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Mean Reversion and Consumption Smoothing

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  • Fischer Black
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    Abstract

    Using a simple conventional model with additive separable utility and constant elasticity, we can explain mean reversion and consumption smoothing. The model uses the price of risk and wealth as state variables, but has only one stochastic variable. The price of risk rises temporarily as wealth falls. We also distinguish between risk aversion and the consumption elasticity of marginal utility. We can use the model to match estimates of the average values of consumption volatility, wealth volatility, mean reversion, the growth rate of consumption, the real interest rate, and the market risk premium.

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    File URL: http://www.nber.org/papers/w2946.pdf
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    Bibliographic Info

    Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 2946.

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    Date of creation: Apr 1989
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    Publication status: published as Review of Financial Studies, Vol. 3, no. 1 (1990): 107-114.
    Handle: RePEc:nbr:nberwo:2946

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    1. 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.
    2. Shmuel Kandel & Robert F. Stambaugh, . "Modeling Expected Stock Returns for Long and Short Horizons," Rodney L. White Center for Financial Research Working Papers 42-88, Wharton School Rodney L. White Center for Financial Research.
    3. Edward C. Prescott, 1986. "Theory ahead of business cycle measurement," Staff Report 102, Federal Reserve Bank of Minneapolis.
    4. Brock, William A., 1980. "Asset Prices in a Production Economy," Working Papers 275, California Institute of Technology, Division of the Humanities and Social Sciences.
    5. R. Mehra & E. Prescott, 2010. "The equity premium: a puzzle," Levine's Working Paper Archive 1401, David K. Levine.
    6. Andrew Abel, . "Stock Prices Under Time-Varying Dividend Risk: An Exact Solution in an Infinite-Horizon General Equilibrium Model," Rodney L. White Center for Financial Research Working Papers 15-88, Wharton School Rodney L. White Center for Financial Research.
    7. Zeldes, Stephen P, 1989. "Consumption and Liquidity Constraints: An Empirical Investigation," Journal of Political Economy, University of Chicago Press, vol. 97(2), pages 305-46, April.
    8. Fischer Black, 1988. "An Equilibrium Model of the Crash," NBER Chapters, in: NBER Macroeconomics Annual 1988, Volume 3, pages 269-276 National Bureau of Economic Research, Inc.
    9. Summers, Lawrence H, 1986. " Does the Stock Market Rationally Reflect Fundamental Values?," Journal of Finance, American Finance Association, vol. 41(3), pages 591-601, July.
    10. Friend, Irwin & Blume, Marshall E, 1975. "The Demand for Risky Assets," American Economic Review, American Economic Association, vol. 65(5), pages 900-922, December.
    11. Robert E. Hall, 1981. "Intertemporal Substitution in Consumption," NBER Working Papers 0720, National Bureau of Economic Research, Inc.
    12. Stephen G. Cecchetti & Pok-sang Lam & Nelson C. Mark, 1988. "Mean Reversion in Equilibrium Asset Prices," NBER Working Papers 2762, National Bureau of Economic Research, Inc.
    13. Fama, Eugene F & French, Kenneth R, 1988. "Permanent and Temporary Components of Stock Prices," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 246-73, April.
    14. Olivier J. Blanchard & N. Gregory Mankiw, 1988. "Consumption: Beyond Certainty Equivalence," NBER Working Papers 2496, National Bureau of Economic Research, Inc.
    15. Epstein, Larry G., 1988. "Risk aversion and asset prices," Journal of Monetary Economics, Elsevier, vol. 22(2), pages 179-192, September.
    16. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-87, September.
    17. G. Constantinides, 1990. "Habit formation: a resolution of the equity premium puzzle," Levine's Working Paper Archive 1397, David K. Levine.
    18. Kim, M.J. & Nelson, C.R. & Startz, R., 1988. "Mean Reversion In Stock Prices? A Reappraisal Of Empirical Evidence," Discussion Papers in Economics at the University of Washington 88-15, Department of Economics at the University of Washington.
    19. Cochrane, John H, 1988. "How Big Is the Random Walk in GNP?," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 893-920, October.
    20. James M. Poterba & Lawrence H. Summers, 1987. "Mean Reversion in Stock Prices: Evidence and Implications," NBER Working Papers 2343, National Bureau of Economic Research, Inc.
    21. R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
    22. Hall, Robert E, 1978. "Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence," Journal of Political Economy, University of Chicago Press, vol. 86(6), pages 971-87, December.
    23. 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.
    24. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
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    Cited by:
    1. Fischer Black, 1989. "Equilibrium Exchange Rate Hedging," NBER Working Papers 2947, National Bureau of Economic Research, Inc.
    2. McKenzie, Michael D. & Kim, Suk-Joong, 2007. "Evidence of an asymmetry in the relationship between volatility and autocorrelation," International Review of Financial Analysis, Elsevier, vol. 16(1), pages 22-40.
    3. Alan J. Marcus, 1989. "An Equilibrium Theory of Excess Volatility and Mean Reversion in Stock Market Prices," NBER Working Papers 3106, National Bureau of Economic Research, Inc.

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