Properties of the beta coefficient of the global minimum variance portfolio
| dc.citation.epage | 21 | |
| dc.citation.issue | 1 | |
| dc.citation.spage | 11 | |
| dc.contributor.affiliation | Національний університет “Львівська політехніка” | |
| dc.contributor.affiliation | Львівський національний університет імені Івана Франка | |
| dc.contributor.affiliation | Lviv Polytechnic National University | |
| dc.contributor.affiliation | Ivan Franko National University of Lviv | |
| dc.contributor.author | Ярошко, С. М. | |
| dc.contributor.author | Заболоцький, М. В. | |
| dc.contributor.author | Заболоцький, Т. М. | |
| dc.contributor.author | Yaroshko, S. M. | |
| dc.contributor.author | Zabolotskyy, M. V. | |
| dc.contributor.author | Zabolotskyy, T. M. | |
| dc.coverage.placename | Львів | |
| dc.coverage.placename | Lviv | |
| dc.date.accessioned | 2023-10-03T09:31:45Z | |
| dc.date.available | 2023-10-03T09:31:45Z | |
| dc.date.created | 2021-03-01 | |
| dc.date.issued | 2021-03-01 | |
| dc.description.abstract | Стаття присвячена дослідженню статистичних властивостей вибіркової оцінки бета коефіцієнта у випадку, коли ваги еталонного портфеля є постійні, а цільовим є портфель з найменшою дисперсією. Знайдено асимптотичний розподіл вибіркової оцінки бета коефіцієнта за припущення, що вектор дохідностей активів має багатовимірний нормальний розподіл. На основі асимптотичного розподілу побудовано довірчий інтервал для бета коефіцієнта. Використовуючи щоденні дохідності акцій, включених до індексу DAX за період з 01.01.2018 по 30.09.2019, порівняно емпіричні та асимптотичні середні, дисперсії та щільності стандартизованої вибіркової оцінки бета коефіцієнта. Зауважено, що для великої кількості активів у портфелі зміщення стандартизованої вибіркової оцінки бета коефіцієнта збігається до нуля дуже повільно. Представлено скориговану оцінку бета коефіцієнта, для якої збіжність емпіричних дисперсій до асимптотичних не є значно повільнішою, ніж для вибіркової оцінки, але зміщення скоригованої оцінки є істотно меншим. | |
| dc.description.abstract | 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. | |
| dc.format.extent | 11-21 | |
| dc.format.pages | 11 | |
| dc.identifier.citation | Yaroshko S. M. Properties of the beta coefficient of the global minimum variance portfolio / S. M. Yaroshko, M. V. Zabolotskyy, T. M. Zabolotskyy // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2021. — Vol 8. — No 1. — P. 11–21. | |
| dc.identifier.citationen | Yaroshko S. M. Properties of the beta coefficient of the global minimum variance portfolio / S. M. Yaroshko, M. V. Zabolotskyy, T. M. Zabolotskyy // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2021. — Vol 8. — No 1. — P. 11–21. | |
| dc.identifier.doi | doi.org/10.23939/mmc2021.01.011 | |
| dc.identifier.uri | https://ena.lpnu.ua/handle/ntb/60326 | |
| dc.language.iso | en | |
| dc.publisher | Видавництво Львівської політехніки | |
| dc.publisher | Lviv Politechnic Publishing House | |
| dc.relation.ispartof | Mathematical Modeling and Computing, 1 (8), 2021 | |
| dc.relation.references | [1] Markowitz H. Portfolio selection. Journal of finance. 7, 77–91 (1952). | |
| dc.relation.references | [2] Merton R. C. An analytical derivation of the efficient frontier. Journal of financial and quantitative analysis. 7 (4), 1851–1872 (1972). | |
| dc.relation.references | [3] Okhrin Y., SchmidW. Distributional properties of optimal portfolio weights. Journal of econometrics. 134 (1), 235–256 (2006). | |
| dc.relation.references | [4] Okhrin Y., SchmidW. Estimation of optimal portfolio weights. International journal of theoretical and applied finance. 11 (3), 249–276 (2008). | |
| dc.relation.references | [5] Ingersoll J. E. Theory of financial decision making. New York, Rowman & Littlefield Publishers (1987). | |
| dc.relation.references | [6] SharpeW. F. The Sharpe ratio. The journal of portfolio management. 21 (1), 49–58 (1994). | |
