WO2019192134A1 - Portfolio optimization method, device, and storage medium - Google Patents

Portfolio optimization method, device, and storage medium Download PDF

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WO2019192134A1
WO2019192134A1 PCT/CN2018/102222 CN2018102222W WO2019192134A1 WO 2019192134 A1 WO2019192134 A1 WO 2019192134A1 CN 2018102222 W CN2018102222 W CN 2018102222W WO 2019192134 A1 WO2019192134 A1 WO 2019192134A1
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portfolio
stock
initial
stocks
return
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PCT/CN2018/102222
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李正洋
周璟
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平安科技(深圳)有限公司
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    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06QINFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q40/00Finance; Insurance; Tax strategies; Processing of corporate or income taxes
    • G06Q40/06Asset management; Financial planning or analysis
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06QINFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00Administration; Management
    • G06Q10/04Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"

Abstract

The present application provides a portfolio optimization method. The method comprises: receiving stocks in an input initial portfolio to be optimized and an initial weight corresponding to each stock in the initial portfolio, and obtaining a market corresponding to each stock and history data of each stock in the initial portfolio in a first preset time period; calculating a weight corresponding to each stock in the initial portfolio, and determining a first portfolio subjected to preliminary optimization; and predicting a prospective logarithmic rate of return of each stock in the first portfolio, and determining a second portfolio. The present application further provides an electronic device and a storage medium. By using the present application, the correlation between each two individual stocks in an initial portfolio is minimized as much as possible, and a weight corresponding to each stock in a portfolio is adjusted by predicting a prospective rate of return of each stock, so as to improve the portfolio return.

Description

投资组合优化方法、装置及存储介质Portfolio optimization method, device and storage medium
本申请基于巴黎公约申明享有2018年4月3日递交的申请号为CN2018102966908、名称为“投资组合优化方法、装置及存储介质”的中国专利申请的优先权,该中国专利申请的整体内容以参考的方式结合在本申请中。The present application is based on the priority of the Chinese Patent Application entitled "Investment Portfolio Optimization Method, Apparatus and Storage Medium" filed on April 3, 2018, the disclosure of which is hereby incorporated by reference. The way is combined in this application.
技术领域Technical field
本申请涉及金融大数据挖掘领域,尤其涉及一种投资组合优化方法、电子装置及计算机可读存储介质。The present application relates to the field of financial big data mining, and in particular, to a portfolio optimization method, an electronic device, and a computer readable storage medium.
背景技术Background technique
投资组合是指金融机构或者投资者所持有的股票、债券、衍生金融产品等组成的集合,以股票为例,如何分配投资组合中每只个股的比例,以实现一定的目标,比如收益对大话或者风险最小化,构建投资组合的目的在于分散风险。A portfolio refers to a collection of stocks, bonds, and derivative financial products held by a financial institution or investor. Taking stocks as an example, how to allocate the proportion of each stock in the portfolio to achieve certain goals, such as income pair To minimize language or risk, the purpose of building a portfolio is to spread risk.
然而,在投资组合中,各只股票对应的权重并不是一成不变的。目前,业内对于投资组合中股票的权重分配通常采用人工调整的形式。此类方法较为依赖研究人员个人的交易经验,缺乏客观性,效率低,且不利于控制风险。However, in the portfolio, the weight of each stock is not static. Currently, the industry's weighting of stocks in portfolios is usually in the form of manual adjustments. Such methods rely more on the individual trading experience of the researchers, lack of objectivity, low efficiency, and are not conducive to controlling risks.
发明内容Summary of the invention
本申请提供一种投资组合优化方法、电子装置及计算机可读存储介质,其主要目的在于尽可能缩小初始投资组合中个股两两之间的相关性,并通过预测各只股票的未来收益率对投资组合中各股票对应的权重进行调整,以提高投资组合收益。The present application provides a portfolio optimization method, an electronic device, and a computer readable storage medium, the main purpose of which is to minimize the correlation between individual stocks in the initial investment portfolio, and to predict the future yield of each stock by comparing The weights corresponding to each stock in the portfolio are adjusted to increase the portfolio income.
为实现上述目的,本申请提供一种投资组合优化方法,该方法包括:To achieve the above objective, the present application provides a portfolio optimization method, the method comprising:
接收输入的待优化的初始投资组合中的股票、初始投资组合中各股票对应的初始权重,获取各股票对应的市场及该初始投资组合中各股票在第一预设时间内的历史数据;Receiving the initial weights of the stocks in the initial portfolio to be optimized and the stocks in the initial portfolio, and obtaining the historical data of the market corresponding to each stock and the stocks in the initial investment portfolio in the first preset time;
根据所述历史数据及预设的第一分析规则,计算得到所述初始投资组合中的各股票之间的相关性最小时,所述初始投资组合中各股票应对应的权重, 并对初始投资组合中的各股票对应的权重进行调整,确定初步优化后的第一投资组合;及Calculating, according to the historical data and the preset first analysis rule, a weight corresponding to each stock in the initial investment portfolio when the correlation between the stocks in the initial investment portfolio is minimum, and initial investment Adjusting the weight corresponding to each stock in the portfolio to determine the first optimized investment portfolio; and
获取所述第一投资组合中的各股票在第二预设时间内的历史数据,构建各股票的特征向量,并输入各股票对应的预先训练好的未来收益率预测模型中,预测所述第一投资组合中的各股票的未来对数收益率,根据预设的第二分析规则对所述第一投资组合中的各股票对应的权重进行调整,确定第二投资组合。Obtaining historical data of each stock in the first investment portfolio in a second preset time, constructing a feature vector of each stock, and inputting a pre-trained future profit rate prediction model corresponding to each stock, predicting the first The future logarithmic yield of each stock in a portfolio is adjusted according to a preset second analysis rule for the weight corresponding to each stock in the first portfolio, and the second portfolio is determined.
此外,为实现上述目的,本申请还提供一种电子装置,该电子装置包括:存储器、处理器,所述存储器上存储有投资组合优化程序,所述投资组合优化程序被所述处理器执行时实现如上所述的投资组合优化方法的步骤。In addition, in order to achieve the above object, the present application further provides an electronic device, including: a memory, a processor, and a portfolio optimization program stored on the memory, where the portfolio optimization program is executed by the processor The steps of the portfolio optimization method as described above are implemented.
此外,为实现上述目的,本申请还提供一种计算机可读存储介质,所述计算机可读存储介质上存储有投资组合优化程序,所述投资组合优化程序被处理器执行时实现如上所述的投资组合优化方法的步骤。In addition, in order to achieve the above object, the present application further provides a computer readable storage medium, where the portfolio optimization program is stored, and the portfolio optimization program is executed by a processor to implement the above The steps of the portfolio optimization method.
相较于现有技术,本申请提出的投资组合优化方法、电子装置及计算机可读存储介质,在保持收益不变的情况下,尽可能缩小初始投资组合中个股两两之间的相关性,对初始投资组合进行初步优化,得到风险最小的第一投资组合;另外,通过LSTM模型预测第一投资组合中各股票对应的未来对数收益率,并对未来收益率相对较高或较低的股票的权重进行调整,得到第二投资组合,在一定程度上提高了投资收益。Compared with the prior art, the portfolio optimization method, the electronic device and the computer readable storage medium proposed by the present application minimize the correlation between individual stocks in the initial investment portfolio while keeping the income unchanged. The initial investment portfolio is initially optimized to obtain the first portfolio with the least risk; in addition, the future logarithmic yield of each stock in the first portfolio is predicted by the LSTM model, and the future yield is relatively high or low. The weight of the stock is adjusted to obtain the second investment portfolio, which improves the investment income to a certain extent.
附图说明DRAWINGS
图1为本申请电子装置较佳实施例的示意图;1 is a schematic diagram of a preferred embodiment of an electronic device of the present application;
图2为图1中投资组合优化程序的程序模块图;2 is a program module diagram of the portfolio optimization program of FIG. 1;
图3为本申请投资组合优化方法较佳实施例的流程图。3 is a flow chart of a preferred embodiment of a portfolio optimization method of the present application.
本申请目的的实现、功能特点及优点将结合实施例,参照附图做进一步说明。The implementation, functional features and advantages of the present application will be further described with reference to the accompanying drawings.
具体实施方式detailed description
应当理解,此处所描述的具体实施例仅仅用以解释本申请,并不用于限定本申请。It is understood that the specific embodiments described herein are merely illustrative of the application and are not intended to be limiting.
本申请提供一种电子装置1。参照图1所示,为本申请电子装置1较佳实施例的示意图。The application provides an electronic device 1 . Referring to FIG. 1 , it is a schematic diagram of a preferred embodiment of the electronic device 1 of the present application.
在本实施例中,该电子装置1包括存储器11、处理器12,网络接口13及通信总线14。In the embodiment, the electronic device 1 includes a memory 11, a processor 12, a network interface 13, and a communication bus 14.
存储器11包括至少一种类型的可读存储介质。所述至少一种类型的可读存储介质可为如闪存、硬盘、多媒体卡、卡型存储器等的非易失性存储介质。在一些实施例中,所述可读存储介质可以是所述电子装置1的内部存储单元,例如该电子装置1的硬盘。在另一些实施例中,所述可读存储介质也可以是所述电子装置1的外部存储设备,例如所述电子装置1上配备的插接式硬盘,智能存储卡(Smart Media Card,SMC),安全数字(Secure Digital,SD)卡,闪存卡(Flash Card)等。The memory 11 includes at least one type of readable storage medium. The at least one type of readable storage medium may be a non-volatile storage medium such as a flash memory, a hard disk, a multimedia card, a card type memory, or the like. In some embodiments, the readable storage medium may be an internal storage unit of the electronic device 1, such as a hard disk of the electronic device 1. In other embodiments, the readable storage medium may also be an external storage device of the electronic device 1, such as a plug-in hard disk equipped on the electronic device 1, a smart memory card (SMC). , Secure Digital (SD) card, Flash Card, etc.
