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

Author

Listed:
  • Ning Sun

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

  • Zaifu Yang

    (Cowles Foundation for Research in Economics, Yale University)

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.

Suggested Citation

  • Ning Sun & Zaifu Yang, 2003. "Existence of Equilibrium and Zero-Beta Pricing Formula in the Capital Asset Pricing Model with Heterogeneous Beliefs," Annals of Economics and Finance, Society for AEF, vol. 4(1), pages 51-71, May.
    • Handle: RePEc:cuf:journl:y:2003:v:4:i:1:p:51-71
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    References listed on IDEAS

    as
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    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Lei Shi, 2010. "Portfolio Analysis and Equilibrium Asset Pricing with Heterogeneous Beliefs," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 9, July-Dece.
    2. Svetlozar T. Rachev & Stoyan V. Stoyanov & Frank J. Fabozzi, 2017. "Financial Markets With No Riskless (Safe) Asset," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(08), pages 1-24, December.
    3. Lei Shi, 2010. "Portfolio Analysis and Equilibrium Asset Pricing with Heterogeneous Beliefs," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2010, January-A.
    4. Ma, Chenghu & Hu, Jianqiang & Xu, Yifan, 2018. "Margins on short sales and equilibrium price indeterminacy," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 79-92.
    5. Tong, Jun & Hu, Jiaqiao & Hu, Jianqiang, 2017. "Computing equilibrium prices for a capital asset pricing model with heterogeneous beliefs and margin-requirement constraints," European Journal of Operational Research, Elsevier, vol. 256(1), pages 24-34.
    6. 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.
    7. W. Brent Lindquist & Svetlozar T. Rachev, 2024. "Alternatives to classical option pricing," Papers 2403.17187, arXiv.org.
    8. Ki Beom Binh & Hogyu Jhang, 2015. "Extraneous Risk: Pricing of Non-Systematic Risk," Annals of Economics and Finance, Society for AEF, vol. 16(2), pages 335-352, November.
    9. Xue-Zhong He & Lei Shi, 2009. "Portfolio Analysis and Zero-Beta CAPM with Heterogeneous Beliefs," Research Paper Series 244, Quantitative Finance Research Centre, University of Technology, Sydney.
    10. 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.
    11. Wang, Tiandu & Ma, Chenghu & Sun, Qian, 2017. "The interaction between security lending market and security trading market," Pacific-Basin Finance Journal, Elsevier, vol. 46(PB), pages 309-322.
    12. Phelim P. Boyle & Chenghu Ma, 2013. "Mean-Preserving-Spread Risk Aversion and The CAPM," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.

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    More about this item

    Keywords

    Capital asset pricing model; Heterogeneity; Equilibrium theorem; Pricing formula;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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