MİNİMUM YAYILAN AĞAÇ İLE PORTFÖY ANALİZİ: BIST100 ÖRNEĞİ

Year 2019, Volume: 4 Issue: 4, 609 - 625, 31.12.2019

Ayşegül İşcanoğlu Çekiç , Buket Taştan

https://doi.org/10.29106/fesa.593881

Abstract

Markowitz (1952)
çalışması iyi bir risk yönetiminde, finansal yatırım araçları arasındaki
korelasyonların dikkate alınmasına işaret etmiş ve yatırımcıların seçimlerinde
korelasyonların önemini vurgulamıştır. Zaman içinde ise bu olgu genel kabul
görmüştür. Birçok araştırmacı ve yatırımcı için risk yönetimi korelasyonlar ile
özdeşleşmiştir.  Son yıllarda, finansal
ürünler arasındaki çapraz korelasyonların saptanması için finansal ağlar önem
kazanmıştır. Çalışmada, bu yöntemlerden Minimum Yayılan Ağaç (MST) dikkate
alınarak, Borsa İstanbul’da işlem gören hisse senetleri arasındaki kısa dönem
çapraz korelasyonların incelenmesi amaçlanmıştır. Bu amaçla, BIST100 endeksine
dahil 94 hisse senedi dikkate alınmış ve Ocak 2018 ve Haziran 2018 dönemine ait
günlük hisse senedi fiyat verisi kullanılmıştır. Bu ağaçtan yola çıkarak, hisse
senetlerinin ağaç üzerinde konumlarının portföy performanslarına etkisi simülasyonlar
yardımı ile araştırılmıştır. Çalışmanın bulgularına göre, büyük hisse senedi
kümelerinin merkezi hisselerinin, THYAO, BIMAS, CEMAS, IEYHO, FLAP ve AYEN kodlu
hisseler olduğu ve bu hisselerin kendi kümelerindeki diğer hisseler üzerinde
güçlü etkiye sahip oldukları gözlemlenmiştir. Ayrıca portföylerin ağaç
üzerindeki konumlarının performanslarında etkin olduğu gözlemlenerek aynı uç
dallara ait bağlantısız kümelerden oluşturulan portföylerinde performanslarının
diğer portföylere göre daha iyi olduğu sonucuna ulaşılmıştır.

Keywords

MST, Çapraz Korelasyon, Hiyerarşik Kümeleme, Portföy Çeşitlendirmesi

PORTFOLIO ANALYSIS WITH MINIMUM SPANNING TREE: AN APPLICATION TO XU100

Abstract

The pioneering work of Markowitz
(1952) emphasized the importance of correlations between financial assets in
risk management and investor preferences. Over time, this phenomenon was
generally accepted. Today, for researchers and investors,  risk management is associated with
correlations. In recent years, in order to determine cross-correlations between
financial products the importance of financial networks are increased. In this
study, it is aimed to investigate the short term cross-correlations between the
stocks traded on Borsa Istanbul, by using Minimum Spanning Tree (MST) methodology.
For this purpose, 94 stocks of XU100 index are included into the analysis and
daily stock price data from January 2018 to June 2018 period are used. Using
the constructed tree, the effects of stocks’ positions on the portfolio
performances are investigated with the help of simulation study. Findings show
that the central stocks of the large stock clusters are coded with THYAO,
BIMAS, CEMAS, IEYHO, FLAP and AYEN and these stocks have a strong effect on the
other stocks in their clusters. In addition, it is concluded that stock
positions are effective in portfolio performances and it is concluded that portfolio
performances are better for the portfolios which contain the stocks of
unconnected clusters in the same end branches.

 

