Portfolio optimization using classification and functional data analysis techniques

In this paper, we propose an algorithm for hierarchical classification, based on an ultrametric distance. We study its properties and develop an application in Microsoft Visual Studio, based on the algorithm proposed, using C# language. The software obtained will be used to classify the shares from Bucharest Stock Exchange which had profit during the last two years, in order to find similarities and differences between these shares and build a diversified portfolio. We prove that this portfolio is representative for the shares from Bucharest Stock Exchange and study the evolution of the obtained portfolio at different moments of time, using functional data analysis methods ( STATIS ) . In order to evaluate our methodology, we provide a numerical experiment .We demonstrate the performance of the proposed algorithm by comparing the obtained results with the evolution of BET index, BET-C index or BET –XT index, which are representatives for the capital market in Romania.