel & Lorenzo Garlappi & Raman Uppal, 2009. "Optimal Versus Naive Diversification: How Inefficient is the 1-N Portfolio Strategy?," Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 1915-1953, May.
    11. Larry G. Epstein & Stanley E. Zin, 2013. "Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 12, pages 207-239, World Scientific Publishing Co. Pte. Ltd..
    12. Jérôme B. Detemple & Ren Garcia & Marcel Rindisbacher, 2003. "A Monte Carlo Method for Optimal Portfolios," Journal of Finance, American Finance Association, vol. 58(1), pages 401-446, February.
    13. 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.
    14. Andrew Ang & Geert Bekaert, 2007. "Stock Return Predictability: Is it There?," Review of Financial Studies, Society for Financial Studies, vol. 20(3), pages 651-707.
    15. Dennis, Richard & Soderstrom, Ulf, 2006. "How Important Is Precommitment for Monetary Policy?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 38(4), pages 847-872, June.
    16. Liu, Jun & Peleg, Ehud & Subrahmanyam, Avanidhar, 2010. "Information, Expected Utility, and Portfolio Choice," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 45(5), pages 1221-1251, October.
    17. 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..
    18. Suleyman Basak & Georgy Chabakauri, 2012. "Dynamic Hedging in Incomplete Markets: A Simple Solution," Review of Financial Studies, Society for Financial Studies, vol. 25(6), pages 1845-1896.
    19. James Andreoni & Charles Sprenger, 2012. "Risk Preferences Are Not Time Preferences," American Economic Review, American Economic Association, vol. 102(7), pages 3357-3376, December.
    20. He, Hua & Pearson, Neil D., 1991. "Consumption and portfolio policies with incomplete markets and short-sale constraints: The infinite dimensional case," Journal of Economic Theory, Elsevier, vol. 54(2), pages 259-304, August.
    21. Cvitanic, Jaksa & Malamud, Semyon, 2011. "Price impact and portfolio impact," Journal of Financial Economics, Elsevier, vol. 100(1), pages 201-225, April.
    22. Ravi Jagannathan & Tongshu Ma, 2003. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," Journal of Finance, American Finance Association, vol. 58(4), pages 1651-1683, August.
    23. Hua He & Neil D. Pearson, 1991. "Consumption and Portfolio Policies With Incomplete Markets and Short‐Sale Constraints: the Finite‐Dimensional Case1," Mathematical Finance, Wiley Blackwell, vol. 1(3), pages 1-10, July.
    24. Andrea Buraschi & Paolo Porchia & Fabio Trojani, 2010. "Correlation Risk and Optimal Portfolio Choice," Journal of Finance, American Finance Association, vol. 65(1), pages 393-420, February.
    25. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    26. Kim, Tong Suk & Omberg, Edward, 1996. "Dynamic Nonmyopic Portfolio Behavior," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 141-161.
    27. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    28. 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.
    29. Jakša Cvitanić & Ali Lazrak & Lionel Martellini & Fernando Zapatero, 2006. "Dynamic Portfolio Choice with Parameter Uncertainty and the Economic Value of Analysts' Recommendations," Review of Financial Studies, Society for Financial Studies, vol. 19(4), pages 1113-1156.
    30. Munk, Claus & Sørensen, Carsten, 2010. "Dynamic asset allocation with stochastic income and interest rates," Journal of Financial Economics, Elsevier, vol. 96(3), pages 433-462, June.
    31. Ravi Jagannathan & Tongshu Ma, 2003. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," Journal of Finance, American Finance Association, vol. 58(4), pages 1651-1684, August.
    32. Isabelle Bajeux-Besnainou & Roland Portait, 1998. "Dynamic Asset Allocation in a Mean-Variance Framework," Management Science, INFORMS, vol. 44(11-Part-2), pages 79-95, November.
    33. Michael J. Brennan & Yihong Xia, 2002. "Dynamic Asset Allocation under Inflation," Journal of Finance, American Finance Association, vol. 57(3), pages 1201-1238, June.
    34. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, Oxford University Press, vol. 112(2), pages 443-478.
    35. Jun Liu, 2007. "Portfolio Selection in Stochastic Environments," Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 1-39, January.
    36. Stefano DellaVigna & Ulrike Malmendier, 2006. "Paying Not to Go to the Gym," American Economic Review, American Economic Association, vol. 96(3), pages 694-719, June.
    37. Abraham Lioui & Patrice Poncet, 2011. "Misunderstanding risk and return?," Finance, Presses universitaires de Grenoble, vol. 32(2), pages 91-136.
    38. Jérome Detemple & Marcel Rindisbacher, 2010. "Dynamic Asset Allocation: Portfolio Decomposition Formula and Applications," Review of Financial Studies, Society for Financial Studies, vol. 23(1), pages 25-100, January.
    39. Antonios Sangvinatsos & Jessica A. Wachter, 2005. "Does the Failure of the Expectations Hypothesis Matter for Long‐Term Investors?," Journal of Finance, American Finance Association, vol. 60(1), pages 179-230, February.
    40. Stambaugh, Robert F., 1999. "Predictive regressions," Journal of Financial Economics, Elsevier, vol. 54(3), pages 375-421, December.
    41. Buraschi, Andrea & Corielli, Francesco, 2005. "Risk management implications of time-inconsistency: Model updating and recalibration of no-arbitrage models," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2883-2907, November.
    42. Kydland, Finn E & Prescott, Edward C, 1977. "Rules Rather Than Discretion: The Inconsistency of Optimal Plans," Journal of Political Economy, University of Chicago Press, vol. 85(3), pages 473-491, June.
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    3. Lu, Jin-Ray & Hwang, Chih-Chiang & Liu, Min-Luan & Lin, Chien-Yi, 2016. "An incentive problem of risk balancing in portfolio choices," The Quarterly Review of Economics and Finance, Elsevier, vol. 61(C), pages 192-200.
    4. Zhou, Zhongbao & Xiao, Helu & Yin, Jialing & Zeng, Ximei & Lin, Ling, 2016. "Pre-commitment vs. time-consistent strategies for the generalized multi-period portfolio optimization with stochastic cash flows," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 187-202.
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    More about this item

    Keywords

    Mean-variance preferences; Dynamic asset allocation; Intertemporal hedging; Predictability; Value and growth investment;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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