Portfolio Selection by Maximizing Omega Function using Differential Evolution

Affiliation(s)

Department of Operations Research and Econometrics, University of Economics, Bratislava, Slovakia.

Department of Operations Research and Econometrics, University of Economics, Bratislava, Slovakia.

ABSTRACT

Paper presents alternative solution seeking approach for portfolio selection problem with Omega function performance measure which allows determining capital allocation over the number of assets. Omega function computability is diffi-cult due to substandard structures and therefore the use of standard techniques seems to be relatively complicated. Dif-ferential evolution from the group of evolutionary algorithms was selected as an alternative computing procedure. Al-ternative approach is analyzed on the Down Jones Industrial Index data. Presented approach enables to determine good real-time solution and the quality of results is comparable with results obtained by professional software.

Paper presents alternative solution seeking approach for portfolio selection problem with Omega function performance measure which allows determining capital allocation over the number of assets. Omega function computability is diffi-cult due to substandard structures and therefore the use of standard techniques seems to be relatively complicated. Dif-ferential evolution from the group of evolutionary algorithms was selected as an alternative computing procedure. Al-ternative approach is analyzed on the Down Jones Industrial Index data. Presented approach enables to determine good real-time solution and the quality of results is comparable with results obtained by professional software.

Cite this paper

P. Juraj, B. Ivan, Č. Zuzana and R. Marian, "Portfolio Selection by Maximizing Omega Function using Differential Evolution,"*Technology and Investment*, Vol. 4 No. 1, 2013, pp. 73-77. doi: 10.4236/ti.2013.41B012.

P. Juraj, B. Ivan, Č. Zuzana and R. Marian, "Portfolio Selection by Maximizing Omega Function using Differential Evolution,"

References

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[2] J. L. Treynor, “How to Rate Management of Investment Funds”, Harvard Business Review, Vol. 43, No. 1, 1965, pp. 63-75.

[3] M. C. Jensen, “The Per-formance of Mutual Funds in the Period 1945-1964”, Journal of Finance, Vol. 23, 1968, pp. 389-416.

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[5] T. H. Goodwin, “The Information Ratio”, Investment Performance Measurement: Evaluation and Presenting Results. Hoboken, NJ: John Wiley & Sons, 2009.

[6] C. S. Pedersen and T. Ruddholm-Alfin, ”Se-lecting risk-adjusted shareholder performance meas-ure”, Journal of Asset Management. Vol. 4, No. 3, 2003, pp. 152-172.

[7] R. Hentati-Kaffel and J. L. Prigent, “Structured portfolio analysis under SharpeOmega ratio”, Documents de Travail du Centre d’Economie de la Sor-bonne, 2012.

[8] C. Keating and W. F. Shadwick, “A Universal Performance Measure”, Journal of Perfor-mance Measurement.Vol. 6, 2002, pp. 59-84.

[9] S. Avouyi-Dovi, A. Morin and D. Neto, “Optimal Asset Allocation with Omega Function”, Technical report, Banque de France, 2004.

[10] R. Storn and K. Price. “Differential Evolution – A simple and efficient heuristic for global optimization over continuous spaces”, Journal of Global Optimization, Vol. 11, 1997, pp. 341–359.

[11] Z.cickova,I. Brezina and J. Pekár, “Al-ternative method for solving traveling salesman problem by evolutionary algorithm”, Management information systems. No. 1, 2008, pp. 17-22.

[12] I. Brezina, Z.cickova and J. Pekár, “Application of evolutionary ap-proach to solving vehicle routing problem with time windows”, Economic review, Vol. 38, No. 4, 2009, pp. 529-539.

[13] I. Brezina, Z.cickova and J. Pekár, “Evolutionary approach as an alternative method for solving the vehicle routing problem”, Economic review, Vol. 41, No. 2, 2012, pp. 137-147.

[14] D. Ardia, K. Boudt, P. Carl, K. M. Mullen and B. G. Peterson, “Differential Evolution with DEoptim”, The R Journal, Vol. 3, No. 1, 2011, pp. 27-34.

