基于序关系重构的恒定再平衡投资组合

中国管理科学 ›› 2014, Vol. 22 ›› Issue (3): 13-19.

基于序关系重构的恒定再平衡投资组合

刘学伟, 贺昌政, 朱兵

四川大学商学院, 四川成都 610064

收稿日期:2012-04-02 修回日期:2012-10-10 出版日期:2014-03-20 发布日期:2014-03-19
作者简介:刘学伟（1970- ），男（汉族），四川成都人，四川大学商学院，博士研究生，讲师，研究方向：金融数据挖掘.
基金资助:
国家自然科学基金资助项目（70771067，71071101）

Rank-Reconstruction Based Constant Rebalanced Portfolios

LIU Xue-wei, HE Chang-zheng, ZHU Bing

Business School of Sichuan University, Chengdu 610064, China

Received:2012-04-02 Revised:2012-10-10 Online:2014-03-20 Published:2014-03-19

摘要/Abstract

摘要： CRP（Constant Rebalancing Portfolios，即恒定再平衡投资组合）是一种重要的投资组合，它要求资产收益率序列必须满足独立同分布条件，这个限定条件影响了CRP在实际金融投资中的应用。为了使CRP发挥与其理论基础相称的实际效果，对真实金融数据进行基于序关系的重构，使得重构后的数据接近于满足独立同分布条件。在重构后的数据上构建最优CRP，这种策略称为rankCRP。证明了在适当的条件下rankCRP具有最优性。运用国际国内多个真实市场的大型历史数据进行检验，检验结果表明rankCRP在真实市场的表现优于CRP，远远超越市场指数，甚至战胜涨幅最大的证券。RankCRP在理论上的最优性表明，通过适当的重构，CRP也可以适用于非独立同分布收益率时间序列，拓宽了CRP理论的适用领域。RankCRP在实践上的有效性对金融投资实务有重要意义。

关键词: 动态投资组合, 独立同分布, 序关系重构, CRP

Abstract: The Constant Rebalanced Portfolio (CRP) is an asset allocation algorithm which keeps the same distribution of wealth among a set of assets along a period of time. The best CRP is optimal when the stock return time series is I.I.D.. However the unrealistic I.I.D. condition set the CRP back from application. By means of reconstructing the real financial data to be I.I.D., it is possible to apply the CRP to investment industry. The optimality of rank-reconstruction based Constant Rebalanced Portfolios (rankCRP proposed in this paper) is proved theoretically. And the empirical study on several markets shows the effective of rankCRP. The study sheds light on the relationship between CRP and non I.I.D. time series.

Key words: dynamic portfolio, rank-reconstruction, rankCRP

中图分类号:

C812

刘学伟, 贺昌政, 朱兵. 基于序关系重构的恒定再平衡投资组合[J]. 中国管理科学, 2014, 22(3): 13-19.

LIU Xue-wei, HE Chang-zheng, ZHU Bing. Rank-Reconstruction Based Constant Rebalanced Portfolios[J]. Chinese Journal of Management Science, 2014, 22(3): 13-19.

参考文献

[1] Markowitz H. Portfolio selection: Efficient diversification of investments[M]. New York: Wiley, 1959.

[2] Luenberger D G. Investment science[M]. New York: Oxford University Press, 1998.

[3] Cover T M, Gluss D H. Empirical Bayes stock market portfolios[J]. Advances in applied mathematics, 1986, 7(2):170-181.

[4] Cover T M, Thomas J A. Elements of information theory[M]. New York: John Wiley & Sons, 1991.

[5] Breiman L. Optimal gambling systems for favorable games[J]. Proceedings of the Berkeley Symposium on Mathematical Statistics and Probability, 1961, 1:65-78.

[6] Gyorfi L, Ottucsák G, Urbán A. Empirical log-optimal portfolio selections: a survey[R]. Working Paper, Budapest University of Technology and Economics, 2007.

[7] Lo A W, MacKinlay A C. Stock market prices do not follow random walks: Evidence from a simple specification test[J]. Review of Financial Studies, 1988, 1(1):41-66.

[8] 刘兴华, 杨建梅. 证券市场的条件可预测性分析[J]. 管理科学学报, 2008, 11(6):77-83.

[9] Gyorfi L, Schafer D. Nonparametric prediction[M]//. Suykens J A K, Horváth G, Basu S, et al. Advances in learning theory: Methods, models and applications. Netherlands: IOS Press, 2003.

[10] Gyorfi L, Urbán A, Vajda I. Kernel-based semi-log-optimal empirical portfolio selection strategies[J]. International Journal of Theoretical and Applied Finance, 2007, 10(3):505-516.

[11] Gyorfi L, Udina F, Walk H. Nonparametric nearest neighbor based empirical portfolio selection strategies[J]. Statistics and Decisions, 2008, 26(2):145-157.

[12] Borodin A, El-Yaniv R, Gogan V. Can we learn to beat the best stock[J]. Journal of Artificial Intelligence Research, 2004, 21:579-594.

[13] Li Bin, Hoi S C, Gopalkrishnan V. CORN: Correlation-driven nonparametric learning approach for portfolio selection[J]. ACM Transactions on Intelligent Systems and Technology, 2010, 2(3):21.

[14] Mori T F. On favourable stochastic games[J]. Annales Univ. Sci. Budapest, 1982, 3:99-103.

[15] Algoet P H, Cover T M. Asymptotic optimality and asymptotic equipartition properties of log-optimum investment[J]. The Annals of Probability, 1988, 16(2):876-898.

[16] Algoet P. The strong law of large numbers for sequential decisions under uncertainty[J]. EE Transactions on Information Theory, 1994, 40:609-634.

[17] Algoet P. Universal schemes for prediction, gambling and portfolio selection[J]. The Annals of Probability, 1992, 20(2):901-941.

[18] Pearl J. Causality: Models, reasoning, and inference[M]. Combridge: Cambridge University Press, 2000.

[19] Li Bin, Zhao Peilin, Hoi S C, et al. PAMR: Passive aggressive mean reversion strategy for portfolio selection[J]. Machine Learning, 2012, 87(2):221 -258.

[20] Cover T M. Universal Portfolios[J]. Mathematical Finance, 1991, 1(1):1-29.

[21] Singer Y. Switching Portfolios[J]. International Journal of Neural Systems, 1997, 8(4):488-495.

[22] Helmbold D P, Schapire R E, Singer Y, et al. On-line portfolio selection using multiplicative updates[J]. Mathematical Finance, 1998, 8(4):325-347.

[23] Blum A, Kalai A. Universal portfolios with and without transaction Costs[J]. Machine Learning, 1999, 35(3):193-205.