  The present article explores the application of randomized control techniques
in empirical asset pricing and performance evaluation. It introduces geometric
random walks, a class of Markov chain Monte Carlo methods, to construct
flexible control groups in the form of random portfolios adhering to investor
constraints. The sampling-based methods enable an exploration of the
relationship between academically studied factor premia and performance in a
practical setting. In an empirical application, the study assesses the
potential to capture premias associated with size, value, quality, and momentum
within a strongly constrained setup, exemplified by the investor guidelines of
the MSCI Diversified Multifactor index. Additionally, the article highlights
issues with the more traditional use case of random portfolios for drawing
inferences in performance evaluation, showcasing challenges related to the
intricacies of high-dimensional geometry.
