Data Mining and Knowledge Discovery

, Volume 32, Issue 6, pp 1708–1734 | Cite as

A kernel-based trend pattern tracking system for portfolio optimization

  • Zhao-Rong Lai
  • Pei-Yi YangEmail author
  • Xiaotian Wu
  • Liangda Fang


We propose a novel kernel-based trend pattern tracking (KTPT) system for portfolio optimization. It includes a three-state price prediction scheme, which extracts both of the following and reverting patterns from the asset price trend to make future price predictions. Moreover, KTPT is equipped with a novel kernel-based tracking system to optimize the portfolio, so as to capture a potential growth of the asset price effectively. The kernel measures the similarity between the current portfolio and the predicted price relative to control the influence of each asset when optimizing the portfolio, which is different from some previous kernels that measure the probability of occurrence of a price relative. Extensive experiments on 5 benchmark datasets from real-world stock markets with various assets in different time periods indicate that KTPT outperforms other state-of-the-art strategies in cumulative wealth and other risk-adjusted metrics, showing its effectiveness in portfolio optimization.


Kernel method Trend pattern analysis Tracking system Portfolio optimization 



The authors would like to thank the Editor-in-Chief, the Area Editor, and the anonymous reviewers for the detailed and constructive comments and suggestions that help to significantly improve this paper. This work is supported by the National Natural Science Foundation of China [Grant Numbers 61703182, 61602211, 61603152]; the Fundamental Research Funds for the Central Universities [Grant Numbers 21617347, 21617404]; the Talent Introduction Foundation of Jinan University [Grant Numbers 88016653, 88016534]; Science and Technology Program of Guangzhou, China [Grant Number 201707010259]; the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) and Jiangsu Collaborative Innovation Center on Atmospheric Environment and Equipment Technology (CICAEET); Guangxi Key Laboratory of Trusted Software [Grant Number kx201606]; the Fundamental Research Funds for the Center for Mathematical Finance in Guangdong Province [Grant Number 50411628].


