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Endogenous Uncertainty and Market Volatility

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  • Mordecai Kurz
  • Maurizio Motolese
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    Abstract

    January 22, 2000 (Revised) Endogenous Uncertainty is that component of economic risk and market volatility which is propagated within the economy by the beliefs and actions of agents. The theory of Rational Belief (see Kurz [1994]) permits rational agents to hold diverse beliefs and consequently, a Rational Belief Equilibrium (in short, RBE) may exhibit diverse patterns of Endogenous Uncertainty. This paper shows that most of the observed volatility in financial markets is generated by the beliefs of the agents and the diverse market puzzles which are examined in this paper, such as the equity premium puzzle, are all driven by the structure of market expectations. To make the case for this theory we present a single RBE model, which builds on developments in Kurz and Beltratti [1997] and Kurz and Schneider [1996], with which we study a list of phenomena that have been viewed as "anomalies" in financial markets. The model is able to predict the correct order of magnitude of: (i) the long term mean and standard deviation of the price\dividend ratio; (ii) the long term mean and standard deviation of the risky rate of return on equities; (iii) the long term mean and standard deviation of the riskless rate; (iv) the long term mean equity premium. In addition, the model predicts (v) the GARCH property of risky asset returns; (vi) the Forward Discount Bias in foreign exchange markets. We also conjecture that an adaptation of the same model to markets with derivative assets will predict the appearance of "smile curves" in derivative prices. The common economic explanation for these phenomena is the existence of heterogenous agents with diverse but correlated beliefs. Given such diversity, some agents are optimistic and some pessimistic. We develop a simple model which allows agents to be in these two states of belief but the identity of the optimists and the pessimists fluctuates over time since at any date any agent may be in these two states of belief. In this model there is a unique parameterization under which the model makes all the above predictions simultaneously. That is, although the parameter space of the RBE is large, all parameterizations outside a small neighborhood of the parameter space fail significantly to reproduce some subset of variables under consideration. Any parameter choice in this small neighborhood requires the optimists to be in the majority but the rationality of belief conditions of the RBE require the pessimists to have a higher intensity level. This higher intensity has a decisive effect on the market: it increases the demand for riskless assets, decreases the equilibrium riskless rate and increases the equity premium. In simple terms, the large equity premium and the lower equilibrium riskless rate are the result of the fact that at any moment of time there are agents who hold extreme pessimistic beliefs and they have a relatively stronger impact on the market. The relative impact of these two groups of agents who are, at any moment of time, in the two states of belief is a direct consequence of the rationality of belief conditions and in that sense it is unique to an RBE. As for the correlation among the beliefs of agents, the paper shows that the dynamics of asset prices are strongly affected by such correlation. The pattern of correlation which was used in the model can be explained intuitively in terms of its effect on the dynamics of prices. The model correlation causes periods of price rises (i.e. bull markets) to develop slower than periods of decline (i.e. bear markets) hence the model dynamics does not permit prices to shoot directly from the bottom to the top but the opposite is possible and takes the form of market crashes. Note: Both the RBE model developed in this paper as well as the associated programs used to solve it are available to the public on Professor Kurz’s web page at http://www.stanford.edu/~mordecai/ JEL Classification Numbers: D5, D84, G12. Key Words: Rational Expectations, Rational Beliefs, Rational Belief Equilibrium (RBE), Endogenous Uncertainty, states of belief, stock price, discount bond, equity premium, market volatility, GARCH, Forward Discount Bias.

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    Bibliographic Info

    Paper provided by Stanford University, Department of Economics in its series Working Papers with number 99005.

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    Handle: RePEc:wop:stanec:99005

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    Keywords: Rational Expectations; Rational Beliefs; Rational Belief Equilibrium (RBE); Endogenous Uncertainty; states of belief; stock price; discount bond; equity premium; market volatility; GARCH; Forward Discount Bias;

