4 The Stochastic Discount Factor Approach

摘要

Modern asset pricing theory posits the existence of a stochastic discount factor, m_(t+1), which is a scalar random variable, such that the following equation holds:rnE(m_(t+1)R_(t+1) - 1|Z_t) = 0, (4.1)rnwhere R_(t+1) is the vector of primitive asset gross returns (payoff divided by price), 1 is an N-vector of ones and Z_t denotes the public information set available at time t. Virtually all asset pricing models may be viewed as specifying a particular stochastic discount factor, m_(t+1). The elements of the vector m_(t+1)R_(t+1) may be viewed as "risk adjusted" gross returns. The returns are risk adjusted by "discounting" them, or multiplying by the discount factor, m_(t+1), so that the expected "present value" per dollar invested is equal to one dollar. Thus, m_(t+1) is called a stochastic discount factor (SDF). We say that a SDF "prices" the assets if Equation (4.1) is satisfied.