The Market-Based Probability of Stock Returns

Olkhov, Victor (2023): The Market-Based Probability of Stock Returns.

Abstract

This paper describes the probability of stock returns through a description of the set of their market-based n-th statistical moments that depended on the n-th statistical moments of market trade values and volumes. We derive these relations as extensions of Markowitz’s definition of a value weighted return of the portfolio. The average return of sale trades during the averaging period coincides with Markowitz’s definition of portfolio return. We highlight the similarity between Markowitz’s definition of portfolio return and the definition of average price as a volume weighted average price. We derive market-based volatility, autocorrelations of return, return-volume correlations, and return-price correlations as functions of the n-th statistical moments of the trade values and volumes. We derive how a finite number of the n-th statistical moments of the trade values and volumes determine the approximations of the characteristic functions and probability density functions of stock returns. To forecast the average stock return or volatility, one should predict the statistical moments of market trades. Our results are important for the largest investors, economic and financial authorities, and all market participants.

• Item Type: MPRA Paper
• Language: English
• Keywords: stock returns; volatility; correlations; probability; market trades
• Subjects: C - Mathematical and Quantitative Methods > C0 - General > C00 - General; D - Microeconomics > D4 - Market Structure, Pricing, and Design > D40 - General; E - Macroeconomics and Monetary Economics > E4 - Money and Interest Rates > E43 - Interest Rates: Determination, Term Structure, and Effects; E - Macroeconomics and Monetary Economics > E5 - Monetary Policy, Central Banking, and the Supply of Money and Credit > E50 - General; G - Financial Economics > G0 - General > G00 - General; G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates; G - Financial Economics > G1 - General Financial Markets > G15 - International Financial Markets

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