6.2.1 Asset pricing frameworks

We focus on linear pricing relationships and examine asset pricing in both the traditional regression framework and the stochastic discount factor framework using GMM. For asset pricing posed in the traditional regression framework, assets excess returns are linear functions of k factors return.

(6.1)

where n is the number of assets and T is the number of time-series observations. If a linear combination of the k factors is efficient, the expected return linear beta relation holds, i.e.,

(6.2)

r _it is the asset return and r _ft is the risk-free rate so that r _it ? r _ft is the excess return at time t, hereafter denoted as . f _jt is the factor return of factor j at time t. ? _{j , i} is factor j s loading of asset i. The assumptions such that equation (6.2) holds are: (1) r _it and f _jt are stationary and spherically distributed, (2) is iid. with zero mean, and (3) each ? _{j , i} is constant through time. Both equation (6.1) and equation (6.2) can be put into linear regression framework using their sample counterpart. We will use equation (6.1) and linear regression to implement the multivariate F test and the average F test.

Asset pricing in the stochastic discount framework is based on the Euler equation, which is the first order condition of the investor s...