Three Remarks On Asset Pricing

We make three remarks to the main CAPM equation presented in the well-known 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 first-order 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 price-volume positive correlations may prohibit existence of ξmax and main CAPM equation. Third, we argue that the economic sense of the conventional frequency-based 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.