在本实施例中,所述存储器11的可读存储介质通常用于存储安装于所述电子装置1的投资组合优化程序10等。所述存储器11还可以用于暂时地存储已经输出或者将要输出的数据。In the present embodiment, the readable storage medium of the memory 11 is generally used to store a portfolio optimization program 10 or the like installed in the electronic device 1. The memory 11 can also be used to temporarily store data that has been output or is about to be output.
处理器12在一些实施例中可以是一中央处理器(Central Processing Unit,CPU),微处理器或其他数据处理芯片,用于运行存储器11中存储的程序代码或处理数据,例如执行投资组合优化程序10等。The processor 12, in some embodiments, may be a Central Processing Unit (CPU), microprocessor or other data processing chip for running program code or processing data stored in the memory 11, such as performing portfolio optimization. Program 10 and so on.
网络接口13可以包括标准的有线接口、无线接口(如WI-FI接口)。通常用于与终端(图中未标识)进行数据传输。The network interface 13 may include a standard wired interface, a wireless interface (such as a WI-FI interface). Usually used for data transmission with terminals (not identified in the figure).
通信总线14用于实现这些组件之间的连接通信。 Communication bus 14 is used to implement connection communication between these components.
图1仅示出了具有组件11-14以及投资组合优化程序10的电子装置1,但是应理解的是,并不要求实施所有示出的组件,可以替代的实施更多或者更少的组件。Figure 1 shows only the electronic device 1 with components 11-14 and portfolio optimization program 10, but it should be understood that not all illustrated components may be implemented, and more or fewer components may be implemented instead.
可选的,该电子装置1还可以包括用户接口,用户接口可以包括显示器(Display)、输入单元比如键盘(Keyboard),可选的用户接口还可以包括标准的有线接口、无线接口。Optionally, the electronic device 1 may further include a user interface, and the user interface may include a display, an input unit such as a keyboard, and the optional user interface may further include a standard wired interface and a wireless interface.
可选地,该电子装置1还可以包括显示器,在一些实施例中可以是LED显示器、液晶显示器、触控式液晶显示器以及有机发光二极管(Organic Light-Emitting Diode,OLED)触摸器等。显示器用于显示在电子装置中处理的信息以及用于显示可视化的用户界面。Optionally, the electronic device 1 may further include a display, and in some embodiments, an LED display, a liquid crystal display, a touch liquid crystal display, and an Organic Light-Emitting Diode (OLED) touch device. The display is used to display information processed in the electronic device and a user interface for displaying visualizations.
在图1所示的装置实施例中,作为一种计算机存储介质的存储器11中包括投资组合优化程序10,处理器12执行存储器11中存储的投资组合优化程序10时实现以下步骤:In the apparatus embodiment shown in FIG. 1, a memory optimization program 10 is included in the memory 11 as a computer storage medium. When the processor 12 executes the portfolio optimization program 10 stored in the memory 11, the following steps are implemented:
接收输入的待优化的初始投资组合中的股票、初始投资组合中各股票对应的初始权重,获取各股票对应的市场及该初始投资组合中各股票在第一预设时间内的历史数据;Receiving the initial weights of the stocks in the initial portfolio to be optimized and the stocks in the initial portfolio, and obtaining the historical data of the market corresponding to each stock and the stocks in the initial investment portfolio in the first preset time;
根据所述历史数据及预设的第一分析规则,计算得到所述初始投资组合中的各股票之间的相关性最小时,所述初始投资组合中各股票应对应的权重,并对初始投资组合中的各股票对应的权重进行调整,确定初步优化后的第一投资组合;及Calculating, according to the historical data and the preset first analysis rule, a weight corresponding to each stock in the initial investment portfolio when the correlation between the stocks in the initial investment portfolio is minimum, and initial investment Adjusting the weight corresponding to each stock in the portfolio to determine the first optimized investment portfolio; and
获取所述第一投资组合中的各股票在第二预设时间内的历史数据,构建各股票的特征向量,并输入各股票对应的预先训练好的未来收益率预测模型中,预测所述第一投资组合中的各股票的未来对数收益率,根据预设的第二分析规则对所述第一投资组合中的各股票对应的权重进行调整,确定第二投资组合。Obtaining historical data of each stock in the first investment portfolio in a second preset time, constructing a feature vector of each stock, and inputting a pre-trained future profit rate prediction model corresponding to each stock, predicting the first The future logarithmic yield of each stock in a portfolio is adjusted according to a preset second analysis rule for the weight corresponding to each stock in the first portfolio, and the second portfolio is determined.
在本实施例中,以沪深300中的股票对本方案进行说明,但不仅限于沪深300。可以理解的是,在调整投资组合中各只股票对应的权重时,一方面是为了控制投资组合的风险,另一方面是为了提高投资组合的收益,本方案既考虑了风险最小化,又考虑了提高收益。需要说明的是,本方案中提到的权重指投资组合中各股票对应的投资金额占投资总金额的比重。In the present embodiment, the scheme is described with stocks in the CSI 300, but is not limited to the CSI 300. Understandably, when adjusting the weights of each stock in the portfolio, on the one hand, it is to control the risk of the portfolio, and on the other hand, to improve the return of the portfolio, the scheme considers both risk minimization and consideration. Increased revenue. It should be noted that the weight mentioned in this scheme refers to the proportion of the investment amount corresponding to each stock in the portfolio to the total amount of investment.
当接收到投资者输入的待优化的初始投资组合时,分别获取初始投资组合中的各股票及各股票对应的权重,例如,初始投资组合中包含N(例如,20)只股票,且该N只股票对应的权重分别为W 0=[w 01,w 02,w 03,…,w 0n]。分别获取初始投资组合中N只股票及市场(例如,沪深300)在第一预设时间内(例如,在对初始投资组合进行优化前的2个月)的历史数据,例如,N只股票在优化前的2个月内各期的收盘价,市场在优化前的2个月内各期的收盘价等。 When receiving the initial investment portfolio to be optimized input by the investor, respectively obtaining the weights corresponding to each stock and each stock in the initial investment portfolio, for example, the initial investment portfolio includes N (for example, 20) stocks, and the N The weights corresponding to only stocks are W 0 =[w 01 ,w 02 ,w 03 ,...,w 0n ]. Obtain historical data of N stocks and markets (for example, CSI 300) in the initial portfolio for the first preset time (for example, 2 months before the optimization of the initial portfolio), for example, N stocks The closing price of each period within 2 months before the optimization, the closing price of each period of the market within 2 months before the optimization.
确定初始投资组合中各股票对应的历史数据及市场的历史上数据后,需 根据已有的数据,对初始投资组合中各股票对应的权重进行调整,在收益率保持不变的条件下,使投资组合中各股票的相关性降到最低,就能使投资组合的风险降到最低。After determining the historical data corresponding to each stock in the initial investment portfolio and the historical data of the market, it is necessary to adjust the weight corresponding to each stock in the initial investment portfolio according to the existing data, and under the condition that the profit rate remains unchanged, Minimizing the correlation of stocks in a portfolio can minimize the risk of a portfolio.
优选地,使投资组合中各股票的相关性降到最低的步骤包括:Preferably, the steps to minimize the correlation of each stock in the portfolio include:
首先,分别计算第一预设时间内所述市场及所述初始投资组合中各股票对应的对数收益率序列。First, a logarithmic rate of return corresponding to each stock in the market and the initial investment portfolio in a first preset time period is separately calculated.
具体地,以每隔一周调整初始投资组合中各股票对应的权重为例,初始投资组合中股票数N=20,第一预设时间T=60。Specifically, taking the weight corresponding to each stock in the initial investment portfolio every other week as an example, the number of stocks in the initial portfolio is N=20, and the first preset time T=60.
在优化初始投资组合当天,分别计算初始投资组合中20只股票在前60个交易日中每天的对数收益率,综合每天的对数收益率,生成对应的对数收益率序列,对数收益率的计算公式为:On the day of optimizing the initial investment portfolio, calculate the logarithmic rate of return of the 20 stocks in the initial portfolio for the first 60 trading days, synthesize the daily logarithmic rate of return, and generate the corresponding logarithmic rate of return, logarithmic returns. The formula for calculating the rate is:
RS it=lnP it-lnP i(t-1) RS it =lnP it -lnP i(t-1)
其中,RS it表示所述初始投资组合中第i只股票对应的对数收益率序列中第t时刻该股票的对数收益率,P it表示第i只股票在t时刻的收盘价,P i(t-1)表示第i只股票在t-1时刻的收盘价,t表示在优化初始投资组合之前的某时刻,即某交易日。 Where RS it represents the logarithmic rate of return of the stock at the t-th time in the logarithmic rate of return corresponding to the i-th stock in the initial portfolio, and P it represents the closing price of the i-th stock at time t, P i (t-1) indicates the closing price of the i-th stock at time t-1, and t indicates a certain time before the optimization of the initial investment portfolio, that is, a trading day.
