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ARFIMA ve FIGARCH yöntemlerinin Markowitz ortalama varyans portföy optimizasyonunda kullanılması: İMKB-30 endeks hisseleri üzerine bir uygulama

Using ARFIMA and FIGARCH methods in Markowitz mean variance portfolio optimization: An application on ISE-30 index stocks

Journal Name:

  • İstanbul Üniversitesi İşletme Fakültesi Dergisi

Publication Year:

  • 2013

Key Words:

Keywords (Original Language):

Author NameUniversity of AuthorFaculty of Author
Abstract (2. Language): 
In finance literature, there are some problems about Markowitz mean variance portfolio optimization model. One of these problems is how to determine the expected return of stocks which are used in calculations of portfolio optimization. In this study, whether enhanced optimized portfolios may be obtained via using fractional integrated models that ensure return forecast is examined. Return forecast data is obtained via ARFIMA model, and variance forecast data is obtained via FIGARCH model and then, dynamic portfolio optimizations for 42 months is formed by using obtained data. Performances of these portfolios are compared with equivalent dynamic optimized portfolios which use classical Markowitz expected returns. According to the results, the hypothesis investigated is not supported on ISE-30 Index stocks for forecast period including “Mortgage Crises”, which is originated from USA.
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Abstract (Original Language): 
Finans yazınında, Markowitz ortalama varyans portföy optimizasyon modeli için bazı problemler söz konusudur. Bu problemlerden biri, optimizasyon hesaplamalarında kullanılan hisse senedi beklenen getirilerin nasıl belirleneceğidir. Bu çalışmada, kesirli bütünleşik modellerden elde edilen öngörü verileri kullanılarak optimize edilen portföylerin daha yüksek performans gösterip gösteremeyeceği test edilmiştir. ARFIMA modeliyle getiri öngörüleri ve FIGARCH modeliyle varyans öngörü verileri elde edilmiş, elde edilen bu veri serileri kullanılarak 42 dönemlik dinamik portföy optimizasyonları oluşturulmuştur. Söz konusu bu portföylerin performansları, klasik Markowitz beklenen getirileri kullanılarak optimize edilen dinamik portföylerle karşılaştırılmıştır. Araştırma sonuçlarına göre, ABD kaynaklı “Mortgage Krizi”ni de içeren bu öngörü döneminde İMKB-30 Endeks hisse senetleri bazında araştırma hipotezindeki görüşü destekleyen sonuçlara ulaşılamamıştır.
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REFERENCES

References: 

