Abstract
In this study, the performances of four different portfolio optimisation methods consisting
of the Omega ratio, conditional value-at-risk (CVaR), maximum drawdown (MDD), and Markowitz
(1952) mean variance methods are compared using monthly data for the period fromJanuary 2000 to
September 2020. Portfolio optimisation methods are applied b y taking into account three different
targeted annual return rates. Sharpe ratio, Treynor ratio, Information ratio, Sortino ratio, Calmar ratio,
and Jensen’s alpha measure are used to evaluate the performance of portfolio optimisation methods.
The study findings indicate that the portfolio optimisation method based on the Omega ratio exhibits
the best performance for the period examined. However, findings also indicate that optimal portfolios
based on the Omega ratio contain significant concentration risk in addition to high market risk.
References
- Almahdi, S., and Yang, S.Y. (2017). An adaptive portfolio trading system: A risk-return portfolio optimization using recurrent reinforcement learning with expected maximum drawdown. Expert Systems With Applications, 87, 267–279.
- Bernard, C., Vanduffel, S., and Ye, J. (2018). Optimal strategies under omega ratio. European Journal of Operational Research, 275 (2), 755-767.
- Castro, J.G., Tito, E.A.H., Brandão,L.E.ET., and Gomes, L.L. (2019). Crypto-assets portfolio optimization under the omega measure. The Engineering Economist, 65 (2), 114-134.
- Chang, T-J., Yang, S.C., and Chang, K-J. (2009). Portfolio optimization problems in different risk measures using genetic algorithm. Expert Systems with Applications, 36, 10529–10537.
- Chekhlov, A., Uryasev,S., and Zabarankin, M. (2003). Portfolio Optimization With Drawdown Constraints.Pardalos, P.M., Migdalas, A. ve Baourakis,G. (Eds.). Supply Chain and Finance içinde (s. 209-228).London, England: World Scientific publishing Co.Pte.Ltd.
- Çelengi, A. Z., Eğrioğlu,E., ve Çorba,B.Ş. (2015). İMKB 30 indeksini oluşturan hisse senetleri için parçacık sürü optimizasyonu yöntemlerine dayalı portföy optimizasyonu. Doğuş Üniversitesi Dergisi, 16(1), 25-33.
- Dai, Z., and Wen, F. (2014). Robust CVaR-based portfolio optimization under a genal affine data perturbation uncertainty set. Journal of Computational Analysis and Applications, 16(1),93-103.
- Deng, L., Ma, C., and Yang,W. (2011). Portfolio optimization via pair copula-GARCH-EVT-CVaR model. Systems Engineering Procedia, 2, 171 – 181.
- Favre-Bulle, A., and Pache, S.(2003). The omega measure: Hedge fund portfolio optimization. (Unpublished MBF master’s thesis). University of Lausanne – Ecole Des Hec.
- Fernandez, A., and Gomez , S. (2007). Portfolio selection using neural networks. Computers & Operations Research, 34, 1177-1191.
- Gökgöz, E. (2006). Riske maruz değer (VaR) ve portföy optimizasyonu (1. Baskı) Ankara: Sermaye Piyasası Kurulu Yayınları, Yayın No: 190.
- Gökmen, Y. (2009). Stokastik programlama ile optimal portföy oluşturma. (Yayınlanmamış Doktora Tezi). Gazi Üniversitesi, Sosyal Bilimler Enstitüsü.
- Grinold R. C. (1989). The fundamental law of active management. Journal of Portfolio Management, 15 (3), 30-37.
- Jensen, M. C. (1968). The performance of mutual funds in the period 1945-1964. The Journal of Finance, 23 (2), 389-416.
- Keating, C., and Shadwick, W. F. (2002). A universal performance measure. Journal of Performance Measurement, 6(3), 59–84.
- Klega, D. (2013). My ventures are not in one bottom trusted: Comparative study to modern portfolio theory and Black-Litterman portfolio formation.( Unpublished Rigorosum Thesis). Charles University, Faculty of Social Sciences.
