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


  • Florentin SERBAN

    (Department of Applied Mathematics, Faculty of Cybernetics, Statistics and Computer Science, Academy of Economic Studies, Bucharest)

  • Mihail BUSU

    (Department of Mathematics, Spiru Haret University, Bucharest, Romania)


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.

Suggested Citation

  • Florentin SERBAN & Mihail BUSU, 2011. "Building an Optimal Portfolio Consisting of two Assets and Its Efficient Frontier," Timisoara Journal of Economics, West University of Timisoara, Romania, Faculty of Economics and Business Administration, vol. 4(4(16)), pages 231-238.
  • Handle: RePEc:wun:journl:tje:v04:y2011:i4(16):a05

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    risk; selection of assets; principal components analysis; optimization; efficient frontier;

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions


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