[1] F.J. Fabozzi, P.N. Kolm, D.A Panhamanova, S.M. Focardi, Robust Portfolio Optimization and Management, John Wiley & Sons, New Jersey, 2007, pp. 139.
[2] R.O. Michaud, Efficient Asset Management, A Practical Guide to Stock Portfolio Optimization and Asset Allocation, Harvard Business School Press, Boston, 1998.
[3] M. Balcılar, “Persistance in Inflation: Long Memory, Aggregation, or Level Shifts?”, Sixth METU International Conference on Economics, September 11-14, 2002, Ankara, Turkey, erişim linki: http://www.emu.edu.tr/mbalcilar/rresearch/ (15 Aralık 2009).
[4] M. Karanasos, S.H. Sekioua, N. Zeng, On the Order of Integration of Monthly US Ex-ante and Ex-post Real Interest Rates: New Evidence from over a Century of Data. Economics Letters, 90, 2, 163–169 (2006).
[5] R. Caballero, S. Jewson A. Brix, Long Memory in Surface Air Temprature: Detection, Modeling, and Aplication to Weather Derivative Valuation. Climate Research, 21, June, 127-140 (2002).
[6] A.D. Roy, Safety First and the Holding of Assets. Econometrica, 20, 3, 431-449 (1952).
[7] H. Markowitz, Portfolio Selection. The Journal of Finance, 7, 1, 77-91 (1952).
[8] J. Tobin, Liquidity Preferences as Behavior Towards Risk. The Review of Economic Studies, 25, 2, 65-86 (1958).
[9] W.F. Sharpe, Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. The Journal of Finance, 19, 3, 425-442 (1964).
[10] J. Lintner, The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets. The Review of Economics and Statistics, 47, 1, 13-37 (1965).
M. Pekkaya, A.S. Albayrak / İstanbul Üniversitesi İşletme Fakültesi Dergisi 42, 1, (2013) 93-112 © 2013
105
[11] J. Mossin, Equilibrium in a Capital Asset Market. Econometrica, 34, 4, 768-783 (1966).
[12] J.P. Morgan, “RiskMetrics™ Monitor”, Fourth Quarter 1995, New York, http://www.riskmetrics.com/system/files/private/rmm4q95.pdf, 15 Ağustos 2010.
[13] S. Wang, Y. Xia, Portfolio Selection and Asset Pricing, Springer, Berlin, 2002, pp. 3-14.
[14] Y. Crama, M. Schyns, Simulated Annealing for Complex Portfolio Selection Problems. European Journal of Operational Research, 150, 3, 546-571 (2003).
[15] A. Gelman, “Prior distribution”, in A.H. El-Shaarawi, W.W. Piegorsch (Ed.), Encyclopedia of Environmetrics, John Wiley & Sons, Ltd, 2002, 1627-1637, erişim linki: http://www.stat.columbia. edu/~gelman/research/published/p039-_o.pdf, 12 Aralık 2010.
[16] S.M. Focardi, P.N. Kolm, F.J. Fabozzi, New Kids on the Block. The Journal of Portfolio Management, 30th Anniversary Issue, 42-54 (2004).
[17] S. Ceria, R.A. Stubbs, Incorporating Estimation Errors into Portfolio Selection: Robust Portfolio Construction. Journal of Asset Management, 7, 2, 109–127 (2006).
[18] R.H. Tütüncü, M. Koenig, Robust Asset Allocation. Annals of Operations Research, 132, 1-4, 157-187 (2004).
[19] F.J. Fabozzi, S.M. Focardi, P.H. Kolm, Financial Modeling of the Equity Market from CAPM to Cointegration, John Wiley & Sons, New Jersey, 2006, pp. 308-316.
[20] H. Zhang, “How Rational is the Stock Market towards Properties of Analyst Consensus Forecasts?”, http://www.fbe.hku.hk/~hzhang/research/diss.pdf, 29 Kasım 2010.
[21] I. Vehvilainen, “Applying Mathematical Finance Tools to the Competitive Nordic Electricity Market”, http://math.tkk.fi/reports/a475.pdf, 29 Kasım 2010.
[22] P. Swisher, G.W. Kasten, Post-Modern Portfolio Theory. Journal of Financial Planning, 18, 9, 74-85 (2005).
