Statistical Inference for the Beta Coefficient
Date
2019-06
Journal Title
Journal ISSN
Volume Title
Publisher
MDPI AG
Abstract
The beta coefficient plays a crucial role in finance as a risk measure of a portfolio in
comparison to the benchmark portfolio. In the paper, we investigate statistical properties of the
sample estimator for the beta coefficient. Assuming that both the holding portfolio and the benchmark
portfolio consist of the same assets whose returns are multivariate normally distributed, we provide
the finite sample and the asymptotic distributions of the sample estimator for the beta coefficient.
These findings are used to derive a statistical test for the beta coefficient and to construct a confidence
interval for the beta coefficient. Moreover, we show that the sample estimator is an unbiased estimator
for the beta coefficient. The theoretical results are implemented in an empirical study.
Description
Keywords
beta coefficient, sampling distribution, test theory, Wishart distribution
Citation
Statistical Inference for the Beta Coefficient / Taras Bodnar, Arjun K. Gupta, Valdemar Vitlinskyi, Taras Zabolotskyy // Risks. – 2019. – Vol. 7, Iss. 2, June. – P. 1–14.