U.A. Bachaev1, N.V. Grineva2
1 National Research University Higher School of Economics (HSE) (Moscow, Russia)
2 Financial University under the Government of the Russian Federation (Moscow, Russia)
1 uabachaev@edu.hse.ru, 2 ngrineva@fa.ru
The question of constructing an optimal securities portfolio is one of the most well-known in the tasks of modeling economic processes. This issue is particularly acute during the economic shocks, which the world economy has been facing lately more and more often. This is due to the impossibility of using classical modeling methods in such periods and the need to apply more sophisticated approaches, such as copula functions. As opposed to classical models, copulas take into consideration multivariate data structure and tails of asset yield distributions, this helps to better account for the risk of large portfolio losses. There are few scientific works devoted to this problem in Russian literature and it is impossible not to mention the relevance of the present article. The purpose of the research is to describe and test a portfolio optimization model taking into account multidimensional assets structure using copula functions. By the example of a portfolio of 10 shares of domestic companies the effectiveness of the model will be considered and a conclusion on its applicability will be made. The R language and its copula packages are used to implement and test the algorithm.
Bachaev U.A, Grineva N.V. Modeling of multidimensional asset structure in the portfolio optimization based on copulas. Information-measuring and Control Systems. 2023. V. 21. № 6. P. 16−28. DOI: https://doi.org/10.18127/j20700814-202306-03 (in Russian)
- Alekseev V.V., Shokolov V.V., Solozhentsev E.D. Logiko-veroyatnostnoe modelirovanie portfelya tsennykh bumag s ispolzovaniem kopul. Upravlenie finansovymi riskami. 2006. № 3. S. 272–283. (in Russian)
- Blagoveshchenskiй Yu.N. Osnovnye elementy teorii kopul. Prikladnaya ekonometrika. 2012. 26 (2). S 113–130. (in Russian)
- Kritskiй O.L., Ulyanova M.K. Opredelenie mnogomernogo finansovogo riska portfelya aktsiй. Prikladnaya ekonometrika. 2007. 8 (4). S. 3–17. (in Russian)
- Fantatstsini D. Ekonometricheskii analiz finansovykh dannykh v zadachakh upravleniya riskom. Prikladnaya ekonometrika. 2008. № 2 (10). S. 91–137. (in Russian)
- Fantatstsini D. Modelirovanie mnogomernykh raspredelenii s ispolzovaniem kopula-funktsii. I. Prikladnaya ekonometrika. 2011a. 22 (2). S. 98–134. (in Russian)
- Fantatstsini D. Modelirovanie mnogomernykh raspredelenii s ispolzovaniem kopula-funktsii. II. Prikladnaya ekonometrika. 2011b. 23 (3). S. 98–132. (in Russian)
- Fantatstsini D. Modelirovanie mnogomernykh raspredelenii s ispolzovaniem kopula-funktsii. III. Prikladnaya ekonometrika. 2011c. 25 (4). S. 100–130. (in Russian)
- Fang K., Kotz S., Ng K. Symmetric multivariate and related distributions. London: Chapman Hall. 1987.
- Fantazzini D. Dynamic copula modeling for Value at Risk. Frontiers in Finance and Economics. 2006. 2 (5). P. 1–38.
- Gumbel E.J. Bivariate exponential distributions. Journal of the American Statistal Association. 1960. 55. P. 698 – 707.
- Hennessy D., Lapan H. The Use of Archimedean Copulas to Model Portfolio Allocations. Mathematical Finance. 2002. № 12. P. 143–154.
- Markowitz H. Portfolio selection. Journal of Finance. 1952. № 7. P. 77–91.
- Nelsen R. An introduction to copulas. Lecture Notes in Statistics. New York: Springer-Verlag. 1999.
- Sklar A. Fonctions de répartition á n dimensions et leurs marges. Publ. Inst. Statis. Univ. Paris. 1959. 8. P. 229–231.
- Sklar A. Random variables. distribution functions. and copulas: Personal look backward and forward. Lecture notes. Monograph series. 1996. 28. P. 1–14.