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Uniqueness of Equilibrium in the Classical Capital Asset Pricing Model

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  • Nielsen, Lars Tyge

Abstract

General equilibrium in the classical two-period mean-variance capital asset pricing model is not unique. Corresponding to one single set of expectations, utility functions, and an initial wealth distribution, there may be several equilibria, and an asset may have different prices, expected rates of return, and betas in different equilibria. However, any equilibrium portfolio is sustained by a unique price system, and if investors have decreasing risk aversion, then any equilibrium allocation of the risky assets is sustained by a unique price system.

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  • Nielsen, Lars Tyge, 1988. "Uniqueness of Equilibrium in the Classical Capital Asset Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(3), pages 329-336, September.
    • Handle: RePEc:cup:jfinqa:v:23:y:1988:i:03:p:329-336_01
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    Cited by:

    1. Rockafellar, R. Tyrrell & Uryasev, Stan & Zabarankin, M., 2007. "Equilibrium with investors using a diversity of deviation measures," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3251-3268, November.
    2. Koch-Medina, Pablo & Wenzelburger, Jan, 2018. "Equilibria in the CAPM with non-tradeable endowments," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 93-107.
    3. Dana, Rose-Anne, 1999. "Existence, uniqueness and determinacy of equilibrium in C.A.P.M. with a riskless asset," Journal of Mathematical Economics, Elsevier, vol. 32(2), pages 167-175, October.
    4. Bottazzi, Jean-Marc & Hens, Thorsten & Loffler, Andreas, 1998. "Market Demand Functions in the Capital Asset Pricing Model," Journal of Economic Theory, Elsevier, vol. 79(2), pages 192-206, April.
    5. Peter Bossaerts & Charles Plott, 2004. "Basic Principles of Asset Pricing Theory: Evidence from Large-Scale Experimental Financial Markets," Review of Finance, European Finance Association, vol. 8(2), pages 135-169.
    6. Christoph Czichowsky & Martin Herdegen & David Martins, 2024. "Existence and uniqueness of quadratic and linear mean-variance equilibria in general semimartingale markets," Papers 2408.03134, arXiv.org.
    7. Jan Wenzelburger, 2010. "The two-fund separation theorem revisited," Annals of Finance, Springer, vol. 6(2), pages 221-239, March.
    8. Matteo Del Vigna, 2011. "Financial market equilibria with heterogeneous agents: CAPM and market segmentation," Working Papers - Mathematical Economics 2011-08, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    9. Bick, Avi, 2004. "The mathematics of the portfolio frontier: a geometry-based approach," The Quarterly Review of Economics and Finance, Elsevier, vol. 44(2), pages 337-361, May.
    10. Matteo Del Vigna, 2014. "A note on the existence of CAPM equilibria with homogeneous cumulative prospect theory preferences," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(2), pages 341-348, October.
    11. Wenzelburger, Jan, 2008. "A Note on the Two-fund Separation Theorem," MPRA Paper 11014, University Library of Munich, Germany, revised 31 Sep 2008.
    12. Bettzuge, Marc Oliver, 1998. "An extension of a theorem by Mitjushin and Polterovich to incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 30(3), pages 285-300, October.
    13. Jun Tong & Jian-Qiang Hu & Jiaqiao Hu, 2017. "A Computational Algorithm for Equilibrium Asset Pricing Under Heterogeneous Information and Short-Sale Constraints," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(05), pages 1-16, October.
    14. Hens, Thorsten & Laitenberger, Jorg & Loffler, Andreas, 2002. "Two remarks on the uniqueness of equilibria in the CAPM," Journal of Mathematical Economics, Elsevier, vol. 37(2), pages 123-132, April.
    15. Thorsten Hens & Joerg Laitenberger & Andreas Loeffler, "undated". "On Uniqueness of Equilibria in the CAPM - (This paper replaces "Existence and Uniqueness of Equilibria in the CAPM")," IEW - Working Papers 039, Institute for Empirical Research in Economics - University of Zurich.

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