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Endogenous Uncertainty: A Unified View of Market Volatility

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  • Mordecai Kurz
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    September 9, 1997 (Updated November 28, 1998) The theory of Rational Belief Equilibria (RBE) offers a unified paradigm for explaining market volatility by the effect of "Endogenous Uncertainty" on financial markets. This uncertainty is propagated within the economy (hence "endogenous") by the beliefs of asset traders. The theory of RBE was developed in a sequence of papers assembled in a recently published book (Kurz [1997]) and the present paper provides a non-mathematical exposition of both the main ideas of the theory of RBE as well as a summary of the main results of the book regarding market volatility. Section I starts by reviewing the standard assumptions underlying models of Rational Expectations Equilibria (REE) and their implications to market volatility. The paper then reviews four basic problems which have constituted puzzles or anomalies in relation to the assumptions of REE : (i) Why are asset prices much more volatile than their underlying fundamentals? (ii) The equity premium puzzle: why under REE the predicted riskless rate is so high and the equity risk premium so low? (iii) Why do asset prices exhibit the "GARCH" behavior without exogenous fundamental variables to explain it? (iv) the "Forward Discount Bias" in foreign exchange: why are interest rate differentials poor predictors of future changes in the exchange rates? Section II outlines the basic assumptions of the theory of RBE and the main propositions which it implies for market volatility. Section III develops the simulation models which are used to study the four problems above and explains that the domestic economy is calibrated, as in Mehra and Prescott [1985], to the U.S. economy. Then for each of the four problems the relevant simulation results of the RBE are presented and compared to the results predicted by a corresponding REE and to the actual empirical observations in the U.S. The paper concludes that the main cause of market volatility is the dynamics of beliefs of agents. The theory of RBE shows that if agents disagree then the state of belief of each agent, represented by his conditional probability, must fluctuate over time. Hence the distribution of the individual states of belief in the market is the root cause of all phenomena of market volatility. The GARCH phenomenon of time varying variance of asset prices is explained in the simulation model by the presence of both persistence in the states of beliefs of agents as well as correlation among these states. Correlation makes beliefs either narrowly distributed (i.e. "consensus") or widely distributed (i.e. "non-consensus"). In a belief regime of consensus (due to persistence it remains in place for a while) agents seek to buy or sell the same portfolio leading to high volatility. In a belief regime of non-consensus there is a widespread disagreement which cause a balance between sellers and buyers leading to low market volatility. In short, the GARCH phenomenon is the result of shifts in the distribution of beliefs in the market induced by the dynamics of the individual states of belief. Turning to the equity risk premium, the key question is what are the distributions of beliefs which ensure that the average riskless rate is low and the average equity risk premium is high. It turns out that the only circumstances when the mean riskless rate falls to around 1% and the mean equity premium rises to around 5.5% arise when, on the average, the majority of agents are relatively optimistic about the prospects of capital gains in the subsequent period. In such a circumstance the rationality of belief conditions imply that the pessimists (who are in the minority) must have a higher intensity of pessimism than the intensity of the optimists. In a large economy with this property the state of belief of any one agent may fluctuate but on the average there will be a minority of intensely pessimistic agents. This asymmetry between optimists and pessimists flows directly from the rationality conditions of beliefs and implies that at most dates the pessimists have a stronger impact on the bill market. At those dates the pessimists protect their wealth by increasing their purchases of the riskless bill. This bids up the price of the bill, lowers the riskless rate and results in a higher equity risk premium. In sum, the theory of Rational Belief offers a very simple explanation to the observed riskless rate and equity premium. It says that the riskless rate is, on average, low and the premium high because at most dates there is a minority of pessimist who, by the rationality of belief conditions, have the higher intensity level of belief about high stock prices in the future. These agents drive the riskless rate lower and the equity premium higher. The "Forward Discount Bias" in foreign exchange markets is the result of the fact that in an RBE agents often make the wrong forecasts although they are right on the average. Hence, in an RBE the exchange rate fluctuates excessively due to the errors of the agents and hence at almost no date is the interest differential between two countries an unbiased estimate of the rate of depreciation of the exchange rate one period later. The bias is positive since agents who invest in foreign currency demand a risk premium on endogenous uncertainty which is above and beyond the risk which exists in an REE. The size of the bias is equal to the added risk premium due to endogenous uncertainty. JEL Classification Numbers: D58, D84, G12. Key Words: rational expectation equilibrium (REE), rational beliefs, rational belief equilibrium (RBE), endogenous uncertainty, state of belief, market volatility, equity risk premium, riskless rate, GARCH, forward discount bias, foreign exchange rates, OLG economy, correlation among beliefs, simulations.

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    Paper provided by Stanford University, Department of Economics in its series Working Papers with number 98013.

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    Handle: RePEc:wop:stanec:98013
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    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. Willaiam A. Brock, 1996. "Asset Price Behavior in Complex Environments," Working Papers 96-04-018, Santa Fe Institute.
    4. Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics,in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038 Elsevier.
    5. Kenneth A. Froot, 1990. "Short Rates and Expected Asset Returns," NBER Working Papers 3247, National Bureau of Economic Research, Inc.
    6. 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.
    7. 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.
    8. Steven N. Durlauf, 1993. "Nonergodic Economic Growth," Review of Economic Studies, Oxford University Press, vol. 60(2), pages 349-366.
    9. Froot, Kenneth A & Thaler, Richard H, 1990. "Foreign Exchange," Journal of Economic Perspectives, American Economic Association, vol. 4(3), pages 179-192, Summer.
    10. Kurz, Mordecai, 1994. "On Rational Belief Equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(6), pages 859-876, October.
    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. Follmer, Hans, 1974. "Random economies with many interacting agents," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 51-62, March.
    13. 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.
    14. 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.
    15. William A. Brock, 1993. "Pathways to randomness in the economy: Emergent nonlinearity and chaos in economics and finance," Estudios Económicos, El Colegio de México, Centro de Estudios Económicos, vol. 8(1), pages 3-55.
    16. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    17. Brock, W.A., 1996. "Asset Price Behavior in Complex Environments," Working papers 9606, Wisconsin Madison - Social Systems.
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