Building an Optimal Portfolio Consisting of two Assets and Its Efficient Frontier

In modern portfolio theory, it is common practice to first compute the risk-reward efficient frontier and then to support an individual investor in selecting a portfolio that meets his/her preferences for profitability and risk. Potential flaws include (a) the assumption that past data provide sufficient evidence for predicting the future performances of the securities under consideration and (b) the necessity to mathematically determine or approximate the investor’s utility function. This paper presents the description of the efficient frontier for a portfolio made of two assets. We use data analysis to obtain two clusters, then, we estimate the risk of each asset corresponding to each class we obtained. Thus, we get the best two assets among the ones we analyzed and for which we will construct the efficient frontier. The originality of our paper consists in the combination of classification theory and risk estimation theory to determine the best assets. To illustrate the efficiency of the method we used, we present a case study which makes reference to the stocks listed at Bucharest Stock Exchange. We consider two stocks with the best features from Bucharest Stock Exchange based on the existent correlation that we obtained by data analyses (for classification), and by the evaluation of the loss repartition (for risk estimation), then we construct the efficient frontier for this portfolio.