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Risk aversion and the elasticity of substitution in general dynamic portfolio theory: Consistent planning by forward looking, expected utility maximizing investors

  • Kihlstrom, Richard
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    Using the measure of risk aversion suggested by Kihlstrom and Mirman [Kihlstrom, R., Mirman, L., 1974. Risk aversion with many commodities. Journal of Economic Theory 8, 361-388; Kihlstrom, R., Mirman, L., 1981. Constant, increasing and decreasing risk aversion with many commodities. Review of Economic Studies 48, 271-280], we propose a dynamic consumption-savings-portfolio choice model in which the consumer-investor maximizes the expected value of a non-additively separable utility function of current and future consumption. Preferences for consumption streams are CES and the elasticity of substitution can be chosen independently of the risk aversion measure. The additively separable case is a special case. Because choices are not dynamically consistent, we follow the "consistent planning" approach of Strotz [Strotz, R., 1956. Myopia and inconsistency in dynamic utility maximization. Review of Economic Studies 23, 165-180] and also interpret our analysis from the game theoretic perspective taken by Peleg and Yaari [Peleg, B., Yaari, M., 1973. On the existence of a consistent course of action when tastes are changing. Review of Economic Studies 40, 391-401]. The equilibrium of the Lucas asset pricing model with i.i.d. consumption growth is obtained and the equity premium is shown to depend on the elasticity of substitution as well as the risk aversion measure. The nature of the dependence is examined. Our results are contrasted with those of the non-expected utility recursive approach of Epstein-Zin and Weil.

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    Article provided by Elsevier in its journal Journal of Mathematical Economics.

    Volume (Year): 45 (2009)
    Issue (Month): 9-10 (September)
    Pages: 634-663

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    Handle: RePEc:eee:mateco:v:45:y:2009:i:9-10:p:634-663
    Contact details of provider: Web page: http://www.elsevier.com/locate/jmateco

