UDC 336.76
UDC 519.852
This paper examines the application of the Markowitz model for investment portfolio optimization in terms of risk minimization at a given level of return. The theoretical foundation of the study is based on the Modern Portfolio Theory, which analyzes the relationship between expected return and financial risk. Shares of companies from different sectors of the economy were selected as the research objects in order to ensure portfolio diversification. During the study, logarithmic returns, standard deviations, and the covariance matrix were calculated. Based on the obtained data, an equally weighted investment portfolio was analyzed and subsequently optimized using the mean-variance model and the Lagrange multiplier method. In addition, Microsoft Excel tools were applied for the numerical solution of the optimization problem. The results of the research demonstrate that the Markowitz model makes it possible to reduce the overall portfolio risk while maintaining the target level of return. The obtained findings confirm the effectiveness of mathematical methods in investment management and illustrate the practical applicability of portfolio theory in financial market analysis.
Markowitz model, investment portfolio, optimization, risk, return, diversification, covariance, financial mathematics
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