A general randomized test for Alpha

2025-07-23

AI Summary

This paper addresses the fundamental problem of joint “zero-alpha” testing in linear factor asset pricing models. We propose a general randomized inference procedure applicable to models with observable tradable factors, unobservable (non-tradable) factors, and latent factors. The method avoids covariance matrix estimation, accommodates asymptotics where both cross-sectional dimension $N$ and time-series dimension $T$ diverge—potentially with $N$ growing faster than $T$—and remains robust to conditional heteroskedasticity, non-Gaussian errors, and strong cross-sectional dependence. By combining equation-by-equation estimation with randomized inference and introducing a derandomized decision rule, the procedure substantially improves test reliability. Monte Carlo simulations demonstrate superior finite-sample performance relative to leading existing methods. In empirical application, the method successfully tests multifactor model specifications using S&P 500 constituent stocks.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Kernel Methods
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

We propose a methodology to construct tests for the null hypothesis that the pricing errors of a panel of asset returns are jointly equal to zero in a linear factor asset pricing model -- that is, the null of "zero alpha". We consider, as a leading example, a model with observable, tradable factors, but we also develop extensions to accommodate for non-tradable and latent factors. The test is based on equation-by-equation estimation, using a randomized version of the estimated alphas, which only requires rates of convergence. The distinct features of the proposed methodology are that it does not require the estimation of any covariance matrix, and that it allows for both N and T to pass to infinity, with the former possibly faster than the latter. Further, unlike extant approaches, the procedure can accommodate conditional heteroskedasticity, non-Gaussianity, and even strong cross-sectional dependence in the error terms. We also propose a de-randomized decision rule to choose in favor or against the correct specification of a linear factor pricing model. Monte Carlo simulations show that the test has satisfactory properties and it compares favorably to several existing tests. The usefulness of the testing procedure is illustrated through an application of linear factor pricing models to price the constituents of the S&P 500.

Problem

• Tests zero alpha hypothesis in linear factor asset pricing models
• Accommodates non-tradable, latent factors and cross-sectional dependence
• Avoids covariance matrix estimation, works with large N and T

Innovation

• Randomized alpha estimation for zero-alpha test
• No covariance matrix estimation required
• Handles heteroskedasticity and cross-sectional dependence