[23] H. Konno, R. Yamamoto, Minimal Concave Cost Rebalance of a Portfolio to the Efficient Frontier. Mathematical Programming, Ser. B 97, 571-585 (2003).
[24] V.A. Aivazian, J.L. Callen, I. Krinsky, C.C.Y. Kwan, Mean-Variance Utility Functions and the Demand for Risky Assets: An Empirical Analysis Using Flexible Functional Forms. Journal of Financial and Quantitative Analysis, 18, 4, 411–424 (1983).
[25] H. Markowitz, Portfolio Selection, Blackwell Publishing, UK, 2006, pp. 116-125.
[26] U. Çelikyurt, S. Özçekici, Multiperiod Portfolio Optimization Models in Stochastic Markets Using the Mean-Variance Approach. European Journal of Operational Research, 179, 1, 186-202 (2007).
[27] G.J. Alexander, A.M. Baptista, Portfolio Selection with a Drawdown Constrants. Journal of Banking & Finance, 30, 11, 3171–3189 (2006).
[28] M. Guidolin, S. Hyde, Equity Portfolio Diversification Under Time-Varying Predictability: Evidence from Ireland, the US, and the UK. Journal of Multinational Financial Management, 18, 4, 293–312 (2008).
[29] P. Grupta, M.K. Mehlawat, A. Saxena, Asset Portfolio Optimization Using Fuzzy Mathematical Programming. Information Sciences, 178, 6, 1734-1755 (2008).
M. Pekkaya, A.S. Albayrak / İstanbul Üniversitesi İşletme Fakültesi Dergisi 42, 1, (2013) 93-112 © 2013
106
[30] J. Branke, B. Scheckenbach, M. Stein, K. Deb, H. Schmeck, Portfolio Optimization with an Envelope-based Multi-objective Evolutionary Algorithm. European Journal of Operational Research, 199, 3, 684-693 (2009).
[31] X. Huang, Portfolio Selection with Fuzzy Returns. Journal of Intelligent & Fuzzy Systems, 18, 4, 383–390 (2007).
[32] L. Yu, S. Wang, K.K. Lai, Neural Network-Based Mean-Variance-Skewness Model for Portfolio Selection. Computers & Operations Research, 35, 1, 34-46 (2008).
[33] J.R.M. Hosking, Fractional Differencing. Biometrika, 68, 1, 165-176 (1981).
[34] L. Bisaglia, Model Selection for Long Memory Models. Quaderni di Statistica, 4, 33-49 (2002), erişim linki: http://www.dipstat.unina.it/Quaderni%20di%20statistica/ volume%204/bisaglia.pdf, 24 Temmuz 2010.
[35] M.J. Hinich, T.T.L. Chong, A Class Test for Fractional Integration. Studies in Nonlinear Dynamics & Econometrics, 11, 2, 1-22 (2007).
[36] T. Lux, T. Kaizoji, Forecasting Volatility and Volume in the Tokyo Stock Market: The Advantage of Long Memory Models. Economic Working Paper No. 05: Christian-Albrechts-Universität Kiel, 1-31 (2004), erişim linki: http://www.econstor.eu/handle/
10419/3244, 15 Mayıs 2010.
[37] J. Kwiatkowski, Bayesian Analysis of Long Memory and Persistence Using ARFIMA Models with an Application to Polish Stock Market. Dynamic Econometric Models, 4, 1-13 (2000), erişim linki: http://www.home.umk.pl/~jkwiat/ARFIMA_eng.pdf, 25 Mayıs 2010.
[38] R.O. Michaud, The Markowitz Optimization Enigma: Is ‘Optimized’ Optimal?. Financial Analysts Journal, 45, 1, 31-42 (1989).
[39] K.L. Fisher, M. Statman, The Mean-Variance-Optimization Puzzle: Security Portfolios and Food Portfolios. Financial Analysts Journal, 53, 4, 41-50 (1997).
[40] G. Zumbach, “Volatility Processes and Volatility Forecast with Long Memory” (2003), http://www.olsen.ch/fileadmin/Publications/Working_Papers/030617LM Processes.pdf, 25 Temmuz 2010.
[41] R.T. Baillic, Long Memory Processes and Fractional Integration in Econometrics. Journal of Econometrics, 73, 1, 5-59 (1996).
