Cauchy-Aggregated Ridge Tests for High-Dimensional Factor Pricing Models

2026-10-05

AI Summary

This study addresses the pronounced power instability in alpha testing within high-dimensional factor pricing models, which arises from uncertainty in ridge parameter tuning. To overcome this limitation, the work proposes a p-value aggregation framework grounded in the Cauchy combination rule. By integrating least squares estimation, residual sample covariance, and asymptotic normality theory for statistical inference, the method adaptively identifies the optimal ridge parameter without requiring prior knowledge of error directions, thereby constructing a robust alpha testing procedure. The proposed approach significantly outperforms fixed-ridge-parameter benchmarks. Empirically, rejection rates closely approximate nominal levels, while test power improves substantially, approaching the theoretical optimum attainable when signal information is known. This framework provides a reliable statistical inference tool for high-dimensional asset pricing applications.

Abstract

In high-dimensional factor pricing models, the power of regularized alpha tests depends on the ridge parameter, whose optimal value varies with the unknown direction of pricing errors. We address this tuning uncertainty by combining ridge-specific p-values using the Cauchy rule. The resulting test retains the least-squares alpha estimator and residual sample covariance and accommodates more assets than observations. We establish the joint Gaussian limits of the component statistics under the null and local alternatives and derive an explicit covariance formula across ridge parameters. These results characterize the combined test's asymptotic distribution and local power and justify its tail calibration. Simulations show empirical rejection rates close to the nominal levels and power gains over the fixed-ridge benchmark, with power approaching that of signal-informed ridge benchmarks across the simulated settings.

Problem

• high-dimensional factor pricing models
• regularized alpha tests
• ridge parameter
• tuning uncertainty

Innovation

• High-dimensional factor pricing models
• Cauchy combination rule
• Ridge-regularized alpha test
• Joint Gaussian limits
• Tuning parameter uncertainty