Olkhov, Victor (2021): Three Remarks On Asset Pricing.

PDF
MPRA_paper_107938.pdf Download (273kB)  Preview 
Abstract
We make three remarks to the main CAPM equation presented in the wellknown textbook by John Cochrane (2001). First, we believe that any economic averaging procedure implies aggregation of corresponding time series during certain time interval Δ and explain the necessity to use math expectation for both sides of the main CAPM equation. Second, the firstorder condition of utility max used to derive main CAPM equation should be complemented by the second one that requires negative utility second derivative. Both define the amount of assets ξmax that delivers max to utility. Expansions of the utility in a Taylor series by price and payoff variations give approximations for ξmax and uncover equations on price, payoff, volatility, skewness, their covariance’s and etc. We discuss why market pricevolume positive correlations may prohibit existence of ξmax and main CAPM equation. Third, we argue that the economic sense of the conventional frequencybased price probability may be poor. To overcome this trouble we propose new price probability measure based on widely used volume weighted average price (VWAP). To forecast price volatility one should predict evolution of squares of the value and the volume of market trades aggregated during averaging interval Δ. The forecast of the new price probability measure may be the main tough puzzle for CAPM and finance. However investors are free to chose any probability measure they prefer as ground for their investment strategies but should be ready for unexpected losses due to possible distinctions with real market trade price dynamics.
Item Type:  MPRA Paper 

Original Title:  Three Remarks On Asset Pricing 
English Title:  Three Remarks On Asset Pricing 
Language:  English 
Keywords:  asset pricing, volatility, price probability, market trades 
Subjects:  C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods D  Microeconomics > D4  Market Structure, Pricing, and Design > D40  General D  Microeconomics > D5  General Equilibrium and Disequilibrium > D53  Financial Markets G  Financial Economics > G1  General Financial Markets > G10  General G  Financial Economics > G1  General Financial Markets > G12  Asset Pricing ; Trading Volume ; Bond Interest Rates 
Item ID:  107938 
Depositing User:  Victor Olkhov 
Date Deposited:  25 May 2021 01:30 
Last Modified:  25 May 2021 01:30 
References:  Andersen, T., Bollerslev, T., Diebold, F.X. and H. Ebens, (2001). The Distribution of Realized Stock Return Volatility, Journal of Financial Economics, 61, 4376 Andersen, T.G., Bollerslev, T., Christoffersen, P.F. and F.X. Diebold, (2005). Volatility Forecasting, CFS WP 2005/08, 1116 Bernanke, B. and M. Gertler, (1999). Monetary Policy and Asset Price Volatility. FRB of Kansas City, Economic Review, 4Q, 136 Borovička, J. and L. P. Hansen, (2012). Examining Macroeconomic Models through the Lens of Asset Pricing. FRB Chicago Brock, W.A. and B.D. LeBaron, (1995). A Dynamic structural model for stock return volatility and trading volume. NBER, WP 4988, 146 Buryak, A. and I. Guo, (2014). Effective And Simple VWAP Options Pricing Model, Intern. J. Theor. Applied Finance, 17, (6), 1450036, https://doi.org/10.1142/S0219024914500356 Busseti, E. and S. Boyd, (2015). Volume Weighted Average Price Optimal Execution, 134, arXiv:1509.08503v1 Campbell, J.Y. and R. J. Shiller, (1988). Stock Prices, Earnings And Expected Dividends. NBER, WP 2511, 142 Campbell, J.Y. (1998). Asset Prices, Consumption, and the Business Cycle. NBER, WP6485, 1111 Campbell, J.Y. (2000). Asset Pricing at the Millennium. The Journal Of Finance, 55(4), 15151567 Campbell, J.Y. (2002). ConsumptionBased Asset Pricing. Harvard Univ., Cambridge, Discussion Paper # 1974, 1116 CME Group, (2020). www.cmegroup.com/confluence/display/EPICSANDBOX/ GovPX+Historical+Data; www.cmegroup.com/confluence/display/EPICSANDBOX/Standard+and+Poors+500+Futures Cochrane, J.H. and L. P. Hansen, (1992). Asset Pricing Explorations for Macroeconomics. Ed., Blanchard, O. J. and S. Fischer, NBER Macroeconomics Annual 1992, v. 7, 115  182 Cochrane, J.H., (2001). Asset Pricing. Princeton Univ. Press, Princeton, US. Cochrane, J.H. and C.L. Culp, (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, 5792. Cochrane, J.H. (2021). Portfolios For LongTerm Investors. NBER, WP28513, 154 DeFusco, A.A., Nathanson, C.G. and E. Zwick, (2017). Speculative Dynamics Of Prices And Volume. NBER WP 