Contrary to the classic framework of passive strategies, if investors exploit return predictability through active strategies then there is a tension between the mean-variance frontiers that drive empirical work and the mean-variance preferences that are used in finance theory. We show that...

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 initial and additional assets share the economically meaningful cost and mean representing portfolios. We prove their asymptotic equivalence to existing tests under local alternatives. We also show that unlike two-step or iterated procedures,...

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...