基于聚类选股的上证50指数跟踪遗传算法优化模型研究

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3.0 周伟光 2024-09-30 5 4 997.23KB 55 页 15积分

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硕士学位论文

摘要

中国的证券市场经过二十多年的发展，已经从一棵幼苗发展成了一棵枝繁叶

茂的参天大树，市场指数体系的建立也已基本完善，建成了上证综合指数、深证

综合指数、沪深 300 指数、上证 180 指数、上证 50 指数、中证 100 指数等等，基

于这些指数的 ETF 和其它投资产品也在不断地出现。截止到 2012 年，指数类产

品管理资金经过将近 10 年的发展，其规模已经超过 4000 亿元，产品形式覆盖分

级基金、ETF、LOF 和开放式指数基金，指数化投资理念已经深入人心。而股指

期货的推出也将推动指数化投资进入一个全新的发展阶段。

随着我国资本市场的不断发展和证券指数体系的日趋成熟，指数基金等各种

指数化投资产品不断的出现，指数跟踪作为指数化投资产品的基本技术也得到许

多投资界人士和理论界学者的重视。指数跟踪是根据某种方法构建一个股票投资

组合，使其表现尽可能与目标指数接近。它可以运用于指数基金、股指期货与标

的指数之间的交易等方面，对股票价值投资和分散化投资有着重要的意义，有利

于促进我国资本市场健康有序地发展。

截止到 2012 年 10 月，跟踪相同标的指数的 A 股指数基金跟踪误差分化十分

显著，因此指数跟踪技术仍然有着巨大的改善空间，对于指数跟踪的研究仍具有

相当的必要性。本文在结合现代投资组合理论和有效市场理论等理论的基础上，

运用统计学、遗传生物学和金融学相关知识对指数跟踪的跟踪效果进行研究，意

在发展和改进优化指数跟踪的方法。

本文主要分为五部分，第一部分为导论，第二部分为指数跟踪的参数选择；

第三部分是本文指数跟踪优化的模型设计，第四部分利用实际数据对本文的优化

模型进行实证分析，最后部分则是结论。

第一部分导论主要介绍本文的选题背景、研究意义、研究的重难点和本文的

创新之处。在导论部分，本文还对指数跟踪的国内外研究成果进行了归纳和总结，

根据前人研究成果的特点和不足之处，本文提出了相应的研究思路和改进方向。

第二部分为指数跟踪的参数选择，主要为本文的指数跟踪优化模型确定相应

的参数。这一部分根据指数跟踪定义和特点，本文确定了指数跟踪优化模型的度

量方法、影响因素和目标指数的选择。

第三部分为本文的核心部分，设计了基于聚类选择的指数跟踪遗传算法优化

模型。根据前人对指数跟踪优化模型的研究成果，本文发现指数跟踪主要采用传

统的优化算法，部分复制的成分股选择采取市值最大化排序或随机抽样，跟踪误

硕士学位论文

差的度量则主要采用收益率序列。正是如此，本文针对这些特点对优化模型加以

改进。首先在优化算法方面引入生物遗传学的遗传算法，得到最优解的概率要大

于传统的点到点的优化算法；其次在成分股选择方面采用聚类选股的方法。前人

在构建跟踪投资组合的成分股时，缺乏对目标指数原始数据信息的进一步利用，

本文采用聚类选股方法弥补这一缺陷，有效地利用了目标指数的原始数据信息；

最后本文综合价格时间序列和收益率时间序列这两方面的信息，降低日均收益率

的波动，提高跟踪组合与目标指数的相关系数，降低数学模型的跟踪误差。据此，

本文设计得到相应的指数跟踪遗传算法优化模型。

第四部分为实证分析部分，主要利用上证 50 指数数据对第三部分设计的指数

指跟踪遗传算法优化模型进行实证检验。首先本文利用聚类分析得到相应股票簇，

挑选出部分复制的投资组合的成分股；其次本文根据传统算法和遗传算法设计不

同的优化方案，得到相应的优化计算结果；最后，本文对比不同方法的优化计算

结果，发现综合了价格时间序列和收益率时间序列的指数跟踪组合的跟踪误差较

单独的时间序列得到的误差要小，说明了更多的时间序列信息可以提高指数跟踪

的精度。

最后部分为结论部分，主要对本文主要内容进行总结，并提出了本文的一些

不足和下一步可能的研究方向。

关键词：指数跟踪；遗传算法；聚类分析；跟踪误差

硕士学位论文

ABSTRACT

With more than two-decade development, China’s security market has been

booming as if a seedling has grown into a tall tree with luxuriant foliage. And the

establishment of market index system also has been completed. For example, Shanghai

stock exchange composite index, Shenzhen securities composite index, Hushen 300

index, Shanghai stock exchange 180 index, Shanghai stock exchange 50 index, China

securities 100 index and so on have been established. EFT base on these indexes is also

continuously appearing. With almost a decade’s development of index products

management funds, the total number has exceeded 400 billion yuan, product forms

have covered grade funds, ETF, LOF and open-end index funds, and index investment

concept has enjoyed popular support by 2012. Furthermore, the development of futures

will also promote index investment to enter into a new development stage.

