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Three Remarks On Asset Pricing

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  • Olkhov, Victor

Abstract

We make three remarks to the main CAPM equation presented in the well-known textbook by John Cochrane (2001). First, we believe that any economic averaging procedure implies aggregation of corresponding time series during certain time interval Δ and explain the necessity to use math expectation for both sides of the main CAPM equation. Second, the first-order condition of utility max used to derive main CAPM equation should be complemented by the second one that requires negative utility second derivative. Both define the amount of assets ξmax that delivers max to utility. Expansions of the utility in a Taylor series by price and payoff variations give approximations for ξmax and uncover equations on price, payoff, volatility, skewness, their covariance’s and etc. We discuss why market price-volume positive correlations may prohibit existence of ξmax and main CAPM equation. Third, we argue that the economic sense of the conventional frequency-based price probability may be poor. To overcome this trouble we propose new price probability measure based on widely used volume weighted average price (VWAP). To forecast price volatility one should predict evolution of squares of the value and the volume of market trades aggregated during averaging interval Δ. The forecast of the new price probability measure may be the main tough puzzle for CAPM and finance. However investors are free to chose any probability measure they prefer as ground for their investment strategies but should be ready for unexpected losses due to possible distinctions with real market trade price dynamics.

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  • Olkhov, Victor, 2021. "Three Remarks On Asset Pricing," MPRA Paper 107938, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:107938
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    Cited by:

    1. Victor Olkhov, 2023. "Economic Complexity Limits Accuracy of Price Probability Predictions by Gaussian Distributions," Papers 2309.02447, arXiv.org.
    2. Victor Olkhov, 2022. "Market-Based Asset Price Probability," Papers 2205.07256, arXiv.org, revised Feb 2024.
    3. Olkhov, Victor, 2023. "The Market-Based Statistics of “Actual” Returns of Investors," MPRA Paper 116896, University Library of Munich, Germany.
    4. Olkhov, Victor, 2022. "Why Economic Theories and Policies Fail? Unnoticed Variables and Overlooked Economics," MPRA Paper 114187, University Library of Munich, Germany.
    5. Olkhov, Victor, 2023. "Economic Theory as Successive Approximations of Statistical Moments," MPRA Paper 118722, University Library of Munich, Germany.

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    More about this item

    Keywords

    asset pricing; volatility; price probability; market trades;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • D40 - Microeconomics - - Market Structure, Pricing, and Design - - - General
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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