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Market-Based Probability of Stock Returns

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  • Victor Olkhov

Abstract

Markets possess all available information on stock returns. The randomness of market trade determines the statistics of stock returns. This paper describes the dependence of the first four market-based statistical moments of stock returns on statistical moments and correlations of current and past trade values. The mean return of trades during the averaging period coincides with Markowitz's definition of portfolio value weighted return. We derive the market-based volatility of return and return-value correlations. We present approximations of the characteristic functions and probability measures of stock return by a finite number of market-based statistical moments. To forecast market-based average return or volatility of return, one should predict the statistical moments and correlations of current and past market trade values at the same time horizon.

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  • Victor Olkhov, 2023. "Market-Based Probability of Stock Returns," Papers 2302.07935, arXiv.org, revised Feb 2024.
    • Handle: RePEc:arx:papers:2302.07935
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    16. Olkhov, Victor, 2022. "Price and Payoff Autocorrelations in the Consumption-Based Asset Pricing Model," MPRA Paper 112255, University Library of Munich, Germany.
    17. Victor Olkhov, 2022. "Price and Payoff Autocorrelations in a Multi-Period Consumption-Based Asset Pricing Model," Papers 2204.07506, arXiv.org, revised Mar 2024.
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    Cited by:

    1. Victor Olkhov, 2023. "Theoretical Economics as Successive Approximations of Statistical Moments," Papers 2310.05971, arXiv.org, revised Apr 2024.
    2. Victor Olkhov, 2023. "Economic Complexity Limits Accuracy of Price Probability Predictions by Gaussian Distributions," Papers 2309.02447, arXiv.org, revised Apr 2024.
    3. Olkhov, Victor, 2023. "Economic Theory as Successive Approximations of Statistical Moments," MPRA Paper 118722, University Library of Munich, Germany.
    4. Olkhov, Victor, 2023. "The Market-Based Statistics of “Actual” Returns of Investors," MPRA Paper 116896, University Library of Munich, Germany.

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    More about this item

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • D40 - Microeconomics - - Market Structure, Pricing, and Design - - - General
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • E50 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - General
    • G00 - Financial Economics - - General - - - General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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