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Optimal Portfolio Diversification Under Cardinality Constraint

Year 2020, Volume: 18 Issue: 2, 171 - 181, 24.06.2020
https://doi.org/10.18026/cbayarsos.600258

Abstract

Portfolio selection is an important selection process in economy and finance. The classic modern portfolio theory is a model that focuses on portfolio return and risk in the light of historical data that is assumed to be normally distributed in portfolio selection problem. However, the past return series of stocks are not normally distributed frequently in real life, and it is meaningful to add skewness and kurtosis to the portfolio model. The entropy function that provides the natural diversity is included in the model in order to add future uncertainty in the model and prevent the accumulation of certain stocks encountered in portfolio selection based on higher order moments. In the study, the model, which has become a np-hard problem with the addition of cardinality constraint limiting the number of stocks that can be found in the portfolio, has been solved by particle swarm optimization. From the assets in the sample dataset, models were set for different scenarios and the effectiveness of the proposed entropy function for selection process, in diversification was discussed.

References

  • Aksaraylı, M. ve Pala, O. (2018b). Bist 30 Endeksinde Portföy Seçimi İçin Yeni Bir Kısmi Hedef Programlama Yaklaşımı. Balkan Sosyal Bilimler Dergisi. 7(13). s. 119-134.
  • Aksaraylı, M., ve Pala, O. (2018a). A polynomial goal programming model for portfolio optimization based on entropy and higher moments. Expert Systems with Applications, 94, s. 185-192.
  • Aladağ, C. H., Yolcu, U., Egrioğlu, E., ve Dalar, A. Z. (2012). A new time invariant fuzzy time series forecasting method based on particle swarm optimization. Applied Soft Computing, 12(10) s. 3291-3299.
  • Beardsley, X. W., Field, B., ve Xiao, M. (2012). Mean-variance-skewness-kurtosis portfolio optimization with return and liquidity. Communications in Mathematical Finance, 1(1), 13-49.
  • Bera, A. K., ve Park, S. Y. (2008). Optimal portfolio diversification using the maximum entropy principle. Econometric Reviews, 27(4-6), s. 484-512.
  • Brito, R. P., Sebastião, H., ve Godinho, P. (2019). Portfolio management with higher moments: the cardinality impact. International Transactions in Operational Research, 26(6), 2531-2560.
  • Chen, C., ve Zhou, Y. S. (2018). Robust multiobjective portfolio with higher moments. Expert Systems with Applications, 100, 165-181.
  • Chunhachinda, P., Dandapani, K., Hamid, S., ve Prakash, A. J. (1997). Portfolio selection and skewness: Evidence from international stock markets. Journal of Banking & Finance, 21(2), s. 143-167.
  • DeMiguel, V., Garlappi, L., ve Uppal, R. (2009). Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy?. Review of Financial Studies, 22(5), s. 1915-1953.
  • Eberhart, R., ve Kennedy, J. (1995, October). A new optimizer using particle swarm theory. In MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science (pp. 39-43). Ieee.
  • Harvey, C. R., Liechty, J. C., Liechty, M. W., ve Müller, P. (2010). Portfolio selection with higher moments. Quantitative Finance, 10(5), s. 469-485.
  • Jurczenko, E., Maillet, B. B., ve Merlin, P. (2005). Hedge funds portfolio selection with higher-order moments: a non-parametric mean-variance-skewness-kurtosis efficient frontier. Available at SSRN 676904.
  • Kendal, G., ve Su, Y. (2005). A Particle Swarm Optimization Approach in the Construction of Optimal Risky Portfolios. In IASTED International Multi Conference Artificial Intelligence and Applications Journal,( 23). s. 14-16.
  • Kenneth French İnternet Sitesi. Çevrimiçi Adres :http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/index.html (erişim tarihi 1 Ekim 2018)
  • Konno, H., ve Suzuki, K. I. (1995). A mean-variance-skewness portfolio optimization model. Journal of the Operations Research Society of Japan, 38(2), 173-187.
  • Lai, K. K., Yu, L., ve Wang, S. (2006, June). Mean-variance-skewness-kurtosis-based portfolio optimization. In Computer and Computational Sciences, 2006. IMSCCS'06. First International Multi-Symposiums on (Vol. 2, pp. 292-297). IEEE.
  • Liu, S. Y. W. S., Wang, S. Y., ve Qiu, W. 2. (2003). Mean-variance-skewness model for portfolio selection with transaction costs. International Journal of Systems Science, 34(4), 255-262.
  • Maringer, D., ve Parpas, P. (2009). Global optimization of higher order moments in portfolio selection. Journal of Global Optimization, 43(2-3), 219-230.
  • Markowitz, H. (1952). Portfolio selection. The journal of finance, 7(1), s. 77-91.
  • Markowitz, H. M. (1991). Foundations of portfolio theory. The journal of finance, 46(2), s. 469-477.
  • Mehlawat, M. K., Kumar, A., Yadav, S., ve Chen, W. (2018). Data envelopment analysis based fuzzy multi-objective portfolio selection model involving higher moments. Information Sciences, 460, 128-150.
  • Nguyen, Thanh Thi. "Portfolio selection under higher moments using fuzzy multi-objective linear programming." Journal of Intelligent & Fuzzy Systems 30, no. 4 (2016): 2139-2156.
  • Pala, O. ve Aksaraylı, M. (2017). Bist 30 Endeksinde Entropi Ve Yüksek Momentlerle TOPSIS Ve PROMETHEE Tabanlı Çok Amaçlı Portföy Seçimi Modeli Önerisi. Adnan Menderes Üniversitesi Sosyal Bilimler Enstitüsü Dergisi. 4(4). s. 171-188.
  • Prakash, A. J., Chang, C. H., ve Pactwa, T. E. (2003). Selecting a portfolio with skewness: Recent evidence from US, European, and Latin American equity markets. Journal of Banking & Finance, 27(7), 1375-1390.
  • Shi, Y., ve Eberhart, R. C. (1999). Empirical study of particle swarm optimization. In Evolutionary Computation, 1999. CEC 99. Proceedings of the 1999 Congress on (Vol. 3, s. 1945-1950). IEEE.
  • Yue, W., ve Wang, Y. (2017). A new fuzzy multi-objective higher order moment portfolio selection model for diversified portfolios. Physica A: Statistical Mechanics and its Applications, 465, s. 124-140.
  • Zhu, H., Wang, Y., Wang, K., ve Chen, Y. (2011). Particle Swarm Optimization (PSO) for the constrained portfolio optimization problem. Expert Systems with Applications, 38(8), s. 10161-10169.