[42] A. Dionisio, R. Menezes, D.A. Mendes; On the Integrated Behaviour of Non-stationary Volatility in Stock Markets. Physica A: Statistical Mechanics and Its Applications, 382, 1, 58–65 (2007).
[43] A. Kasman, E. Torun, Long Memory in the Turkish Stock Market Return and Volatility. Central Bank Review, ISSN 1303-0701, Central Bank of the Republic of Turkey, 7, 2, 13-27 (2007).
[44] J. Cuñado, L.A. Gil-Alana, F.P. de Gracia, Stock Market Volatility in US Bull and Bear Markets. Journal of Money, Investment and Banking, 1, 24-32 (2008).
[45] L.A. Gil-Alana, P.M. Robinson, Testing of Unit Root and other Nonstaionary Hypotheses in Macroeconomic Time Series. Journal of Econometrics, 80, 2, 241-268 (1997).
[46] M. Balcılar, “Long Memory and Structural Breaks in Turkish Inflation Rates”, VI. Ulusal Ekonometri ve İstatistik Sempozyumu, Mayıs 2003, Gazi Üniversitesi, Ankara, erişim linki: http://www.emu.edu.tr/mbalcilar/rresearch/ (15 Aralık 2009).
M. Pekkaya, A.S. Albayrak / İstanbul Üniversitesi İşletme Fakültesi Dergisi 42, 1, (2013) 93-112 © 2013
107
[47] X. Shao, W.B. Wu, Local Asymptotic Powers of Nonparametric and Semiparametric Tests for Fractional Integration. Stochastic Processes and their Applications, 117, 2, 251–261 (2007).
[48] Y-W. Chung, K.S. Lai, A Fractional Cointegration Analysis of Purchasing Power Parity. Journal of Busness & Economic Statistics, 11, 1, 103-112 (1993).
[49] D.C. Yıldırtan, A.G. Bölükbaşı, “Testing for Long Memory Models in Turkish Derivatives Exchange Using ARFIMA FIGARCH Model”, 9th Special Conference of the Hellenic Operational Research Society, 27-29 May 2010, Agios Nikolaos, Greece, erişim linki: http://www.helors2010.gr (29 Kasım 2010).
[50] Ö. Demirtaş, Z. Güngör, Portföy Yönetimi ve Portföy Seçimine Yönelik Uygulama. Havacılık ve Uzay Teknolojileri Dergisi, 1, 4, 103-109 (2004).
[51] A. Kapusuzoğlu, S. Karacaer, The Process of Stock Portfolio Construction with Respect to the Relationship between Index, Return and Risk Evidence from Turkey. International Research Journal of Finance and Economics, 23, 193-206 (2009).
[52] G. Sayılgan, A.D. Mut, Portföy Optimizasyonunda Alt Kısmi Moment ve Yarı-Varyans Ölçütlerinin Kullanılması. BDDK Bankacılık ve Finansal Piyasalar, 4, 1, 47-73 (2010).
[53] M. Pekkaya, Kriz Dönemlerinde Hisse Senedi Portföylerinin Riske Maruz Değerlerinin Hesaplanması: İMKB-30 Endeks Uygulaması, Yayınlanmamış Yüksek Lisans Tezi, Zonguldak Karaelmas Üniversitesi Sosyal Bilimler Enstitüsü, 2002.
[54] S. Bozkuş, Risk Ölçümünde Alternatif Yaklaşımlar: Riske Maruz Değer (VaR) ve Beklenen Kayıp (ES) Uygulamaları. Dokuz Eylül Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, 20, 2, 27-46 (2005).
[55] B. Altaylıgil, Portföy Seçimi için Ortalama-Varyans-Çarpıklık Modeli. İstanbul Üniversitesi İşletme Fakültesi Dergisi, 37, 2, 65-78 (2008).
[56] A.A. Karacabey, Is Mean Variance Efficient than MAD in Istanbul. International Research Journal of Finance and Economics, 3, 113-120 (2006).
[57] Z. Haklı, Tam Sayılı Doğrusal Programlama Modeli ile Optimal Portföy Oluşturma ve İMKB’de bir Uygulama, Yayınlanmamış Yüksek Lisans Tezi, Süleyman Demirel Üniversitesi Sosyal Bilimler Enstitüsü, 2006.
[58] F. Kardiyen, Portföy Optimizasyonunda Ortalama Mutlak Sapma Modeli ve Markowitz Modelinin Kullanımı ve İMKB Verilerine Uygulanması. Süleyman Demirel Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, 13, 2, 335-350 (2008).
