The Market-Based Statistics of “Actual” Returns of Investors

Olkhov, Victor (2023): The Market-Based Statistics of “Actual” Returns of Investors.

Abstract

The paper presents the unified theoretical description of three levels of the market-based statistical moments of “actual” returns, which Investors gain within their market sales. The market-based statistics of “actual” returns takes into account the size of the trade sale values, purchased values and volumes of stocks and that differs it from conventional regular statistics based on frequency analysis of returns time-series. We start with description of statistical moments of returns, which Investor gains via a single sale due to his multiple purchases in the past. The second level describes statistics of returns, which Investor gains performing numerous market sales during the “trading day”. The third level describes statistics of returns that different Investors gain during the “trading day”. We derive dependence of statistical moments of returns on statistical moments of market sale values, purchased values and volumes of stocks. In its turn, statistical moments of trade values and volumes for finite number of market trades during the “trading day” are assessed via regular frequency-based probability.

• Item Type: MPRA Paper
• Language: English
• Keywords: asset pricing, stock returns, volatility, correlations, probability, market trades
• Subjects: C - Mathematical and Quantitative Methods > C0 - General; C - Mathematical and Quantitative Methods > C8 - Data Collection and Data Estimation Methodology ; Computer Programs > C80 - General; G - Financial Economics > G1 - General Financial Markets; G - Financial Economics > G1 - General Financial Markets > G11 - Portfolio Choice ; Investment Decisions; G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates

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

Baker, M. and J. Wurgler, (2004). Investor Sentiment And The Cross-Section Of Stock Returns, NBER, Cambridge, WP 10449, 1-47

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

Daniel, K. and D. Hirshleifer, (2016). Overconfident Investors, Predictable Returns, And Excessive Trading, NBER, Cambridge, WP 21945, 1-36

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

Greenwood, R. and A. Shleifer, (2013). Expectations of Returns and Expected Returns, WP18686, NBER, Cambridge, 1-52

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

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

Gabaix, X., Gopikrishnan, P., Plerou, V. and H. E. Stanley, (2005). Institutional Investors And Stock Market Volatility, NBER, Cambridge, WP 11722, 1-50

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

Hardouvelis, G., Karalas, G. and D. Vayanos, (2021). The Distribution of Investor Beliefs, Stock Ownership and Stock Returns, NBER, Cambridge, WP 28697, 1-47

Ivković, Z., Sialm, C. and S. Weisbenner, (2004). Portfolio Concentration and The Performance of Individual Investors, NBER, Cambridge, WP 10675, 1-52

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

Koijen, R.S., Richmond, R.J. and M. Yogo (2020). Which Investors Matter For Equity Valuations And Expected Returns?, NBER, Cambridge, WP 27402, 1-53

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

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, 1-24, https://ssrn.com/abstract=3852261

Olkhov, V. (2022a). The Market-Based Asset Price Probability, MPRA WP115382, 1-21, https://mpra.ub.uni-muenchen.de/115382/

Olkhov, V. (2022b). Price and Payoff Autocorrelations in the Consumption-Based Asset Pricing Model, SSRN, WP 4050652, 1- 18

Olkhov, V. (2023). The Market-Based Probability of Stock Returns, SSRN, WP 4350975, 1- 25, https://ssrn.com/abstract=4350975

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

Stanley, K.L., Lewellen, W.G. and G.G. Schlarbaum, (1980). Further Evidence of on the Value of Professional Investment Research, NBER, Cambridge, WP 536, 1-19

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