Abstract
Modern portfolio theory introduced by Markowitz in 1952 is the most popular portfolio optimization framework established based on the trade-off between risk and return as an operation research model. The main shortcoming of applying Markowitz portfolio optimization in practice is that the obtained optimal weights are really sensitive to the embedded uncertainty in return series of stocks. In this paper, it is demonstrated how using a new methodology of time series clustering as a remedy can lead to a more robust and accurate portfolio in terms of the gap between mean variance efficient frontier obtained from the optimization model and the one observed in reality. In this regard, two similarity measures, the autocorrelation coefficients and the weighted dynamic time warping, are used in an innovative way to construct the desired portfolio optimization model. Moreover, the effectiveness of proposed approach is investigated in two different market conditions: semi-realistic and full-realistic. In the first one, it is assumed that the forecasted and realized stocks mean returns are the same; however, these returns are not necessarily equal in the second market conditions. Finally, a database of stock prices from the literature is utilized to show the robustness and accuracy of the proposed approach in empirical results in comparison with applied similarity measures in previous researches.
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References
Aghabozorgi S, Shirkhorshidi AS, Wah TY (2015) Time-series clustering—a decade review. Inf Syst 53:16–38
Amenc N, Le Sourd V (2005) Portfolio theory and performance analysis. Wiley, Hoboken
Au S-T, Duan R, Hesar SG, Jiang W (2010) A framework of irregularity enlightenment for data pre-processing in data mining. Ann Oper Res 174:47–66
Basalto N, Bellotti R, De Carlo F, Facchi P, Pascazio S (2005) Clustering stock market companies via chaotic map synchronization. Phys A 345:196–206
Berndt DJ, Clifford J (1994) Using dynamic time warping to find patterns in time series. In: KDD workshop, vol 16. Seattle, WA, pp 359–370
Best MJ (2010) Portfolio optimization. CRC Press, Boca Raton
Bonanno G, Lillo F, Mantegna RN (2001) High-frequency cross-correlation in a set of stocks. Quant Finance 96:104
Bouguettaya A, Yu Q, Liu X, Zhou X, Song A (2015) Efficient agglomerative hierarchical clustering. Expert Syst Appl 42:2785–2797
Caiado J, Crato N, Peña D (2006) A periodogram-based metric for time series classification. Comput Stat Data Anal 50:2668–2684
Caiado J, Crato N, Peña D (2009) Comparison of times series with unequal length in the frequency domain. Commun Stat Simul Comput 38:527–540
Capitani P, Ciaccia P (2007) Warping the time on data streams. Data Knowl Eng 62:438–458
Cong F, Oosterlee C (2016) Multi-period mean-variance portfolio optimization based on monte-carlo simulation. J Econ Dyn Control 64:23–38
D’Urso P, Maharaj EA (2009) Autocorrelation-based fuzzy clustering of time series. Fuzzy Sets Syst 160:3565–3589
Ehrgott M, Klamroth K, Schwehm C (2004) An MCDM approach to portfolio optimization. Eur J Oper Res 155:752–770
Fangwen Z, Zehong Y, Yixu S, Yi L (2010) A novel similarity measure framework on financial data mining. In: 2010 second international conference on networks security wireless communications and trusted computing (NSWCTC). IEEE, pp 505–508
Han J, Kamber M, Pei J (2006) Data mining, southeast Asia edition: concepts and techniques. Morgan Kaufmann, Burlington
Irani J, Pise N, Phatak M (2016) Clustering techniques and the similarity measures used in clustering: a survey. Int J Comput Appl 134:9–14
Jeong Y-S, Jayaraman R (2015) Support vector-based algorithms with weighted dynamic time warping kernel function for time series classification. Knowl Based Syst 75:184–191
Jeong Y-S, Jeong MK, Omitaomu OA (2011) Weighted dynamic time warping for time series classification. Pattern Recognit 44:2231–2240
