Econophysics of Asset Price, Return and Multiple Expectations

Olkhov, Victor (2019): Econophysics of Asset Price, Return and Multiple Expectations.

Abstract

This paper describes asset price and return disturbances as result of relations between transactions and multiple kinds of expectations. We show that disturbances of expectations can cause fluctuations of trade volume, price and return. We model price disturbances for transactions made under all types of expectations as weighted sum of partial price and trade volume disturbances for transactions made under separate kinds of expectations. Relations on price allow present return as weighted sum of partial return and trade volume “return” for transactions made under separate expectations. Dependence of price disturbances on trade volume disturbances as well as dependence of return on trade volume “return” cause dependence of volatility and statistical distributions of price and return on statistical properties of trade volume disturbances and trade volume “return” respectively.

• Item Type: MPRA Paper
• Language: English
• Keywords: financial transactions; expectations; economic space; asset price; return
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C58 - Financial Econometrics; E - Macroeconomics and Monetary Economics > E4 - Money and Interest Rates > E44 - Financial Markets and the Macroeconomy; G - Financial Economics > G0 - General > G02 - Behavioral Finance: Underlying Principles; G - Financial Economics > G1 - General Financial Markets; G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates; G - Financial Economics > G3 - Corporate Finance and Governance > G32 - Financing Policy ; Financial Risk and Risk Management ; Capital and Ownership Structure ; Value of Firms ; Goodwill

References

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

Batchelor, G.K., (1967). An introduction to fluid dynamics. Cambridge University Press, Cambridge, UK. 615 p.

van Binsbergen, J. H., Koijen, R., (2017). The term structure of returns: Facts and theory, NBER WP 21234, Cambridge, MA

Blume, L.E., Easley, D., (1984). Rational Expectations Equilibrium: An Alternative Approach, Journal Of Economic Theory, 34, 116-129

Brock, W.A., Hommes, C.H., (1998). Heterogeneous beliefs and routes to chaos in a simple asset pricing model. Journal of Economic Dynamics and Control, 22, 1235-1274

Brunnermeier, M.K., Parker, J.A., (2005). Optimal Expectations. American Economic Review, 95 (4), 1092-1118

Campbell, J.Y., (1985). Stock Returns and The Term Structure, WP1626, NBER, Cambridge

Campbell, J.Y., Cochrane, J.H., (1995). By Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior, NBER WP 4995, Cambridge, US

Chane-Kon, L., Neugebauer, M., Pak, A., Trebach, K., Tsang, E., (2010). Structured Finance. Global Rating Criteria for Structured Finance CDOs, Fitch Ratings, 1-27

Cochrane, J.H., (2001). Asset pricing. Princeton University Press, Princeton, N. Jersey, US

Cochrane, J.H., Cupl, C.L., (2003). Equilibrium Asset Pricing and Discount Factors: Overview and Implications for Derivatives Valuation and Risk Management. In Modern Risk Management. A History, Ed. S.Jenkins, 57-92.

Cochrane, J.H., (2017). Macro-Finance. Review of Finance, European Finance Association, 21(3), 945-985.

Dominitz, J., Manski, C.F., (2005). Measuring And Interpreting Expectations Of Equity Returns. NBER, WP 11313, Cambridge, MA.

Fama, E.F., (1965). The Behavior of Stock-Market Prices. Jour. of Business, 38 (1), 34-105.

Fama, E.F., (1998). Market efficiency, long-term returns, and behavioral finance, Journal of Financial Economics 49, 283-306

Gabaix, X., Gopikrishnan, P., Plerou, V., Stanley, H,E., (2003). A theory of power-law distributions in financial market fluctuations, Nature, 423, 267-270

Gontis, V., Havlin, S., Kononovicius, A., Podobnik, B., Stanley, H.E., (2016). Stochastic model of financial markets reproducing scaling and memory in volatility return intervals. Physica A, 462, 1091–1102

Greenwald, D.L., Lettau, M., Ludvigson, S., (2014). Origins of Stock Market Fluctuations. NBER, WP 19818, Cambridge, MA

Greenwood, R., Shleifer, A., (2014). Expectations of Returns and Expected Returns. The Review of Financial Studies, 27 (3), 714–746, https://doi.org/10.1093/rfs/hht082

Hansen, L. P., (2013). Uncertainty outside and inside economic models. Nobel lecture.