Keywords

MST, Cross Correlation, Hierarchical Cluster

References

• Akgüller, Ö., Öcal, S., Balcı, M.A. (2017). A New Topological Measure for The Communities of Stock Market Networks, Mugla Journal of Science and Technology, 3(2), 104-109
• Birch, J., Pantelous, A.A., Soramäki, K. (2016). Analysis Of Correlation Based Networks Representing DAX 30 Stock Price Returns, Computational Economics, 47(4), 501–525.
• Bonanno, G., Vandewalle, N., Mantegna, R.N. (2000). Taxonomy Of Stock Market Indices, Physical Review E, 62(6), 7615–7618.
• Bonanno, G., Lillo, F., Mantegna, R.N. (2001). High-Frequency Cross-Correlation in a Set of Stocks, Quantitative Finance, 1, 96-104
• Bonanno, G., Caldarelli, G., Lillo, F, Mantegna, R.N. (2003). Topology of Correlation-Based Minimal Spanning Trees in Real and Model Markets, Physical Review E, 68, 046130
• Bonanno, G., Caldarelli, G., Lillo, F., Micciché, S., Vandewalle, N., Mantegna, R.N. (2004). Networks of Equities in Financial Markets, The European Physical Journal B, 38(2), 363-371.
• Coelho, R., Gilmore, C.G., Lucey, B., Richmond, P., Hutzler, S. (2007). The Evolution of Interdependence İn World Equity Markets - Evidence From Minimum Spanning Trees, Physica A, 376, 455–466.
• Coelho, R., Hutzler, S., Repetowicz, P., Richmond, P. (2007). Sector Analysis for A FTSE Portfolio of Stocks, Physica A, 373, 615–626.
• Danko, J., Soltes, V. (2018). Portfolio Creation Using Graph Characteristics, Investment Management and Financial Innovations, 15(1), 180-189.
• Eryiğit, M., Eryiğit, R. (2009). Network Structure of Cross Correlations Among the World Market Indices, Physica A, 388, 3551–3562.
• Gilmore, C.G., Lucey, B.M., Boscia, M. (2008). A Never-Closer Union? Examining The Evolution of Linkages Of European Equity Markets Via Minimum Spanning Trees, Physica A, 387 (2008) 6319–6329.
• Gilmore, C.G., Lucey, B.M., Boscia, M.W. (2010). Comovements In Government Bond Markets: Aminimum Spanning Tree Analysis. Physica A, 389(21), 4875–4886.
• Guo, X., Zhang, H., Tian, T. (2018). Development Of Stock Correlation Networks Using Mutual İnformation And Financial Big Data, PLoS ONE, 13(4): e0195941.
• Hatipoğlu, V.F., (2017). Application of a New Quantitative Approach to Stock Markets: Minimum Spanning Tree, Alphanumeric Journal, 5(2).
• Mantegna, R. N. (1999). Hierarchical Structure in Financial Markets. The European Physical Journal B, 11, 193-197.
• Mantegna, R.N., Stanley, H.E. (2000). An Introduction To Econophysics: Corrleations and Complexity in Finance. Cambridge:Cambridge Universiy Press.
• Markowitz, H. M. (1952). Portfolio Selection, The Journal of Finance, 7(1), 77-91.
• Micciche, S., Bonanno, G., Lillo, F., Mantegna, R.N. (2003). Degree Stability Of A Minimum Spanning Tree Of Price Return and Volatility, Physica A, 324 66.
• Onnela, J.P., Chakraborti, A., Kaski, K., Kertesz, J. (2002). Dynamic Asset Trees And Portfolio Analysis, The European Physical Journal B, 30(3), 285–288
• Onnela, J.-P., Chakraborti, A., Kaski, K., Kertesz, J., Kanto, A. (2003a). Asset Trees and Asset Graphs in Financial Markets, Physica Scripta, T106, 48-54.
• Onnela, J.-P., Chakraborti, A., Kaski, K., Kertesz, J., Kanto, A. (2003b). Dynamics Of Market Correlations: Taxonomy and Portfolio Analysis, Physical Review E, 68(5), 68-79.
• Tse, C.K., Liu, J., Lau, F.C.M. (2010). A Network Perspective Of The Stock Market, Journal of Empirical Finance, 17(4), 659–667.
• Vandewalle, N., Brisbois, F., Tordoir, X. (2001). Self-organized Critical Topology of Stock Markets, Quantitative Finance, 1, 372–375
• Vizgunov, A., Goldengorin, V., Kalyagin, V., Koldanov, A., Koldanov, P., Pardalos, P. M. (2014). Network Approach For The Russian Stock Market, Computational Management Science, 11(1–2), 45–55.
• Wang, G.-J., Xie, H.C., Stanley, E. (2018). Correlation Structure and Evolution of World Stock Markets: Evidence from Pearson and Partial Correlation-Based Networks, Computational Economics, 51( 3), 607–635.
• Zhang, X., Zheng, X., Zeng, D.D. (2017). The Dynamic Interdependence Of International Financial Markets: An Empirical Study On Twenty-Seven Stock Markets, Physica A, 472, 32-42