The Permutation Test for Event Studies When the Number of Firms Is Small
ADIA Lab Research Paper Series
Authors:
Phuong Anh Nguyen
International University - Vietnam National University of Ho Chi Minh City
Michael Wolf
University of Zurich - Department of Economics; ADIA Lab
Date Written: November 25, 2025
In this research paper, Phuong Anh Nguyen & Professor Michael Wolf examine a fundamental challenge in empirical finance: how to conduct reliable event studies when the number of firms under analysis is too small for conventional statistical methods to apply.
While grounded in financial econometrics, this research contributes to the broader toolkit of nonparametric and simulation-based methods that underpin robust empirical validation in data-constrained, algorithm-driven financial analysis.
Traditional tests of average abnormal returns (AAR) and cumulative average abnormal returns (CAAR) rely on large-sample assumptions, typically invoking central limit theorems that break down when only a handful of firms—or even just two—are available. In such settings, widely used parametric and nonparametric tests can become ineffective or entirely uninformative.
To address this gap, the authors propose a nonparametric permutation testing framework that remains valid for arbitrarily small samples. The approach constructs exact or near-exact finite-sample inference without relying on asymptotic approximations, making it particularly well suited to niche event studies, policy shocks affecting limited firms, or tightly defined market events.
The paper develops an alternative test statistic tailored to cumulative abnormal returns, details the permutation procedure, and evaluates its finite-sample performance through extensive Monte Carlo simulations. The methodology is further demonstrated using two empirical applications based on real financial data, highlighting its practical relevance alongside its theoretical contribution.
By extending permutation testing techniques to multi-firm event studies with very small samples, this research provides a robust and flexible tool for empirical analysis in finance and economics where data limitations would otherwise preclude formal statistical testing.