| dc.relation.references | [7] SchmidW., Zabolotskyy T. On the existence of unbiased estimators for the portfolio weights obtained by maximizing the Sharpe ratio. ASTA - Advances in Statistical Analysis. 92, 29–34 (2008). | |
| dc.relation.references | [8] Bodnar T., Zabolotskyy T. Maximization of the Sharpe ratio of an asset portfolio in the context of risk minimization. Economic annals - ХХI. 11-12 (1), 110–113 (2013). | |
| dc.relation.references | [9] Bodnar T., Zabolotskyy T. How risky is the optimal portfolio which maximizes the Sharpe ratio? ASTA -Advances in statistical analysis. 101 (1), 1–28 (2017). | |
| dc.relation.references | [10] Alexander G. J., Baptista M. A. Economic implication of using a mean-VaR model for portfolio selection: a comparison with mean-variance analysis. Journal of economic dynamics & control. 26 (7-8), 1159–1193 (2002). | |
| dc.relation.references | [11] Alexander G. J., Baptista M. A. A comparison of VaR and CVaR constraints on portfolio selection with the mean-variance model. Management Science. 50 (9), 1261–1273 (2004). | |
| dc.relation.references | [12] Bodnar T., SchmidW., Zabolotskyy T. Minimum VaR and Minimum CVaR optimal portfolios: estimators, confidence regions, and tests. Statistics & Risk Modeling. 29 (4), 281–314 (2012). | |
| dc.relation.references | [13] Bodnar T., SchmidW. A test for the weights of the global minimum variance portfolio in an elliptical model. Metrika. 67, 12–143 (2008). | |
| dc.relation.references | [14] Bodnar T., Mazur S., Okhrin Y. Bayesian estimation of the global minimum variance portfolio. European journal of operational research. 256 (1), 292–307 (2017). | |
| dc.relation.references | [15] Kan R., Smith D. R. The distribution of the sample minimum-variance frontier. Management. 54 (7), 1364–1380 (2008). | |
| dc.relation.references | [16] Chan L. K. C., Karceski J., Lakonishok J. On portfolio optimization: forecasting and choosing the risk model. The review of financial study. 12 (5), 937–974 (1999). | |
| dc.relation.references | [17] Bodnar T., SchmidW. Econometrical analysis of the sample efficient frontier. The European journal of finance. 15 (3), 317–335 (2009). | |
| dc.relation.references | [18] Bodnar T., Gupta A. K., Vitlinskiy V., Zabolotskyy T. Statistical inference for the β coefficient. Risks. 7 (2), 56 (2019). | |
| dc.relation.references | [19] Markowitz H. Foundations of portfolio theory. Journal of finance. 7, 469–477 (1991). | |
| dc.relation.references | [20] Ling S., McAleer M. Asymptotic theory for a vector ARMA-GARCH model. Econometric theory. 19 (2), 280–310 (2003). | |
| dc.relation.references | [21] Harville D. A. Matrix algebra from a statistician’s perspective. New York, Springer Science+Business Media (2008). | |
| dc.relation.references | [22] Brockwell P. J., Davis R. A. Time series: theory and methods. New York, Springer Science+Business Media (2006). | |
| dc.relation.references | [23] DasGupta A. Asymptotic theory of statistics and probability. New York, Springer (2008). | |
| dc.relation.references | [24] Muirhead R. J. Aspects of multivariate statistical theory. New York, Wiley (1982). | |
| dc.relation.referencesen | [1] Markowitz H. Portfolio selection. Journal of finance. 7, 77–91 (1952). | |
| dc.relation.referencesen | [2] Merton R. C. An analytical derivation of the efficient frontier. Journal of financial and quantitative analysis. 7 (4), 1851–1872 (1972). | |
| dc.relation.referencesen | [3] Okhrin Y., SchmidW. Distributional properties of optimal portfolio weights. Journal of econometrics. 134 (1), 235–256 (2006). | |
| dc.relation.referencesen | [4] Okhrin Y., SchmidW. Estimation of optimal portfolio weights. International journal of theoretical and applied finance. 11 (3), 249–276 (2008). | |
| dc.relation.referencesen | [5] Ingersoll J. E. Theory of financial decision making. New York, Rowman & Littlefield Publishers (1987). | |
| dc.relation.referencesen | [6] SharpeW. F. The Sharpe ratio. The journal of portfolio management. 21 (1), 49–58 (1994). | |
