Two main approaches are commonly used to empirically evaluate linear factor pricing models: regression 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...

We propose new spanning tests that assess if the economically meaningful cost and mean representing portfolios are shared by the initial and additional assets. We show that our proposed tests are asymptotically equivalent to existing ones under local alternatives, and analyse their asymptotic...

Two main approaches are commonly used to empirically evaluate linear factor pricing models: regression and stochastic discount factor (SDF) methods, with centered and uncentered versions of the latter. We show that unlike standard two-step or iterated generalized method of moments (GMM)...

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...