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Existence of Equilibrium and Zero-Beta Pricing Formula in the Capital Asset Pricing Model with Heterogeneous Beliefs

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  • Ning Sun

    ()
    (Faculty of System Science and Technology, Akita Prefectural University)

  • Zaifu Yang

    ()
    (Cowles Foundation for Research in Economics, Yale University)

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    Abstract

    We study a mean-variance capital asset pricing model (CAPM) in which investors have different probability beliefs about assets returns and different attitudes towards risk, all assets are risky, short-selling is allowed and satiation is possible. First, we prove that there exists a competitive equilibrium in the model under a rather general condition. This condition indicates a simple relationship among initial endowment vectors, risk aversion ratio functions, perceived mean vectors and covariance matrices of all investors. Secondly, we derive a zero-beta pricing formula for the model which generalizes the well known Black¡¯s zero-beta pricing formula. In addition, we find in closed form an equilibrium price vector expressed in terms of perceived mean vectors, covariance matrices, and initial endowments of all investors.

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    Bibliographic Info

    Article provided by Society for AEF in its journal Annals of Economics and Finance.

    Volume (Year): 4 (2003)
    Issue (Month): 1 (May)
    Pages: 51-71

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    Handle: RePEc:cuf:journl:y:2003:v:4:i:1:p:51-71

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    Related research

    Keywords: Capital asset pricing model; Heterogeneity; Equilibrium theorem; Pricing formula;

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    References

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    1. Owen, Joel & Rabinovitch, Ramon, 1983. " On the Class of Elliptical Distributions and Their Applications to the Theory of Portfolio Choice," Journal of Finance, American Finance Association, vol. 38(3), pages 745-52, June.
    2. Berk, Jonathan B., 1997. "Necessary Conditions for the CAPM," Journal of Economic Theory, Elsevier, vol. 73(1), pages 245-257, March.
    3. Duffie, Darrell, 1987. "Stochastic equilibria with incomplete financial markets," Journal of Economic Theory, Elsevier, vol. 41(2), pages 405-416, April.
    4. Duffie, Darrell & Shafer, Wayne, 1985. "Equilibrium in incomplete markets: I : A basic model of generic existence," Journal of Mathematical Economics, Elsevier, vol. 14(3), pages 285-300, June.
    5. Williams, Joseph T., 1977. "Capital asset prices with heterogeneous beliefs," Journal of Financial Economics, Elsevier, vol. 5(2), pages 219-239, November.
    6. Gonedes, Nicholas J, 1976. "Capital Market Equilibrium for a Class of Heterogeneous Expectations in a Two-Parameter World," Journal of Finance, American Finance Association, vol. 31(1), pages 1-15, March.
    7. Hart, Oliver D., 1974. "On the existence of equilibrium in a securities model," Journal of Economic Theory, Elsevier, vol. 9(3), pages 293-311, November.
    8. Werner, Jan, 1985. "Equilibrium in economies with incomplete financial markets," Journal of Economic Theory, Elsevier, vol. 36(1), pages 110-119, June.
    9. Black, Fischer, 1972. "Capital Market Equilibrium with Restricted Borrowing," The Journal of Business, University of Chicago Press, vol. 45(3), pages 444-55, July.
    10. Nielsen, Lars Tyge, 1989. "Asset Market Equilibrium with Short-Selling," Review of Economic Studies, Wiley Blackwell, vol. 56(3), pages 467-73, July.
    11. Nielsen, Lars Tyge, 1990. "Existence of equilibrium in CAPM," Journal of Economic Theory, Elsevier, vol. 52(1), pages 223-231, October.
    12. Allingham, Michael, 1991. "Existence Theorems in the Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 59(4), pages 1169-74, July.
    13. Hiroshi Konno & Hiroshi Shirakawa, 1995. "Existence Of A Nonnegative Equilibrium Price Vector In The Mean-Variance Capital Market," Mathematical Finance, Wiley Blackwell, vol. 5(3), pages 233-246.
    14. Nielsen, Lars Tyge, 1990. "Equilibrium in CAPM without a Riskless Asset," Review of Economic Studies, Wiley Blackwell, vol. 57(2), pages 315-24, April.
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    Cited by:
    1. Lei Shi, 2010. "Analysis and Equilibrium Asset Pricing with Heterogeneous Beliefs," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 9.
    2. D. Won & G. Hahn & N. Yannelis, 2008. "Capital market equilibrium without riskless assets: heterogeneous expectations," Annals of Finance, Springer, vol. 4(2), pages 183-195, March.
    3. repec:wyi:wpaper:001969 is not listed on IDEAS

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