Hansen, L.P., Sargent, T.J., (1979). Formulating and Estimating Dynamic Rational Expectations Models. NBER, WP 127

Heaton, J., Lucas, D., (2000). Stock Prices and Fundamentals, in Ed. Bernanke, B.S., Rotemberg, J.J. NBER Macroeconomics Annual 1999, Volume 14, 213 - 264

Horcher, K.A., (2005). Essentials of Financial Risk Management. J.Wiley & Sons, NJ

Keim, D.B., Stambaugh, R.F., (1986). Predicting Returns In The Stock And Bond Markets, Journal of Financial Economics, 17, 357-390

Kraemer, N., Vazza, D., (2012). 2011 Annual U.S. Corporate Default Study And Rating Transitions, S&P: 1-96

Landau, L.D., Lifshitz, E.M., (1987). Fluid Mechanics. NY: Pergamon Press Ltd

Lof, M., (2014). Essays on Expectations and the Econometrics of Asset Pricing, MPRA WP 59064, http://mpra.ub.uni-muenchen.de/59064/

Lucas, R.E., (1972). Expectations and the Neutrality of Money. Jour. of Economic Theory 4, 103-124

McNeil, A,J., Frey, R., Embrechts, P., (2005). Quantitative Risk Management. Concepts, Techniques and Tools. Princeton Univ. Press, Princeton.

Mandelbrot, B., Fisher, A., Calvet, L., (1997). A Multifractal Model of Asset Returns. Cowles Foundation Discussion Paper #1164

Manski, C.F., (2017). Survey Measurement Of Probabilistic Macroeconomic Expectations: Progress and Promise. NBER Macro Annual Conference, 1-76.

Metz, A. and Cantor, R., (2007). Introducing Moody's Credit Transition Model, Moody’s Investor Service, 1-26

Muth, J.F., (1961). Rational Expectations and the Theory of Price Movements. Econometrica, 29 (3), 315-335

Olkhov, V., (2016a). On Economic space Notion, Int. Rev. Financial Analysis, 47, 372-381

Olkhov, V., (2016b). Finance, Risk and Economic space, ACRN Oxford J. of Finance and Risk Perspectives, Special Issue of Finance Risk and Accounting Perspectives, 5, 209-221

Olkhov, V., (2017a). Quantitative Wave Model of Macro-Finance. Int. Rev. Financial Analysis, 50, 143-150

Olkhov, V., (2017b). Quantitative Description of Financial Transactions and Risks” ACRN Oxford Journal of Finance and Risk Perspectives 6, (2), 41-54.

Olkhov, V., (2017c). Credit-Loans Non-Local Transactions and Surface-Like Waves. https://ssrn.com/abstract=2971417

Olkhov, V., (2017d). Econophysics of Business Cycles: Aggregate Economic Fluctuations, Mean Risks and Mean Square Risks. arxiv.org/abs/1709.00282,

Olkhov, V., (2018a). Economic Transactions Govern Business Cycles. MPRA, WP 87207, https://mpra.ub.uni-muenchen.de/id/eprint/87207

Olkhov, V., (2018b). Expectations, Price Fluctuations and Lorenz Attractor. MPRA WP89105, https://mpra.ub.uni-muenchen.de/89105/

Pitman, T., Moss, J., (2016). The Ratings Process. Fitch Ratings, Business Relationship Management, NY

Plerou, V., Gopikrishnan, P., Amaral, L., Meyer, M., Stanley, H.E., (1999). Scaling of the distribution of price fluctuations of individual companies. Phys. Rev. E, 60 (6), 6519-6529

Plerou, V., Gabaix, X., Gopikrishnan, P., Amaral, L.A.N., Meyer, M., Stanley, H.E., (2001). Price fluctuations, market activity and trading volume. Quantitative Finance, 1, 262–269

Resibois, P., De Leener, M., (1977). Classical Kinetic Theory of Fluids, John Wiley, NY.

Sargent, T.J., Wallace, N., (1976). Rational Expectations And The Theory Of Economic Policy, Journal of Monetary Economics 2 (1976) 169-183

Skoglund, J., Chen, W., (2015). Financial Risk Management: Applications in Market, Credit, Asset and Liability Management, and Firmwide Risk. John Wiley&Sons Inc.

S&P, (2014). Guide To Credit Rating Essentials. What are credit ratings and how do they work? McGraw Hill Financial Staff of the U.S.

SEC, (2012). Credit Rating Standardization Study. Report to Congress.

Stanley, H.E., Pleroua, V., Gabaixb, X., (2008). A statistical physics view of financial fluctuations: Evidence for scaling and universality. Physica A, 387, 3967–3981

Strauss, W.A., (2008). Partial Differential Equations. An Introduction. John Wiley&Sons, Inc., NJ, US. p.179.

Wilier, A.H., (1901). The Economic Theory Of Risk And Insurance. Introduction by Glenn Meyers. Reprinted 1951. Richard D. Irwin, Inc., Homewood, Illinois