23449, 174 Duffie, D. and P. Dworczak, (2018). Robust Benchmark Design. NBER, WP 20540, 156 Fama, E.F. (1965). The Behavior of StockMarket Prices. J. of Business, 38 (1), 34105 Fama, E.F. and K. R. French, (2015). A fivefactor asset pricing model. J. Financial Economics, 116,122 Ferson, W.E., Sarkissian, S. and T. Simin, (1999). The alpha factor asset pricing model: A parable. J. Financial Markets, 2, 4968 Friedman, D.D., (1990). Price Theory: An Intermediate Text. SouthWestern Pub. Co., US. Gallant, A.R., Rossi, P.E. and G. Tauchen., (1992). Stock Prices And Volume. The Review of Financial Studies, 5(2), 199242 Goldsmith, R.W. and R. E. Lipsey, (1963). Asset Prices and the General Price Level, NBER, 166 – 189, in Studies in the National Balance Sheet of the United States, Ed. Goldsmith, R.W. and R. E. Lipsey. Greenwood, R. and A. Shleifer, (2014). Expectations of Returns and Expected Returns. The Review of Financial Studies, 27 (3), 714–746 Guéant, O. and G. Royer, 2014. VWAP execution and guaranteed VWAP, SIAM J. Finan. Math., 5(1), 445–471 Hall, R.L. and C.J. Hitch, (1939). Price Theory and Business Behaviour, Oxford Economic Papers, 2. Reprinted in T. Wilson and P. W. S. Andrews (eds.), Oxford Studies in the Price Mechanism (Oxford, 1951) Heaton, J. and D. Lucas, (2000). Stock Prices and Fundamentals. Ed. Ben S. Bernanke, B.S and J. J. Rotemberg, NBER Macroeconomics Annual 1999, v. 14., 213  264 Hördahl, P. and F. Packer. (2007). Understanding asset prices: an overview. Bank for International Settlements, WP 34, 138 Karpoff, J.M. (1987). The Relation Between Price Changes and Trading Volume: A Survey. The Journal of Financial and Quantitative Analysis, 22 (1),109126 Klyatskin, V.I. (2005). Stochastic Equations through the Eye of the Physicist, Elsevier B.V. Klyatskin, V.I. (2015). Stochastic Equations: Theory and Applications in Acoustics, Hydrodynamics, Magnetohydrodynamics, and Radiophysics, v.1, 2, Springer, Switzerland Lucas, R.E., 1972. Expectations and the Neutrality of Money. J. Econ. Theory, 4, 103124 Mankiw, N.G., Romer, D. and M.D. Shapiro, 1991. Stock Market Forecastability and Volatility: A Statistical Appraisal, Rev.Economic Studies, 58,455477 Mackey, M.C. (1989). Commodity Price Fluctuations: Price Dependent Delays and Nonlinearities as Explanatory Factors. J. Economic Theory, 48, 497509 Malkiel, B. and J. G. Cragg, (1980). Expectations and valuations of shares. NBER, WP 471, 170 Merton, R.C., (1973). An Intertemporal Capital Asset Pricing Model, Econometrica, 41, (5), 867887. Mills, F.C. (1946). PriceQuantity Interactions in Business Cycles. NBER, Princeton Univ. Press, NY. Muth, J.F., (1961). Rational Expectations and the Theory of Price Movements, Econometrica, 29, (3) 315335. Olkhov, V., (2020a). Volatility Depend on Market Trades and Macro Theory. MPRA, WP102434, https://mpra.ub.unimuenchen.de/102434/1/MPRA_paper_102434.pdf Olkhov, V., (2020b). Price, Volatility and the SecondOrder Economic Theory. SSRN, WP 3688109, https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3688109 Olkhov, V., (2021). To VaR, or Not to VaR, That is the Question. SSRN, WP 3770615, https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3770615 Padungsaksawasdi, C. and R.T. Daigler, (2018). Volume weighted volatility: empirical evidence for a new realized volatility measure, Int. J. Banking, Accounting and Finance, 9, (1), 6187 Perold, A.F. (2004). The Capital Asset Pricing Model. J. Economic Perspectives, 18(3), 3–24 Poon, SH., and C.W.J. Granger, 2003. Forecasting Volatility in Financial Markets: A Review, J. of Economic Literature, 41, 478–539 Sharpe, W.F. (1964). Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. The Journal of Finance, 19 (3), 425442 Stigler, G.J., and J.K. Kindahl, (1970). The Dispersion of Price Movements, NBER, 88  94 in Ed. Stigler,G.J., and J.K. Kindahl, The Behavior of Industrial Prices Schwert, G.W., (1988). Why Does Stock Market Volatility Change Over Time? NBER WP2798 Shiryaev, A.N. (1999). Essentials Of Stochastic Finance: Facts, Models, Theory. World Sc. Pub., Singapore. 1852 Tauchen, G.E. and M. Pitts, (1983). The Price VariabilityVolume Relationship On Speculative Markets, Econometrica, 51, (2), 485505 Weyl, E.G., (2019). Price Theory, AEA J. of Economic Literature, 57(2), 329–384 Xu, J. (2007). Price Convexity and Skewness. Jour Of Finance, 67 (5), 25212552 Ying, C. C., (1966). Stock Market Prices and Volumes of Sales. Econometrica, 34, 676686 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/107938 