DEA STRATEGIES IN INTERNATIONAL PORTFOLIO INVESTMENT
Main Article Content
Abstract
Introduction. International investment activity in the global economy determines the development of countries, regions, and corporations. Its flexibility and efficiency enable improvements in competitiveness, market expansion, and the formation of global economic networks. In modern international investment management, it is crucial to make timely decisions regarding portfolio diversification, analyze key financial and economic indicators when assessing its risks and profitability.
Purpose. The purpose of the article is to develop new DEA-based evaluation methods for the studied objects that do not require solving linear and quadratic programming tasks.
Results. The proposed methods make it possible to evaluate the position of the studied objects relative to the convex hull of their states and virtual extreme points. These methods were tested on a sample of twenty exchange-traded funds (ETFs). The input indicators selected were annual indices of total asset value and fund share prices. The study was conducted in two alternative coordinate systems: logarithms of the indices and exponents of growth rates. The proposed methods identified the optimal object for portfolio investment. A combined portfolio was examined, consisting of investments in the optimal ETF and another efficient fund adjacent to it on the convex hull. Using the proposed methods, alternative structures of combined portfolios were identified and compared. It was found that the combined portfolios constructed based on deviations from virtual extreme states were very similar in structure and contained a significantly larger share of the optimal fund. In combined portfolios constructed based on differences in the areas of opposite parts of the studied set, the share of the optimal fund slightly exceeded 50%.
Originality. A rectangle was constructed around the convex hull of the studied objects.
According to the selected indicators, the upper right part of the convex hull, along with the adjacent segments of the sides of the described rectangle, is considered as the frontier of zero-order efficiency. The frontiers of lower (negative) orders of efficiency are formed by successively subtracting from the investigated set those objects located on the previous frontier. Similarly, the lower left part of the convex hull, together with the adjacent segments of the sides of the described rectangle, is regarded as the frontier of zero-order inefficiency. The inefficiency frontiers of higher (positive) orders are formed by successively subtracting from the investigated set those objects located on the previous frontier.
The efficiency frontier where a specific object is located and the zero-order (worst) inefficiency frontier form a polygon whose area characterizes the deviation of this object from the inefficient set. Similarly, the inefficiency frontier where a specific object is located and the zero-order (best) efficiency frontier form a polygon whose area characterizes the deviation of this object from the efficient set. It has been demonstrated that the relative difference in these areas, the relative difference in the functions of these areas, and the function of the area difference can be used as a basis for forming a combined investment portfolio.
The opposite vertices of the rectangle enclosing the convex hull of the investigated objects are interpreted as the best ("ideal") and worst ("horrible") virtual states. The diagonal connecting these states intersects the set of real states, efficiency frontiers, and inefficiency frontiers. The segment of the zero-efficiency frontier through which the diagonal of the extreme virtual states passes is considered distinguished. It has been shown that as alternative bases for forming a combined investment portfolio, the function of the differences in Euclidean distances of a specific object to the extreme virtual states and the function of the difference in the squares of these distances can be used. It has been found that for better comparability of portfolios formed on alternative planes, it is advisable to use inverse functions—exponential on a logarithmic plane and logarithmic on an exponential plane.
Conclusion. The proposed approach can be generalized in several directions. The first direction of such generalization is increasing the dimensionality of the DEA model by incorporating data on other indicators of companies’ financial status. The second direction of generalization of the proposed model is transitioning from elementary indices characterizing the performance of exchange-traded investment funds to statistical parameters reflecting their correlations with the market as a whole. The third direction of generalization can reflect the time factor. Another potential direction of generalization involves creating a "paramodel" in which the coordinates represent certain properties of the investigated financial investment models—for example, their reliability (forecast error), cost of creation, and use of the model. The proposed DEA evaluation methods can also be applied to studies of the primary securities market, commodity markets, and operational management of companies in the real sector. Non-financial companies can utilize them in their business planning and assessment of the efficiency of their internal divisions.
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