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Excess covariance and dynamic instability in a multi-asset model

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  • Anufriev, Mikhail
  • Bottazzi, Giulio
  • Marsili, Matteo
  • Pin, Paolo

Abstract

The presence of excess covariance in financial price returns is an accepted empirical fact: the price dynamics of financial assets tend to be more correlated than their fundamentals would justify. We advance an explanation of this fact based on an intertemporal equilibrium multi-assets model of financial markets with an explicit and endogenous price dynamics. The market is driven by an exogenous stochastic process of dividend yields paid by the assets that we identify as market fundamentals. The model is rather flexible and allows for the coexistence of different trading strategies. The evolution of assets price and traders' wealth is described by a high-dimensional stochastic dynamical system. We identify the equilibria of the model consistent with a baseline assumption of procedural rationality. We show that these equilibria are characterized by excess covariance in prices with respect to the dividend process. Moreover, we show that in equilibrium there is a positive expected marginal profit in choosing more risky portfolios. As a consequence, the evolutionary pressure generates a trend towards more remunerative strategies, which, in turn, increase the variance of prices and the dynamic instability of the system.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 36 (2012)
Issue (Month): 8 ()
Pages: 1142-1161

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Handle: RePEc:eee:dyncon:v:36:y:2012:i:8:p:1142-1161

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Web page: http://www.elsevier.com/locate/jedc

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Keywords: Excess covariance; Capital asset pricing model; Efficient market hypothesis; Heterogeneous agents; Procedurally consistent equilibrium;

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  1. Anufriev, Mikhail & Dindo, Pietro, 2010. "Wealth-driven selection in a financial market with heterogeneous agents," Journal of Economic Behavior & Organization, Elsevier, vol. 73(3), pages 327-358, March.
  2. Karl Schmedders, 2005. "Two-Fund Separation in Dynamic General Equilibrium," Discussion Papers 1398, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Anufriev, Mikhail & Bottazzi, Giulio, 2010. "Market equilibria under procedural rationality," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1140-1172, November.
  4. Igor V. Evstigneev & Thorsten Hens & Klaus Reiner Schenk-Hoppé, 2008. "Evolutionary Finance," Swiss Finance Institute Research Paper Series 08-14, Swiss Finance Institute.
  5. Xue-Zhong (Tony) He & Carl Chiarella, 2001. "Asset Price and Wealth Dynamics under Heterogeneous Expectations," CeNDEF Workshop Papers, January 2001 5A.2, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  6. Carl Chiarella & Roberto Dieci & Xue-Zhong He, 2010. "Time-Varying Beta: A Boundedly Rational Equilibrium Approach," Research Paper Series 275, Quantitative Finance Research Centre, University of Technology, Sydney.
  7. Lux, Thomas, 1995. "Herd Behaviour, Bubbles and Crashes," Economic Journal, Royal Economic Society, vol. 105(431), pages 881-96, July.
  8. Stefano Battiston & Domenico Delli Gatti & Mauro Gallegati & Bruce C. Greenwald & Joseph E. Stiglitz, 2009. "Liaisons Dangereuses: Increasing Connectivity, Risk Sharing, and Systemic Risk," NBER Working Papers 15611, National Bureau of Economic Research, Inc.
  9. Carl Chiarella & Roberto Dieci & Laura Gardini, 2005. "The Dynamic Interaction of Speculation and Diversification," Applied Mathematical Finance, Taylor and Francis Journals, vol. 12(1), pages 17-52.
  10. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215.
  11. Anufriev, Mikhail & Bottazzi, Giulio & Pancotto, Francesca, 2006. "Equilibria, stability and asymptotic dominance in a speculative market with heterogeneous traders," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1787-1835.
  12. Kallberg, Jarl & Pasquariello, Paolo, 2008. "Time-series and cross-sectional excess comovement in stock indexes," Journal of Empirical Finance, Elsevier, vol. 15(3), pages 481-502, June.
  13. Follmer, Hans & Horst, Ulrich & Kirman, Alan, 2005. "Equilibria in financial markets with heterogeneous agents: a probabilistic perspective," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 123-155, February.
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