Risk Return Optimization Using the Knapsack Problem in The Formation of a Stocks Portfolio. Case Study of a Brazilian Investment Site.

Main Article Content

Nicolas Sampaio Bevilaqua
OCILEIDE Custodio da Silva


In this work, the composition of a portfolio was proposed by using the Knapsack problem and verified its effectiveness in comparison to a portfolio of shares on an investment website. The programming variables were based on the Markowitz risk theory of variance and following collaborators for their studies. And from the chosen portfolio, the efficient frontier was elaborated analyzing the performance of the investment site portfolio during 30 days. The portfolio obtained exceeded the percentage performance obtained from the investment site in the same period when considering the maximum possible return, the minimum global variance and also in the naive distribution.


Download data is not yet available.

Article Details

How to Cite
Sampaio Bevilaqua, N., Custodio da Silva, O., & DE MATTOS VERONEZE, G. (2020). Risk Return Optimization Using the Knapsack Problem in The Formation of a Stocks Portfolio. Case Study of a Brazilian Investment Site. International Journal for Innovation Education and Research, 8(9), 280-289. https://doi.org/10.31686/ijier.vol8.iss9.2629


Cibulskienė, D. and Grigaliūnienė, Z. (2007). The Genesis and Development of Modern Portfolio Theory, Economics and Management: Current Issues and Perspectives, p. 52–61, Šiauliai University.

Galinienė, B and Stravinskytė, J.(2016). Constructing an optimal investment portfolio for the bank of Lithuania, Ekonomika, 2016, Vol. 95(1).

Gupta, P, Mehlawat, K and Saxena, A.(2010). “A hybrid approach to asset allocation with simultaneous consideration of suitability and optimality,” Information Sciences, vol. 180, no. 11, pp. 2264–2285, 2010.

Investment and Finance. Portfolio Management. (2020). Available at: https://www.investment-and-finance.net/portfolio-management/e/efficient-frontier.html. Acessado em 30 de julho.

Konno, H and Yamazaki, H. (1991). “Mean-absolute deviation portfolio. Optimization model and its applications to Tokyo stockmarket,”. Management Science, vol. 37, no. 5, pp. 519–531.

Malaj, E and Malaj, V. (2016). Portfolio Allocation: An Empirical Analysis of Ten American Stocks for the Period 2010-2015. International Journal of Accounting, Finance and Risk Management. Vol. 1, No. 1, 2016, pp. 11-18.

Markowitz, H. (1952). Portfolio selection. The Journal of Finance, vol.7, no. 1, pp. 77–91, 1952.

Morita, H. (1989). Stochastic linear knapsack programming problem and its application to a portfolio selection problem. European Journal of operational Research, vol. 3, no. 4, pp. 329-336, 1989.

Sekar, G. (2012). “Portfolio optimization using neuro fuzzy system in Indian stock market,” Journal of Global Research in Computer Science, vol. 3, no. 4, pp. 44–47, 2012.

Sharpe, W. (1971). A linear programming approximation for the general portfolio.(1971a).

analysis problem. Journal of Financial and Quantitative Analysis 6, 1263–1275.

Sharpe, W.(1971). Mean-absolute deviation characteristic lines for securities and portfolios. Management Science 18, B1–B13

Speranza, M. (1993). “Linear programming models for portfolio optimization,” Finance, vol. 14, pp. 107–123, 1993..+

Most read articles by the same author(s)