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Stock Price Volatility, Learning, and the Equity Premium

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  • Brennan, Michael
  • Xia, Yihong
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    Abstract

    The determination of stock prices and equilibrium expected rates of return in a general equilibrium setting is still imperfectly understood. In particular, as Grossman and Shiller (1981) and others have argued, stock returns appear to be too volatile given the smooth process for dividends and consumption growth. Mehra and Prescott (1985) claim that this smoothness in consumption and dividend growth gives rise to an “equity premium paradox†since it makes it impossible to explain the equity risk premium with a risk aversion parameter of less than an implausible 35. This paper reconciles the apparent smoothness of aggregate dividends and the volatility of observed stock prices by developing a model of stock prices in a dynamic general equilibrium setting in which learning is important. Dividends, which are one component of the aggregate consumption endowment, are assumed to follow a stochastic process with a mean-reverting drift that is not directly observable by the representative agent but must be estimated from the realized growth rates of dividends and aggregate consumption. The stock price-dividend ratio is shown to depend on the current estimate of the dividend growth rate as well as on the level of uncertainty about the true growth rate. This non-observability of the growth rate of dividends introduces an element of learning into the stock valuation process which is shown to increase the volatility of the stock price and therefore reduce the level of risk aversion required to explain the equity premium. The model is calibrated to the observed joint dividend and consumption process for the US, and is shown to yield an interest rate and stock price process that conform closely to the stylized facts for US capital markets.

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    Bibliographic Info

    Paper provided by Anderson Graduate School of Management, UCLA in its series University of California at Los Angeles, Anderson Graduate School of Management with number qt3zw2w634.

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    Date of creation: 01 Feb 1997
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    Handle: RePEc:cdl:anderf:qt3zw2w634

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    1. Wayne E. Ferson & George M. Constantinides, 1991. "Habit Persistence and Durability in Aggregate Consumption: Empirical Tests," NBER Working Papers 3631, National Bureau of Economic Research, Inc.
    2. Gennotte, Gerard, 1986. " Optimal Portfolio Choice under Incomplete Information," Journal of Finance, American Finance Association, vol. 41(3), pages 733-46, July.
    3. Barsky, Robert B & De Long, J Bradford, 1993. "Why Does the Stock Market Fluctuate?," The Quarterly Journal of Economics, MIT Press, vol. 108(2), pages 291-311, May.
    4. Gollier, Christian & Pratt, John W, 1996. "Risk Vulnerability and the Tempering Effect of Background Risk," Econometrica, Econometric Society, vol. 64(5), pages 1109-23, September.
    5. Timmermann, Allan G, 1993. "How Learning in Financial Markets Generates Excess Volatility and Predictability in Stock Prices," The Quarterly Journal of Economics, MIT Press, vol. 108(4), pages 1135-45, November.
    6. Goetzmann, William Nelson & Jorion, Philippe, 1993. " Testing the Predictive Power of Dividend Yields," Journal of Finance, American Finance Association, vol. 48(2), pages 663-79, June.
    7. S.G. Cecchetti & P. Lam & N.C. Mark, 2010. "The equity premium and the risk-free rate: matching the moments," Levine's Working Paper Archive 1396, David K. Levine.
    8. Andrew B. Abel, 1990. "Asset Prices under Habit Formation and Catching up with the Joneses," NBER Working Papers 3279, National Bureau of Economic Research, Inc.
    9. Fama, Eugene F, 1991. " Efficient Capital Markets: II," Journal of Finance, American Finance Association, vol. 46(5), pages 1575-617, December.
    10. S. Grossman & R. Shiller, . "The Determinants of the Variability of Stock Market Price," Rodney L. White Center for Financial Research Working Papers 18-80, Wharton School Rodney L. White Center for Financial Research.
    11. Hodrick, Robert J, 1992. "Dividend Yields and Expected Stock Returns: Alternative Procedures for Inference and Measurement," Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 357-86.
    12. Andrew B. Abel, 1992. "Exact Solutions for Expected Rates of Return Under Markov Regime Switching: Implications for the Equity Premium Puzzle," NBER Working Papers 4110, 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. R. Mehra & E. Prescott, 2010. "The equity premium: a puzzle," Levine's Working Paper Archive 1401, David K. Levine.
    15. Timmermann, Allan, 1996. "Excess Volatility and Predictability of Stock Prices in Autoregressive Dividend Models with Learning," Review of Economic Studies, Wiley Blackwell, vol. 63(4), pages 523-57, October.
    16. Hagiwara, May & Herce, Miguel A, 1997. "Risk Aversion and Stock Price Sensitivity to Dividends," American Economic Review, American Economic Association, vol. 87(4), pages 738-45, September.
    17. Fama, Eugene F. & French, Kenneth R., 1988. "Dividend yields and expected stock returns," Journal of Financial Economics, Elsevier, vol. 22(1), pages 3-25, October.
    18. John Y. Campbell, 1996. "Consumption and the Stock Market: Interpreting International Experience," NBER Working Papers 5610, National Bureau of Economic Research, Inc.
    19. Kocherlakota, Narayana R., 1990. "On the 'discount' factor in growth economies," Journal of Monetary Economics, Elsevier, vol. 25(1), pages 43-47, January.
    20. Friend, Irwin & Blume, Marshall E, 1975. "The Demand for Risky Assets," American Economic Review, American Economic Association, vol. 65(5), pages 900-922, December.
    21. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-84, March.
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