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Heterogeneous Beliefs, Risk and Learning in a Simple Asset Pricing Model with a Market Maker

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This paper attempts to study the dynamics of a simple discounted present value asset price model where agents have different risk attitudes and follow different expectation formulation schemes for both first and second moments of the price distribution. Instead of using a Walrasian auctioneer scenario as the market clearing mechanism, a market maker scenario is used. In particular, the paper concentrates on models of fundamentalists and trend traders who follow least squares learning processes. An analysis is made of the effects of lag lengths on the stability of the fundamental equilibrium. Some necessary and/or sufficient conditions on the stability of the fundamental equilibrium associated with the speed of the adjustment of the market maker, different risk attitudes and different risk attitudes and different values of lags (used in the learning process) are established. The results lead to the following observations: (I) Compared with the findings with the Walrasian market clearing scenario in Brock and Hommes [8] and Chiarella and He [14], different price dynamics are obtained when the speed of the adjustment of the market maker increases and, in particular, when the contrarians are involved in the model; (ii) In contrast to homogeneous beliefs, where the larger is the lag length the more stable is that in general (for both the Walrasian and the market maker equilibrium) different lag lengths can complicate the price dynamics; (iii) In the model of trend followers versus contrarians, the stability of the fundamental equilibrium is determined by risk-adjusted aggregated extrapolation rates. This indicates that although every individual forecasting rule may lead to divergence from the equilibrium, these may "cancel out" in the aggregate and the actual dynamics with learning may thus be locally stable. On the other hand, only a small group of traders with expectation functions involving significant divergence can in fact destabilize the whole system.

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File URL: http://www.business.uts.edu.au/qfrc/research/research_papers/rp35.pdf
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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 35.

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Date of creation: 01 Mar 2000
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Handle: RePEc:uts:rpaper:35

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  1. Campbell, John Y & Kyle, Albert S, 1993. "Smart Money, Noise Trading and Stock Price Behaviour," Review of Economic Studies, Wiley Blackwell, vol. 60(1), pages 1-34, January.
  2. Grandmont, Jean-Michel, 1994. "Expectations formation and stability of large socioeconomic systems," CEPREMAP Working Papers (Couverture Orange) 9424, CEPREMAP.
  3. 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.
  4. Alan P. Kirman, 1992. "Whom or What Does the Representative Individual Represent?," Journal of Economic Perspectives, American Economic Association, vol. 6(2), pages 117-136, Spring.
  5. Brock, W.A. & Hommes, C.H., 1996. "A Rational Route to Randomness," Working papers 9530r, Wisconsin Madison - Social Systems.
  6. Balasko, Yves & Royer, Daniel, 1996. "Stability of Competitive Equilibrium with Respect to Recursive and Learning Processes," Journal of Economic Theory, Elsevier, vol. 68(2), pages 319-348, February.
  7. Evans, George W. & Honkapohja, Seppo, 1999. "Learning dynamics," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 7, pages 449-542 Elsevier.
  8. James Bullard & John Duffy, 2010. "Using genetic algorithms to model the evolution of heterogenous beliefs," Levine's Working Paper Archive 550, David K. Levine.
  9. repec:att:wimass:9621 is not listed on IDEAS
  10. Day, Richard H. & Huang, Weihong, 1990. "Bulls, bears and market sheep," Journal of Economic Behavior & Organization, Elsevier, vol. 14(3), pages 299-329, December.
  11. 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 703-38, August.
  12. Reiner Franke & Tim Nesemann, 1999. "Two destabilizing strategies may be jointly stabilizing," Journal of Economics, Springer, vol. 69(1), pages 1-18, February.
  13. Routledge, Bryan R, 1999. "Adaptive Learning in Financial Markets," Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 1165-1202.
  14. Lux, Thomas, 1998. "The socio-economic dynamics of speculative markets: interacting agents, chaos, and the fat tails of return distributions," Journal of Economic Behavior & Organization, Elsevier, vol. 33(2), pages 143-165, January.
  15. 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.
  16. Franke, Reiner & Sethi, Rajiv, 1998. "Cautious trend-seeking and complex asset price dynamics," Research in Economics, Elsevier, vol. 52(1), pages 61-79, March.
  17. Brock, William A. & Hommes, Cars H., 1998. "Heterogeneous beliefs and routes to chaos in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1235-1274, August.
  18. Sethi, Rajiv, 1996. "Endogenous regime switching in speculative markets," Structural Change and Economic Dynamics, Elsevier, vol. 7(1), pages 99-118, March.
  19. Marcet, Albert & Sargent, Thomas J., 1989. "Convergence of least squares learning mechanisms in self-referential linear stochastic models," Journal of Economic Theory, Elsevier, vol. 48(2), pages 337-368, August.
  20. James Bullard, 1991. "Learning equilibria," Working Papers 1991-004, Federal Reserve Bank of St. Louis.
  21. repec:att:wimass:9706 is not listed on IDEAS
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