Paper: arXiv 2309.02447

Authors: Victor Olkhov

Abstract

We discuss the economic reasons why the predictions of price and return statistical moments in the coming decades, in the best case, will be limited by their averages and volatilities. That limits the accuracy of the forecasts of price and return probabilities by Gaussian distributions. The economic origin of these restrictions lies in the fact that the predictions of the market-based n-th statistical moments of price and return for n=1,2,.., require the description of the economic variables of the n-th order that are determined by sums of the n-th degrees of values or volumes of market trades. The lack of existing models that describe the evolution of the economic variables determined by the sums of the 2nd degrees of market trades results in the fact that even predictions of the volatilities of price and return are very uncertain. One can ignore existing economic barriers that we highlight but cannot overcome or resolve them. The accuracy of predictions of price and return probabilities substantially determines the reliability of asset pricing models and portfolio theories. The restrictions on the accuracy of predictions of price and return statistical moments reduce the reliability and veracity of modern asset pricing and portfolio theories.

Complexity vs Empirical Score

  • Math Complexity: 3.0/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Philosophers — conceptual discussion, limited math and data

Why this score: The paper presents a conceptual and theoretical argument regarding the fundamental economic limits of predicting higher-order statistical moments in market prices. However, it lacks robust empirical testing, quantitative backtests, or formal mathematical proofs to substantiate its claims.

Research Flowchart

  flowchart TD
    A[Research Goal: Evaluate limits of price probability predictions via Gaussian distributions] --> B[Input Data: Market trade values, volumes & n-th order economic variables]
    B --> C[Methodology: Analyze n-th statistical moments of prices & returns]
    C --> D[Process: Assess economic complexity & models for 2nd-degree trade sums]
    D --> E[Key Finding: Lack of models for 2nd-degree trade sums causes high volatility uncertainty]
    E --> F[Outcome: Economic barriers cap predictions at basic averages & reduce reliability of Asset Pricing & Portfolio Theories]