计算初始投资组合中20只股票对应的市场在前60个交易日中每天的对数收益率,综合每天的对数收益率,生成对应的对数收益率序列,对数收益率的计算公式为:Calculate the daily logarithmic rate of return of the market corresponding to 20 stocks in the initial portfolio for the first 60 trading days, and synthesize the daily logarithmic rate of return to generate a corresponding logarithmic rate of return. The formula for calculating the logarithmic rate of return is :
RM t=lnPM t-lnPM t-1 RM t =lnPM t -lnPM t-1
其中,RM t表示市场对应的对数收益率序列中第t时刻市场的对数收益率,PM t表示t时刻市场的收盘价,PM t-1表示t-1时刻市场的收盘价,t表示在优化初始投资组合之前的某时刻,即某交易日。 Where RM t represents the logarithmic rate of return of the market at the t-th time in the logarithmic rate of return corresponding to the market, PM t represents the closing price of the market at time t, PM t-1 represents the closing price of the market at time t-1, and t represents At some point before the optimization of the initial portfolio, that is, a trading day.
最终得到的第一预设时间内初始投资组合中各股票对应的对数收益率序列为[RS i1,RS i2,RS i3,…,RS it],市场对应的对数收益率序列为[RM 1,RM 2,RM 3,…,RM t]其中,t=T=60,0<i≤N=20。 The log yield series corresponding to each stock in the initial investment portfolio in the first preset time is [RS i1 , RS i2 , RS i3 ,..., RS it ], and the market corresponding log yield series is [RM 1 , RM 2 , RM 3 , . . . , RM t ] wherein t=T=60, 0<i≤N=20.
然后,将所述初始投资组合中各股票对应的对数收益序列分别与所述市场的对数收益序列进行回归,分别计算所述初始投资组合中各股票对应的残差序列,并求得所述初始投资组合对应的协方差矩阵。Then, the logarithmic income sequence corresponding to each stock in the initial investment portfolio is respectively regressed with the logarithmic income sequence of the market, and the residual sequence corresponding to each stock in the initial investment portfolio is calculated respectively, and the obtained residue is obtained. The covariance matrix corresponding to the initial portfolio.
具体地,对于初始投资组合中的各股票而言,分别以其对数收益率序列 与市场的对数收益率序列作回归,得:Specifically, for each stock in the initial portfolio, the logarithmic rate of return series and the market's logarithmic rate of return series are respectively returned to obtain:
RM t=α ii*RS it+e it RM tii *RS it +e it
通过回归分别求得:α i=[α 123,…,α n],β i=[β 123,…,β n],并根据:e it=RM t-(α ii*RS it),求得初始投资组合中第i只股票在第一预设时间(60天)内的残差序列。其中,对于第i只股票而言,α i表示该股票相对于市场的超额收益,β i表示该股票对数收益率走势与市场对数收益率走势的联动程度,e it为残差项,表示除α i、β i之外的随机干扰项,即所述初始投资组合中该股票对应的残差序列,且e it=[e 1i,e 2i,e 3i,…,e Ti]。 By regression, we obtain: α i =[α 123 ,...,α n ], β i =[β 123 ,...,β n ], and according to: e it = RM t -(α ii *RS it ), and obtain the residual sequence of the i-th stock in the initial investment portfolio within the first preset time (60 days). Among them, for the i-th stock, α i represents the excess return of the stock relative to the market, β i represents the degree of linkage between the trend of the logarithmic yield of the stock and the trend of the market logarithmic yield, and e it is the residual item. Represents a random interference term other than α i , β i , that is, a residual sequence corresponding to the stock in the initial portfolio, and e it =[e 1i , e 2i , e 3i , . . . , e Ti ].
最后,计算所述初始投资组合对应的协方差矩阵中各股票之间的协方差加权和最小的解,根据计算结果确定所述初始投资组合中各股票对应的权重。Finally, the solution of the covariance weighted sum between the stocks in the covariance matrix corresponding to the initial portfolio is calculated, and the weight corresponding to each stock in the initial portfolio is determined according to the calculation result.
具体地,利用各股票在第一预设时间内的残差序列,分别计算每只股票两两之间的协方差为:Specifically, using the residual sequence of each stock in the first preset time, the covariance between each stock is calculated as:
X=e it=[e 1i,e 2i,e 3i,…,e Ti] X=e it =[e 1i ,e 2i ,e 3i ,...,e Ti ]
Cov(X,Y)=E[(X-E[X])(Y-E[Y])]=E[XY]-E[X]E[Y]Cov(X,Y)=E[(X-E[X])(Y-E[Y])]=E[XY]-E[X]E[Y]
协方差(Covariance)在概率论和统计学中用于衡量两个变量的总体误差。由每只股票两两之间的协方差可以写出一个N*N(即,20*20)的协方差矩阵,记为Σ。Covariance is used in probability theory and statistics to measure the overall error of two variables. A covariance matrix of N*N (ie, 20*20) can be written by the covariance between two and two stocks, denoted as Σ.
可以理解的是,协方差矩阵代表了投资组合中个股之间的相关程度,当协方差越小的同时,往往代表着风险的越分散。因此,在确认初始投资组合对应的协方差矩阵Σ后,需求得使各股票之间的协方差加权和最小的解,其计算公式为:It can be understood that the covariance matrix represents the degree of correlation between individual stocks in the portfolio. When the covariance is smaller, it often represents the more dispersed risk. Therefore, after confirming the covariance matrix corresponding to the initial portfolio, the demand is to minimize the covariance weighted sum between the stocks. The formula is:
min W T∑W Min W T ∑W
s.t∑ iw 0i*RS i=R St∑ i w 0i *RS i =R
e TW=1 e T W=1
其中,W为待求解,W=[w 1,w 2,…,w n],表示每只个股应该对应的权重,∑表示所述初始投资组合对应的协方差矩阵,RS i表示优化投资组合前一时刻各股票对应的对数收益率,w 0i表示初始投资组合中各股票对应的初始权重,RS为常数,表示优化投资组合前一时刻初始投资组合对应的总对数收益率,意思是控制优化后的投资组合的收益与优化前一个交易日的收益持平的情况下,尽可能缩小个股两两之间的相关性,e TW=1表示W中各股票对应的 权重总和为1。 Where W is to be solved, W=[w 1 ,w 2 ,...,w n ], indicating the weight corresponding to each stock, ∑ represents the covariance matrix corresponding to the initial portfolio, and RS i represents the optimized portfolio The logarithmic rate of return corresponding to each stock in the previous moment, w 0i represents the initial weight corresponding to each stock in the initial portfolio, and RS is a constant, indicating the total logarithmic yield of the initial portfolio at the previous moment of the optimized investment portfolio, meaning In the case of controlling the profit of the optimized portfolio to be equal to the gain of the previous trading day, the correlation between the two stocks is reduced as much as possible, and e T W=1 indicates that the sum of the weights of each stock in W is 1.
通过上述步骤求得W=[w 1,w 2,…,w n]后,对比W=[w 1,w 2,…,w n]和W 0=[w 01,w 02,w 03,…,w 0n],当初始投资组合中每只股票对应的权重与W=[w 1,w 2,…,w n]不一致时,对初始投资组合需调整权重的各股票的权重进行相应调整,得到第一投资组合。需要说明的是,上述步骤的主要目的在于,控制收益不变,且尽可能大地分散风险,即,第一投资组合在保持上一期收益率的前提下,使投资组合风险控制到了最低。 After obtaining W=[w 1 , w 2 , . . . , w n ] by the above steps, comparing W=[w 1 , w 2 , . . . , w n ] and W 0 =[w 01 ,w 02 ,w 03 , ...,w 0n ], when the weight corresponding to each stock in the initial portfolio is inconsistent with W=[w 1 , w 2 ,...,w n ], the weights of the stocks whose initial portfolio needs to be adjusted are adjusted accordingly. , get the first portfolio. It should be noted that the main purpose of the above steps is to control the income unchanged and to spread the risk as much as possible, that is, the first investment portfolio controls the portfolio risk to the minimum while maintaining the previous yield.
针对初始投资组合惊醒初步优化的频率除了按周优化外,在其他实施例中,还可以按月优化。例如,每月计算目标函数W=[w 1,w 2,…,w n],确定下一期的最佳投资组合。 The frequency of initial optimization for the initial portfolio awakening is not only optimized by week, but in other embodiments, it can also be optimized monthly. For example, the objective function W = [w 1 , w 2 , ..., w n ] is calculated monthly to determine the best investment portfolio for the next period.
可以理解的是,投资者的决策目标有两个:尽可能低的不确定性风险和尽可能高的收益率,但不是一味最求低风险也不是一味追求高收益,最好的目标应是使这两个相互制约的目标达到最佳平衡。Understandably, there are two investors' decision-making goals: the lowest possible uncertainty risk and the highest possible rate of return, but not the pursuit of the lowest risk or the pursuit of high returns. The best goal should be The best balance between these two mutually constrained goals.
通过上述步骤确定了最低风险的第一投资组合之后,需进一步考虑第一投资组合的收益情况,也就是以风险换收益,追求超额收益,例如,对第一投资组合中预测未来收益率较高的个股采取增持操作,对预测未来收益率较低的个股采取减持操作。那么,需要对第一投资组合中各股票对应的未来收益率进行预测。After determining the minimum risk of the first investment portfolio through the above steps, it is necessary to further consider the income of the first investment portfolio, that is, to convert the risk into profit, and pursue excess returns. For example, the predicted future return rate is higher in the first investment portfolio. The individual stocks adopt an increase in holding operation and take a reduction operation for individual stocks with lower forecasting future yields. Then, it is necessary to predict the future rate of return corresponding to each stock in the first portfolio.
