带交易成本的二阶在线投资组合选择策略

瞿菁晶; 郁顺昌; 黄定江

doi:10.3969/j.issn.1000-5641.2019.04.008

带交易成本的二阶在线投资组合选择策略

doi: 10.3969/j.issn.1000-5641.2019.04.008

瞿菁晶^1,,
郁顺昌¹,
黄定江^1,2, ,

1.
华东理工大学理学院, 上海 200237
2.
华东师范大学数据科学与工程学院, 上海 200062

基金项目:

国家自然科学基金 11501204

国家自然科学基金 U1711262

上海市自然科学基金 15ZR1408300

详细信息

作者简介:
瞿菁晶, 女, 硕士研究生, 研究领域为机器学习与金融投资组合选择.E-mail:Jolinqu@hotmail.com

通讯作者:
黄定江, 男, 教授, 研究领域为机器学习与人工智能及其在计算金融、教育等跨领域的大数据解析和应用.E-mail:djhuang@ecust.edu.cn

中图分类号: TP399
计量
- 文章访问数: 105
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- PDF下载量: 75
- 被引次数: 0
出版历程
- 收稿日期: 2018-08-07
- 刊出日期: 2019-07-25

Second-order online portfolio selection strategy with transaction costs

1.
School of Science, East China University of Science and Technology, Shanghai 200237, China
2.
School of Data Science and Engineering, East China Normal University, Shanghai 200062, China

摘要

摘要: 针对基于在线牛顿步（Online Newton Step，ONS）算法的投资组合选择策略没有考虑交易成本的问题，而交易成本是真实市场中不可或缺的部分，提出了一种新的带交易成本的在线投资组合选择策略，简称在线牛顿步交易成本策略（Online Newton Step Transaction Cost，ONSC）：首先，结合投资组合向量的二阶信息和交易成本惩罚项构造优化函数，并推导得出投资组合的更新公式；然后，通过理论分析得到ONSC算法的次线性后悔边界O（log（T））.实证研究表明，与半常数再调整投资组合策略（Semiconstant RebalancedPortfolios，SCRP）以及其他考虑交易成本的策略相比，在SP500、NYSE（O）、NYSE（N）和TSE这4个真实市场的数据集上，ONSC获得了最高的累计净收益和最小的周转率，表明了所提算法的有效性.
- 投资组合选择 /
- 在线牛顿步 /
- 交易成本
Abstract: Existing portfolio selection strategies based on the online Newton step (ONS) algorithm ignore the role of transaction costs, an indispensable factor in real markets. This paper proposes a new online portfolio selection strategy, the online Newton step transaction cost (ONSC) method, to address this issue. First, we constructed the optimal function by combining second order information of a portfolio with the transaction cost penalty term, and the portfolio was subsequently updated. Then, the sublinear regret bound O(log(T)) was achieved by theoretical analysis. Empirical research on the data sets of four real markets-namely, SP500, NYSE(O), NYSE(N) and TSE-showed that in comparison to semiconstant rebalanced portfolios (SCRP) and other strategies with transaction costs, ONSC achieves the highest accumulated wealth and the smallest turnover. Hence, the research demonstrates the efiectiveness of the algorithm.
- portfolio selection /
- online Newton step /
- transaction costs

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图 1 6个策略在数据集SP500上的周转率结果($ c = 0.05 $)

Fig. 1 The turnover results for six strategies on the SP500 dataset ($ c = 0.05 $)

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图 2 6个策略在数据集NYSE(O)上的周转率结果($ c = 0.05 $)

Fig. 2 The turnover results for six strategies on the NYSE(O) dataset ($ c = 0.05 $)

下载: 全尺寸图片幻灯片

图 3 6个策略在数据集NYSE(N)上的周转率结果($ c = 0.05 $)

Fig. 3 The turnover results for six strategies on the NYSE(N) dataset ($ c = 0.05 $)

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图 4 6个策略在数据集TSE上的周转率结果($ c = 0.05 $)

Fig. 4 The turnover results for six strategies on the TSE dataset ($ c = 0.05 $)

