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Market-based variance of market portfolio and of entire market

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  • Olkhov, Victor

Abstract

We present the unified market-based description of returns and variances of the trades with shares of a particular security, of the trades with shares of all securities in the market, and of the trades with the market portfolio. We consider the investor who doesn’t trade the shares of his portfolio he collected at time t0 in the past. The investor observes the time series of the current trades with all securities made in the market during the averaging interval. The investor may convert these time series into the time series that model the trades with all securities as the trades with a single security and into the time series that model the trades with the market portfolio as the trades with a single security. That establishes the same description of the returns and variances of the trades with a single security, the trades with all securities in the market, and the market portfolio. We show that the market-based variance, which accounts for the impact of random change of the volumes of consecutive trades with securities, takes the form of Markowitz’s (1952) portfolio variance if the volumes of consecutive trades with all market securities are assumed constant. That highlights that Markowitz’s (1952) variance ignores the effects of random volumes of consecutive trades. We compare the market-based variances of the market portfolio and of the trades with all market securities, consider the importance of the duration of the averaging interval, and explain the economic obstacles that limit the accuracy of the predictions of the returns and variances at best by Gaussian distributions. The same methods describe the returns and variances of any portfolio and the trades with its securities.

Suggested Citation

  • Olkhov, Victor, 2025. "Market-based variance of market portfolio and of entire market," MPRA Paper 126487, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:126487
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    References listed on IDEAS

    as
    1. Bryan T. Kelly & Semyon Malamud & Kangying Zhou, 2022. "The Virtue of Complexity in Return Prediction," NBER Working Papers 30217, National Bureau of Economic Research, Inc.
    2. Athanasoulis, Stefano G & Shiller, Robert J, 2000. "The Significance of the Market Portfolio," The Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 301-329.
    3. Victor Olkhov, 2022. "Market-Based Asset Price Probability," Papers 2205.07256, arXiv.org, revised Dec 2024.
    4. Kandel, Shmuel & Stambaugh, Robert F, 1996. "On the Predictability of Stock Returns: An Asset-Allocation Perspective," Journal of Finance, American Finance Association, vol. 51(2), pages 385-424, June.
    5. Campbell, John Y. & Yogo, Motohiro, 2006. "Efficient tests of stock return predictability," Journal of Financial Economics, Elsevier, vol. 81(1), pages 27-60, July.
    6. Victor Olkhov, 2025. "Markowitz Variance May Vastly Undervalue or Overestimate Portfolio Variance and Risks," Papers 2507.21824, arXiv.org.
    7. Nelson, C.R. & Kim, M.J., 1990. "Predictable Stock Returns: Reality Or Statistical Illusion?," Working Papers 90-15, University of Washington, Department of Economics.
    8. Victor Olkhov, 2025. "Market-Based Portfolio Variance," Papers 2504.07929, arXiv.org, revised Jul 2025.
    9. Victor Olkhov, 2023. "Economic Complexity Limits Accuracy of Price Probability Predictions by Gaussian Distributions," Papers 2309.02447, arXiv.org, revised Apr 2024.
    10. Victor Olkhov, 2024. "Lower Bounds of Uncertainty of Observations of Macroeconomic Variables and Upper Limits on the Accuracy of Their Forecasts," Papers 2408.04644, arXiv.org, revised Oct 2024.
    11. Koutmos, Gregory, 1997. "Is the Market Portfolio a Dynamic Factor? Evidence from Individual Stock Returns," The Financial Review, Eastern Finance Association, vol. 32(3), pages 411-430, August.
    12. Olkhov, Victor, 2021. "Theoretical Economics and the Second-Order Economic Theory. What is it?," MPRA Paper 110893, University Library of Munich, Germany.
    13. Lakonishok, Josef, 1980. "Stock Market Return Expectations: Some General Properties," Journal of Finance, American Finance Association, vol. 35(4), pages 921-931, September.
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    Keywords

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    JEL classification:

    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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