在本实施例中,利用各股票在第二预设时间(例如,前30个交易日)内的历史数据,对各股票对应的未来收益率进行预测,鉴于长短期记忆网络(Long Short-Term Memory,LSTM),是一种时间递归神经网络,更适合处理和预测时间序列中间隔和延迟相对较长的重要事件,目前已经证明,LSTM是解决长序依赖问题的有效技术。因此,选择LSTM对初步优化后的第一投资组合中的各只股票对应的未来收益率进行预测。In this embodiment, the historical yield data of each stock in the second preset time (for example, the first 30 trading days) is used to predict the future profit rate corresponding to each stock, in view of the long-short-term memory network (Long Short-Term) Memory, LSTM) is a time recurrent neural network that is more suitable for processing and predicting important events with relatively long intervals and delays in time series. LSTM has been proven to be an effective technique for solving long-order dependent problems. Therefore, the LSTM is selected to predict the future rate of return corresponding to each stock in the initially optimized first portfolio.
在对第一投资组合中的各股票的未来收益率进行预测之前,需对LSTM进行训练,具体包括以下步骤:Before predicting the future rate of return of each stock in the first portfolio, the LSTM needs to be trained, including the following steps:
构建样本数据:分别获取第一投资组合中各只股票在第三预设时间(过去两年)内每个交易日的特征数据,未来扩充样本数据,随机采集任意连续的30天的特征数据及对应的未来5个交易日的对数收益率作为样本集,从样 本集中抽取第一比例(例如,80%)的样本数据作为训练集,第二比例(例如,20%)的样本数据作为验证集;及Construct sample data: obtain the characteristic data of each stock in the first investment portfolio for each trading day in the third preset time (the past two years), expand the sample data in the future, and randomly collect the arbitrarily 30 days of characteristic data and The corresponding logarithmic rate of return for the next 5 trading days is used as a sample set, and the first proportion (for example, 80%) of the sample data is extracted from the sample set as the training set, and the second ratio (for example, 20%) of the sample data is used as the verification. Set; and
模型训练:利用训练集对LSTM模型进行有监督的训练得到未来收益率预测模型,利用验证集对未来收益率预测模型进行验证,直到满足条件为止,例如,模型预测准确率达到90%为止。Model training: The training set is used to supervise the LSTM model to obtain the future rate prediction model. The verification set is used to verify the future rate prediction model until the condition is met. For example, the model prediction accuracy reaches 90%.
重复上述步骤,为每只股票拟合一个未来收益率预测模型,训练完毕后,第一投资组合中每只股票对应一个模型,即Model=[Model1,Model2,…,ModelN]。Repeat the above steps to fit a future yield prediction model for each stock. After the training, each stock in the first portfolio corresponds to one model, namely Model=[Model1, Model2,...,ModelN].
当需要对第一投资组合中第i只股票对应的未来收益率进行预测时,首先获取该股票在第二预设时间(例如,前30个交易日)内的特征数据,特征数据有5个,分别为['close','open','high','low','volume'],构建第i只股票对应的30*5的特征向量;调用第i只股票对应的未来收益率预测模型,将特征向量作为Input输入第i只股票对应的模型,对其未来5个交易日的对数收益率进行预测,模型Output为未来5个交易日的逐日对数收益率。When it is required to predict the future profit rate corresponding to the i-th stock in the first investment portfolio, firstly, the feature data of the stock in the second preset time (for example, the first 30 trading days) is obtained, and the feature data has 5 ,['close', 'open', 'high', 'low', 'volume'], construct the feature vector of 30*5 corresponding to the i-th stock; call the future yield prediction corresponding to the i-th stock The model uses the feature vector as the input to input the model corresponding to the i-th stock, and predicts the logarithmic rate of return for the next five trading days. The model Output is the daily logarithmic yield of the next five trading days.
在确定经初步优化后的第一投资组合中每只股票对应的未来5个交易日的对数收益率后,为了追求利益最大化,需根据每只股票在未来5个交易日的综合对数收益率进行调整。After determining the logarithmic rate of return for each of the stocks in the first optimized investment portfolio for the next 5 trading days, in order to maximize the benefits, the total logarithm of each stock in the next 5 trading days is required. The rate of return is adjusted.
具体地,根据预设的第二分析规则对所述第一投资组合中的各股票对应的权重进行调整的步骤包括:Specifically, the step of adjusting the weight corresponding to each stock in the first investment portfolio according to the preset second analysis rule includes:
分别计算各股票对应的未来综合对数收益率,按照各股票的未来综合对数收益率的高低顺序,对所述第一投资组合中的各股票进行排序;鉴于未来收益率预测模型输出的结果为各股票在未来5个交易日的对数收益率,因此,分别对第一投资组合中每只股票未来5个交易日的对数收益率进行加总,作为每只股票的未来综合对数收益率,并根据未来综合对数收益率的高低顺序对第一投资组合中各股票进行排序。Calculating the future comprehensive logarithmic rate of return for each stock separately, sorting the stocks in the first portfolio according to the order of the future comprehensive logarithm of each stock; in view of the output of the future yield prediction model For the logarithmic rate of return of each stock in the next 5 trading days, therefore, the logarithmic rate of return for each stock in the first portfolio for the next 5 trading days will be added as the future comprehensive logarithm of each stock. Yield, and sort the stocks in the first portfolio according to the order of future comprehensive logarithmic returns.
对于未来综合对数收益率大于或等于第一预设阈值的第一类股票,将该类股票对应的权重上调;例如,对于未来综合对数收益率大于或等于10%的股票,说明未来涨幅较大,故可对其进行增持操作,假设其在第一投资组合中的权重为a,调整该股票对应的权重至(1+50%)a。For the first type of stocks whose future comprehensive logarithmic rate of return is greater than or equal to the first preset threshold, the weight corresponding to the stocks is raised; for example, for stocks with a future comprehensive logarithm of return greater than or equal to 10%, indicating future gains It is larger, so it can be overweighted, assuming that its weight in the first portfolio is a, and the weight corresponding to the stock is adjusted to (1+50%)a.
对于未来综合对数收益率小于或等于第二预设阈值的第二类股票,将该 类股票对应的权重调整为第三预设阈值;例如,对于未来综合对数收益率小于-10%的股票,说明未来跌幅较大,故可对其进行减持甚至空仓操作,假设其在第一投资组合中的权重为a,调整该股票对应的权重至(1-80%)a或者直接将其对应的权重调整为0。For the second type of stocks whose future comprehensive logarithmic rate of return is less than or equal to the second predetermined threshold, the weight corresponding to the stocks is adjusted to a third preset threshold; for example, for a future comprehensive logarithmic yield of less than -10% Stocks, indicating a large decline in the future, it can be reduced or even short-selling operations, assuming that its weight in the first portfolio is a, adjust the corresponding weight of the stock to (1-80%) a or directly The corresponding weight is adjusted to 0.
对于预设比例的排序靠后的第三类股票,将该类股票对应的权重下调;例如,第一投资组合中的20只股票,对于未来综合收益率排序为后20%的4只股票,说明其在第一投资组合中未来收益相对较低,故可对该股票进行减持操作,假设原始比重为a,调整该个股对应的比重至(1-50%)a。For the third type of stocks with a predetermined proportion, the corresponding weights of the stocks are lowered; for example, 20 stocks in the first portfolio are sorted into the next 20% of the 4 stocks for the future comprehensive rate of return. It shows that its future income in the first investment portfolio is relatively low, so the stock can be reduced. Assuming the original proportion is a, adjust the proportion of the stock to (1-50%) a.
经过上述步骤,确定了第一投资组合中应调整权重的各股票后,对第一投资组合中各股票对应的权重进行调整,确定第二投资组合中各股票对应的权重W *=[w 1 *,w 2 *,w 3 *,…,w n *],即,确定目标投资组合。 After the above steps, after determining the stocks in the first portfolio that should be adjusted in weight, the weights corresponding to the stocks in the first portfolio are adjusted to determine the weights corresponding to the stocks in the second portfolio W * = [w 1 * , w 2 * , w 3 * , ..., w n * ], that is, determine the target portfolio.
上述实施例提出的电子装置1,通过在保持收益不变的情况下,尽可能缩小初始投资组合中个股两两之间的相关性,对初始投资组合进行初步优化,得到风险最小的第一投资组合;另外,通过LSTM模型预测第一投资组合中各股票对应的未来对数收益率,并对未来收益率相对较高或较低的股票的权重进行调整,得到第二投资组合,在一定程度上提高了投资收益。The electronic device 1 proposed in the above embodiment optimizes the initial investment portfolio by minimizing the correlation between the individual stocks in the initial investment portfolio while maintaining the same income, and obtains the first investment with the least risk. In addition, the LSTM model predicts the future logarithmic yield of each stock in the first portfolio, and adjusts the weight of stocks with relatively higher or lower yields to obtain a second portfolio, to a certain extent. Increased investment income.
