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Existence Of A Nonnegative Equilibrium Price Vector In The Mean‐Variance Capital Market

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  • Hiroshi Konno
  • Hiroshi Shirakawa

Abstract

We derive a necessary and sufficient condition for the existence of a nonnegative equilibrium price vector under which the total demand and supply of each asset balances in the standard mean‐variance capital market. Also, we give an explicit formula for such a price vector. This formula shows that the price of assets is an increasing function of p̄, the weighted average of the requested rate of return of individual investors, which tends to infinity as p̄ approaches the expected rate of return on the market portfolio. Further, we construct a macroeconomic index which gives information about the soundness of the capital market.

Suggested Citation

  • 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, July.
    • Handle: RePEc:bla:mathfi:v:5:y:1995:i:3:p:233-246
    DOI: 10.1111/j.1467-9965.1995.tb00066.x
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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. Deng, Xiao-Tie & Li, Zhong-Fei & Wang, Shou-Yang, 2005. "A minimax portfolio selection strategy with equilibrium," European Journal of Operational Research, Elsevier, vol. 166(1), pages 278-292, October.
    3. Pınar, Mustafa Ç., 2014. "Equilibrium in an ambiguity-averse mean–variance investors market," European Journal of Operational Research, Elsevier, vol. 237(3), pages 957-965.
    4. 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.
    5. Bin, Liu, 2015. "A new risk measure and its application in portfolio optimization: The SPP–CVaR approach," Economic Modelling, Elsevier, vol. 51(C), pages 383-390.
    6. 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.

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