- Lim, A.E.B., Shanthikumar, J.G., and Vahn, G-Y. (2011). Conditional value-at-risk in portfolio optimization: Coherent but fragile. Operations Research Letters, 39(3),163-171.
- Ma, Y., Han, R., and Wang,W. (2021). Portfolio optimization with return prediction using deep learning and machine learning. Expert Systems with Applications,165(1),1139-73.
- Magdon-Ismail, M., and Atiya, A. (2004). An analysis of the maximum drawdown risk measure. Risk Magazine, 17 (10): 99–102.
- Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77-91.
- Mishra, A. K., Pisipati, S., and Vyas, I. (2011). An equilibrium approach for tactical asset allocation: Assessing Black-Litterman model to Indian stock market. Journal of Economics and International Finance, 3 (10), 553-563.
- Najafi, A. A,. and Mushakhian, S. (2015). Multi-stage stochastic mean–semivariance–CVaR portfolio optimization under transaction costs. Applied Mathematics and Computation, 256, 445–458.
- Özdemir, M. (2011). Genetik algoritma kullanılarak portföy seçimi. İktisat Isletme ve Finans, 26 (299), 43-66.
- Receiz, A. and León, C.E. (2008). Efficient Portfolio Optimization in the Wealth Creation and Maximum Drawdown Space. Berkelaar, A., Coche, J. ve Nyholm, K. (Eds.). Interest Rate Models, Asset Allocation and Quantitative Techniques For Central Banks And Sovereıgn Wealth Funds içinde (s.1-23). Bogota, Colombia: Palgrave Macmillan.
- Rejeb, A.B., and Boughrara, A.(2013). Financial liberalization and stock markets efficiency: New evidence from emerging economies. Emerging Markets Review, 17, 186–208.
- Rockafellar, R.T., and Uryasev, S. (2000). Optimization of conditional value-at-risk. Journal of Risk, 2, 21–41.
- Roy, A. D. (1952). Safety first and the holding of assets. Econometrica: Journal of the Econometric Society, 20 (3), 431-449.
- Sharma, A., Utz, S., and Mehra, A. (2017). Omega-CVaR portfolio optimization and its worst case analysis. OR Spectrum, 39, 505–539.
- Sharpe, W. F. (1966). Mutual fund performance. The Journal of Business, 39(S1), 119.
- Solatikia, F., Kiliç, E ., and Weber, G.W. (2014). Fuzzy optimization for portfolio selectionbased on embedding theorem in fuzzy normed linear spaces. Organizacija, 47(2), 90-97.
- Sortino F. A. (2000). Measuring risk: Upside-potential ratios vary by ınvestment style. Pensions and Investments, 28(22), 30–35.
- Treynor, J. L. (1965). How to rate management of investment funds. Harvard Business Review, 43 (1), 63-75.
- Uyar, U., ve Küçükşahin, H. (2017). Portföy seçiminde expected maximum drawdown yaklaşımı: BİST100-S&P500 Uygulaması. Business and Economics Research Journal, 8 (4), 727-748.
- Uygurtürk, H., ve Korkmaz, T. (2015). Portföy optimizasyonunda markowitz modelinin kullanımı: bireysel emeklilik yatırım fonları üzerine bir uygulama. Muhasebe ve Finansman Dergisi,68, 67-82.
- Yakut, E., ve Çankal, A. (2016). Çok amaçlı genetik algoritma ve hedef programlama metotlarını kullanarak hisse senedi portföy optimizasyonu: BİST 30’da bir uygulama. Business and Economics Research Journal, 7(2),43.62.
- Young T. W. (1991). Calmar ratio: A smoother tool. Futures (Cedar Falls, Iowa), 20 (11),1-22.
