Efficient Factor Selection: Explaining Risk and Mean Returns Jointly

An asset pricing model is customarily evaluated by how well it explains means of returns. But how well the model explains fluctuations of returns is similarly important though often overlooked in the literature. We derive “efficient” factors that combine both objectives and turn out to maximize average time-series (first-pass) R-square for given cross-sectional (second-pass) R-square. Efficient factors work better out of sample and even explain mean returns better than structural models. The reason is that structural models emphasize factors that as a group are close to the tangency portfolio. But this portfolio, by necessity, has relatively low variance that explains individual asset return fluctuations poorly and impedes factor identification. These findings explain many of the puzzling results in empirical asset pricing. Further, intended holding period becomes essential now for model evaluation and shorter holding periods require more emphasis on first-pass fit, which is another key issue overlooked in the literature.