Nicelik Kısıtı Altında Optimal Portföy Çeşitlendirme

Year 2020, Volume: 18 Issue: 2, 171 - 181, 24.06.2020
https://doi.org/10.18026/cbayarsos.600258

Abstract

Portföy seçimi ekonomi ve finans alanında önem verilen bir seçim sürecidir. Klasik modern portföy teorisi portföy seçim probleminde normal dağıldığı varsayılan tarihsel veriler ışığında portföy getiri ve riskine odaklanan bir modeldir. Öte yandan hisse senetlerinin geçmiş dönem getiri serileri gerçek hayatta çoğunlukla normal dağılmamakta, çarpıklık ve basıklığın modele eklenmesi anlamlı olmaktadır. Yüksek dereceden momentler ile portföy optimizasyonunda karşılaşılan belirli hisse senetlerine yığılmayı önlemek ve gelecek belirsizliği modele dahil etmek için doğal çeşitlilik sağlayan entropi fonksiyonu modele eklenmektedir. Çalışmada, portföyde bulunabilecek hisse senedi sayısını kısıtlayan nicelik kısıtı eklenmesi ile np-zor hale gelen model, parçacık sürü optimizasyonu ile çözülmüştür. Örnek veri setinde bulunan hisse senetlerinden, farklı senaryolar için modeller kurulmuş ve seçim süreci için önerilmiş olan entropi fonksiyonunun çeşitlendirmede etkinliği tartışılmıştır.

