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Martingale-Like Behavior of Prices

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Christopher A. Sims

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Abstract

Asset prices set in a competitive market need not be martingales; that is, it need not be true that the best predictor of future prices is the current price. Nonetheless, statistical tests for this property are sometimes treated as tests for the proper functioning of an asset market; asset prices often seem to have the property to a close approximation, and it is sometimes supposed that the martingale ought to be imposed on econometric models of asset markets and forecasts made from them. This paper shows that under general conditions, which allow among other things for risk aversion among market participants, competitive asset prices ought to be locally -- over small units of time -- martingale-like. This implies that tests of proper functioning of the market ought to be conducted with data at fine time intervals; results of such tests should not be used to justify imposing the martingale property on a model's long-term projections of asset prices.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 0489.

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Date of creation: Jun 1980
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Handle: RePEc:nbr:nberwo:0489

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Ross, Stephen A, 1978. "A Simple Approach to the Valuation of Risky Streams," Journal of Business, University of Chicago Press, vol. 51(3), pages 453-75, July. [Downloadable!] (restricted)
  2. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June. [Downloadable!] (restricted)
  3. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November. [Downloadable!] (restricted)
  4. LeRoy, Stephen F, 1973. "Risk Aversion and the Martingale Property of Stock Prices," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(2), pages 436-46, June. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Michael Cooper & David H. Downs, 1999. "Real Estate Securities and a Filter-based, Short-term Trading Strategy," Journal of Real Estate Research, American Real Estate Society, vol. 18(2), pages 313-334. [Downloadable!]
  2. Bruce N. Lehmann, 1990. "Fads, Martingales, and Market Efficiency," NBER Working Papers 2533, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  3. John Barkoulas & Christopher F. Baum & Joseph Onochie, 1996. "Nonlinear Nonparametric Prediction of the 90-Day T-Bill Rate," Boston College Working Papers in Economics 320., Boston College Department of Economics. [Downloadable!]
  4. René Garcia & Éric Renault, 1998. "Risk Aversion, Intertemporal Substitution, and Option Pricing," CIRANO Working Papers 98s-02, CIRANO. [Downloadable!]
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  5. Andrew W. Lo & Jiang Wang, 1994. "Implementing Option Pricing Models When Asset Returns Are Predictable," NBER Working Papers 4720, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
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