Abstract
Bu çalışmada koşullu riske maruz değer (Conditional value-at-risk, CVaR), maksimum düşüş oranı (Maximum drawndown, MDD), Omega rasyosu ve Markowitz (1952) ortalama-varyans yönteminden oluşan dört farklı portföy optimizasyon yönteminin performansları aylık veriler kullanılarak Ocak 2000 ile Eylül 2020 dönemi için karşılaştırılmıştır. Portföy optimizasyon yöntemleri hedeflenen üç farklı yıllık getiri oranı dikkate alınarak uygulanmıştır. Portföy optimizasyon yöntemlerinin performanslarının değerlendirilmesinde Sharpe rasyosu, Treynorrasyosu, Bilgi rasyosu, Sortino rasyosu, Calmar rasyosu ve Jensen (alfa) kriterinden yararlanılmıştır. Çalışma bulguları incelenen dönem için en iyi performansı Omega rasyosuna dayalı portföy optimizasyon yönteminin sergilediği sonucuna işaret etmektedir. Fakat, bulgular Omega rasyosuna dayalı portföylerin yoğunlaşma riskine ilaveten önemli oranda piyasa riski de içerdiğini göstermektedir.
References
- Almahdi, S., and Yang, S.Y. (2017). An adaptive portfolio trading system: A risk-return portfolio optimization using recurrent reinforcement learning with expected maximum drawdown. Expert Systems With Applications, 87, 267–279.
- Bernard, C., Vanduffel, S., and Ye, J. (2018). Optimal strategies under omega ratio. European Journal of Operational Research, 275 (2), 755-767.
- Castro, J.G., Tito, E.A.H., Brandão,L.E.ET., and Gomes, L.L. (2019). Crypto-assets portfolio optimization under the omega measure. The Engineering Economist, 65 (2), 114-134.
- Chang, T-J., Yang, S.C., and Chang, K-J. (2009). Portfolio optimization problems in different risk measures using genetic algorithm. Expert Systems with Applications, 36, 10529–10537.
- Chekhlov, A., Uryasev,S., and Zabarankin, M. (2003). Portfolio Optimization With Drawdown Constraints.Pardalos, P.M., Migdalas, A. ve Baourakis,G. (Eds.). Supply Chain and Finance içinde (s. 209-228).London, England: World Scientific publishing Co.Pte.Ltd.
- Çelengi, A. Z., Eğrioğlu,E., ve Çorba,B.Ş. (2015). İMKB 30 indeksini oluşturan hisse senetleri için parçacık sürü optimizasyonu yöntemlerine dayalı portföy optimizasyonu. Doğuş Üniversitesi Dergisi, 16(1), 25-33.
- Dai, Z., and Wen, F. (2014). Robust CVaR-based portfolio optimization under a genal affine data perturbation uncertainty set. Journal of Computational Analysis and Applications, 16(1),93-103.
- Deng, L., Ma, C., and Yang,W. (2011). Portfolio optimization via pair copula-GARCH-EVT-CVaR model. Systems Engineering Procedia, 2, 171 – 181.
- Favre-Bulle, A., and Pache, S.(2003). The omega measure: Hedge fund portfolio optimization. (Unpublished MBF master’s thesis). University of Lausanne – Ecole Des Hec.
- Fernandez, A., and Gomez , S. (2007). Portfolio selection using neural networks. Computers & Operations Research, 34, 1177-1191.
- Gökgöz, E. (2006). Riske maruz değer (VaR) ve portföy optimizasyonu (1. Baskı) Ankara: Sermaye Piyasası Kurulu Yayınları, Yayın No: 190.
- Gökmen, Y. (2009). Stokastik programlama ile optimal portföy oluşturma. (Yayınlanmamış Doktora Tezi). Gazi Üniversitesi, Sosyal Bilimler Enstitüsü.
- Grinold R. C. (1989). The fundamental law of active management. Journal of Portfolio Management, 15 (3), 30-37.
- Jensen, M. C. (1968). The performance of mutual funds in the period 1945-1964. The Journal of Finance, 23 (2), 389-416.
- Keating, C., and Shadwick, W. F. (2002). A universal performance measure. Journal of Performance Measurement, 6(3), 59–84.
- Klega, D. (2013). My ventures are not in one bottom trusted: Comparative study to modern portfolio theory and Black-Litterman portfolio formation.( Unpublished Rigorosum Thesis). Charles University, Faculty of Social Sciences.
- Lim, A.E.B., Shanthikumar, J.G., and Vahn, G-Y. (2011). Conditional value-at-risk in portfolio optimization: Coherent but fragile. Operations Research Letters, 39(3),163-171.
