The efficiency of the SDF and Beta methods at evaluating multi-factor asset-pricing models

The classical beta method and the stochastic discount factor (SDF) method may be
considered competing paradigms for empirical work in asset pricing. The two methods are equally efficient at estimating risk premiums in the context of the single-factor model. We show this does not hold for multi-factor models. Inference is consistently more reliable in the Beta method for the estimates in models which include size, value and momentum factors. However, our evidence also illustrates that the SDF method is generally more efficient at estimating sample pricing errors. Finally, the specification test in the Beta method tends to under-reject in finite samples while the SDF method has approximately the correct size. Our Monte Carlo simulation results are consistent whether we use a normal or empirical distribution, or different sets and sizes of tests portfolios.