| dc.relation.referencesen | [7] SchmidW., Zabolotskyy T. On the existence of unbiased estimators for the portfolio weights obtained by maximizing the Sharpe ratio. ASTA - Advances in Statistical Analysis. 92, 29–34 (2008). | |
| dc.relation.referencesen | [8] Bodnar T., Zabolotskyy T. Maximization of the Sharpe ratio of an asset portfolio in the context of risk minimization. Economic annals - KhKhI. 11-12 (1), 110–113 (2013). | |
| dc.relation.referencesen | [9] Bodnar T., Zabolotskyy T. How risky is the optimal portfolio which maximizes the Sharpe ratio? ASTA -Advances in statistical analysis. 101 (1), 1–28 (2017). | |
| dc.relation.referencesen | [10] Alexander G. J., Baptista M. A. Economic implication of using a mean-VaR model for portfolio selection: a comparison with mean-variance analysis. Journal of economic dynamics & control. 26 (7-8), 1159–1193 (2002). | |
| dc.relation.referencesen | [11] Alexander G. J., Baptista M. A. A comparison of VaR and CVaR constraints on portfolio selection with the mean-variance model. Management Science. 50 (9), 1261–1273 (2004). | |
| dc.relation.referencesen | [12] Bodnar T., SchmidW., Zabolotskyy T. Minimum VaR and Minimum CVaR optimal portfolios: estimators, confidence regions, and tests. Statistics & Risk Modeling. 29 (4), 281–314 (2012). | |
| dc.relation.referencesen | [13] Bodnar T., SchmidW. A test for the weights of the global minimum variance portfolio in an elliptical model. Metrika. 67, 12–143 (2008). | |
| dc.relation.referencesen | [14] Bodnar T., Mazur S., Okhrin Y. Bayesian estimation of the global minimum variance portfolio. European journal of operational research. 256 (1), 292–307 (2017). | |
| dc.relation.referencesen | [15] Kan R., Smith D. R. The distribution of the sample minimum-variance frontier. Management. 54 (7), 1364–1380 (2008). | |
| dc.relation.referencesen | [16] Chan L. K. C., Karceski J., Lakonishok J. On portfolio optimization: forecasting and choosing the risk model. The review of financial study. 12 (5), 937–974 (1999). | |
| dc.relation.referencesen | [17] Bodnar T., SchmidW. Econometrical analysis of the sample efficient frontier. The European journal of finance. 15 (3), 317–335 (2009). | |
| dc.relation.referencesen | [18] Bodnar T., Gupta A. K., Vitlinskiy V., Zabolotskyy T. Statistical inference for the b coefficient. Risks. 7 (2), 56 (2019). | |
| dc.relation.referencesen | [19] Markowitz H. Foundations of portfolio theory. Journal of finance. 7, 469–477 (1991). | |
| dc.relation.referencesen | [20] Ling S., McAleer M. Asymptotic theory for a vector ARMA-GARCH model. Econometric theory. 19 (2), 280–310 (2003). | |
| dc.relation.referencesen | [21] Harville D. A. Matrix algebra from a statistician’s perspective. New York, Springer Science+Business Media (2008). | |
| dc.relation.referencesen | [22] Brockwell P. J., Davis R. A. Time series: theory and methods. New York, Springer Science+Business Media (2006). | |
| dc.relation.referencesen | [23] DasGupta A. Asymptotic theory of statistics and probability. New York, Springer (2008). | |
| dc.relation.referencesen | [24] Muirhead R. J. Aspects of multivariate statistical theory. New York, Wiley (1982). | |
| dc.rights.holder | © Національний університет “Львівська політехніка”, 2021 | |
| dc.subject | портфель з найменшою дисперсією | |
| dc.subject | бета коефіцієнт | |
| dc.subject | теорія тестування | |
| dc.subject | асимптотичний розподіл | |
| dc.subject | невизначеність параметрів | |
| dc.subject | global minimum variance portfolio | |
| dc.subject | beta coefficient | |
| dc.subject | test theory | |
| dc.subject | asymptotic distribution | |
| dc.subject | parameter uncertainty | |
| dc.subject | sample estimator | |
| dc.title | Properties of the beta coefficient of the global minimum variance portfolio | |
| dc.title.alternative | Властивості бета коефіцієнта портфеля з найменшою дисперсією | |
| dc.type | Article |
Files
License bundle
1 - 1 of 1