The Market-Based Probability of Stock Returns

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

Abstract

This paper introduces a new economic, market-based probability of stock return that takes into account the impact of the size of the market’s trade values and volumes. We define how the statistical moments of trade values and volumes determine the statistical moments of stock returns. To assess the statistical moments of the trade values and volumes, one should use conventional frequency-based probabilities. The market-based average return takes a form similar to Markowitz’s definition of the weighted value return of the portfolio. We derive market-based volatility, autocorrelations of return, return-volume correlations, and return-price correlations as functions of the statistical moments of the trade values and volumes. We derive how a finite number of the 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 and banks, 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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