Portfolio and stochastic discount factor (SDF) frontiers are usually regarded as dual objects, and researchers sometimes use one to answer questions about the other. However, the introduction of conditioning information and active portfolio strategies alters this relationship. For instance, the...

We propose new approaches to test for spanning in the return and stochastic discount factor mean-variance frontiers, which assess if either the centred or uncentred mean and cost representing portfolios are shared by the initial and extended sets of assets. We show that our proposed tests are...

Two main approaches are commonly used to empirically evaluate linear factor pricing models: regrassion and SDF methods, with centred and uncentred versions of the latter. We show that unlike standard two-step or iterated GMM procedures, single-step estimators such as continuously updated GMM...