Cite this article as:

Vygodchikova I. Y., Selivanova A. A. Investment Portfolio Risk Assessment on the Basis of Hierarchical Model. Izv. Saratov Univ. (N. S.), Ser. Economics. Management. Law, 2016, vol. 16, iss. 1, pp. 80-?. DOI:


Investment Portfolio Risk Assessment on the Basis of Hierarchical Model

Introduction. Efficiency of investments is an important factor at the micro- and macroanalysis of economy, investment in venture capital depends on the development of firms, regions, States. Especially actual this problem for portfolio investment. The aim of this work is to develop a new minimax method for modeling the dynamics of risk of portfolio investment, which allows to assess the distribution of equity is a structural component of a financial portfolio.

Methods. Suggested new method for modeling and rationalizing the structure of equity investments using the minimax criterion. Drill through the decision of the investor as from the original portfolio preferences, specific risk assessments for each lower level in the hierarchy (topdown) and a calculation of expediency of inclusion in the portfolio of each asset of the lower level, with specific risk assessments (bottomup), which is consistent with the approaches of fundamental analysis of securities market. Provided step-by-step algorithm for grouping, clustering and data analysis along the branches of the hierarchy.

Results. Is developed the scheme the implementation of the model for a three-tier structure for complete binary decision tree. Is given the iterative computational algorithm and its implementation.

Conclusion. The recommendations can be applied to rationalize the funding of innovations that improve the quality of development of regions in the rehabilitation plan for selected executives of corporate sector.


1. Firsovа A. A. Teoriia i metodologiia investirovaniia innovatsionnoi deiatel’nosti na osnove gosudarstvennochastnogo partnerstva [Theory and Methodology of investment innovation through public-private partnership]. Saratov, Saratov Univ. Press, 2012. 320 p.
2. Vygodchikova I. Yu. O primenenii minimaksnoi modeli dlya ratsionalizatsii raskhodov potrebitelya [On the application of the minimax model for rationalization expenses of the consumer]. Izv. Saratov Univ. (N.S.), Ser. Economics. Management. Law, 2014, vol. 14, iss. 1, pt. 1, pp. 96–100.
3. Vygodchikova I. Yu. O modelirovanii dolevoi struktury fi nansirovaniya premial’nykh vyplat s ispol’zovaniem minimaksnogo kriteriya kachestva [About the Modeling of the Shared Structure of Finances Using the Minimax Criterion of Laboriousness]. Izv. Saratov Univ. (N.S.), Ser. Economics. Management. Law, 2015, vol. 15, iss. 2, pp. 202–206.
4. Vygodchikova I. Yu. O minimaksnom modelirovanii otsenki riska fi nansovogo portfelya [Minimax risk assessment modeling fi nancial portfolio]. Matematicheskoe modelirovanie v ekonomike i upravlenii riskami [Mathematical Modeling in Economics and Risk Management. Proc. III Int. youth sci. and pract. conf. (Saratov, 5–8 November 2014)]. Saratov, Saratov Univ. Press, 2014, pp. 63–66.
5. Vygodchikova I.Yu. Nailuchshee priblizhenie dinamiki ekonomicheskikh pokazatelei fundamental’nogo i tekhnicheskogo analiza rynka tsennykh bumag algebraicheskimi polinomami [The best approximation of the dynamics of economic indicators of fundamental and technical analysis of securities market by algebraic polynomials]. Saratov, Saratov Univ. Press, 2007. 88 p.
6. Rynok tsennykh bumag [The securities market. Textbook. Ed. by V. A. Galanov, A. I. Basov. 2nd ed., rev. and add.]. Moscow, Finance and statistics, 2006. 448 p.
7. Vygodchikova I. Yu. O modelirovanii riska s ispol’- zovaniem mnogoznachnykh tsenovykh dannykh [About the risk’s modeling using ultivalued price data]. Matematicheskoe modelirovanie v jekonomike, strakhovanii i upravlenii riskami [Mathematical Modeling in Economics, Insurance and Risk Management. Proc. Int. youth sci. and pract. conf. (Saratov, 5–8 November 2013)]. Saratov, Saratov Univ. Press, 2013, pp. 39–45.
8. Vygodchikova I. Yu. Priemy otsenki fi nansovogo riska [The methods of fi nancial risk’s valuing]. Izv. Saratov Univ. (N.S.), Ser. Economics. Management. Law, 2010, vol. 10, iss. 1, pp. 41–45.
9. Vygodchikova I. Yu. O matematicheskom modelirovanii struktury tekhnicheskoi sistemy s ravnomerno raspredelennymi riskami [About the mathematical modeling of the technical system’s structure with the evenly distributed riscs]. Vestnik Saratovskogo gosudarstvennogo tekhnicheskogo universiteta [Vestnik Saratov State Technical University], 2012, iss. 4 (68), pp. 17–22.

Full Text (PDF): 
Short Text (PDF):