Stochastic Discount Factor, Asset Pricing, and Dependence of Random Variables in Discrete Period

Fundamental theory of asset pricing states that current price of an asset equals expected value of multiplication between stochastic discount factor and future cash flows of the asset in a discrete period. If we assume that such theory holds, 1) discount factor and cash flow of an asset are independent in which case expected value of returns of the asset equals risk-free rate of return if discount factor and cash flow realize at the same point in time, 2) discount factor and cash flows are interdependent via dependence of risk-free rate of return on cash flows in which case expected asset return is explained by risk-free rate of return and its dependence on asset return if realization of cash flows precedes realization of discount factor, or 3) discount factor and cash flows are interdependent via dependence of expected value of cash flows on stochastic discount factor in which case expected asset return over a period is, via the dependence, explained by expected asset returns over sub-periods if realization of discount factor precedes realization of cash flows. In this paper, I provide the rationale behind these conclusions