可选地,在其他的实施例中,投资组合优化程序10还可以被分割为一个或者多个模块,一个或者多个模块被存储于存储器11中,并由一个或多个处理器12所执行,以完成本申请。本申请所称的模块是指能够完成特定功能的一系列计算机程序指令段。参照图2所示,为图1中投资组合优化程序的程序模块图。在本实施例中,投资组合优化程序10可以被分割为:接收模块110、第一优化模块120及第二优化模块130。所述模块110-130所实现的功能或操作步骤均与上文类似,此处不再详述,示例性地,例如其中:Alternatively, in other embodiments, portfolio optimization program 10 may also be partitioned into one or more modules, one or more modules being stored in memory 11 and executed by one or more processors 12 To complete this application. A module as referred to in this application refers to a series of computer program instructions that are capable of performing a particular function. Referring to FIG. 2, it is a program module diagram of the portfolio optimization program in FIG. In this embodiment, the portfolio optimization program 10 can be divided into: a receiving module 110, a first optimization module 120, and a second optimization module 130. The functions or operational steps implemented by the modules 110-130 are similar to the above, and are not described in detail herein, by way of example, for example:
接收模块110,用于接收输入的待优化的初始投资组合中的股票、初始投资组合中各股票对应的初始权重,获取各股票对应的市场及该初始投资组合中各股票在第一预设时间内的历史数据;The receiving module 110 is configured to receive the input stocks in the initial portfolio to be optimized, the initial weights corresponding to the stocks in the initial investment portfolio, obtain the market corresponding to each stock, and obtain the stocks in the initial investment portfolio at the first preset time. Historical data within;
第一优化模块120,用于根据所述历史数据及预设的第一分析规则,计算得到所述初始投资组合中的各股票之间的相关性最小时,所述初始投资组合中各股票应对应的权重,并对初始投资组合中的各股票对应的权重进行调整, 确定初步优化后的第一投资组合;及a first optimization module 120, configured to calculate, according to the historical data and a preset first analysis rule, when the correlation between each stock in the initial investment portfolio is minimum, each stock in the initial investment portfolio should respond The weights should be adjusted, and the weights corresponding to the stocks in the initial portfolio should be adjusted to determine the first optimized investment portfolio; and
第二优化模块130,用于获取所述第一投资组合中的各股票在第二预设时间内的历史数据,构建各股票的特征向量,并输入各股票对应的预先训练好的未来收益率预测模型中,预测所述第一投资组合中的各股票的未来对数收益率,根据预设的第二分析规则对所述第一投资组合中的各股票对应的权重进行调整,确定第二投资组合。The second optimization module 130 is configured to acquire historical data of each stock in the first investment portfolio in a second preset time, construct a feature vector of each stock, and input a pre-trained future profit rate corresponding to each stock. In the prediction model, predicting a future logarithmic yield of each stock in the first portfolio, and adjusting a weight corresponding to each stock in the first portfolio according to a preset second analysis rule to determine a second portfolio.
此外,本申请还提供一种投资组合优化方法。参照图3所示,为本申请投资组合优化方法较佳实施例的流程图。该方法可以由一个装置执行,该装置可以由软件和/或硬件实现。In addition, the present application also provides a portfolio optimization method. Referring to FIG. 3, it is a flowchart of a preferred embodiment of the portfolio optimization method of the present application. The method can be performed by a device that can be implemented by software and/or hardware.
在本实施例中,投资组合优化方法包括:步骤S1-S4。In this embodiment, the portfolio optimization method includes: steps S1-S4.
步骤S1,接收输入的待优化的初始投资组合中的股票、初始投资组合中各股票对应的初始权重,获取各股票对应的市场及该初始投资组合中各股票在第一预设时间内的历史数据;Step S1, receiving the initial weights of the stocks in the initial portfolio to be optimized and the stocks in the initial portfolio, and obtaining the market corresponding to each stock and the history of each stock in the initial investment portfolio in the first preset time. data;
步骤S2,根据所述历史数据及预设的第一分析规则,计算得到所述初始投资组合中的各股票之间的相关性最小时,所述初始投资组合中各股票应对应的权重,并对初始投资组合中的各股票对应的权重进行调整,确定初步优化后的第一投资组合;及Step S2: calculating, according to the historical data and the preset first analysis rule, a weight corresponding to each stock in the initial investment portfolio when the correlation between the stocks in the initial investment portfolio is minimum, and Adjusting the weights corresponding to the stocks in the initial portfolio to determine the first optimized investment portfolio; and
步骤S3,获取所述第一投资组合中的各股票在第二预设时间内的历史数据,构建各股票的特征向量,并输入各股票对应的预先训练好的未来收益率预测模型中,预测所述第一投资组合中的各股票的未来对数收益率,根据预设的第二分析规则对所述第一投资组合中的各股票对应的权重进行调整,确定第二投资组合。Step S3: acquiring historical data of each stock in the first investment portfolio in a second preset time, constructing a feature vector of each stock, and inputting a pre-trained future profit rate prediction model corresponding to each stock, and predicting The future logarithmic yield of each stock in the first investment portfolio is adjusted according to a preset second analysis rule, and the weight corresponding to each stock in the first investment portfolio is adjusted to determine a second investment portfolio.
在本实施例中,以沪深300中的股票对本方案进行说明,但不仅限于沪深300。可以理解的是,在调整投资组合中各只股票对应的权重时,一方面是为了控制投资组合的风险,另一方面是为了提高投资组合的收益,本方案既考虑了风险最小化,又考虑了提高收益。需要说明的是,本方案中提到的权重指投资组合中各股票对应的投资金额占投资总金额的比重。In the present embodiment, the scheme is described with stocks in the CSI 300, but is not limited to the CSI 300. Understandably, when adjusting the weights of each stock in the portfolio, on the one hand, it is to control the risk of the portfolio, and on the other hand, to improve the return of the portfolio, the scheme considers both risk minimization and consideration. Increased revenue. It should be noted that the weight mentioned in this scheme refers to the proportion of the investment amount corresponding to each stock in the portfolio to the total amount of investment.
当接收到投资者输入的待优化的初始投资组合时,分别获取初始投资组合中的各股票及各股票对应的权重,例如,初始投资组合中包含N(例如, 20)只股票,且该N只股票对应的权重分别为W 0=[w 01,w 02,w 03,…,w 0n]。分别获取初始投资组合中N只股票及市场(例如,沪深300)在第一预设时间内(例如,在对初始投资组合进行优化前的2个月)的历史数据,例如,N只股票在优化前的2个月内各期的收盘价,市场在优化前的2个月内各期的收盘价等。 When receiving the initial investment portfolio to be optimized input by the investor, respectively obtaining the weights corresponding to each stock and each stock in the initial investment portfolio, for example, the initial investment portfolio includes N (for example, 20) stocks, and the N The weights corresponding to only stocks are W 0 =[w 01 ,w 02 ,w 03 ,...,w 0n ]. Obtain historical data of N stocks and markets (for example, CSI 300) in the initial portfolio for the first preset time (for example, 2 months before the optimization of the initial portfolio), for example, N stocks The closing price of each period within 2 months before the optimization, the closing price of each period of the market within 2 months before the optimization.
确定初始投资组合中各股票对应的历史数据及市场的历史上数据后,需根据已有的数据,对初始投资组合中各股票对应的权重进行调整,在收益率保持不变的条件下,使投资组合中各股票的相关性降到最低,就能使投资组合的风险降到最低。After determining the historical data corresponding to each stock in the initial investment portfolio and the historical data of the market, it is necessary to adjust the weight corresponding to each stock in the initial investment portfolio according to the existing data, and under the condition that the profit rate remains unchanged, Minimizing the correlation of stocks in a portfolio can minimize the risk of a portfolio.
优选地,使投资组合中各股票的相关性降到最低的步骤包括:Preferably, the steps to minimize the correlation of each stock in the portfolio include:
首先,分别计算第一预设时间内所述市场及所述初始投资组合中各股票对应的对数收益率序列。First, a logarithmic rate of return corresponding to each stock in the market and the initial investment portfolio in a first preset time period is separately calculated.
具体地,以每隔一周调整初始投资组合中各股票对应的权重为例,初始投资组合中股票数N=20,第一预设时间T=60。Specifically, taking the weight corresponding to each stock in the initial investment portfolio every other week as an example, the number of stocks in the initial portfolio is N=20, and the first preset time T=60.
在优化初始投资组合当天,分别计算初始投资组合中20只股票在前60个交易日中每天的对数收益率,综合每天的对数收益率,生成对应的对数收益率序列,对数收益率的计算公式为:On the day of optimizing the initial investment portfolio, calculate the logarithmic rate of return of the 20 stocks in the initial portfolio for the first 60 trading days, synthesize the daily logarithmic rate of return, and generate the corresponding logarithmic rate of return, logarithmic returns. The formula for calculating the rate is:
RS it=lnP it-lnP i(t-1) RS it =lnP it -lnP i(t-1)
其中,RS it表示所述初始投资组合中第i只股票对应的对数收益率序列中第t时刻该股票的对数收益率,P it表示第i只股票在t时刻的收盘价,P i(t-1)表示第i只股票在t-1时刻的收盘价,t表示在优化初始投资组合之前的某时刻,即某交易日。 Where RS it represents the logarithmic rate of return of the stock at the t-th time in the logarithmic rate of return corresponding to the i-th stock in the initial portfolio, and P it represents the closing price of the i-th stock at time t, P i (t-1) indicates the closing price of the i-th stock at time t-1, and t indicates a certain time before the optimization of the initial investment portfolio, that is, a trading day.
计算初始投资组合中20只股票对应的市场在前60个交易日中每天的对数收益率,综合每天的对数收益率,生成对应的对数收益率序列,对数收益率的计算公式为:Calculate the daily logarithmic rate of return of the market corresponding to 20 stocks in the initial portfolio for the first 60 trading days, and synthesize the daily logarithmic rate of return to generate a corresponding logarithmic rate of return. The formula for calculating the logarithmic rate of return is :
RM t=lnPM t-lnPM t-1 RM t =lnPM t -lnPM t-1
其中,RM t表示市场对应的对数收益率序列中第t时刻市场的对数收益率,PM t表示t时刻市场的收盘价,PM t-1表示t-1时刻市场的收盘价,t表示在优化初始投资组合之前的某时刻,即某交易日。 Where RM t represents the logarithmic rate of return of the market at the t-th time in the logarithmic rate of return corresponding to the market, PM t represents the closing price of the market at time t, PM t-1 represents the closing price of the market at time t-1, and t represents At some point before the optimization of the initial portfolio, that is, a trading day.
