Hostname: page-component-7b7567c8c-kwt9d Total loading time: 0 Render date: 2026-11-12T20:31:39.095Z Has data issue: false hasContentIssue false
  • English
  • Français

On Equilibrium Pricing under Parameter Uncertainty

Published online by Cambridge University Press:  06 April 2009

Jeffrey L. Coles,
Uri Loewenstein and
Jose Suay
Jeffrey L. Coles
Affiliation:
College of Business, Arizona State University, Tempe, AZ 85287
Uri Loewenstein
Affiliation:
David Eccles School of Business, University of Utah, Salt Lake City, UT 84112
Jose Suay
Affiliation:
College of Business and Public Administration, Department of Finance, University of Arizona, Tucson, AZ 85721
Get accessRights & Permissions [Opens in a new window]

Abstract

Prior theoretical work on estimation risk generally has been restricted to single-period, returns-based models in which the investor must estimate the vector of expected returns but the covariance matrix is known. This paper extends the literature on parameter uncertainty in several ways. First, we analyze asymmetric parameter uncertainty in a model based on payoffs. Second, we explore the effects of both symmetric and asymmetric estimation risk on equilibrium asset prices when the covariance matrix for payoffs must also be estimated. Finally, we investigate the effects on equilibrium of asymmetric parameter uncertainty in a simple multiperiod model.

Information

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 30 , Issue 3 , September 1995, pp. 347 - 364
Copyright
Copyright © School of Business Administration, University of Washington 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Anderson, T. W. “Cochran's Theorem for Elliptically Contoured Distributions.” Sankhya, 49 A (1987), 305–315.Google Scholar
Barry, C. “Portfolio Analysis under Uncertain Means, Variances, and Covariances.” Journal of Finance, 29 (1974), 515–522.CrossRefGoogle Scholar
Barry, C. “Effects of Uncertain and Nonstationary Parameters upon Capital Market Equilibrium Conditions.” Journal of Financial and Quantitative Analysis, 13 (1978), 419–433.CrossRefGoogle Scholar
Barry, C., and Brown, S.. “Differential Information and Security Market Equilibrium.” Journal of Financial and Quantitative Analysis, 20 (1985), 407–422.CrossRefGoogle Scholar
Bawa, V. “Admissible Portfolios for All Individuals.” Journal of Finance, 31 (1976), 1169–1183.CrossRefGoogle Scholar
Bawa, V. S., and Brown, S. J.. “Capital Market Equilibrium: Does Estimation Risk Really Matter?” In Estimation Risk and Optimal Portfolio Choice, Bawa, V. S., Brown, S. J., and Klein, R. W., eds. Amsterdam: North Holland (1979).Google Scholar
Bawa, V. S.; Brown, S. J.; and Klein, R. W.. Estimation Risk and Optimal Portfolio Choice. Amsterdam: North Holland (1979).Google Scholar
Brown, S. J. “The Effect of Estimation Risk on Capital Market Equilibrium.” Journal of Financial and Quantitative Analysis, 15 (1979a), 215–222.CrossRefGoogle Scholar
Brown, S. J. “Optimal Portfolio Choice under Uncertainty: a Bayesian Approach.” In Estimation Risk and Optimal Portfolio Choice. Bawa, V. S., Brown, S. J., and Klein, R. W., eds. Amsterdam: North Holland (1979b).Google Scholar
Chamberlain, G. “A Characterization of the Distributions That Imply Mean-Variance Utility Functions.” Journal of Economic Theory, 29 (1983), 185–201.CrossRefGoogle Scholar
Clarkson, P. M., and Thompson, R.. “Empirical Estimates of Beta when Investors Face Estimation Risk.” Journal of Finance, 45 (1990), 431–454.CrossRefGoogle Scholar
Clarkson, P. M.; Thompson, R.; and Guedes, J.. “Is Estimation Risk Priced? Is it Observable?” Working Paper, Southern Methodist Univ. (1994).Google Scholar
Coles, J., and Loewenstein, U.. “Equilibrium Pricing and Portfolio Composition in the Presence of Uncertain Parameters.” Journal of Financial Economics, 22 (1988), 279–303.CrossRefGoogle Scholar
Degroot, M.Optimal Statistical Decisions. New York, NY.: McGraw Hill (1970).Google Scholar
Devlin, S.; Gnanadesikan, R.; and Kettenring, J.. “Some Multivariate Applications of Elliptical Distributions.” In Essays in Probability and Statistics, Ikeda, S., ed. Tokyo: Shinko Tsusho Co. Ltd. (1976).Google Scholar
Handa, P., and Linn, S.. “Arbitrage Pricing with Estimation Risk.” Journal of Financial and Quantitative Analysis, 28 (1993), 81–100.CrossRefGoogle Scholar
Ingersoll, J.Theory of Financial Decision Making. Totowa, NJ.: Rowman and Littlefield (1987).Google Scholar
Kalymon, B. “Estimation Risk in the Portfolio Selection Model.” Journal of Financial and Quantitative Analysis, 6 (1971), 559–582.CrossRefGoogle Scholar
Kelker, D. “Distribution Theory of Spherical Distributions and a Locations-Scale Parameter Generalization.” Sankhya, A32 (1979), 419–430.Google Scholar
Klein, R., and Bawa, V.. “The Effect of Estimation Risk on Optimal Portfolio Choice.” Journal of Financial Economics, 3 (1976), 215–231.CrossRefGoogle Scholar
Klein, R., and Bawa, V.. “Effect of Limited Information and Estimation Risk on Optimal Portfolio Diversification.” Journal of Financial Economics, 5 (1977), 89–111.CrossRefGoogle Scholar
Lence, S. H., and Hayes, D. J.. “Parameter-Based Decision Making under Estimation Risk: an Application to Futures Trading.” Journal of Finance, 49 (1994), 345–357.Google Scholar
Muirhead, R.Aspects of Multivariate Statistical Theory. New York, NY.: Wiley (1982).CrossRefGoogle Scholar
Owen, J., and Rabinovitch, R.. “On the Class of Elliptical Distributions and Their Application to the Theory of Portfolio Choice.” Journal of Finance, 38 (1983), 745–752.CrossRefGoogle Scholar
Press, J.Applied Multivariate Analysis. New York, NY.: Holt, Rinehart, and Winston (1972).Google Scholar
Raiffa, H., and Schlaifer, R.. Applied Statistical Decision Theory. Boston, MA.: Harvard Univ. Press (1961).Google Scholar
Winkler, R., and Barry, C.. “A Bayesian Model for Portfolio Selection and Revision.” Journal of Finance, 30 (1975), 179–192.CrossRefGoogle Scholar
Zellner, A.An Introduction to Bayesian Inference in Econometrics. New York, NY.: Wiley (1971).Google Scholar
Zellner, A., and Chetty, V. K.. “Prediction and Decision Problems in Regression Models from the Bayesian Point of View.” Journal of the American Statistical Association, 66 (1965), 608–615.CrossRefGoogle Scholar