An Equilibrium Model of Market Efficiency with Bayesian Learning: Explicit Modes of Convergence to Rational Expectations Equilibrium in the Presence of Noise Traders

16 Pages Posted: 5 Jan 2015 Last revised: 19 Feb 2015

See all articles by Omri Ross

Omri Ross

University of Copenhagen

Stephen E. Satchell

University of Cambridge - Faculty of Economics and Politics

Michael Tehranchi

University of Cambridge

Date Written: February 18, 2015

Abstract

A simple discrete-time financial market model is introduced. The market participants consist of a collection of noise traders as well as a distinguished agent who uses the price information as it arrives to update her demand for the assets. It is shown that the distinguished agent's demand converges, both almost surely and in mean square, to a demand consistent with the rational expectations hypothesis, and the rate of convergence is calculated explicitly. Furthermore, the convergence of the standardised deviations from this limit is established. The rate of convergence, and hence the efficiency of this market, is an increasing function of both the risk-free interest rate and the relative number of noise traders in the market. An efficient market, therefore, measured in terms of a high proportion of informed traders, seems incompatible with the notion that efficient markets converge quickly.

Keywords: Market efficiency, asymptotic rationality, Bayesian updating, mode of convergence

JEL Classification: G14, D53, C62

Suggested Citation

Ross, Omri and Satchell, Stephen E. and Tehranchi, Michael, An Equilibrium Model of Market Efficiency with Bayesian Learning: Explicit Modes of Convergence to Rational Expectations Equilibrium in the Presence of Noise Traders (February 18, 2015). Available at SSRN: https://ssrn.com/abstract=2545031 or http://dx.doi.org/10.2139/ssrn.2545031

Omri Ross (Contact Author)

University of Copenhagen ( email )

Nørregade 10
Copenhagen, København DK-1165
Denmark

Stephen E. Satchell

University of Cambridge - Faculty of Economics and Politics ( email )

Austin Robinson Building
Sidgwick Avenue
Cambridge, CB3 9DD
United Kingdom
44 (0)1223 335213 (Phone)
44 (0)1223 335475 (Fax)

HOME PAGE: http://www.econ.cam.ac.uk/faculty/satchell/index.h

Michael Tehranchi

University of Cambridge ( email )

Centre for Mathematical Sciences
Cambridge, CB3 0WB
United Kingdom

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