Стиснена оцінка ваг портфеля з найменшою дисперсією на основі максимізації відношення сподівана дохідність–дисперсія

• Дата: 2026
• Автори: Zabolotskyy, T. M.; Львівський національний університет ім. Івана Франка, Львів, Tsiapa, O. V.; Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України, Львів
• Формат: Стаття
• Опубліковано: Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine 2026
• Теми: математичне моделювання; статистичний аналіз; вибіркова оцінка; портфель; ризик; математичні методи; оцінка параметра; консистент-ність; УДК 519.2: 336.7
• Онлайн доступ: http://journals.iapmm.lviv.ua/ojs/index.php/APMM/article/view/3661
• Назва журналу: Prykladni Problemy Mekhaniky i Matematyky

The paper is dedicated to the problem of estimating the global minimum variance portfolio weights in the case of high-dimensional problems, i.e. when the sample size of the historical values of the asset return vector and its dimension are commensurate. The paper proposes a shrinkage estimator of the global minimum variance portfolio weights, which is based on maximization of the out-of-sample expected return–variance ratio. The method does not require any assumption about the distribution of the asset returns. Two cases are considered: the ratio of the number of portfolio assets to the sample size of historical values is less than one, the ratio of the number of portfolio assets to the sample size of historical values is greater than one. In the second case, a generalized inverse matrix is used to construct the inverse covariance matrix of the asset return vector. An analytical expression for shrinkage intensity is found, and since the shrinkage intensity depends on the distribution parameters of the asset return vector, in the paper consistent estimators for the shrinkage intensity are constructed in both cases. Based on the obtained consistent estimators of shrinkage intensity, consistent shrinkage estimators of global minimum variance portfolio weights are proposed. Based on simulation modeling, the behavior of shrinkage intensity and the difference between out-of-sample expected return-variance ratios of shrinkage and sample estimators are investigated, depending on the value of the ratio of the number of portfolio assets to the sample size of historical values and the maximum eigenvalue of the covariance matrix of the asset returns vector. It is noted that when the ratio of the number of portfolio assets to the sample size of historical values is close to 0, the out-of-sample expected return-variance ratios of both estimators are comparable, but with an increase in the value of the ratio, the estimator proposed in the paper is significantly more effective. Cite as: T. M. Zabolotskyy, O. V. Tsiapa, “Shrinkage estimator of the global minimum variance portfolio weights based on maximization of the expected return–variance ratio,” Prykl. Probl. Mekh. Mat., Issue 23, 94–105 (2025) (in Ukrainian), https://doi.org/10.15407/apmm2025.23.94-105