Modeling the Sample Estimator of the Beta-Coefficient of the Constant Weights Portfolio Under Autocorrelation of the Asset Returns ; Моделювання вибіркової оцінки бета-коефіцієнта портфеля зі сталими вагами за наявності автокореляції дохідностей активів

The paper is dedicated to the study of the properties of the sample estimator of the betacoefficientin the case when the benchmark and investors’ portfolios consist of the same assets and theirweights are constant. The beta-coefficient is one of the tools most frequently used for systematic riskmeasurement. It indicates whether systematic risk of investor’s portfolio is higher or lower than the risk ofsome benchmark portfolio. In general, it depends on the parameters of the distribution of the asset returnsvector that are unknown in practice. That is why we operate with estimators which are random variables.We use the following assumption concerning the vector of the asset returns included into the benchmark andinvestors’ portfolios: it is multivariate normally distributed and it is autocorrelated. Under this assumption,the asymptotic distribution of the sample estimator of the beta-coefficient is found. For simulation studywith 100,000 repetitions, we use vector autoregressive process with normally distributed residuals of orderp for modelling the behavior of the asset returns vector. The true values of the parameters of the consideredmodel of the asset returns vector behavior are taken as the corresponding estimators from the sample ofhistorical values of daily returns of assets included into the Dow Jones index for the period from January01, 2017 to April 14, 2021. For the benchmark portfolio, we take the DJIA portfolio as of April 14, 2021.For the investors portfolio we take the equally-weighted portfolio of six dimensions, viz. {5, 10, 15, 20, 25,30}, which consists of the corresponding first k assets included into the Dow Jones index in the alphabeticalorder. It is shown that, according to our assumption, the asymptotic density provides good approximation tothe empiric density even for sample size equal to 120 observations.Keywords: beta-coefficient, assets portfolio, sample estimator, asymptotic distribution, simulationstudy. ; Анотація. Стаття присвячена дослідженню властивостей вибіркової ...