[15] I. Zelinka, “Umělá inteligence v problémech globální optimalizace”, BEN-technická literature, Praha, 2002.

[16] V.Marik,o.stepankova and J.Lazansky, “Umělá inteligence 4”, Academia Praha, 2003.

[17] G. C. Onwubolu and B. V. Babu, “New Optimization Techniques in Engineering”, Springer-Verlag, Berlin-Heidelberg, 2004.

[18] Z.cickova, I. Brezina and J. Pekár, “A memetic algo-rithm for solving the vehicle routing problem”, In Mathematical methods in Economics 2011, 29th international conference, Praha, Professional Publishing, 2011, pp. 125-128.

[1] W. F. Sharpe, “The Sharpe Ratio”, The Journal of Port-folio Management, Vol. 21, No. 1, 1994, pp. 49–58.

[2] J. L. Treynor, “How to Rate Management of Investment Funds”, Harvard Business Review, Vol. 43, No. 1, 1965, pp. 63-75.

[3] M. C. Jensen, “The Per-formance of Mutual Funds in the Period 1945-1964”, Journal of Finance, Vol. 23, 1968, pp. 389-416.

[4] F. A. Sortino and R. Meer, “Downside Risk”, The Journal of Portfolio Management, Vol. 17, No. 4, 1991, pp. 27–31.

[5] T. H. Goodwin, “The Information Ratio”, Investment Performance Measurement: Evaluation and Presenting Results. Hoboken, NJ: John Wiley & Sons, 2009.

[6] C. S. Pedersen and T. Ruddholm-Alfin, ”Se-lecting risk-adjusted shareholder performance meas-ure”, Journal of Asset Management. Vol. 4, No. 3, 2003, pp. 152-172.

[7] R. Hentati-Kaffel and J. L. Prigent, “Structured portfolio analysis under SharpeOmega ratio”, Documents de Travail du Centre d’Economie de la Sor-bonne, 2012.

[8] C. Keating and W. F. Shadwick, “A Universal Performance Measure”, Journal of Perfor-mance Measurement.Vol. 6, 2002, pp. 59-84.

[9] S. Avouyi-Dovi, A. Morin and D. Neto, “Optimal Asset Allocation with Omega Function”, Technical report, Banque de France, 2004.

[10] R. Storn and K. Price. “Differential Evolution – A simple and efficient heuristic for global optimization over continuous spaces”, Journal of Global Optimization, Vol. 11, 1997, pp. 341–359.

[11] Z.cickova,I. Brezina and J. Pekár, “Al-ternative method for solving traveling salesman problem by evolutionary algorithm”, Management information systems. No. 1, 2008, pp. 17-22.

[12] I. Brezina, Z.cickova and J. Pekár, “Application of evolutionary ap-proach to solving vehicle routing problem with time windows”, Economic review, Vol. 38, No. 4, 2009, pp. 529-539.

[13] I. Brezina, Z.cickova and J. Pekár, “Evolutionary approach as an alternative method for solving the vehicle routing problem”, Economic review, Vol. 41, No. 2, 2012, pp. 137-147.

[14] D. Ardia, K. Boudt, P. Carl, K. M. Mullen and B. G. Peterson, “Differential Evolution with DEoptim”, The R Journal, Vol. 3, No. 1, 2011, pp. 27-34.

[15] I. Zelinka, “Umělá inteligence v problémech globální optimalizace”, BEN-technická literature, Praha, 2002.

[16] V.Marik,o.stepankova and J.Lazansky, “Umělá inteligence 4”, Academia Praha, 2003.

[17] G. C. Onwubolu and B. V. Babu, “New Optimization Techniques in Engineering”, Springer-Verlag, Berlin-Heidelberg, 2004.

[18] Z.cickova, I. Brezina and J. Pekár, “A memetic algo-rithm for solving the vehicle routing problem”, In Mathematical methods in Economics 2011, 29th international conference, Praha, Professional Publishing, 2011, pp. 125-128.