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Statistical Inference for the Beta Coefficient

Author

Listed:
  • Taras Bodnar

    (Department of Mathematics, Stockholm University, Roslagsvägen 101, SE-10691 Stockholm, Sweden)

  • Arjun K. Gupta

    (Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, USA)

  • Valdemar Vitlinskyi

    (Department of Economic and Mathematical Modelling, Kyiv National Economic University, Peremoga Avenue 54/1, 03680 Kyiv, Ukraine)

  • Taras Zabolotskyy

    (Department of Programming, Ivan Franko Lviv National University, Universytetska str. 1, 79000 Lviv, Ukraine)

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.

Suggested Citation

  • Taras Bodnar & Arjun K. Gupta & Valdemar Vitlinskyi & Taras Zabolotskyy, 2019. "Statistical Inference for the Beta Coefficient," Risks, MDPI, vol. 7(2), pages 1-14, May.
    • Handle: RePEc:gam:jrisks:v:7:y:2019:i:2:p:56-:d:231435
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    References listed on IDEAS

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    Cited by:

    1. Pankaj Agrrawal, 2023. "The Gibbons, Ross, and Shanken Test for Portfolio Efficiency: A Note Based on Its Trigonometric Properties," Mathematics, MDPI, vol. 11(9), pages 1-19, May.

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