Kaufman L, Rousseeuw PJ (2009) Finding groups in data: an introduction to cluster analysis, vol 344. Wiley, Hoboken
Keogh E, Kasetty S (2003) On the need for time series data mining benchmarks: a survey and empirical demonstration. Data Min Knowl Disc 7:349–371
Keogh EJ, Pazzani MJ (1998) An enhanced representation of time series which allows fast and accurate classification, clustering and relevance feedback. In: KDD, pp 239–243
Keogh E, Ratanamahatana CA (2005) Exact indexing of dynamic time warping. Knowl Inf Syst 7:358–386
Liao TW (2005) Clustering of time series data—a survey. Pattern Recognit 38:1857–1874
Lin C-C, Liu Y-T (2008) Genetic algorithms for portfolio selection problems with minimum transaction lots. Eur J Oper Res 185:393–404
Madhulatha TS (2012) An overview on clustering methods. arXiv preprint arXiv:12051117
Markowitz H (1952) Portfolio selection. J Finance 7:77–91
Markowitz HM (1959) Portfolio selection: efficient diversification of investments, 2nd edn. Wiley, Hoboken
Merton RC (1980) On estimating the expected return on the market: an exploratory investigation. J Financ Econ 8:323–361
Mitsa T (2010) Temporal data mining. CRC Press, Boca Raton
Murtagh F, Contreras P (2012) Algorithms for hierarchical clustering: an overview. Wiley Interdiscip Rev Data Min Knowl Discov 2:86–97
Nanda S, Mahanty B, Tiwari M (2010) Clustering Indian stock market data for portfolio management. Expert Syst Appl 37:8793–8798
Sharpe WF (1964) Capital asset prices: a theory of market equilibrium under conditions of risk. J Finance 19:425–442
Shirkhorshidi AS, Aghabozorgi S, Wah TY (2015) A comparison study on similarity and dissimilarity measures in clustering continuous data. PLoS ONE 10:e0144059
Soon L-K, Lee SH (2007) An empirical study of similarity search in stock data. In: Proceedings of the 2nd international workshop on Integrating artificial intelligence and data mining, vol 84. Australian Computer Society, Inc., pp 31–38
Taillard G (2004) Le point sur? L’optimisation de portefeuille. Bankers, Markets & Investors No. 65
Tola V, Lillo F, Gallegati M, Mantegna RN (2008) Cluster analysis for portfolio optimization. J Econ Dyn Control 32:235–258
Vaclavik M, Jablonsky J (2012) Revisions of modern portfolio theory optimization model. CEJOR 20:473–483
Weng S-S, Liu Y-H (2006) Mining time series data for segmentation by using ant colony optimization. Eur J Oper Res 173:921–937
Witten IH, Frank E (2005) Data mining: practical machine learning tools and techniques. Morgan Kaufmann, Burlington
Wöllmer M, Al-Hames M, Eyben F, Schuller B, Rigoll G (2009) A multidimensional dynamic time warping algorithm for efficient multimodal fusion of asynchronous data streams. Neurocomputing 73:366–380
Xi X, Keogh E, Shelton C, Wei L, Ratanamahatana CA (2006) Fast time series classification using numerosity reduction. In: Proceedings of the 23rd international conference on machine learning. ACM, pp 1033–1040
Yim O, Ramdeen KT (2015) Hierarchical cluster analysis: comparison of three linkage measures and application to psychological data. Quant Methods Psychol 11:8–21
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We are grateful to Institute for Plasma Research of Kharazmi University for all their kindness and help in terms of providing us with their super computer and facilities.
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Massahi, M., Mahootchi, M. & Arshadi Khamseh, A. Development of an efficient cluster-based portfolio optimization model under realistic market conditions. Empir Econ 59, 2423–2442 (2020). https://doi.org/10.1007/s00181-019-01802-5
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DOI: https://doi.org/10.1007/s00181-019-01802-5
Keywords
- Portfolio optimization
- Realized efficient frontier
- Time series clustering
- Weighted dynamic time warping
- Autocorrelation coefficient
- Realistic market condition