References

  • Aksaraylı, M. ve Pala, O. (2018b). Bist 30 Endeksinde Portföy Seçimi İçin Yeni Bir Kısmi Hedef Programlama Yaklaşımı. Balkan Sosyal Bilimler Dergisi. 7(13). s. 119-134.
  • Aksaraylı, M., ve Pala, O. (2018a). A polynomial goal programming model for portfolio optimization based on entropy and higher moments. Expert Systems with Applications, 94, s. 185-192.
  • Aladağ, C. H., Yolcu, U., Egrioğlu, E., ve Dalar, A. Z. (2012). A new time invariant fuzzy time series forecasting method based on particle swarm optimization. Applied Soft Computing, 12(10) s. 3291-3299.
  • Beardsley, X. W., Field, B., ve Xiao, M. (2012). Mean-variance-skewness-kurtosis portfolio optimization with return and liquidity. Communications in Mathematical Finance, 1(1), 13-49.
  • Bera, A. K., ve Park, S. Y. (2008). Optimal portfolio diversification using the maximum entropy principle. Econometric Reviews, 27(4-6), s. 484-512.
  • Brito, R. P., Sebastião, H., ve Godinho, P. (2019). Portfolio management with higher moments: the cardinality impact. International Transactions in Operational Research, 26(6), 2531-2560.
  • Chen, C., ve Zhou, Y. S. (2018). Robust multiobjective portfolio with higher moments. Expert Systems with Applications, 100, 165-181.
  • Chunhachinda, P., Dandapani, K., Hamid, S., ve Prakash, A. J. (1997). Portfolio selection and skewness: Evidence from international stock markets. Journal of Banking & Finance, 21(2), s. 143-167.
  • DeMiguel, V., Garlappi, L., ve Uppal, R. (2009). Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy?. Review of Financial Studies, 22(5), s. 1915-1953.
  • Eberhart, R., ve Kennedy, J. (1995, October). A new optimizer using particle swarm theory. In MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science (pp. 39-43). Ieee.
  • Harvey, C. R., Liechty, J. C., Liechty, M. W., ve Müller, P. (2010). Portfolio selection with higher moments. Quantitative Finance, 10(5), s. 469-485.
  • Jurczenko, E., Maillet, B. B., ve Merlin, P. (2005). Hedge funds portfolio selection with higher-order moments: a non-parametric mean-variance-skewness-kurtosis efficient frontier. Available at SSRN 676904.
  • Kendal, G., ve Su, Y. (2005). A Particle Swarm Optimization Approach in the Construction of Optimal Risky Portfolios. In IASTED International Multi Conference Artificial Intelligence and Applications Journal,( 23). s. 14-16.
  • Kenneth French İnternet Sitesi. Çevrimiçi Adres :http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/index.html (erişim tarihi 1 Ekim 2018)
  • Konno, H., ve Suzuki, K. I. (1995). A mean-variance-skewness portfolio optimization model. Journal of the Operations Research Society of Japan, 38(2), 173-187.
  • Lai, K. K., Yu, L., ve Wang, S. (2006, June). Mean-variance-skewness-kurtosis-based portfolio optimization. In Computer and Computational Sciences, 2006. IMSCCS'06. First International Multi-Symposiums on (Vol. 2, pp. 292-297). IEEE.
  • Liu, S. Y. W. S., Wang, S. Y., ve Qiu, W. 2. (2003). Mean-variance-skewness model for portfolio selection with transaction costs. International Journal of Systems Science, 34(4), 255-262.
  • Maringer, D., ve Parpas, P. (2009). Global optimization of higher order moments in portfolio selection. Journal of Global Optimization, 43(2-3), 219-230.
  • Markowitz, H. (1952). Portfolio selection. The journal of finance, 7(1), s. 77-91.
  • Markowitz, H. M. (1991). Foundations of portfolio theory. The journal of finance, 46(2), s. 469-477.
  • Mehlawat, M. K., Kumar, A., Yadav, S., ve Chen, W. (2018). Data envelopment analysis based fuzzy multi-objective portfolio selection model involving higher moments. Information Sciences, 460, 128-150.
  • Nguyen, Thanh Thi. "Portfolio selection under higher moments using fuzzy multi-objective linear programming." Journal of Intelligent & Fuzzy Systems 30, no. 4 (2016): 2139-2156.
  • Pala, O. ve Aksaraylı, M. (2017). Bist 30 Endeksinde Entropi Ve Yüksek Momentlerle TOPSIS Ve PROMETHEE Tabanlı Çok Amaçlı Portföy Seçimi Modeli Önerisi. Adnan Menderes Üniversitesi Sosyal Bilimler Enstitüsü Dergisi. 4(4). s. 171-188.
  • Prakash, A. J., Chang, C. H., ve Pactwa, T. E. (2003). Selecting a portfolio with skewness: Recent evidence from US, European, and Latin American equity markets. Journal of Banking & Finance, 27(7), 1375-1390.
  • Shi, Y., ve Eberhart, R. C. (1999). Empirical study of particle swarm optimization. In Evolutionary Computation, 1999. CEC 99. Proceedings of the 1999 Congress on (Vol. 3, s. 1945-1950). IEEE.
  • Yue, W., ve Wang, Y. (2017). A new fuzzy multi-objective higher order moment portfolio selection model for diversified portfolios. Physica A: Statistical Mechanics and its Applications, 465, s. 124-140.
  • Zhu, H., Wang, Y., Wang, K., ve Chen, Y. (2011). Particle Swarm Optimization (PSO) for the constrained portfolio optimization problem. Expert Systems with Applications, 38(8), s. 10161-10169.
There are 27 citations in total.

Details

Primary Language Turkish
Journal Section İktisadi ve idari Bilimler Sayısı
Authors

Osman Pala 0000-0002-2634-2653

Mehmet Aksaraylı 0000-0003-1590-4582

Publication Date June 24, 2020
Published in Issue Year 2020 Volume: 18 Issue: 2

Cite

APA Pala, O., & Aksaraylı, M. (2020). Nicelik Kısıtı Altında Optimal Portföy Çeşitlendirme. Manisa Celal Bayar Üniversitesi Sosyal Bilimler Dergisi, 18(2), 171-181. https://doi.org/10.18026/cbayarsos.600258