Иерархическая кластеризация как метод снижения размерности в задаче оптимизации инвестиционного портфеля Марковица

Optimal portfolio selection is a common and important application of an optimization problem. Practical applications of an existing optimal portfolio selection methods is often difficult due to high data dimensionality (as a consequence of the large number of securities available for investment). In this paper, a method of dimension reduction based on hierarchical clustering is proposed. Clustering is widely used in computer science, a lot of algorithms and computational methods have been developed for it. As a measure of securities proximity for hierarchical clustering Pearson pair correlation coefficient is used. Further, the proposed method’s influence on the quality of the optimal solution is investigated on several examples of optimal portfolio selection according to the Markowitz Model. The influence of hierarchical clustering parameters (intercluster distance metrics and clustering threshold) on the quality of the obtained optimal solution is also investigated. The dependence between the target return of the portfolio and the possibility of reducing the dimension using the proposed method is investigated too. For each considered example in the paper graphs and tables with the main results of the proposed method - application which are the decrease of the dimension and the drop of the yield (the decrease of the quality of the optimal solution) - for a portfolio constructed using the proposed method compared to a portfolio constructed without the proposed method are given. For the experiments the Python programming language and its libraries: scipy for clustering and cvxpy for solving the optimization problem (building an optimal portfolio) are used.Составление оптимального портфеля ценных бумаг является важным и частым случаем решения задачи оптимизации. Практическое применение существующих методов составления оптимального портфеля часто затруднено из-за большого числа доступных для инвестирования ценных бумаг (и, как следствие, большой размерности исходных данных). В данной работе предлагается метод снижения размерности исходных данных, основанный на иерархической кластеризации доступных для инвестирования ценных бумаг. Для кластеризации, широко используемой в компьютерных науках, уже разработано множество алгоритмов и методов. В качестве меры близости ценных бумаг для иерархической кластеризации используется коэффициент парной корреляции Пирсона. Далее исследуется влияние предложенного метода на качество получаемого оптимального решения на нескольких примерах составления оптимального портфеля ценных бумаг по модели Марковица. Также исследуется влияние параметров иерархической кластеризации (метрики межкластерного расстояния и порогового значения кластеризации) на изменение качества получаемого оптимального решения. Исследуется зависимость между целевой доходностью портфеля и возможностью снижения размерности с помощью предложенного метода. Для каждого рассмотренного примера приводятся графики и таблицы с основными полученными результатами применения метода — понижением размерности и падением доходности (снижением качества оптимального решения) у портфеля, построенного с применением предложенного метода по сравнению с портфелем, построенным без применения предложенного метода. Для проведения экспериментов используется язык программирования Python и его библиотеки: scipy для проведения кластеризации и cvxpy для решения задачи оптимизации (построения оптимального портфеля)

Hierarchical Clustering as a Dimension Reduction Technique for Markowitz Portfolio Optimization

Optimal portfolio selection is a common and important application of an optimization problem. Practical applications of an existing optimal portfolio selection methods is often difficult due to high data dimensionality (as a consequence of the large number of securities available for investment). In this paper, a method of dimension reduction based on hierarchical clustering is proposed. Clustering is widely used in computer science, a lot of algorithms and computational methods have been developed for it. As a measure of securities proximity for hierarchical clustering Pearson pair correlation coefficient is used. Further, the proposed method’s influence on the quality of the optimal solution is investigated on several examples of optimal portfolio selection according to the Markowitz Model. The influence of hierarchical clustering parameters (intercluster distance metrics and clustering threshold) on the quality of the obtained optimal solution is also investigated. The dependence between the target return of the portfolio and the possibility of reducing the dimension using the proposed method is investigated too. For each considered example in the paper graphs and tables with the main results of the proposed method - application which are the decrease of the dimension and the drop of the yield (the decrease of the quality of the optimal solution) - for a portfolio constructed using the proposed method compared to a portfolio constructed without the proposed method are given. For the experiments the Python programming language and its libraries: scipy for clustering and cvxpy for solving the optimization problem (building an optimal portfolio) are used

Structure, Conductivity, and Sensor Properties of Nanosized ZnO-In₂O₃ Composites: Influence of Synthesis Method

The influence of the method used for synthesizing ZnO-In2O3 composites (nanopowder mixing, impregnation, and hydrothermal method) on the structure, conductivity, and sensor properties is investigated. With the nanopowder mixing, the size of the parent nanoparticles in the composite remains practically unchanged in the range of 50–100 nm. The impregnation composites consist of 70 nm In2O3 nanoparticles with ZnO nanoclusters 2 is 1.3–1.5 times higher than the response of the mixed composite. Additives of 15–20 and 85 wt.% ZnO to mixed and impregnated composites lead to an increase in the response compared with pure In2O3. In the case of hydrothermal composite, up to 20 wt.% ZnO addition leads to a decrease in response, but 65 wt.% ZnO addition increases response by almost two times compared with pure In2O3. The sensor activity of a hydrothermal composite depends on the phase composition of In2O3. The maximum efficiency is reached for the composite containing cubic In2O3 and the minimum for rhombohedral In2O3. An explanation is provided for the observed effects