由于大宗交易下边际交易费用递减,因此用线性加凹的函数拟合实际交易费用函数, 建立了均值-方差框架下的组合优化模型并给出了相应的求解算法.通过对恒生指数样本股的实证分析发现:考虑大宗交易的组合有效边缘介于线性交易费用和无交易费用的组合有效边缘之间; 大宗交易稀释了“分散化降低风险”的效应; 大宗交易下交易费用越大, 相对于线性交易费用而言组合集中度越高.
Abstract
In this paper, we consider the portfolio optimal problem under block trading. As the decrease of marginal transaction cost under block trading, we establish the mean-variance portfolio optimization model and the corresponding algorithm by means of fit transaction cost function with linear and concave form. Computational results are presented by considering the stocks involved in Hang Seng Index to show that: The efficient frontier under block trading is between that with linear transaction cost and without transaction cost; The investment risk can be eliminated by portfolio diversification, but the effect of that is dilute under block trading; In terms of linear transaction cost, the greater the transaction cost under block trading, the higher the portfolio concentration.
关键词
大宗交易 /
线性加凹交易费用 /
组合规模 /
分散化效应 /
分枝定界算法
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Key words
block trading /
linear and concave transaction cost /
portfolio size /
diversification effect /
branchbound algorithm
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中图分类号:
F830.9
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参考文献
[1] Markowitz H. Portfolio selection[J]. Journal of Finance, 1952(1): 77-91.
[2] BestM J, Kale J K. Quadratic Programming for Large Scale Portfolio Optimization[M]// Jessica Keyes. Financial Services Information Systems, CRC Press: Boca Raton, 2000.
[3] Best M J, Hlouskova J. Portfolio selection and transaction costs[J]. Computational Optimization and Application, 2003(24): 95-116.
[4] Lobo M S, Fazel M, Boyd S. Portfolio optimization with linear and fixed transaction costs[J]. Annals of Operations Research, 2007(152): 341-365.
[5] Schattman J B. Portfolio selection under nonconvex transaction cost and capital gains taxes[D]. Rugters Center for Operations Research, Rugters University, USA, 2000.
[6] Li D, Sun X L, Wang J. Optimal lot solution to cardinality constrained mean-variance formulation for portfolio selection[J]. Mathematical Finance, 2006(16): 83-101.
[7] Evans J L, Archer S H. Diversification and the reduction of dispersion: An empirical analysis[J]. Journal of Finance, 1968(23): 761-767.
[8] Fisher L, Lorie J H. Some studies of variability of returns on investments in common stocks[J]. Journal of Business, 1970(43): 90-l34.
[9] Statman M. How many stocks make a diversified portfolio?[J]. Journal of Financial and Quantitative Analysis, 1987(22): 353-363.
[10] Tang G Y N. How efficient is naive portfolio diversification? An educational note[J]. Omega — The International Journal of Management Science, 2004(32): 155-160.
[11] 施东晖. 上海股票市场风险性实证研究[J]. 经济研究, 1996(10): 44-48. Shi D H. The empirical research of the risk in Shanghai market[J]. Economic Research, 1996(10): 44-48.
[12] 吴世农, 韦绍永. 上海股市投资组合规模和风险关系的实证研究[J]. 经济研究, 1998(4): 21-29. Wu S N, Wei S Y. The empirical study of the portfolio size and risk in Shanghai stock market[J]. Economic Research, 1998(4): 21-29.
[13] 杨继平, 张力健. 沪市股票投资组合规模与风险分散化关系的进一步研究[J]. 系统工程理论与实践, 2005, 25(10): 21-28. Yang J P, Zhang L J. The further study of the relationship between portfolio size and risk diversification in Shanghai stock market[J]. Systems Engineering — Theory & Practice, 2005, 25(10): 21-28.
[14] http://baike.baidu.com/view/1000275.htm?fr=ala0??1??1.
[15] 薛宏刚. 投资组合VaR的计算与考虑交易费用的投资组合最优选择[D]. 西安: 西安交通大学, 2004. Xue H G. The calculation of the portfolio’s VaR and portfolio optimization under transaction costs[D]. Xi’an: Xi’an Jiaotong University, 2004.
[16] Konno H, Wijayanayake A. Portfolio optimization problem under concave transaction costs and minimal transaction unit constraints[J]. Mathematical Programming, 2001, 89: 233-250.
[17] Xue H G, Xu C X, Feng Z X. Mean-variance portfolio optimal problem under concave transaction cost[J]. Applied Mathematics and Computation, 2006, 174: 1-12.
[18] Rockafellar R T. Convex Analysis[M]. Princeton: Princeton University Press, 1970.
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基金
国家自然科学基金(71171158); 教育部新世纪优秀人才支持计划项目(NCET-10-0646); 教育部人文社会科学研究项目基金(09XJAZH005, 10YJCZH043)
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