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    1. R. Mehra & E. Prescott, 2010. "The equity premium: a puzzle," Levine's Working Paper Archive 1401, David K. Levine.
    2. Brock, William A & LeBaron, Blake D, 1996. "A Dynamic Structural Model for Stock Return Volatility and Trading Volume," The Review of Economics and Statistics, MIT Press, vol. 78(1), pages 94-110, February.
    3. 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.
    4. Hansen, Lars Peter & Sargent, Thomas J & Tallarini, Thomas D, Jr, 1999. "Robust Permanent Income and Pricing," Review of Economic Studies, Wiley Blackwell, vol. 66(4), pages 873-907, October.
    5. Lucas, Robert E, Jr, 1973. "Some International Evidence on Output-Inflation Tradeoffs," American Economic Review, American Economic Association, vol. 63(3), pages 326-34, June.
    6. Weil, Philippe, 1989. "The equity premium puzzle and the risk-free rate puzzle," Journal of Monetary Economics, Elsevier, vol. 24(3), pages 401-421, November.
    7. Chang-Jin Kim & James C. Morley & Charles Nelson, 2000. "Does an Interpemporal Trade Off Between Risk and Return Explain Mean Reversion in Stock Prices?," Discussion Papers in Economics at the University of Washington 0011, Department of Economics at the University of Washington.
    8. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
    9. John Heaton & Deborah Lucas, 1993. "Evaluating the Effects of Incomplete Markets on Risk Sharing and Asset Pricing," NBER Working Papers 4249, National Bureau of Economic Research, Inc.
    10. Kandel, Eugene & Pearson, Neil D, 1995. "Differential Interpretation of Public Signals and Trade in Speculative Markets," Journal of Political Economy, University of Chicago Press, vol. 103(4), pages 831-72, August.
    11. Engel, Charles, 1996. "The forward discount anomaly and the risk premium: A survey of recent evidence," Journal of Empirical Finance, Elsevier, vol. 3(2), pages 123-192, June.
    12. Sanford J Grossman & Joseph E Stiglitz, 1997. "On the Impossibility of Informationally Efficient Markets," Levine's Working Paper Archive 1908, David K. Levine.
    13. 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.
    14. Radner, Roy, 1979. "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Econometrica, Econometric Society, vol. 47(3), pages 655-78, May.
    15. Stephen G. Cecchetti & Pok-sang Lam & Nelson C. Mark, 1990. "Mean Reversion in Equilibrium Asset Prices," NBER Working Papers 2762, National Bureau of Economic Research, Inc.
    16. Wang, Jiang, 1993. "A Model of Intertemporal Asset Prices under Asymmetric Information," Review of Economic Studies, Wiley Blackwell, vol. 60(2), pages 249-82, April.
    17. 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.
    18. R. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Bibliography 513, UCLA Department of Economics.
    19. 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.
    20. Mankiw, N. Gregory, 1986. "The equity premium and the concentration of aggregate shocks," Journal of Financial Economics, Elsevier, vol. 17(1), pages 211-219, September.
    21. Grossman, Sanford J, 1981. "An Introduction to the Theory of Rational Expectations under Asymmetric Information," Review of Economic Studies, Wiley Blackwell, vol. 48(4), pages 541-59, October.
    22. 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 519-43, June.
    23. Shinji Takagi, 1991. "Exchange Rate Expectations: A Survey of Survey Studies," IMF Staff Papers, Palgrave Macmillan, vol. 38(1), pages 156-183, March.
    24. Paul Milgrom & Nancy L.Stokey, 1979. "Information, Trade, and Common Knowledge," Discussion Papers 377R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    25. Lucas, Robert Jr, 1976. "Econometric policy evaluation: A critique," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 1(1), pages 19-46, January.
    26. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-35, November.
    27. Shiller, Robert J, 1981. "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?," American Economic Review, American Economic Association, vol. 71(3), pages 421-36, June.
    28. Jeffrey A. Frankel and Andrew K. Rose., 1995. "A Survey of Empirical Research on Nominal Exchange Rates," Center for International and Development Economics Research (CIDER) Working Papers C95-051, University of California at Berkeley.
    29. Narayana R. Kocherlakota, 1996. "The Equity Premium: It's Still a Puzzle," Journal of Economic Literature, American Economic Association, vol. 34(1), pages 42-71, March.
    30. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
    31. Lucas, Robert E, Jr, 1981. "Tobin and Monetarism: A Review Article," Journal of Economic Literature, American Economic Association, vol. 19(2), pages 558-67, June.
    32. Andrew B. Abel, 1998. "Risk Premia and Term Premia in General Equilibrium," NBER Working Papers 6683, National Bureau of Economic Research, Inc.
    33. Poterba, James M. & Summers, Lawrence H., 1988. "Mean reversion in stock prices : Evidence and Implications," Journal of Financial Economics, Elsevier, vol. 22(1), pages 27-59, October.
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