The Market-Based Probability of Stock Returns

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

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

• 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

References

Amaral, L.I., Plerou, V., Gopikrishnan, P., Meyer, M. and H. E. Stanley, (2000). The Distribution of Returns of Stock Prices, Int.J.Theoretical and Applied Finance, 3(3), 365-369

Andersen, T., Bollerslev, T., Diebold, F.X, Ebens, H. (2001). The Distribution of Realized Stock Return Volatility, Journal of Financial Economics, 61, 43-76

Andersen, T. and T. Bollerslev, (2006). Realized Return Volatility, Asset Pricing, and Risk Management, NBER Reporter Online, NBER, Cambridge, 7-10

Andersen, T. and L. Benzoni, (2009). Realized Volatility, 555-570, in Andersen, T., Davis, R., Kreiß, J-P. and T. Mikosch, Handbook of Financial Time Series, Springer, Berlin, 1-1031

Bachelier, L., (1900). Théorie de la speculation, Ann. Scientifiques, 3e série, 17, 21-86

Berkowitz, S.A., Dennis, E., Logue, D.E., Noser, E.A. Jr. (1988). The Total Cost of Transactions on the NYSE, The Journal of Finance, 43, (1), 97-112

van Binsbergen, J.H. and R. Koijen, (2015). The Term Structure Of Returns: Facts And Theory, NBER WP 21234, Cambridge, 1-38

Brown, S.J. (1989). The Number of Factors in Security Returns, J. Finance, 44(5), 1247-1262

Campbell, J. (1985). Stock Returns And The Term Structure, NBER WP1626, 1-53

Campbell, J., Grossman, S.J. and J.Wang, (1993). Trading Volume And Serial Correlation In Stock Returns, Quatr. Jour. Economics, 108 (4), 905-939

Davis, J.L., Fama, E.F. and K. R. French, (2000). Characteristics, Covariances, and Average Returns: 1929 to 1997, J. Finance, 55(1), 389-406

Diebold, F.X. and K. Yilmaz, (2009). Measuring Financial Asset Return And Volatility Spillovers, With Application To Global Equity Markets, The Economic J., 119, 158–171

Dorn, D., Huberman, G. and P. Sengmueller, (2008). Correlated Trading and Returns, J. Finance, 63(2), 885-920

Duffie, D. and P. Dworczak, (2018). Robust Benchmark Design, NBER WP 20540, 1-56

Fama, E.F. (1990). Stock Returns, Expected Returns, and Real Activity, J. Finance, 45(4), 1089-1108

Fama, E.F. and K. R. French, (1992). The Cross-Section of Expected Stock Returns, J.Finance, 47 (2), 427-465

Ferreira, M.A. and P. Santa-Clara, (2008). Forecasting Stock Market Returns: The Sum Of The Parts Is More Than The Whole, WP 14571, NBER, Cambridge, 1-34

Fisher, L. and J. H. Lorie, (1964). Rates Of Return On Investments In Common Stocks, J. Business, 37(1), 1-21

Greenwood, R. and A. Shleifer, (2013). Expectations Of Returns And Expected Returns, NBER, Cambridge, WP 18686, 1-51

Kelly, B.T., Malamud, S. and K. Zhou, (2022). The Virtue Of Complexity In Return Prediction, WP30217, NBER, Cambridge, 1-127

Knight, J. and S. Satchell, (Ed). (2001). Return Distributions In Finance, Butterworth-Heinemann, Oxford, 1-328

Kon, S.J. (1984). Models of Stock Returns-A Comparison, J.Finance, 39(1), 147-165

Lettau, M. and S. C. Ludvigson, (2003). Expected Returns And Expected Dividend Growth, WP 9605, NBER, Cambridge, 1-48

Llorente, G., Michaely R., Saar, G. and J. Wang. (2001). Dynamic Volume-Return Relation of Individual Stocks. NBER, WP 8312, Cambridge, MA., 1-55

Lochstoer, L.A. and T. Muir, (2022). Volatility Expectations and Returns, J. Finance, 77 (2), 1055-1096

McAleer, M. and M. C. Medeiros, (2008). Realized Volatility: A Review, Econometric Reviews, 27(1–3), 10–45

Mandelbrot, B., Fisher, A. and L. Calvet, (1997). A Multifractal Model of Asset Returns, Yale University, Cowles Foundation Discussion WP1164, 1-39

Markowitz, H. (1952). Portfolio Selection, J. Finance, 7(1), 77-91

Martin, I. and C. Wagner, (2019). What Is the Expected Return on a Stock?, J. Finance, 74(4), 1887-1929

Olkhov, V. (2021). Three Remarks On Asset Pricing, SSRN WP3852261, 1-21

Olkhov, V. (2022). The Market-Based Asset Price Probability, MPRA WP115382, 1-19

Schlarbaum, G.G., Lewellen, W.G. and R.C. Lease, (1978). Realized Returns on Common Stock Investments: The Experience of Individual Investors, J. of Business, 51(2), 299-325

Shephard, N.G. (1991). From Characteristic Function to Distribution Function: A Simple Framework for the Theory. Econometric Theory, 7 (4), 519-529

Shiryaev, A.N. (1999). Essentials Of Stochastic Finance: Facts, Models, Theory. World Sc. Pub., Singapore. 1-852

Shreve, S. E. (2004). Stochastic calculus for finance, Springer finance series, NY, USA

Tsay, R.S. (2005). Analysis of Financial Time Series, J.Wiley&Sons, Inc., New Jersey, 1-638