  1. Agarwal A, Hazan E, Kale S, Schapire RE (2006) Algorithms for portfolio management based on the Newton method. In: Proceedings of the 23rd international conference on machine learningGoogle Scholar
  2. Algoet PH, Cover TM (1988) Asymptotic optimality and asymptotic equipartition properties of log-optimum investment. Ann Probab 16(2):876–898MathSciNetzbMATHGoogle Scholar
  3. Bertsekas D (1999) Nonlinear programming. Athena Scientific, BelmontzbMATHGoogle Scholar
  4. Blum A, Kalai A (1999) Universal portfolios with and without transaction costs. Mach Learn 35(3):193–205zbMATHGoogle Scholar
  5. Borodin A, El-Yaniv R, Gogan V (2004) Can we learn to beat the best stock. J Artif Intell Res 21(1):579–594MathSciNetzbMATHGoogle Scholar
  6. Breiman L (1961) Optimal gambling systems for favorable games. In: Proceedings of the the Berkeley symposium on mathematical statistics and probability, vol 1, pp 65–78Google Scholar
  7. Cover TM (1991) Universal portfolios. Math Finance 1(1):1–29MathSciNetzbMATHGoogle Scholar
  8. Cover TM, Thomas JA (1991) Elements of information theory. Wiley, New YorkzbMATHGoogle Scholar
  9. Cui X, Li X, Li D (2014) Unified framework of mean-field formulations for optimal multi-period mean–variance portfolio selection. IEEE Trans Autom Control 59(7):1833–1844MathSciNetzbMATHGoogle Scholar
  10. Duchi J, Shalev-Shwartz S, Singer Y, Chandra T (2008) Efficient projections onto the \(\ell ^1\)-ball for learning in high dimensions. In: Proceedings of the International Conference on Machine Learning (ICML 2008)Google Scholar
  11. Friedman J, Tibshirani R, Hastie T (2010) Regularization paths for generalized linear models via coordinate descent. J Stat Softw 33(1):1–22Google Scholar
  12. Graham JR, Harvey CR (1996) Market timing ability and volatility implied in investment newsletters’ asset allocation recommendations. J Finance Econ 42:397–421Google Scholar
  13. Grinold RC, Kahn RN (1999) Active portfolio management: a quantitative approach for producing superior returns and controlling risk. McGraw-Hill, New YorkGoogle Scholar
  14. Grinold RC, Kahn RN (2000) Active portfolio management, 2nd edn. McGraw-Hill, New YorkGoogle Scholar
  15. Györfi L, Lugosi G, Udina F (2006) Nonparametric kernel-based sequential investment strategies. Math Finance 16(2):337–357MathSciNetzbMATHGoogle Scholar
  16. Györfi L, Udina F, Walk H (2008) Nonparametric nearest neighbor based empirical portfolio selection strategies. Stat Decis 26(2):145–157MathSciNetzbMATHGoogle Scholar
  17. He J, Wang QG, Cheng P, Chen J, Sun Y (2015) Multi-period mean–variance portfolio optimization with high-order coupled asset dynamics. IEEE Trans Autom Control 60(5):1320–1335MathSciNetzbMATHGoogle Scholar
  18. Hoerl A, Kennard R (1988) Ridge regression. In: Kotz S, Johnson NL (eds) Encyclopedia of statistical sciences, vol 8. Wiley, New York, pp 129–136Google Scholar
  19. Huang D, Zhou J, Li B, Hoi S.C.H, Zhou S (2013) Robust median reversion strategy for on-line portfolio selection. In: Proceeding of the twenty-third international joint conference on artificial intelligence, pp 2006–2012Google Scholar
  20. Huang D, Zhou J, Li B, Hoi SCH, Zhou S (2016) Robust median reversion strategy for online portfolio selection. IEEE Trans Knowl Data Eng 28(9):2480–2493Google Scholar
  21. Jegadeesh N (1990) Evidence of predictable behavior of security returns. J Finance 45(3):881–898Google Scholar
  22. Jegadeesh N (1991) Seasonality in stock price mean reversion: evidence from the U.S. and the U.K. J Finance 46(4):1427–1444Google Scholar
  23. Li B, Hoi SCH (2014) Online portfolio selection: a survey. ACM Comput Surv (CSUR) 46(3):35-1–35-36zbMATHGoogle Scholar
  24. Li B, Hoi SCH, Gopalkrishnan V (2011) Corn: Correlation-driven nonparametric learning approach for portfolio selection. ACM Trans Intell Syst Technol 2(3):21Google Scholar
  25. Li B, Zhao P, Hoi SCH, Gopalkrishnan V (2012) Pamr: passive aggressive mean reversion strategy for portfolio election. Mach Learn 87(2):221–258MathSciNetzbMATHGoogle Scholar
  26. Li B, Hoi SCH, Zhao P, Gopalkrishnan V (2013) Confidence weighted mean reversion strategy for online portfolio selection. ACM Trans Knowl Discov Data 7(1):4Google Scholar
  27. Li B, Hoi SCH, Sahoo D, Liu ZY (2015) Moving average reversion strategy for on-line portfolio selection. Artif Intell 222:104–123MathSciNetGoogle Scholar
  28. Li B, Sahoo D, Hoi SCH (2016) OLPS: a toolbox for on-line portfolio selection. J Mach Learn Res 17(35):1–5MathSciNetGoogle Scholar
  29. Lintner J (1965) The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Rev Econ Stat 47(1):13–37Google Scholar
  30. Liu Q, Dang C, Huang T (2013) A one-layer recurrent neural network for real-time portfolio optimization with probability criterion. IEEE Trans Cybern 43(1):14–23Google Scholar
  31. Markowitz HM (1952) Portfolio selection. J Finance 7(1):77–91Google Scholar
  32. Mercer J (1909) Functions of positive and negative type and their connection with the theory of integral equations. R Soc Lond Philos Trans 209:415–446zbMATHGoogle Scholar
  33. Merton RC (1969) Lifetime portfolio selection under uncertainty: the continuous-time case. Rev Econ Stat 51(3):247–257Google Scholar
  34. Mossin J (1966) Equilibrium in a capital asset market. Econometrica 34(4):768–783Google Scholar
  35. Nguyen TT, Lee GB, Khosravi A, Creighton D, Nahavandi S (2015) Fuzzy portfolio allocation models through a new risk measure and fuzzy sharpe ratio. IEEE Trans Fuzzy Syst 23(3):656–676Google Scholar
  36. Pola G, Pola G (2012) A stochastic reachability approach to portfolio construction in finance industry. IEEE Trans Control Syst Technol 20(1):189–195Google Scholar
  37. Raudys S (2013) Portfolio of automated trading systems: complexity and learning set size issues. IEEE Trans Neural Netw Learn Syst 24(3):448–459Google Scholar
  38. Sharpe WF (1964) Capital asset prices: a theory of market equilibrium under conditions of risk. J Finance 19(3):425–442MathSciNetGoogle Scholar
  39. Sharpe WF (1966) Mutual fund performance. J Bus 39(1):119–138Google Scholar
  40. Shiller RJ (2000) Irrational exuberance. Princeton University Press, PrincetonGoogle Scholar
  41. Tibshirani R (1996) Regression shrinkage and selection via the lasso. J R Stat Soc 58(1):267–288MathSciNetzbMATHGoogle Scholar
  42. Treynor JL, Black F (1973) How to use security analysis to improve portfolio selection. J Bus 46(1):66–86Google Scholar
  43. Vardi Y, Zhang CH (2000) The multivariate \(\ell ^1\)-median and associated data depth. Proc Natl Acad Sci USA 97(4):1423–1426MathSciNetzbMATHGoogle Scholar
  44. Vercher E, Bermúdez JD (2013) A possibilistic mean-downside risk-skewness model for efficient portfolio selection. IEEE Trans Fuzzy Syst 21(3):585–595Google Scholar
  45. Weber A (1909) Uber den Standort der Industrien. Mohr, TubingenGoogle Scholar
  46. Weiszfeld E (1937) Sur le point pour lequel la somme des distances de n points donnes est minimum. Tohoku Math J 43:355–386zbMATHGoogle Scholar
  47. Yang L, Couillet R, McKay MR (2015) A robust statistics approach to minimum variance portfolio optimization. IEEE Trans Signal Process 63(24):6684–6697MathSciNetzbMATHGoogle Scholar
  48. Zou H, Hastie T (2005) Regularization and variable selection via the elastic net. J R Stat Soc Ser B (Stat Methodol) 67(2):301–320MathSciNetzbMATHGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Department of Mathematics, College of Information Science and TechnologyJinan UniversityGuangzhouChina
  2. 2.School of MathematicsSun Yat-Sen UniversityGuangzhouChina
  3. 3.Department of Computer Science, College of Information Science and TechnologyJinan UniversityGuangzhouChina
  4. 4.State Key Laboratory of Information Security, Institute of Information EngineeringChinese Academy of SciencesBeijingChina
  5. 5.Nanjing University of Information Science and TechnologyNanjingChina
  6. 6.Guangxi Key Laboratory of Trusted SoftwareGuilin University of Electronic TechnologyGuilinChina

Personalised recommendations