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Heterogeneous Beliefs and the Performances of Optimal Portfolios



The market selection depends on agent's survival index, which is a function of agent's belief and risk preference. When preferences are identical, the survival index of an agent is a decreasing function of his belief accuracy and therefore agent survives if and only if he has the lowest survival index. Following this result, one maybe tempted to think that an agent is expected to perform at least as good as the market if he survives, and he is expected to outperform the market if his belief is more accurate than all other agents' beliefs. We show that the these statements are false in general. In terms of long-run performance, market outperforms those agents who do not have the minimum survival index in the long-run. When multiple agents survive, we show that no agent can outperform the market in the long-run. In terms of the expected performance, all agents are expected to underperform the market even when they all survive in the long-run. When survival indices differ, the fittest agent with the lowest survival index is expected to outperform the market consistently with any given finite investment horizons if and only if his subjective belief is much more accurate than the other agents' beliefs.

Suggested Citation

  • Xue-Zhong He & Lei Shi, 2012. "Heterogeneous Beliefs and the Performances of Optimal Portfolios," Research Paper Series 301, Quantitative Finance Research Centre, University of Technology, Sydney.
  • Handle: RePEc:uts:rpaper:301

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    References listed on IDEAS

    1. Elyès Jouini & Clotilde Napp, 2007. "Consensus Consumer and Intertemporal Asset Pricing with Heterogeneous Beliefs," Review of Economic Studies, Oxford University Press, vol. 74(4), pages 1149-1174.
    2. Elyès Jouini & Clotilde Napp, 2010. "Unbiased Disagreement in Financial Markets, Waves of Pessimism and the Risk-Return Trade-off," Review of Finance, European Finance Association, vol. 15(3), pages 575-601.
    3. Jaksa Cvitanic & Fernando Zapatero, 2004. "Introduction to the Economics and Mathematics of Financial Markets," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262532654, January.
    4. repec:dau:papers:123456789/78 is not listed on IDEAS
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    More about this item


    heterogeneous beliefs; equilibrium asset prices; survival; consensus belief; portfolio performance;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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