PCA for the Construction of Stock Portfolio

Imane Rezgui
Department of Mathematics University Frères Mentouri-Constantine1

Abstract

One of the most important problems in finance is the construction of an efficient portfolio that balances returns and risk. In order to deal with this problem, various strategies and methods were used. Indeed, H. Lowenfeld was the first to announce the strategy of diversification and its benefits for spreading risk.H. Markowitz in 1952, announced his theory of mean-variance theory , and it became the foundation of modern portfolio theory, his main idea was to invest in low-correlation assets to diversify risk. W. Sharpe and Treynor definedportfolio performance criteria. Respecting the principle of the modern theory ofMarkowitz a, Partovi and Caputo, and inspired by the work of LIban Yang, we presente a method based on Principal Component Analysis (PCA) method to construct an optimal stock portfolio of some of the 20 stocks of the BEL 20 is the benchmark stock market index of Euronext Brussels, using R language

Presentation