最终得到的第一预设时间内初始投资组合中各股票对应的对数收益率序列为[RS i1,RS i2,RS i3,…,RS it],市场对应的对数收益率序列为[RM 1,RM 2,RM 3,…,RM t]其中,t=T=60,0<i≤N=20。 The log yield series corresponding to each stock in the initial investment portfolio in the first preset time is [RS i1 , RS i2 , RS i3 ,..., RS it ], and the market corresponding log yield series is [RM 1 , RM 2 , RM 3 , . . . , RM t ] wherein t=T=60, 0<i≤N=20.
然后,将所述初始投资组合中各股票对应的对数收益序列分别与所述市场的对数收益序列进行回归,分别计算所述初始投资组合中各股票对应的残差序列,并求得所述初始投资组合对应的协方差矩阵。Then, the logarithmic income sequence corresponding to each stock in the initial investment portfolio is respectively regressed with the logarithmic income sequence of the market, and the residual sequence corresponding to each stock in the initial investment portfolio is calculated respectively, and the obtained residue is obtained. The covariance matrix corresponding to the initial portfolio.
具体地,对于初始投资组合中的各股票而言,分别以其对数收益率序列与市场的对数收益率序列作回归,得:Specifically, for each stock in the initial portfolio, the logarithmic rate of return series and the market's logarithmic rate of return series are respectively returned to obtain:
RM t=α ii*RS it+e it RM tii *RS it +e it
通过回归分别求得:α i=[α 123,…,α n],β i=[β 123,…,β n],并根据:e it=RM t-(α ii*RS it),求得初始投资组合中第i只股票在第一预设时间(60天)内的残差序列。其中,对于第i只股票而言,α i表示该股票相对于市场的超额收益,β i表示该股票对数收益率走势与市场对数收益率走势的联动程度,e it为残差项,表示除α i、β i之外的随机干扰项,即所述初始投资组合中该股票对应的残差序列,且e it=[e 1i,e 2i,e 3i,…,e Ti]。 By regression, we obtain: α i =[α 123 ,...,α n ], β i =[β 123 ,...,β n ], and according to: e it = RM t -(α ii *RS it ), and obtain the residual sequence of the i-th stock in the initial investment portfolio within the first preset time (60 days). Among them, for the i-th stock, α i represents the excess return of the stock relative to the market, β i represents the degree of linkage between the trend of the logarithmic yield of the stock and the trend of the market logarithmic yield, and e it is the residual item. Represents a random interference term other than α i , β i , that is, a residual sequence corresponding to the stock in the initial portfolio, and e it =[e 1i , e 2i , e 3i , . . . , e Ti ].
最后,计算所述初始投资组合对应的协方差矩阵中各股票之间的协方差加权和最小的解,根据计算结果确定所述初始投资组合中各股票对应的权重。Finally, the solution of the covariance weighted sum between the stocks in the covariance matrix corresponding to the initial portfolio is calculated, and the weight corresponding to each stock in the initial portfolio is determined according to the calculation result.
具体地,利用各股票在第一预设时间内的残差序列,分别计算每只股票两两之间的协方差为:Specifically, using the residual sequence of each stock in the first preset time, the covariance between each stock is calculated as:
X=e it=[e 1i,e 2i,e 3i,…,e Ti] X=e it =[e 1i ,e 2i ,e 3i ,...,e Ti ]
Cov(X,Y)=E[(X-E[X])(Y-E[Y])]=E[XY]-E[X]E[Y]Cov(X,Y)=E[(X-E[X])(Y-E[Y])]=E[XY]-E[X]E[Y]
协方差(Covariance)在概率论和统计学中用于衡量两个变量的总体误差。由每只股票两两之间的协方差可以写出一个N*N(即,20*20)的协方差矩阵,记为Σ。Covariance is used in probability theory and statistics to measure the overall error of two variables. A covariance matrix of N*N (ie, 20*20) can be written by the covariance between two and two stocks, denoted as Σ.
可以理解的是,协方差矩阵代表了投资组合中个股之间的相关程度,当协方差越小的同时,往往代表着风险的越分散。因此,在确认初始投资组合对应的协方差矩阵Σ后,需求得使各股票之间的协方差加权和最小的解,其计算公式为:It can be understood that the covariance matrix represents the degree of correlation between individual stocks in the portfolio. When the covariance is smaller, it often represents the more dispersed risk. Therefore, after confirming the covariance matrix corresponding to the initial portfolio, the demand is to minimize the covariance weighted sum between the stocks. The formula is:
min W T∑W Min W T ∑W
s.t∑ iw 0i*RS i=R St∑ i w 0i *RS i =R
e TW=1 e T W=1
其中,W为待求解,W=[w 1,w 2,…,w n],表示每只个股应该对应的权重,∑表示所述初始投资组合对应的协方差矩阵,RS i表示优化投资组合前一时刻各股票对应的对数收益率,w 0i表示初始投资组合中各股票对应的初始权重,RS为常数,表示优化投资组合前一时刻初始投资组合对应的总对数收益率,意思是控制优化后的投资组合的收益与优化前一个交易日的收益持平的情况下,尽可能缩小个股两两之间的相关性,e TW=1表示W中各股票对应的权重总和为1。 Where W is to be solved, W=[w 1 ,w 2 ,...,w n ], indicating the weight corresponding to each stock, ∑ represents the covariance matrix corresponding to the initial portfolio, and RS i represents the optimized portfolio The logarithmic rate of return corresponding to each stock in the previous moment, w 0i represents the initial weight corresponding to each stock in the initial portfolio, and RS is a constant, indicating the total logarithmic yield of the initial portfolio at the previous moment of the optimized investment portfolio, meaning In the case of controlling the profit of the optimized portfolio to be equal to the gain of the previous trading day, the correlation between the two stocks is reduced as much as possible, and e T W=1 indicates that the sum of the weights of each stock in W is 1.
通过上述步骤求得W=[w 1,w 2,…,w n]后,对比W=[w 1,w 2,…,w n]和W 0=[w 01,w 02,w 03,…,w 0n],当初始投资组合中每只股票对应的权重与W=[w 1,w 2,…,w n]不一致时,对初始投资组合需调整权重的各股票的权重进行相应调整,得到第一投资组合。需要说明的是,上述步骤的主要目的在于,控制收益不变,且尽可能大地分散风险,即,第一投资组合在保持上一期收益率的前提下,使投资组合风险控制到了最低。 After obtaining W=[w 1 , w 2 , . . . , w n ] by the above steps, comparing W=[w 1 , w 2 , . . . , w n ] and W 0 =[w 01 ,w 02 ,w 03 , ...,w 0n ], when the weight corresponding to each stock in the initial portfolio is inconsistent with W=[w 1 , w 2 ,...,w n ], the weights of the stocks whose initial portfolio needs to be adjusted are adjusted accordingly. , get the first portfolio. It should be noted that the main purpose of the above steps is to control the income unchanged and to spread the risk as much as possible, that is, the first investment portfolio controls the portfolio risk to the minimum while maintaining the previous yield.
针对初始投资组合惊醒初步优化的频率除了按周优化外,在其他实施例中,还可以按月优化。例如,每月计算目标函数W=[w 1,w 2,…,w n],确定下一期的最佳投资组合。 The frequency of initial optimization for the initial portfolio awakening is not only optimized by week, but in other embodiments, it can also be optimized monthly. For example, the objective function W = [w 1 , w 2 , ..., w n ] is calculated monthly to determine the best investment portfolio for the next period.
可以理解的是,投资者的决策目标有两个:尽可能低的不确定性风险和尽可能高的收益率,但不是一味最求低风险也不是一味追求高收益,最好的目标应是使这两个相互制约的目标达到最佳平衡。Understandably, there are two investors' decision-making goals: the lowest possible uncertainty risk and the highest possible rate of return, but not the pursuit of the lowest risk or the pursuit of high returns. The best goal should be The best balance between these two mutually constrained goals.
通过上述步骤确定了最低风险的第一投资组合之后,需进一步考虑第一投资组合的收益情况,也就是以风险换收益,追求超额收益,例如,对第一投资组合中预测未来收益率较高的个股采取增持操作,对预测未来收益率较低的个股采取减持操作。那么,需要对第一投资组合中各股票对应的未来收益率进行预测。After determining the minimum risk of the first investment portfolio through the above steps, it is necessary to further consider the income of the first investment portfolio, that is, to convert the risk into profit, and pursue excess returns. For example, the predicted future return rate is higher in the first investment portfolio. The individual stocks adopt an increase in holding operation and take a reduction operation for individual stocks with lower forecasting future yields. Then, it is necessary to predict the future rate of return corresponding to each stock in the first portfolio.
在本实施例中,利用各股票在第二预设时间(例如,前30个交易日)内的历史数据,对各股票对应的未来收益率进行预测,鉴于长短期记忆网络(Long Short-Term Memory,LSTM),是一种时间递归神经网络,更适合处理和预测时间序列中间隔和延迟相对较长的重要事件,目前已经证明,LSTM 是解决长序依赖问题的有效技术。因此,选择LSTM对初步优化后的第一投资组合中的各只股票对应的未来收益率进行预测。In this embodiment, the historical yield data of each stock in the second preset time (for example, the first 30 trading days) is used to predict the future profit rate corresponding to each stock, in view of the long-short-term memory network (Long Short-Term) Memory, LSTM) is a time recurrent neural network that is more suitable for processing and predicting important events with relatively long intervals and delays in time series. LSTM has been proven to be an effective technique for solving long-order dependent problems. Therefore, the LSTM is selected to predict the future rate of return corresponding to each stock in the initially optimized first portfolio.