- Ma, Y., Han, R., and Wang,W. (2021). Portfolio optimization with return prediction using deep learning and machine learning. Expert Systems with Applications,165(1),1139-73.
- Magdon-Ismail, M., and Atiya, A. (2004). An analysis of the maximum drawdown risk measure. Risk Magazine, 17 (10): 99–102.
- Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77-91.
- Mishra, A. K., Pisipati, S., and Vyas, I. (2011). An equilibrium approach for tactical asset allocation: Assessing Black-Litterman model to Indian stock market. Journal of Economics and International Finance, 3 (10), 553-563.
- Najafi, A. A,. and Mushakhian, S. (2015). Multi-stage stochastic mean–semivariance–CVaR portfolio optimization under transaction costs. Applied Mathematics and Computation, 256, 445–458.
- Özdemir, M. (2011). Genetik algoritma kullanılarak portföy seçimi. İktisat Isletme ve Finans, 26 (299), 43-66.
- Receiz, A. and León, C.E. (2008). Efficient Portfolio Optimization in the Wealth Creation and Maximum Drawdown Space. Berkelaar, A., Coche, J. ve Nyholm, K. (Eds.). Interest Rate Models, Asset Allocation and Quantitative Techniques For Central Banks And Sovereıgn Wealth Funds içinde (s.1-23). Bogota, Colombia: Palgrave Macmillan.
- Rejeb, A.B., and Boughrara, A.(2013). Financial liberalization and stock markets efficiency: New evidence from emerging economies. Emerging Markets Review, 17, 186–208.
- Rockafellar, R.T., and Uryasev, S. (2000). Optimization of conditional value-at-risk. Journal of Risk, 2, 21–41.
- Roy, A. D. (1952). Safety first and the holding of assets. Econometrica: Journal of the Econometric Society, 20 (3), 431-449.
- Sharma, A., Utz, S., and Mehra, A. (2017). Omega-CVaR portfolio optimization and its worst case analysis. OR Spectrum, 39, 505–539.
- Sharpe, W. F. (1966). Mutual fund performance. The Journal of Business, 39(S1), 119.
- Solatikia, F., Kiliç, E ., and Weber, G.W. (2014). Fuzzy optimization for portfolio selectionbased on embedding theorem in fuzzy normed linear spaces. Organizacija, 47(2), 90-97.
- Sortino F. A. (2000). Measuring risk: Upside-potential ratios vary by ınvestment style. Pensions and Investments, 28(22), 30–35.
- Treynor, J. L. (1965). How to rate management of investment funds. Harvard Business Review, 43 (1), 63-75.
- Uyar, U., ve Küçükşahin, H. (2017). Portföy seçiminde expected maximum drawdown yaklaşımı: BİST100-S&P500 Uygulaması. Business and Economics Research Journal, 8 (4), 727-748.
- Uygurtürk, H., ve Korkmaz, T. (2015). Portföy optimizasyonunda markowitz modelinin kullanımı: bireysel emeklilik yatırım fonları üzerine bir uygulama. Muhasebe ve Finansman Dergisi,68, 67-82.
- Yakut, E., ve Çankal, A. (2016). Çok amaçlı genetik algoritma ve hedef programlama metotlarını kullanarak hisse senedi portföy optimizasyonu: BİST 30’da bir uygulama. Business and Economics Research Journal, 7(2),43.62.
- Young T. W. (1991). Calmar ratio: A smoother tool. Futures (Cedar Falls, Iowa), 20 (11),1-22.
Details
| Primary Language | Turkish |
|---|---|
| Journal Section | Makaleler |
| Authors | |
| Publication Date | August 31, 2021 |
| Acceptance Date | May 16, 2021 |
| Published in Issue | Year 2021 Issue: 59 |
Cited By
Performans değerlendirmesinde risk temelli ölçütlerin kullanımı: BİST şehir endeksleri uygulaması
Balıkesir Üniversitesi Sosyal Bilimler Enstitüsü Dergisi
https://doi.org/10.31795/baunsobed.1512643
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