IDEAS home Printed from https://ideas.repec.org/p/wop/stanec/99005.html
   My bibliography  Save this paper

Endogenous Uncertainty and Market Volatility

Author

Listed:
  • Mordecai Kurz
  • Maurizio Motolese

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.

Suggested Citation

  • Mordecai Kurz & Maurizio Motolese, "undated". "Endogenous Uncertainty and Market Volatility," Working Papers 99005, Stanford University, Department of Economics.
  • Handle: RePEc:wop:stanec:99005
    as

    Download full text from publisher

    File URL: http://www-econ.stanford.edu/faculty/workp/swp99005.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
    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. Cecchetti, Stephen G. & Lam, Pok-sang & Mark, Nelson C., 1993. "The equity premium and the risk-free rate : Matching the moments," Journal of Monetary Economics, Elsevier, vol. 31(1), pages 21-45, February.
    4. Philippe Weil, 1989. "The Equity Premium Puzzle and the Riskfree Rate Puzzle," Working Papers hal-03399133, HAL.
    5. Kurz, Mordecai, 1994. "On the Structure and Diversity of Rational Beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(6), pages 877-900, October.
    6. Epstein, Larry G. & Zin, Stanley E., 1990. "'First-order' risk aversion and the equity premium puzzle," Journal of Monetary Economics, Elsevier, vol. 26(3), pages 387-407, December.
    7. 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 831-872, August.
    8. Grossman, Sanford J & Stiglitz, Joseph E, 1980. "On the Impossibility of Informationally Efficient Markets," American Economic Review, American Economic Association, vol. 70(3), pages 393-408, June.
    9. Radner, Roy, 1979. "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Econometrica, Econometric Society, vol. 47(3), pages 655-678, May.
    10. 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 246-273, April.
    11. Sarno,Lucio & Taylor,Mark P., 2003. "The Economics of Exchange Rates," Cambridge Books, Cambridge University Press, number 9780521485845, May.
    12. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    13. 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.
    14. 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.
    15. Kenneth A. Froot, 1990. "Short Rates and Expected Asset Returns," NBER Working Papers 3247, National Bureau of Economic Research, Inc.
    16. 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.
    17. Kim, Chang-Jin & Morley, James C. & Nelson, Charles R., 2001. "Does an intertemporal tradeoff between risk and return explain mean reversion in stock prices?," Journal of Empirical Finance, Elsevier, vol. 8(4), pages 403-426, September.
    18. Milgrom, Paul & Stokey, Nancy, 1982. "Information, trade and common knowledge," Journal of Economic Theory, Elsevier, vol. 26(1), pages 17-27, February.
    19. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Permanent Income and Pricing," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 3, pages 33-81, World Scientific Publishing Co. Pte. Ltd..
    20. De Long, J Bradford & Andrei Shleifer & Lawrence H. Summers & Robert J. Waldmann, 1990. "Noise Trader Risk in Financial Markets," Journal of Political Economy, University of Chicago Press, vol. 98(4), pages 703-738, August.
    21. Jiang Wang, 1993. "A Model of Intertemporal Asset Prices Under Asymmetric Information," Review of Economic Studies, Oxford University Press, vol. 60(2), pages 249-282.
    22. Feldman, M, 1991. "On the Generic Nonconvergence of Bayesian Actions and Beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(4), pages 301-321, October.
    23. 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 421-436, June.
    24. 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.
    25. Jeffrey A. Frankel & Andrew K. Rose, 1994. "A Survey of Empirical Research on Nominal Exchange Rates," NBER Working Papers 4865, National Bureau of Economic Research, Inc.
    26. Brunner, Karl & Meltzer, Allan H., 1976. "The Phillips curve," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 1(1), pages 1-18, January.
    27. Heaton, John & Lucas, Deborah J, 1996. "Evaluating the Effects of Incomplete Markets on Risk Sharing and Asset Pricing," Journal of Political Economy, University of Chicago Press, vol. 104(3), pages 443-487, June.
    28. 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 519-543, June.
    29. 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 357-384, March.
    30. Carsten Krabbe Nielsen, 2003. "Floating exchange rates versus a monetary union under rational beliefs: the role of endogenous uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(2), pages 293-315, March.
    31. Philippe Weil, 1989. "The Equity Premium Puzzle and the Riskfree Rate Puzzle," Post-Print hal-03393298, HAL.
    32. Morris, Stephen, 1995. "The Common Prior Assumption in Economic Theory," Economics and Philosophy, Cambridge University Press, vol. 11(2), pages 227-253, October.
    33. Lucas, Robert E, Jr, 1973. "Some International Evidence on Output-Inflation Tradeoffs," American Economic Review, American Economic Association, vol. 63(3), pages 326-334, June.
    34. Sanford J. Grossman, 1981. "An Introduction to the Theory of Rational Expectations Under Asymmetric Information," Review of Economic Studies, Oxford University Press, vol. 48(4), pages 541-559.
    35. Frankel, Jeffrey A. & Rose, Andrew K., 1995. "Empirical research on nominal exchange rates," Handbook of International Economics, in: G. M. Grossman & K. Rogoff (ed.), Handbook of International Economics, edition 1, volume 3, chapter 33, pages 1689-1729, Elsevier.