在对第一投资组合中的各股票的未来收益率进行预测之前,需对LSTM进行训练,具体包括以下步骤:Before predicting the future rate of return of each stock in the first portfolio, the LSTM needs to be trained, including the following steps:
构建样本数据:分别获取第一投资组合中各只股票在第三预设时间(过去两年)内每个交易日的特征数据,未来扩充样本数据,随机采集任意连续的30天的特征数据及对应的未来5个交易日的对数收益率作为样本集,从样本集中抽取第一比例(例如,80%)的样本数据作为训练集,第二比例(例如,20%)的样本数据作为验证集;及Construct sample data: obtain the characteristic data of each stock in the first investment portfolio for each trading day in the third preset time (the past two years), expand the sample data in the future, and randomly collect the arbitrarily 30 days of characteristic data and The corresponding logarithmic rate of return for the next 5 trading days is used as a sample set, and the first proportion (for example, 80%) of the sample data is extracted from the sample set as the training set, and the second ratio (for example, 20%) of the sample data is used as the verification. Set; and
模型训练:利用训练集对LSTM模型进行有监督的训练得到未来收益率预测模型,利用验证集对未来收益率预测模型进行验证,直到满足条件为止,例如,模型预测准确率达到90%为止。Model training: The training set is used to supervise the LSTM model to obtain the future rate prediction model. The verification set is used to verify the future rate prediction model until the condition is met. For example, the model prediction accuracy reaches 90%.
重复上述步骤,为每只股票拟合一个未来收益率预测模型,训练完毕后,第一投资组合中每只股票对应一个模型,即Model=[Model1,Model2,…,ModelN]。Repeat the above steps to fit a future yield prediction model for each stock. After the training, each stock in the first portfolio corresponds to one model, namely Model=[Model1, Model2,...,ModelN].
当需要对第一投资组合中第i只股票对应的未来收益率进行预测时,首先获取该股票在第二预设时间(例如,前30个交易日)内的特征数据,特征数据有5个,分别为['close','open','high','low','volume'],构建第i只股票对应的30*5的特征向量;调用第i只股票对应的未来收益率预测模型,将特征向量作为Input输入第i只股票对应的模型,对其未来5个交易日的对数收益率进行预测,模型Output为未来5个交易日的逐日对数收益率。When it is required to predict the future profit rate corresponding to the i-th stock in the first investment portfolio, firstly, the feature data of the stock in the second preset time (for example, the first 30 trading days) is obtained, and the feature data has 5 ,['close', 'open', 'high', 'low', 'volume'], construct the feature vector of 30*5 corresponding to the i-th stock; call the future yield prediction corresponding to the i-th stock The model uses the feature vector as the input to input the model corresponding to the i-th stock, and predicts the logarithmic rate of return for the next five trading days. The model Output is the daily logarithmic yield of the next five trading days.
在确定经初步优化后的第一投资组合中每只股票对应的未来5个交易日的对数收益率后,为了追求利益最大化,需根据每只股票在未来5个交易日的综合对数收益率进行调整。After determining the logarithmic rate of return for each of the stocks in the first optimized investment portfolio for the next 5 trading days, in order to maximize the benefits, the total logarithm of each stock in the next 5 trading days is required. The rate of return is adjusted.
具体地,根据预设的第二分析规则对所述第一投资组合中的各股票对应的权重进行调整的步骤包括:Specifically, the step of adjusting the weight corresponding to each stock in the first investment portfolio according to the preset second analysis rule includes:
分别计算各股票对应的未来综合对数收益率,按照各股票的未来综合对数收益率的高低顺序,对所述第一投资组合中的各股票进行排序;鉴于未来收益率预测模型输出的结果为各股票在未来5个交易日的对数收益率,因此,分别对第一投资组合中每只股票未来5个交易日的对数收益率进行加总,作 为每只股票的未来综合对数收益率,并根据未来综合对数收益率的高低顺序对第一投资组合中各股票进行排序。Calculating the future comprehensive logarithmic rate of return for each stock separately, sorting the stocks in the first portfolio according to the order of the future comprehensive logarithm of each stock; in view of the output of the future yield prediction model For the logarithmic rate of return of each stock in the next 5 trading days, therefore, the logarithmic rate of return for each stock in the first portfolio for the next 5 trading days will be added as the future comprehensive logarithm of each stock. Yield, and sort the stocks in the first portfolio according to the order of future comprehensive logarithmic returns.
对于未来综合对数收益率大于或等于第一预设阈值的第一类股票,将该类股票对应的权重上调;例如,对于未来综合对数收益率大于或等于10%的股票,说明未来涨幅较大,故可对其进行增持操作,假设其在第一投资组合中的权重为a,调整该股票对应的权重至(1+50%)a。For the first type of stocks whose future comprehensive logarithmic rate of return is greater than or equal to the first preset threshold, the weight corresponding to the stocks is raised; for example, for stocks with a future comprehensive logarithm of return greater than or equal to 10%, indicating future gains It is larger, so it can be overweighted, assuming that its weight in the first portfolio is a, and the weight corresponding to the stock is adjusted to (1+50%)a.
对于未来综合对数收益率小于或等于第二预设阈值的第二类股票,将该类股票对应的权重调整为第三预设阈值;例如,对于未来综合对数收益率小于-10%的股票,说明未来跌幅较大,故可对其进行减持甚至空仓操作,假设其在第一投资组合中的权重为a,调整该股票对应的权重至(1-80%)a或者直接将其对应的权重调整为0。For the second type of stocks whose future comprehensive logarithmic rate of return is less than or equal to the second predetermined threshold, the weight corresponding to the stocks is adjusted to a third preset threshold; for example, for a future comprehensive logarithmic yield of less than -10% Stocks, indicating a large decline in the future, it can be reduced or even short-selling operations, assuming that its weight in the first portfolio is a, adjust the corresponding weight of the stock to (1-80%) a or directly The corresponding weight is adjusted to 0.
对于预设比例的排序靠后的第三类股票,将该类股票对应的权重下调;例如,第一投资组合中的20只股票,对于未来综合收益率排序为后20%的4只股票,说明其在第一投资组合中未来收益相对较低,故可对该股票进行减持操作,假设原始比重为a,调整该个股对应的比重至(1-50%)a。For the third type of stocks with a predetermined proportion, the corresponding weights of the stocks are lowered; for example, 20 stocks in the first portfolio are sorted into the next 20% of the 4 stocks for the future comprehensive rate of return. It shows that its future income in the first investment portfolio is relatively low, so the stock can be reduced. Assuming the original proportion is a, adjust the proportion of the stock to (1-50%) a.
经过上述步骤,确定了第一投资组合中应调整权重的各股票后,对第一投资组合中各股票对应的权重进行调整,确定第二投资组合中各股票对应的权重W *=[w 1 *,w 2 *,w 3 *,…,w n *],即,确定目标投资组合。 After the above steps, after determining the stocks in the first portfolio that should be adjusted in weight, the weights corresponding to the stocks in the first portfolio are adjusted to determine the weights corresponding to the stocks in the second portfolio W * = [w 1 * , w 2 * , w 3 * , ..., w n * ], that is, determine the target portfolio.
上述实施例提出投资组合优化方法,通过在保持收益不变的情况下,尽可能缩小初始投资组合中个股两两之间的相关性,对初始投资组合进行初步优化,得到风险最小的第一投资组合;另外,通过LSTM模型预测第一投资组合中各股票对应的未来对数收益率,并对未来收益率相对较高或较低的股票的权重进行调整,得到第二投资组合,在一定程度上提高了投资收益。The above embodiment proposes a portfolio optimization method, which minimizes the correlation between individual stocks in the initial investment portfolio while keeping the returns unchanged, and initially optimizes the initial investment portfolio to obtain the first investment with the least risk. In addition, the LSTM model predicts the future logarithmic yield of each stock in the first portfolio, and adjusts the weight of stocks with relatively higher or lower yields to obtain a second portfolio, to a certain extent. Increased investment income.
此外,本申请实施例还提出一种计算机可读存储介质,所述计算机可读存储介质上存储有投资组合优化程序,所述投资组合优化程序被处理器执行时实现如下操作:In addition, the embodiment of the present application further provides a computer readable storage medium, where the portfolio optimization program is stored, and when the portfolio optimization program is executed by the processor, the following operations are implemented:
接收输入的待优化的初始投资组合中的股票、初始投资组合中各股票对应的初始权重,获取各股票对应的市场及该初始投资组合中各股票在第一预设时间内的历史数据;Receiving the initial weights of the stocks in the initial portfolio to be optimized and the stocks in the initial portfolio, and obtaining the historical data of the market corresponding to each stock and the stocks in the initial investment portfolio in the first preset time;
根据所述历史数据及预设的第一分析规则,计算得到所述初始投资组合中的各股票之间的相关性最小时,所述初始投资组合中各股票应对应的权重,并对初始投资组合中的各股票对应的权重进行调整,确定初步优化后的第一投资组合;及Calculating, according to the historical data and the preset first analysis rule, a weight corresponding to each stock in the initial investment portfolio when the correlation between the stocks in the initial investment portfolio is minimum, and initial investment Adjusting the weight corresponding to each stock in the portfolio to determine the first optimized investment portfolio; and
获取所述第一投资组合中的各股票在第二预设时间内的历史数据,构建各股票的特征向量,并输入各股票对应的预先训练好的未来收益率预测模型中,预测所述第一投资组合中的各股票的未来对数收益率,根据预设的第二分析规则对所述第一投资组合中的各股票对应的权重进行调整,确定第二投资组合。Obtaining historical data of each stock in the first investment portfolio in a second preset time, constructing a feature vector of each stock, and inputting a pre-trained future profit rate prediction model corresponding to each stock, predicting the first The future logarithmic yield of each stock in a portfolio is adjusted according to a preset second analysis rule for the weight corresponding to each stock in the first portfolio, and the second portfolio is determined.
