  Beta-sorted portfolios -- portfolios comprised of assets with similar
covariation to selected risk factors -- are a popular tool in empirical finance
to analyze models of (conditional) expected returns. Despite their widespread
use, little is known of their statistical properties in contrast to comparable
procedures such as two-pass regressions. We formally investigate the properties
of beta-sorted portfolio returns by casting the procedure as a two-step
nonparametric estimator with a nonparametric first step and a beta-adaptive
portfolios construction. Our framework rationalize the well-known estimation
algorithm with precise economic and statistical assumptions on the general data
generating process and characterize its key features. We study beta-sorted
portfolios for both a single cross-section as well as for aggregation over time
(e.g., the grand mean), offering conditions that ensure consistency and
asymptotic normality along with new uniform inference procedures allowing for
uncertainty quantification and testing of various relevant hypotheses in
financial applications. We also highlight some limitations of current empirical
practices and discuss what inferences can and cannot be drawn from returns to
beta-sorted portfolios for either a single cross-section or across the whole
sample. Finally, we illustrate the functionality of our new procedures in an
empirical application.
