Randomized Control in Performance Analysis and Empirical Asset Pricing

TL;DR

The paper develops a framework for using randomized control via geometric random walks to create constrained random portfolios (RPs) for empirical asset pricing and performance evaluation. It shows that naive RP approaches can mislead skill inferences, and proposes a constrained RP use-case to study factor premia under investor guidelines, enabling analysis of non-linear and asymmetric relationships between portfolio characteristics and performance. It comprehensively surveys and implements a suite of geometric random walks (Ball Walk, HaR, CDHR, BiW, Dikin, Vaidya, John, HMC variants) with exact and approximate sampling capabilities, and provides an open-source C++/R toolset (volesti) for reproducible RP analysis. An empirical study using MSCI DMF constraints demonstrates how value, momentum, quality, and size tilt relationships with return and risk persist, albeit with altered magnitudes and risk profiles under practical constraints. The work offers a practical, flexible toolkit for exploring asset-pricing puzzles within realistic investment bounds and paves the way for deeper exploration of constraint-driven anomalies in financial markets.

Abstract

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.

Figures (7)

• Figure 1: Risk-return distribution of different RPs (red to yellow level sets) together with the corresponding statistics for the 26 letter strategies (grey dots), realizations of the RPs (yellow small dots), the capitalization-weighted benchmark given by the S&P 500 index (black dot) and the equal-weighted portfolio of the index constituents. In the top charts, RPs are constructed to center on the equal-weighted (left chart) and capitalization-weighted benchmark (right chart). The bottom chart displays the distributions of three RPs created through the dartboard game approach, selecting $4$, $30$, and all stocks from the investable universe from right to left.
• Figure 2: Factor exposures
• Figure 3: The relation between portfolio performance and exposure towards towards the letter 'Z' in the company names of the portfolio constituents (first row) or towards the momentum factor (second row).
• Figure 4: a) naive RP with a uniform density defined over the unit simplex, $\omega \sim \mathcal{D}(\mathbf{1})$. b) naive RP with a concentrated Dirichlet model, centered on the naive $1/n$ portfolio, $\omega \sim \mathcal{D}(\mathbf{1}\lambda)$, where $\lambda = 4$ (or $\lambda < 1$ for more mass towards the boundaries). c) Basic RP with weights following a Dirichlet distribution, $\omega \sim \mathcal{D}(\alpha)$, where $\alpha = (0.5, 0.3, 0.2)$. d) Shadow of the Dirichlet distribution in c), denoted as $\omega \sim \mathcal{SD}(M, \alpha)$, where the weights are restricted by a monotonic matrix $M$ with a specific column structure. The constrained weights satisfy the ordering $\omega_1 > \omega_2 > ... > \omega_n$. e) Generally regularized RP defined by the intersection of the simplex with a polytope, resulting in a truncated distribution of the weights. f) Generally regularized RP defined by the intersection of the simplex with the boundary of an ellipsoid, also leading to a truncated distribution of the weights.
• Figure 5: Illustration of HaR, BiW, Dikin walk, HMC (from left to right)