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 …