With the continuous development of China's capital market and the maturity of

stock index system, index funds and other index-based investment products are

constantly appearing. As a basic technology of index investment products, index

tracking has attracted more and more attention of investors in investment field and

academics in theory field. Stock index tracking is to build a stock portfolio in some

way in order to make its performance as much as possible close to the target index. It

can be applied to index funds, transactions between the stock index futures and the

target, and so on, playing a great part in value investment and diversification

investment, and being helpful to promote the healthy and orderly development of

China's capital market. On the basis of combining with modern portfolio theory,

efficient market theory and other theories, this paper uses relevant knowledge of

statistics, biogenetics and finance to study the tracking performance of the index

tracking so as to develop and improve the methods of solving the portfolio.

This paper is mainly divided into five parts including introduction, parameter

selection of index tracking, model design of index tracking optimization, empirical

analysis of the optimization model with the aid of actual data and finally conclusion.

The introduction mainly introduces subject background, significance of study, key

and difficult points of study, innovation of this paper. And in this part, this paper

concludes the domestic and overseas research achievements of index tracking and

硕士学位论文

formulates the corresponding research thinking and improvement direction according

to characteristics and deficiencies of the previous research achievements.

The second part is about parameter selection of index tracking, mainly

determining corresponding parameter for optimization model of index tracking in this

paper. In this part, this paper determines the selection of the measurement methods,

influencing factors and target index of index tracking optimization model according to

the definition and characteristics of index tracking.

The third part is the core part of this paper, designing optimization model of

genetic algorithm of index tracking based on clustering selection. According to the

previous research achievements of index tracking optimization model, this paper

discovers that conventional optimization methods are used in common index tracking,

that market value maximization sequencing or random sampling is adopted in some

replicated constituent stocks, and that yield rate series are mainly used for

measurement of tracking error. Therefore, this paper aims to improve the optimization

model according to these characteristics. Firstly, genetic algorithm is introduced from

biogenetics in the aspect of optimization computation, and the probability of getting

optimal solution is bigger than conventional point-to-point optimization method.

Secondly, clustering method is used for selection of constituent stocks. Since the initial

group of genetic algorithm is selected randomly in the convergence space leading to

lack of further deployment of original data information of target index, this paper

adopts clustering method to make up for it and effectively uses the original data

information of target index. Finally, this paper combines the information of price time

series with time series of yield rate in order to reduce fluctuation of average daily yield

rate and tracking error of mathematical model and improve correlation coefficients of

tracking portfolio and target index. Accordingly, this paper designs and obtains

corresponding optimization model of index tracking genetic algorithm.

The fourth part is about empirical analysis, mainly deploying the actual Shanghai

Stock Exchange 50 index data to make an empirical test of optimization model of

index tracking genetic algorithm designed in the third part. Firstly, this paper uses

clustering analysis to obtain stock cluster and then selects constituent stocks of some

replicated portfolio. Secondly, this paper designs different optimization plans

according to conventional computing method and genetic algorithm to get

corresponding results of optimization computing. Eventually, this paper compares

different results of optimization computing with different methods and finds that the

硕士学位论文

III

tracking error of index tracking portfolio is smaller when combining price time series

and time series of yield rate compared with the error got from the single time series,

which shows that more time series information can improve the accuracy of index

tracking.

The final part is about conclusion including a summary of the main contents in

this paper, some shortcomings of this paper and the possible future research directions.

Key words: index tracking; Cluster analysis; genetic algorithms; tracking error

硕士学位论文

第 1 章导言 ......................................................... 5

1.1 论文的写作背景和意义 ..........................................5

1.2 国内外相关文献 ................................................8

1.3 论文的研究思路及创新 .........................................13

第 2 章指数跟踪的参数确定 .......................................... 15

2.1 指数跟踪的基本内涵 ...........................................15

2.2 指数跟踪的必要性 .............................................18

2.3 指数跟踪误差的度量选择 .......................................20

2.4 影响跟踪误差的因素 ...........................................24

2.5 目标指数的选择 ...............................................25

2.6 小结 .........................................................27

第 3 章基于聚类选股的遗传算法优化模型设计 .......................... 28

3.1 遗传算法的引入 ...............................................28

3.2 跟踪组合的聚类选股 ...........................................33

3.3 跟踪模型的构建 ...............................................35

3.4 跟踪组合成分股权重的设定 .....................................37

3.5 小结 .........................................................37

第 4 章基于上证 50 指数的实证 ....................................... 38

4.1 数据的选取和处理 .............................................38

4.2 跟踪组合成分股的聚类选择 .....................................38

4.3 实证方案的设计 ...............................................42

4.4 实证结果 .....................................................43

4.5 小结 .........................................................47

第 5 章总结 ........................................................ 48

5.1 结论 .........................................................48

5.2 研究展望 .....................................................50

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摘要：

硕士学位论文V摘要中国的证券市场经过二十多年的发展，已经从一棵幼苗发展成了一棵枝繁叶茂的参天大树，市场指数体系的建立也已基本完善，建成了上证综合指数、深证综合指数、沪深300指数、上证180指数、上证50指数、中证100指数等等，基于这些指数的ETF和其它投资产品也在不断地出现。截止到2012年，指数类产品管理资金经过将近10年的发展，其规模已经超过4000亿元，产品形式覆盖分级基金、ETF、LOF和开放式指数基金，指数化投资理念已经深入人心。而股指期货的推出也将推动指数化投资进入一个全新的发展阶段。随着我国资本市场的不断发展和证券指数体系的日趋成熟，指数基金等各种指数化投资产品不断的出现，指...

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