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Open AccessFeature PaperArticle

Statistical Inference for the Beta Coefficient

Department of Mathematics, Stockholm University, Roslagsvägen 101, SE-10691 Stockholm, Sweden
Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, USA
Department of Economic and Mathematical Modelling, Kyiv National Economic University, Peremoga Avenue 54/1, 03680 Kyiv, Ukraine
Department of Programming, Ivan Franko Lviv National University, Universytetska str. 1, 79000 Lviv, Ukraine
Authors to whom correspondence should be addressed.
Risks 2019, 7(2), 56;
Received: 26 March 2019 / Revised: 24 April 2019 / Accepted: 8 May 2019 / Published: 15 May 2019
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. View Full-Text
Keywords: beta coefficient; sampling distribution; test theory; Wishart distribution beta coefficient; sampling distribution; test theory; Wishart distribution
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Bodnar, T.; Gupta, A.K.; Vitlinskyi, V.; Zabolotskyy, T. Statistical Inference for the Beta Coefficient. Risks 2019, 7, 56.

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