Properties of the Pukthuanthong-Roll Stochastic Discount Factor

Pukthuanthong and Roll (2016) (PR) construct a clever candidate stochastic discount factor (SDF) that uses a vast collection of individual security returns. I show that the PR approach provides a consistent estimate of a valid SDF when the SDF is an affine function of a finite number of economy wide pervasive factors. I show how to modify the approach in PR to the case where the number of securities varies over time. The PR approach automatically selects all of the pervasive factors in an economy without the need for specifying the number of factors.