The thesis addresses factor models and different approaches to the estimation of covariance matrices as fundamental tools in portfolio optimization and risk management. In the theoretical part, single-factor, multi-factor, and fundamental factor models are systematically presented, with special emphasis on the Barra model and its ability to segment portfolios based on style, industry, and country factors. Such an overview establishes a methodological basis for further empirical analyses and enables a critical evaluation of the effectiveness of different models in real market conditions.
The central part of the analytical work provides a detailed comparison of classical methods for estimating covariance matrices (the historical covariance matrix, exponentially weighted moving average) with advanced approaches based on random matrix theory. Among the latter, shrinkage methods, eigenvalue clipping, rotationally invariant estimators, and power-law cleaning methods are analyzed in detail. It has been shown that these approaches are generally more effective in separating signal from noise in financial data, which significantly reduces errors in portfolio optimization. The comparison of methods thus highlights their relative strengths and weaknesses and shows under which conditions particular techniques prove to be more reliable.
The thesis also includes the practical application of an adjusted factor model, which enables a detailed decomposition of risk into systematic and idiosyncratic components and the identification of factors that most influence the performance of optimized portfolios. The findings confirm that the combination of factor models with advanced methods of covariance matrix estimation leads to more robust and more transparent strategies that achieve a favorable risk-return profile.
|