[59] M. Cihangir, A.K. Güzeler, İ. Sabuncu, Optimal Portföy Seçiminde Konno-Yamazaki Modeli Yaklaşımı ve İMKB Mali Sektör Hisse Senetlerine Uygulanması. Gazi Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, 10, 3, 125-142 (2008).
[60] M. Atan, “Karesel Programlama ile Portföy Optimizasyonu”, VII Ulusal Ekonometri ve İstatistik Sempozyumu, 26-27 Mayıs 2005, İstanbul, erişim linki: http://muratatan.info (15 Mayıs 2008).
[61] A.C. Çetin, Markowitz Kuadratik Programlama ile Optimal Portföy Seçimi. Süleyman Demirel Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, 12, 1, 63-81 (2007).
[62] G. Küçükkocaoğlu, “Optimal Portföyün Seçimi ve İMKB Ulusal-30 Endeksi Üzerine Bir Uygulama”, http://www.baskent.edu.tr/~gurayk/kisiseloptimization.pdf, 15 Mayıs 2009.
[63] E. Küçüksille, Veri Madenciliği Süreci Kullanılarak Portföy Performansının Değerlendirilmesi ve İMKB Hisse Senetleri Piyasasında Bir Uygulama,
M. Pekkaya, A.S. Albayrak / İstanbul Üniversitesi İşletme Fakültesi Dergisi 42, 1, (2013) 93-112 © 2013
108
Yayınlanmamış Doktora Tezi, Süleyman Demirel Üniversitesi Sosyal Bilimler Enstitüsü, 2009.
[64] K. Kayalıdere, H. Aktaş, “Alternatif Portföy Seçim Modellerinin Performanslarının Karşılaştırılması (İmkb Örneği)”, http://www.sbe.deu.edu.tr/ dergi/cilt10.say%C4 %B11/10.1%20kayal%C4%B1dere%20akta%C5%9F.pdf, 16 Eylül 2010.
[65] N. Bozdağ, Ş. Altan, S. Duman, “Minimaks Portföy Modeli ile Markowitz Ortalamavaryans Portföy Modelinin Karşılaştırılması”, http://www. ekonometridernegi.org/bildiriler/o24s1.pdf, 16 Eylül 2010.
[66] N. Bozdağ, H. Türe, Bulanık Doğrusal Programlama ve İMKB Üzerine Bir Uygulama, Gazi Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, 10, 1, 1-18 (2008).
[67] İstanbul Menkul Kıymetler Borsası, http://imkb.gov.tr, 15 Mart 2011.
[68] A.F. Yüzer, E. Ağaoğlu, H. Talıdil, A. Özmen, E. Şıklar, İstatistik, 6. Baskı, Anadolu Üniversitesi Yayın No: 1448, Eskişehir, 2009, 297.
[69] M. Pekkaya, ARFIMA ve FIGARCH Yöntemlerinin Markowitz Ortalama Varyans Portföy Optimizasyonunda Kullanılması: İMKB-30 Endeks Hisseleri Üzerine Bir Uygulama, Yayınlanmamış Doktora Tezi, Zonguldak Karaelmas Üniversitesi Sosyal Bilimler Enstitüsü, 2011.
[70] C. Conrad, B.R. Haag, Inequality Constraints in the Fractionally Integrated GARCH Model. Journal of Financial Econometrics, 4, 3, 413-449 (2006), http://www.uni-konstanz.de/micfinma/conference/Files/papers/Conrad_Haag.pdf, 26 Temmuz 2010.
[71] J. Duan, K. Jacobs, Is Long Memory Necessary? An Empirical Investigation of Nonnegative Interest Rate Processes. Journal of Empirical Finance, 15, 3, 567–581 (2008), http://www.rotman.utoronto.ca/~jcduan/LongMemoryInterest Rate.pdf, 25 Temmuz 2010.
[72] Türkiye Cumhuriyeti Merkez Bankası, http://www.tcmb.gov.tr, 05 Ocak 2011.
[73] W.F. Sharpe, The Sharpe Ratio. Journal of Financial Portfolio Management, 21, 1, 49-58 (1994).
[74] H.A. Taha, Operations Research an Introduction, Prentice-Hall Inc., International Edition, London, 1997, pp. 86.
[75] K. Niemczak, Eastern European Equity Markets and the Subprime Crisis Does Emerging Europe Still Offer Diversification Benefits?. Finansowy Kwartalnik Internetowy e-Finanse, 6, 3, 47-63 (2010).
[76] C.N.V. Krishnan, R. Petkova, P. Ritchken, Correlation Risk. Journal of Empirical Finance, 16, 3, 353-367 (2009).
[77] D.M. Rey, Time-varying Stock Market Correlations and Correlation Breakdown. Finanzmark und Portfolio Management, 4, 387-412 (2000).

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