Оптимізаційна модель розподілу фінансових ресурсів з урахуванням ризиків

Abstract

The article proposes an optimization model for the allocation of enterprise financial resources among investment assets under conditions of uncertainty and market risk. The relevance of the study is determined by the growing volatility of financial markets and the necessity for enterprises to ensure an effective balance between profitability and risk when managing free capital. Traditional intuitive approaches to capital allocation often lead either to excessive exposure to financial losses or to inefficient use of investment opportunities. Therefore, the study focuses on the development of a formalized quantitative approach that allows enterprises to optimize investment decisions using modern portfolio management methods. The research is based on the classical Markowitz portfolio theory, according to which portfolio risk depends not only on the volatility of individual assets but also on the correlation structure between them. The optimization problem is formulated as a quadratic programming task aimed at minimizing portfolio variance while maintaining a target level of expected return and ensuring full allocation of available financial resources. To improve the adequacy of risk assessment under crisis conditions, the model is supplemented with modern coherent risk measures, namely Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). Unlike variance, CVaR enables the evaluation of expected losses in the worst market scenarios and therefore provides a more realistic assessment of downside risk. A numerical example involving five classes of investment assets, including bonds, stocks, real estate, futures, and commodities, is used to demonstrate the practical application of the proposed model. The optimal portfolio structure is determined by maximizing the Sharpe ratio, which reflects the relationship between excess return and portfolio volatility. The obtained results indicate that the largest share of resources should be allocated to low-risk instruments, while highly volatile assets should occupy smaller positions despite their potentially higher profitability. The study also includes stress testing and sensitivity analysis of the optimized portfolio. Several crisis scenarios of different severity are modeled to evaluate portfolio stability under adverse market conditions. The results confirm that the optimized portfolio demonstrates higher resilience compared to an equally weighted benchmark portfolio. Sensitivity analysis reveals that market volatility and correlation between assets are the most influential parameters affecting portfolio efficiency. The proposed optimization model can be applied by enterprises for strategic financial planning and investment decisionmaking under uncertainty. The practical value of the research lies in the possibility of improving financial stability, reducing tail risks, and increasing the efficiency of capital allocation in turbulent market environments.

У статті розроблено оптимізаційну модель розподілу фінансових ресурсів підприємства між інвестиційними активами з урахуванням ризику. На основі теорії Марковіца та сучасних метрик ризику VaR і CVaR сформовано задачу оптимізації структури інвестиційного портфеля. Визначено оптимальну структуру розподілу для числового прикладу з п'яти класів активів. Проведено стрес-тестування та аналіз чутливості отриманого розв'язку до ключових параметрів моделі.