U.S. Stock Returns, the Berry-Esseen Theorem, and Statistical Testing

38 Pages Posted: 27 Jul 2020

See all articles by Timothy Falcon Crack

Timothy Falcon Crack

University of Otago - Department of Accountancy and Finance

Lynn McAlevey

University of Otago - Department of Accountancy and Finance

Anindya Sen

University of Otago - Department of Accountancy and Finance

Date Written: February 4, 2020

Abstract

Neither existing theory nor prior empirical work can tell us the impact of non-normality on required sample sizes for Student-t tests of the mean in U.S. stock returns. Prior empirical work and bounds from a modified Berry-Esseen theorem do suggest, however, that the answer should vary with market capitalization, driven by third moments. For two-tailed nominally 5%-sized one-sample tests, we find that at least 100 observations are needed for large-capitalization stocks, and at least 200 observations are needed for small-capitalization stocks. Larger sample sizes are required for significance levels below 5%, or if one-tailed tests are used with skewed data.

Keywords: Berry-Esseen Theorem, Central Limit Theorem, Kurtosis, Size Effect, Skewness

JEL Classification: B23, C12, C46, C58, G12

Suggested Citation

Crack, Timothy Falcon and McAlevey, Lynn and Sen, Anindya, U.S. Stock Returns, the Berry-Esseen Theorem, and Statistical Testing (February 4, 2020). Available at SSRN: https://ssrn.com/abstract=3641266 or http://dx.doi.org/10.2139/ssrn.3641266

Timothy Falcon Crack (Contact Author)

University of Otago - Department of Accountancy and Finance ( email )

Dunedin
New Zealand

Lynn McAlevey

University of Otago - Department of Accountancy and Finance ( email )

Dunedin
New Zealand

Anindya Sen

University of Otago - Department of Accountancy and Finance ( email )

PO Box 56
Dunedin, 9054
New Zealand

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