We show that unconditionally efficient returns do not achieve the maximum unconditional Sharpe ratio, neither display zero unconditional Jensen’s alphas, when returns are predictable. Next, we define a new type of efficient returns that is characterized by those unconditional properties. We...

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,...

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...