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    1. Sanford J. Grossman & Robert J. Shiller, 1980. "The Determinants of the Variability of Stock Market Prices," NBER Working Papers 0564, National Bureau of Economic Research, Inc.
    2. Svensson, L.E.O., 1988. "Portfolio Choice With Non-Expected Utility In Continuous Time," Papers 423, Stockholm - International Economic Studies.
    3. Kreps, David M. & Porteus, Evan L., 1979. "Temporal von neumann-morgenstern and induced preferences," Journal of Economic Theory, Elsevier, vol. 20(1), pages 81-109, February.
    4. Kihlstrom, Richard E. & Mirman, Leonard J., 1974. "Risk aversion with many commodities," Journal of Economic Theory, Elsevier, vol. 8(3), pages 361-388, July.
    5. R. Mehra & E. Prescott, 2010. "The equity premium: a puzzle," Levine's Working Paper Archive 1401, David K. Levine.
    6. Bulow, Jeremy I, 1982. "Durable-Goods Monopolists," Journal of Political Economy, University of Chicago Press, vol. 90(2), pages 314-32, April.
    7. Luttmer, Erzo G.J. & Mariotti, Thomas, 2007. "Efficiency and equilibrium when preferences are time-inconsistent," Journal of Economic Theory, Elsevier, vol. 132(1), pages 493-506, January.
    8. Andrew B. Abel, . "Asset Prices Under Habit Formation and Catching Up With the Jones," Rodney L. White Center for Financial Research Working Papers 1-90, Wharton School Rodney L. White Center for Financial Research.
    9. Epstein, Larry G & Zin, Stanley E, 1989. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework," Econometrica, Econometric Society, vol. 57(4), pages 937-69, July.
    10. G. Constantinides, 1990. "Habit formation: a resolution of the equity premium puzzle," Levine's Working Paper Archive 1397, David K. Levine.
    11. Kreps, David M & Porteus, Evan L, 1979. "Dynamic Choice Theory and Dynamic Programming," Econometrica, Econometric Society, vol. 47(1), pages 91-100, January.
    12. Coase, Ronald H, 1972. "Durability and Monopoly," Journal of Law and Economics, University of Chicago Press, vol. 15(1), pages 143-49, April.
    13. Diamond, Peter A. & Stiglitz, Joseph E., 1974. "Increases in risk and in risk aversion," Journal of Economic Theory, Elsevier, vol. 8(3), pages 337-360, July.
    14. Hakansson, Nils H, 1970. "Optimal Investment and Consumption Strategies Under Risk for a Class of Utility Functions," Econometrica, Econometric Society, vol. 38(5), pages 587-607, September.
    15. Bhamra, Harjoat S. & Uppal, Raman, 2005. "The Role of Risk Aversion and Intertemporal Substitution in Dynamic Consumption-Portfolio Choicewith Recursive Utility," CEPR Discussion Papers 5020, C.E.P.R. Discussion Papers.
    16. Bezalel Peleg & Menahem E. Yaari, 1973. "On the Existence of a Consistent Course of Action when Tastes are Changing," Review of Economic Studies, Oxford University Press, vol. 40(3), pages 391-401.
    17. John Y. Campbell & John H. Cochrane, 1994. "By Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior," CRSP working papers 412, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
    18. Philippe Weil, 1989. "The Equity Premium Puzzle and the Riskfree Rate Puzzle," NBER Working Papers 2829, National Bureau of Economic Research, Inc.
    19. Breeden, Douglas T., 1979. "An intertemporal asset pricing model with stochastic consumption and investment opportunities," Journal of Financial Economics, Elsevier, vol. 7(3), pages 265-296, September.
    20. Nancy L. Stokey, 1979. "Intertemporal Price Discrimination," The Quarterly Journal of Economics, Oxford University Press, vol. 93(3), pages 355-371.
    21. Philippe Weil, 1990. "Nonexpected Utility in Macroeconomics," The Quarterly Journal of Economics, Oxford University Press, vol. 105(1), pages 29-42.
    22. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
    23. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-87, September.
    24. Ravi Bansal & Amir Yaron, 2000. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," NBER Working Papers 8059, National Bureau of Economic Research, Inc.
    25. Sanford J. Grossman & Angelo Melino & Robert J. Shiller, 1985. "Estimating the Continuous Time Consumption Based Asset Pricing Model," NBER Working Papers 1643, National Bureau of Economic Research, Inc.
    26. R. A. Pollak, 1968. "Consistent Planning," Review of Economic Studies, Oxford University Press, vol. 35(2), pages 201-208.
    27. Samuelson, Paul A, 1969. "Lifetime Portfolio Selection by Dynamic Stochastic Programming," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 239-46, August.
    28. Epstein, Larry G & Zin, Stanley E, 1991. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 263-86, April.
    29. 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 247-57, August.
    30. Harris, Christopher & Laibson, David, 2001. "Dynamic Choices of Hyperbolic Consumers," Econometrica, Econometric Society, vol. 69(4), pages 935-57, July.
    31. Richard E. Kihlstrom & Leonard J. Mirman, 1981. "Constant, Increasing and Decreasing Risk Aversion with Many Commodities," Review of Economic Studies, Oxford University Press, vol. 48(2), pages 271-280.
    32. Pamela Labadie, 1986. "Comparative Dynamics and Risk Premia in an Overlapping Generations Model," Review of Economic Studies, Oxford University Press, vol. 53(1), pages 139-152.
    33. Andrew B. Abel, 1998. "Risk Premia and Term Premia in General Equilibrium," NBER Working Papers 6683, National Bureau of Economic Research, Inc.
    34. Jerusalem D. Levhari & T. N. Srinivasan, 1969. "Optimal Savings under Uncertainty," Review of Economic Studies, Oxford University Press, vol. 36(2), pages 153-163.
    35. Epstein, Larry G., 1988. "Risk aversion and asset prices," Journal of Monetary Economics, Elsevier, vol. 22(2), pages 179-192, September.
    36. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, Oxford University Press, vol. 112(2), pages 443-478.
    37. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
    38. Skander J. van den Heuvel, 2008. "Temporal risk aversion and asset prices," Finance and Economics Discussion Series 2008-37, Board of Governors of the Federal Reserve System (U.S.).
    39. Hansen, Lars Peter & Singleton, Kenneth J, 1983. "Stochastic Consumption, Risk Aversion, and the Temporal Behavior of Asset Returns," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 249-65, April.
    40. Debreu, Gerard, 1976. "Least concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 121-129, July.
    41. Erzo G. J. Luttmer & Thomas Mariotti, 2003. "Subjective Discounting in an Exchange Economy," Journal of Political Economy, University of Chicago Press, vol. 111(5), pages 959-989, October.
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