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

Abstract

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.qfrc.uts.edu.au/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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Length: 42 pages
Date of creation: 01 Mar 2000
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Publication status: Published as: Chiarella, C. and He, X., 2003, "Heterogeneous Beliefs, Risk and Learning in a Simple Asset-Pricing Model with a Market Maker", Macroeconomic Dynamics, 7(4), 503-536.
Handle: RePEc:uts:rpaper:35
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  1. Brock, W.A. & Hommes, C.H., 1997. "Models of Compelxity in Economics and Finance," Working papers 9706, Wisconsin Madison - Social Systems.
  2. Seppo Honkapohja & Kaushik Mitra, . "Learning with Bounded Memory in Stochastic Models," Discussion Papers 00/42, Department of Economics, University of York.
  3. Garman, Mark B., 1976. "Market microstructure," Journal of Financial Economics, Elsevier, vol. 3(3), pages 257-275, June.
  4. Carl Chiarella, 1992. "The Dynamics of Speculative Behaviour," Working Paper Series 13, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
  5. Kyle, Albert & Campbell, John, 1993. "Smart Money, Noise Trading and Stock Price Behaviour," Scholarly Articles 3208217, Harvard University Department of Economics.
  6. 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.
  7. Barucci, Emilio, 2001. "Fading memory learning in a class of forward-looking models with an application to hyperinflation dynamics," Economic Modelling, Elsevier, vol. 18(2), pages 233-252, April.
  8. 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.
  9. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
  10. GRANDMONT, Jean-Michel, 1997. "Expectations formation and stability of large socioeconomic systems," CORE Discussion Papers 1997088, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  11. Thomas Ho & Hans Stoll, . "Optimal Dealer Pricing Under Transactions and Return Uncertainty," Rodney L. White Center for Financial Research Working Papers 27-79, Wharton School Rodney L. White Center for Financial Research.
  12. Routledge, Bryan R, 1999. "Adaptive Learning in Financial Markets," Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 1165-1202.
  13. Reiner Franke & Tim Nesemann, 1999. "Two destabilizing strategies may be jointly stabilizing," Journal of Economics, Springer, vol. 69(1), pages 1-18, February.
  14. Stoll, Hans R, 1978. "The Supply of Dealer Services in Securities Markets," Journal of Finance, American Finance Association, vol. 33(4), pages 1133-51, September.
  15. Bullard James, 1994. "Learning Equilibria," Journal of Economic Theory, Elsevier, vol. 64(2), pages 468-485, December.
  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. Cars H. Hommes, 2001. "Financial Markets as Nonlinear Adaptive Evolutionary Systems," Tinbergen Institute Discussion Papers 01-014/1, Tinbergen Institute.
  18. Chiarella, Carl & He, Xue-Zhong, 2003. "Dynamics of beliefs and learning under aL-processes -- the heterogeneous case," Journal of Economic Dynamics and Control, Elsevier, vol. 27(3), pages 503-531, January.
  19. Xue-Zhong He & Carl Chiarella, 1999. "Heterogeneous Beliefs, Risk and Learning in a Simple Asset-Pricing Model," Computing in Economics and Finance 1999 223, Society for Computational Economics.
  20. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
  21. 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.
  22. Carl Chiarella & Xue-Zhong He, 2001. "Dynamics of Beliefs and Learning Under aL Processes - The Homogeneous Case," Research Paper Series 53, Quantitative Finance Research Centre, University of Technology, Sydney.
  23. Bullard, James & Duffy, John, 1999. "Using Genetic Algorithms to Model the Evolution of Heterogeneous Beliefs," Computational Economics, Society for Computational Economics, vol. 13(1), pages 41-60, February.
  24. Chen, Shu-Heng & Yeh, Chia-Hsuan, 1997. "Toward a computable approach to the efficient market hypothesis: An application of genetic programming," Journal of Economic Dynamics and Control, Elsevier, vol. 21(6), pages 1043-1063, June.
  25. 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.
  26. 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.
  27. Lux, Thomas, 1995. "Herd Behaviour, Bubbles and Crashes," Economic Journal, Royal Economic Society, vol. 105(431), pages 881-96, July.
  28. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-35, November.
  29. Miller, Edward M, 1977. "Risk, Uncertainty, and Divergence of Opinion," Journal of Finance, American Finance Association, vol. 32(4), pages 1151-68, September.
  30. Chiarella, Carl & He, Xue-Zhong, 2003. "Heterogeneous Beliefs, Risk, And Learning In A Simple Asset-Pricing Model With A Market Maker," Macroeconomic Dynamics, Cambridge University Press, vol. 7(04), pages 503-536, September.
  31. Sethi, Rajiv, 1996. "Endogenous regime switching in speculative markets," Structural Change and Economic Dynamics, Elsevier, vol. 7(1), pages 99-118, March.
  32. Evans George W. & Honkapohja Seppo, 1994. "On the Local Stability of Sunspot Equilibria under Adaptive Learning Rules," Journal of Economic Theory, Elsevier, vol. 64(1), pages 142-161, October.
  33. Peck, James, 1990. "Liquidity without money: A General equilibrium model of market microstructure," Journal of Financial Intermediation, Elsevier, vol. 1(1), pages 80-103, March.
  34. 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.
  35. Lux, Thomas, 1997. "Time variation of second moments from a noise trader/infection model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(1), pages 1-38, November.
  36. Brock, W.A. & Hommes, C.H., 1996. "Hetergeneous Beliefs and Routes to Chaos in a Simple Asset Pricing Model," Working papers 9621, Wisconsin Madison - Social Systems.
  37. Day, Richard H. & Huang, Weihong, 1990. "Bulls, bears and market sheep," Journal of Economic Behavior & Organization, Elsevier, vol. 14(3), pages 299-329, December.
  38. Farmer, J. Doyne & Joshi, Shareen, 2002. "The price dynamics of common trading strategies," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 149-171, October.
  39. 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.
  40. 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.
  41. Beja, Avraham & Goldman, M Barry, 1980. " On the Dynamic Behavior of Prices in Disequilibrium," Journal of Finance, American Finance Association, vol. 35(2), pages 235-48, May.
  42. 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.
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