The Application of the Monte Carlo Method in the Management of Value at Risk of an Investment Portfolio (Zastosowanie metody Monte Carlo w zarzadzaniu Value at Risk portfela inwestycyjnego)

This paper describes the use of the Monte Carlo method in the management of Value at Risk (VaR) of an investment portfolio. The essence of calculating the VaR is the use of a multi-component investment portfolio approach based on calculations matrix algebra where the main role is played by the variance-covariance matrix. As part of the calculation of the variance-covariance matrix, the changes in volatility matrix of assets are made depending on the level of statistic significance. Taking into account the correlation effects, the VaR of the diversified portfolio can thus be estimated. If we do not take into account the correlation effects, then we get non-diversified portfolio value at risk. The concept of diversified and non-diversified VaR allows for the use of simulation based on the Monte Carlo method. The most important area of application of simulation based on the Monte Carlo method in the concept of diversified and non-diversified VaR is the future trading of assets within a portfolio. The presented Monte Carlo application methods in the concept of diversified and non-diversified VaR can be used to build risk management systems for sophisticated investment portfolios based on underlying assets such as stocks, currencies, stock indices, commodities.