下载: 全尺寸图片幻灯片

表 1 实验数据集

Tab. 1 Databases used for experiments

数据集	时间范围	天数/d	股票数/只
SP500	1998.01.02-2003.01.30	1 276	25
NYSE(O)	1962.07.0-1984.12.31	2 826	36
NYSE(N)	1985.01.01-2010.06.30	6 431	23
TSE	1994.01.04-1998.12.31	1 259	88

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表 2 在数据集SP500上50次独立试验($ {c}{ = 0.05} $, 0.02, 0.01, 0.001, 0)

Tab. 2 Average net wealth for 50 independent trails ($ c = 0.05 $, 0.02, 0.01, 0.001, 0) on the SP500 dataset

策略	$ c $
策略	0.05	0.02	0.01	0.001	0
ONSC	2.146	2.235	2.265	2.293	2.296
ONS	0.582	1.133	1.419	1.740	1.823
UP	1.196	1.603	1.804	2.016	2.091
SUP	1.790	1.836	1.880	1.915	1.987
CRP	0.855	1.448	1.727	2.024	2.060
SCRP	1.651	1.789	1.841	1.890	1.895

下载: 导出CSV

表 3 在数据集NYSE(O)上50次独立试验($ {c}{ = 0.05} $, 0.02, 0.01, 0.001, 0)的平均净收益

Tab. 3 Average net wealth for 50 independent trails ($ c = 0.05 $, 0.02, 0.01, 0.001, 0) on the NYSE(O) dataset

策略	$ c $
策略	0.05	0.02	0.01	0.001	0
ONSC	38.562	38.866	40.315	40.724	40.770
ONS	4.379	16.158	25.557	38.959	40.786
UP	22.911	23.705	27.583	29.520	35.111
SUP	29.079	30.640	32.393	34.221	36.702
CRP	3.562	14.532	23.587	2.024	40.125
SCRP	19.381	23.708	25.673	27.429	27.752

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表 4 在数据集NYSE(N)上50次独立试验($ {c}{ = 0.05} $, 0.02, 0.01, 0.001, 0)的平均净收益

Tab. 4 Average net wealth for 50 independent trails ($ c = 0.05 $, 0.02, 0.01, 0.001, 0) on the NYSE(N) Dataset

策略	$ c $
策略	0.05	0.02	0.01	0.001	0
ONSC	27.014	28.327	28.778	29.190	29.236
ONS	1.468	6.659	11.238	18.128	19.125
UP	10.521	12.385	16.091	20.400	22.137
SUP	14.931	15.943	16.849	17.867	19.636
CRP	1.187	6.823	12.266	20.828	22.092
SCRP	11.679	14.592	15.930	17.372	17.549

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表 5 在数据集TSE上50次独立试验($ {c}{ = 0.05} $, 0.02, 0.01, 0.001, 0)的平均净收益

Tab. 5 Average net wealth for 50 independent trails ($ c = 0.05, 0.02, 0.01, 0.001, 0 $) on the TSE dataset

策略	$ c $
策略	0.05	0.02	0.01	0.001	0
ONSC	2.812	2.931	2.971	3.008	3.012
ONS	0.430	0.887	1.131	1.408	1.443
UP	1.149	1.297	1.591	1.816	2.143
SUP	1.671	1.841	1.952	2.090	2.219
CRP	0.781	1.216	1.414	1.621	1.646
SCRP	1.694	1.815	1.860	1.899	1.907

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表 6 6个策略在4个数据集上的周转率的数值结果

Tab. 6 The numerical turnover results of six strategies on the four datasets

策略	数据集
策略	SP500	NYSE(O)	NYSE(N)	TSE
ONSC	0.001 18	0.000 54	0.000 25	0.001 09
ONS	0.017 32	0.014 21	0.007 80	0.019 00
UP	0.148 63	0.882 00	1.096 39	0.164 89
SUP	0.004 62	0.015 71	0.002 73	0.004 44
CRP	0.622 26	1.123 00	1.187 33	0.780 97
SCRP	0.011 05	0.002 83	0.003 63	0.002 69

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