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Divergence of opinion and valuation in a mean-variance framework


  • Jacques A. Schnabel


Purpose - The purpose of this paper is to examine the impact of heterogeneous expectations on the equilibrium value of a risky asset in a capital market populated by investors that choose mean-variance efficient portfolios. Design/methodology/approach - A single-period, discrete-time version of Williams' capital asset pricing model that incorporates heterogeneous beliefs regarding the mean vector of rates of return and homogeneous beliefs regarding the variance-covariance matrix of rates of return is developed. It is then employed to gauge the impact of both divergence of opinion and increases thereof on the equilibrium price of a risky asset. Findings - The value of a risky asset under heterogeneous beliefs differs from that under homogeneous beliefs as the former is biased towards the beliefs of wealthier and/or more risk tolerant investors. If the latter set of investors is optimistic (pessimistic), the value is higher (lower) than that which prevails in the absence of divergence of beliefs. Increasing divergence of opinion likewise affects the equilibrium price of a risky asset to accord more with the beliefs of wealthier and/or more risk tolerant investors. If the latter set of investors is optimistic (pessimistic), increasing dispersion of beliefs causes the value of a risky asset to rise (fall). Originality/value - A novel simplification and application of Williams' model of capital asset pricing is presented. The findings differ from conclusions derived in previous theoretical treatments of divergence of opinions in capital markets.

Suggested Citation

  • Jacques A. Schnabel, 2009. "Divergence of opinion and valuation in a mean-variance framework," Studies in Economics and Finance, Emerald Group Publishing, vol. 26(3), pages 148-154, July.
  • Handle: RePEc:eme:sefpps:v:26:y:2009:i:3:p:148-154

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    References listed on IDEAS

    1. Danthine, Jean-Pierre & Donaldson, John B., 2014. "Intermediate Financial Theory," Elsevier Monographs, Elsevier, edition 3, number 9780123865496.
    2. Karl B. Diether & Christopher J. Malloy & Anna Scherbina, 2002. "Differences of Opinion and the Cross Section of Stock Returns," Journal of Finance, American Finance Association, vol. 57(5), pages 2113-2141, October.
    3. Jouini, Elyes & Napp, Clotilde, 2006. "Heterogeneous beliefs and asset pricing in discrete time: An analysis of pessimism and doubt," Journal of Economic Dynamics and Control, Elsevier, vol. 30(7), pages 1233-1260, July.
    4. repec:dau:papers:123456789/341 is not listed on IDEAS
    5. Varian, Hal R, 1985. " Divergence of Opinion in Complete Markets: A Note," Journal of Finance, American Finance Association, vol. 40(1), pages 309-317, March.
    6. Bart, John & Masse, Isidore J., 1981. "Divergence of Opinion and Risk," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 16(01), pages 23-34, March.
    7. Williams, Joseph T., 1977. "Capital asset prices with heterogeneous beliefs," Journal of Financial Economics, Elsevier, vol. 5(2), pages 219-239, November.
    8. John G. Cragg & Burton G. Malkiel, 1982. "Expectations and the Structure of Share Prices," NBER Books, National Bureau of Economic Research, Inc, number crag82-1, June.
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