Optimal characteristic portfolios

Characteristic-sorted portfolios are the workhorses of modern empirical finance, deployed widely to evaluate anomalies and construct asset pricing models. We propose a new method for their estimation that is simple to compute, makes no ex-ante assumption on the nature of the relationship between the characteristic and returns, and does not require ad hoc selections of percentile breakpoints or portfolio weighting schemes. Characteristic portfolio weights are implied directly from data, through maximizing a Mean-Variance objective function with mean and variance estimated non-parametrically from the cross-section of assets. To illustrate the method, we evaluate the size, value and momentum anomalies and find overwhelming empirical evidence of the outperformance of our methodology compared to standard methods for constructing characteristic-sorted portfolios.