Statistical Inference for the Beta Coefficient

Bodnar, Taras; Gupta, Arjun K.; Vitlinskyi, Valdemar; Zabolotskyy, Taras

doi:10.3390/risks7020056

Cited by 6 publications

(9 citation statements)

References 23 publications

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“…. , X kt ) ′ the k-dimensional vector of asset returns at time point t, i.e., X it = 100 ln(P it /P i(t−1) ) stands for the return of i-th asset at time point t, where P it denotes the price of the i-th asset at time point t. From [18] assuming that X t follows a weakly stationary process with the mean E(X t ) = µ and the covariance matrix Var(X t ) = Σ we get that the beta coefficient can be calculated in the following way…”

Section: Theoretical Resultsmentioning

confidence: 99%

“…The β-coefficient plays a crucial role in CAPM theory and is an important practical tool for portfolios comparison. In [18] probabilistic properties of the β-coefficient estimator are investigated in the case of constant weights of the compared portfolios. These results are not applicable in the case of the global minimum variance portfolio since the weights of this portfolio depend on unknown parameters of the asset returns distribution.…”

Section: Introductionmentioning

confidence: 99%

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Properties of the beta coefficient of the global minimum variance portfolio

Yaroshko¹,

Zabolotskyy²,

Zabolotskyy³

2020

Math. Model. Comput.

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The paper is devoted to the investigation of statistical properties of the sample estimator of the beta coefficient in the case when the weights of benchmark portfolio are constant and for the target portfolio, the global minimum variance portfolio is taken. We provide the asymptotic distribution of the sample estimator of the beta coefficient assuming that the asset returns are multivariate normally distributed. Based on the asymptotic distribution we construct the confidence interval for the beta coefficient. We use the daily returns on the assets included in the DAX index for the period from 01.01.2018 to 30.09.2019 to compare empirical and asymptotic means, variances and densities of the standardized estimator for the beta coefficient. We obtain that the bias of the sample estimator converges to zero very slowly for a large number of assets in the portfolio. We present the adjusted estimator of the beta coefficient for which convergence of the empirical variances to the asymptotic ones is not significantly slower than for a sample estimator but the bias of the adjusted estimator is significantly smaller.

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Section: Theoretical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Properties of the beta coefficient of the global minimum variance portfolio

Yaroshko¹,

Zabolotskyy²,

Zabolotskyy³

2020

Math. Model. Comput.

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“…Дослідження ймовірнісних властивостей оцінки бета-коефіцієнта різних портфелів фінансових активів проведено у [8]- [11]. Зокрема, в [8] знайдено точний розподіл вибіркової оцінки бета-коефіцієнта за припущення, що ваги портфелів інвестора та еталонного сталі та вектор дохідностей активів портфелів нормально розподілений, а також побудовано статистичний тест та інтервал довіри для бета-коефіцієнта. У [9] результати праці [8] поширено на випадок, коли вектор дохідностей активів поводиться як стаціонарний процес Гауса, а в [10]- [11] -на випадок портфеля інвестора з найменшим рівнем дисперсії та з максимальним відношенням Шарпа відповідно.…”

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Probabilistic Analysis of Beta-Coefficient Sample Estimator for Minimum Value-at-Risk Portfolio

Vitlinskyi,

Zabolotskyy,

Zabolotskyy

et al. 2022

SNOAE

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The problems of financial assets portfolio beta-coefficient diversification and evaluation play an important role among aspects of risk management in the financial institutions activities. The paper is dedicated to statistical properties of the sample estimator of the financial assets minimum Value-at-Risk portfolio beta-coefficient. We assume that the weights of the portfolio benchmark are constant and the vector of portfolio assets returns is multivariate normally distributed. We find an analytical expression for calculating the beta-coefficient if the parameters of the portfolio assets returns distribution vector are known. In practice, these parameters are usually unknown, so we make use of distribution parameters sample estimators. By replacing the unknown parameters in the expression for calculating the beta-coefficient with their sample estimators, we obtain a sample estimator of the beta-coefficient, which is a random variable. We provide an asymptotic distribution of this sample estimator. We investigate the rate of empirical distributions convergence to asymptotic ones using simulation modeling with 100,000 repetitions. We take the corresponding sample estimators as the precise value of the distribution parameters of the portfolio assets returns vector. These estimators are obtained from the data on daily stock prices of companies included in the Dow Jones list for the period from 01.07.2020 to 11.01.2022. Six portfolios with different dimensions ({5, 10, 15, 20, 25, 30} of the first companies from the Dow Jones list sorted in alphabetically order) are considered. We select the equally weighted portfolio for the benchmark portfolio. It is noted that the beta-coefficient sample estimator is significantly biased and the bias increases with the number of assets in portfolio. We propose a corrected estimator whose bias is significantly smaller and does not depend on the number of assets in portfolio. It is concluded that the obtained asymptotic results can be used in practice for modeling the behavior of the sample estimator of the beta-coefficient in the presence of moderate dimension historical data samples (500-1000 observations).

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Nexuses between induction training and on the-job-training on employee job performance: the mediating role of organizational culture

Iddrisu,

Adam

2024

IJOA

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Purpose The study aims to explore the mediating role of organizational culture in the relationship between on-the-job training (OJT), induction training and employee job performance. This study is conceptually grounded in Albert Bandura’s Social Cognitive Theory. The function that organizational culture plays as a mediator in the links between employee performance and on-the-job training and induction is a unique aspect of this study. Design/methodology/approach An industry-wide representation was ensured in the study by using a stratified random sampling technique to choose participants. The main characteristics pertaining to organizational culture, training initiatives and worker job performance were measured by using validated scales from earlier studies. For the purpose of validating the measurement model, factor loadings, internal consistency reliability and discriminant validity were evaluated through the use of partial least squares structural equation modelling in SmartPLS. Findings In support of Bandura’s Social Cognitive Theory, the study’s results show a strong association between work performance, organizational culture, on-the-job training and induction training. The study highlights the positive synergistic effect that supportive organizational culture and well-designed training programmes have on improving employee job performance. The unique contribution of this study is the provision of empirical support for these correlations across a wide range of industries, highlighting the crucial roles that organizational culture plays in promoting employee success. Originality/value Authors’ knowledge of how organizations may create environments that maximize worker productivity and potential is expanded by the study’s practical insights.

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Statistical Inference for the Beta Coefficient

Cited by 6 publications

References 23 publications

Properties of the beta coefficient of the global minimum variance portfolio

Properties of the beta coefficient of the global minimum variance portfolio

Probabilistic Analysis of Beta-Coefficient Sample Estimator for Minimum Value-at-Risk Portfolio

Nexuses between induction training and on the-job-training on employee job performance: the mediating role of organizational culture

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