    36. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    37. Cecchetti, Stephen G & Lam, Pok-sang & Mark, Nelson C, 1990. "Mean Reversion in Equilibrium Asset Prices," American Economic Review, American Economic Association, vol. 80(3), pages 398-418, June.
    38. Shinji Takagi, 1991. "Exchange Rate Expectations: A Survey of Survey Studies," IMF Staff Papers, Palgrave Macmillan, vol. 38(1), pages 156-183, March.
    39. Wang, Jiang, 1994. "A Model of Competitive Stock Trading Volume," Journal of Political Economy, University of Chicago Press, vol. 102(1), pages 127-168, February.
    40. Lucas, Robert Jr, 1976. "Econometric policy evaluation: A critique," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 1(1), pages 19-46, January.
    41. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    42. Radner, Roy, 1972. "Existence of Equilibrium of Plans, Prices, and Price Expectations in a Sequence of Markets," Econometrica, Econometric Society, vol. 40(2), pages 289-303, March.
    43. 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.
    44. Lucas, Robert E, Jr, 1981. "Tobin and Monetarism: A Review Article," Journal of Economic Literature, American Economic Association, vol. 19(2), pages 558-567, June.
    45. Abel, Andrew B., 1999. "Risk premia and term premia in general equilibrium," Journal of Monetary Economics, Elsevier, vol. 43(1), pages 3-33, February.
    46. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mordecai Kurz & Hehui Jin & Maurizio Motolese, 2005. "Determinants of stock market volatility and risk premia," Annals of Finance, Springer, vol. 1(2), pages 109-147, July.
    2. Campbell, John Y., 2003. "Consumption-based asset pricing," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 13, pages 803-887, Elsevier.
    3. John Y. Campbell, 2000. "Asset Pricing at the Millennium," Journal of Finance, American Finance Association, vol. 55(4), pages 1515-1567, August.
    4. Yeung Lewis Chan & Leonid Kogan, 2002. "Catching Up with the Joneses: Heterogeneous Preferences and the Dynamics of Asset Prices," Journal of Political Economy, University of Chicago Press, vol. 110(6), pages 1255-1285, December.
    5. Mordecai Kurz, 2007. "Rational Diverse Beliefs and Economic Volatility," Discussion Papers 06-045, Stanford Institute for Economic Policy Research.
    6. Kris Jacobs, 2002. "The Rate of Risk Aversion May Be Lower Than You Think," CIRANO Working Papers 2002s-08, CIRANO.
    7. Pok-sang Lam & Stephen G. Cecchetti & Nelson C. Mark, 2000. "Asset Pricing with Distorted Beliefs: Are Equity Returns Too Good to Be True?," American Economic Review, American Economic Association, vol. 90(4), pages 787-805, September.
    8. Nengjiu Ju & Jianjun Miao, 2012. "Ambiguity, Learning, and Asset Returns," Econometrica, Econometric Society, vol. 80(2), pages 559-591, March.
    9. Mordecai Kurz, "undated". "Endogenous Uncertainty: A Unified View of Market Volatility," Working Papers 97027, Stanford University, Department of Economics.
    10. Sialm, Clemens, 2006. "Stochastic taxation and asset pricing in dynamic general equilibrium," Journal of Economic Dynamics and Control, Elsevier, vol. 30(3), pages 511-540, March.
    11. Cochrane, John H., 2005. "Financial Markets and the Real Economy," Foundations and Trends(R) in Finance, now publishers, vol. 1(1), pages 1-101, July.
    12. John Y. Campbell, 1996. "Consumption and the Stock Market: Interpreting International Experience," Harvard Institute of Economic Research Working Papers 1763, Harvard - Institute of Economic Research.
    13. Bonomo, Marco & Garcia, Rene, 1996. "Consumption and equilibrium asset pricing: An empirical assessment," Journal of Empirical Finance, Elsevier, vol. 3(3), pages 239-265, September.
    14. Jón Daníelsson & Jean-Pierre Zigrand, 2008. "Equilibrium asset pricing with systemic risk," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(2), pages 293-319, May.
    15. Nelson C. Mark & S.G. Cecchetti & P-s. Lam, 1997. "Asset Pricing under Distorted Beliefs: Are Equity Returns Too Good to Be True?," Working Papers 017, Ohio State University, Department of Economics.
    16. John Y. Campbell, 2003. "Two Puzzles of Asset Pricing and Their Implications for Investors," The American Economist, Sage Publications, vol. 47(1), pages 48-74, March.
    17. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2015. "Wave function method to forecast foreign currencies exchange rates at ultra high frequency electronic trading in foreign currencies exchange markets," MPRA Paper 67470, University Library of Munich, Germany.
    18. Committee, Nobel Prize, 2013. "Understanding Asset Prices," Nobel Prize in Economics documents 2013-1, Nobel Prize Committee.
    19. Mao-Wei Hung & Jr-Yan Wang, 2011. "Loss aversion and the term structure of interest rates," Applied Economics, Taylor & Francis Journals, vol. 43(29), pages 4623-4640.
    20. Nicholas Barberis & Ming Huang & Tano Santos, "undated". "Prospect Theory and Asset Prices," CRSP working papers 494, Center for Research in Security Prices, Graduate School of Business, University of Chicago.

    More about this item

    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;
    All these keywords.

    JEL classification:

    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wop:stanec:99005. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/destaus.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thomas Krichel (email available below). General contact details of provider: https://edirc.repec.org/data/destaus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.