A general randomized test for Alpha

TL;DR

This paper introduces a flexible, covariance-free randomized testing methodology for zero alpha in asset pricing models, applicable with large N and T, accommodating complex error structures.

Contribution

It develops a novel randomized test for zero alpha that does not require covariance estimation and handles various error dependencies and model complexities.

Findings

Test performs well in simulations, showing good size and power.

Method compares favorably to existing tests in Monte Carlo studies.

Application to S&P 500 demonstrates practical utility.

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.