本申请之计算机可读存储介质的具体实施方式与上述投资组合优化方法的具体实施方式大致相同,在此不再赘述。The specific implementation manner of the computer readable storage medium of the present application is substantially the same as the specific implementation manner of the above-mentioned portfolio optimization method, and details are not described herein again.
需要说明的是,在本文中,术语“包括”、“包含”或者其任何其他变体意在涵盖非排他性的包含,从而使得包括一系列要素的过程、装置、物品或者方法不仅包括那些要素,而且还包括没有明确列出的其他要素,或者是还包括为这种过程、装置、物品或者方法所固有的要素。在没有更多限制的情况下,由语句“包括一个……”限定的要素,并不排除在包括该要素的过程、装置、物品或者方法中还存在另外的相同要素。It is to be understood that the term "comprises", "comprising", or any other variants thereof, is intended to encompass a non-exclusive inclusion, such that a process, apparatus, article, or method that comprises a series of elements includes those elements. It also includes other elements not explicitly listed, or elements that are inherent to such a process, device, item, or method. An element that is defined by the phrase "comprising a ..." does not exclude the presence of additional equivalent elements in the process, the device, the item, or the method that comprises the element.
上述本申请实施例序号仅仅为了描述,不代表实施例的优劣。通过以上的实施方式的描述,本领域的技术人员可以清楚地了解到上述实施例方法可借助软件加必需的通用硬件平台的方式来实现,当然也可以通过硬件,但很多情况下前者是更佳的实施方式。基于这样的理解,本申请的技术方案本质上或者说对现有技术做出贡献的部分可以以软件产品的形式体现出来,该计算机软件产品存储在如上所述的一个存储介质(如ROM/RAM、磁碟、光盘)中,包括若干指令用以使得一台终端设备(可以是手机,计算机,服务器,或者网络设备等)执行本申请各个实施例所述的方法。The serial numbers of the embodiments of the present application are merely for the description, and do not represent the advantages and disadvantages of the embodiments. Through the description of the above embodiments, those skilled in the art can clearly understand that the foregoing embodiment method can be implemented by means of software plus a necessary general hardware platform, and of course, can also be through hardware, but in many cases, the former is better. Implementation. Based on such understanding, the technical solution of the present application, which is essential or contributes to the prior art, may be embodied in the form of a software product stored in a storage medium (such as ROM/RAM as described above). , a disk, an optical disk, including a number of instructions for causing a terminal device (which may be a mobile phone, a computer, a server, or a network device, etc.) to perform the methods described in the various embodiments of the present application.
以上仅为本申请的优选实施例,并非因此限制本申请的专利范围,凡是利用本申请说明书及附图内容所作的等效结构或等效流程变换,或直接或间接运用在其他相关的技术领域,均同理包括在本申请的专利保护范围内。The above is only a preferred embodiment of the present application, and is not intended to limit the scope of the patent application, and the equivalent structure or equivalent process transformations made by the specification and the drawings of the present application, or directly or indirectly applied to other related technical fields. The same is included in the scope of patent protection of this application.

Claims (20)

  1. 一种投资组合优化方法,应用于电子装置,其特征在于,该方法包括:A portfolio optimization method for an electronic device, the method comprising:
    接收输入的待优化的初始投资组合中的股票、初始投资组合中各股票对应的初始权重,获取各股票对应的市场及该初始投资组合中各股票在第一预设时间内的历史数据;Receiving the initial weights of the stocks in the initial portfolio to be optimized and the stocks in the initial portfolio, and obtaining the historical data of the market corresponding to each stock and the stocks in the initial investment portfolio in the first preset time;
    根据所述历史数据及预设的第一分析规则,计算得到所述初始投资组合中的各股票之间的相关性最小时,各股票应对应的权重,并对初始投资组合中的各股票对应的权重进行调整,确定初步优化后的第一投资组合;及Calculating, according to the historical data and the preset first analysis rule, a weight corresponding to each stock when the correlation between the stocks in the initial investment portfolio is minimum, and corresponding to each stock in the initial investment portfolio The weights are adjusted to determine the first optimized investment portfolio; and
    获取所述第一投资组合中的各股票在第二预设时间内的历史数据,构建各股票的特征向量,并输入各股票对应的预先训练好的未来收益率预测模型中,预测所述第一投资组合中的各股票的未来对数收益率,根据预设的第二分析规则对所述第一投资组合中的各股票对应的权重进行调整,确定第二投资组合。Obtaining historical data of each stock in the first investment portfolio in a second preset time, constructing a feature vector of each stock, and inputting a pre-trained future profit rate prediction model corresponding to each stock, predicting the first The future logarithmic yield of each stock in a portfolio is adjusted according to a preset second analysis rule for the weight corresponding to each stock in the first portfolio, and the second portfolio is determined.
  2. 根据权利要求1所述的投资组合优化方法,其特征在于,所述“根据所述历史数据及预设的第一分析规则,计算得到所述初始投资组合中的各股票之间的相关性最小时,所述初始投资组合中各股票应对应的权重”的步骤包括:The portfolio optimization method according to claim 1, wherein said "based on said historical data and a preset first analysis rule, calculating a correlation between each stock in said initial portfolio In the hour, the steps in which the stocks in the initial portfolio should correspond to the weights include:
    分别计算第一预设时间内所述市场及所述初始投资组合中各股票对应的对数收益率序列;Calculating a logarithmic rate of return sequence corresponding to each stock in the market and the initial investment portfolio in a first preset time period;
    将所述初始投资组合中各股票对应的对数收益序列分别与所述市场的对数收益序列进行回归,分别计算所述初始投资组合中各股票对应的残差序列,并求得所述初始投资组合对应的协方差矩阵;及Regressing the logarithmic income sequence corresponding to each stock in the initial portfolio with the logarithmic yield sequence of the market, respectively calculating a residual sequence corresponding to each stock in the initial portfolio, and obtaining the initial The covariance matrix corresponding to the portfolio; and
    计算所述初始投资组合对应的协方差矩阵中各股票之间的协方差加权和最小的解,根据计算结果确定所述初始投资组合中各股票应对应的权重。Calculating a minimum solution of the covariance weighted sum between the stocks in the covariance matrix corresponding to the initial portfolio, and determining a weight corresponding to each stock in the initial portfolio according to the calculation result.
  3. 如权利要求2所述的投资组合优化方法,其特征在于,所述“根据预设的第二分析规则对所述第一投资组合中的各股票对应的权重进行调整”的步骤包括:The portfolio optimization method according to claim 2, wherein the step of "adjusting the weight corresponding to each stock in the first portfolio according to a preset second analysis rule" comprises:
    分别计算各股票对应的未来综合对数收益率,按照各股票的未来综合对数收益率的高低顺序,对所述第一投资组合中的各股票进行排序;Calculating the future comprehensive logarithmic rate of return corresponding to each stock, and sorting the stocks in the first portfolio according to the order of the future comprehensive logarithmic returns of each stock;
    对于未来综合对数收益率大于或等于第一预设阈值的第一类股票,将该 类股票对应的权重上调;For the first type of stocks whose future comprehensive logarithm rate of return is greater than or equal to the first preset threshold, the weight corresponding to the stocks is raised;
    对于未来综合对数收益率小于或等于第二预设阈值的第二类股票,将该类股票对应的权重调整为第三预设阈值;及For the second type of stocks whose future comprehensive logarithmic rate of return is less than or equal to the second predetermined threshold, the weight corresponding to the stocks is adjusted to a third preset threshold;
    对于预设比例的排序靠后的第三类股票,将该类股票对应的权重下调。For the third type of stocks that are sorted by the preset ratio, the weights corresponding to the stocks are lowered.
  4. 如权利要求1至3中任意一项所述的投资组合优化方法,其特征在于,所述预先训练好的未来收益率预测模型为长短期记忆网络(Long Short-Term Memory,LSTM)。The portfolio optimization method according to any one of claims 1 to 3, wherein the pre-trained future rate of return prediction model is a Long Short-Term Memory (LSTM).
  5. 根据权利要求4所述的投资组合优化方法,其特征在于,所述市场对应的对数收益率序列的计算公式为:The portfolio optimization method according to claim 4, wherein the calculation formula of the logarithmic rate of return corresponding to the market is:
    RM t=lnPM t-lnPM t-1 RM t =lnPM t -lnPM t-1
    其中,RM t表示市场对应的对数收益率序列中第t时刻市场的对数收益率,PM t表示t时刻市场的收盘价,t表示在优化初始投资组合之前的某时刻。 Where RM t represents the logarithmic rate of return of the market at time t in the logarithmic rate of return corresponding to the market, PM t represents the closing price of the market at time t, and t represents a certain time before the optimization of the initial investment portfolio.
  6. 根据权利要求5所述的投资组合优化方法,其特征在于,所述初始投资组合中各股票对应的对数收益率序列的计算公式为:The portfolio optimization method according to claim 5, wherein the calculation formula of the logarithmic rate of return sequence corresponding to each stock in the initial investment portfolio is:
    RS it=lnP it-lnP i(t-1) RS it =lnP it -lnP i(t-1)
    其中,RS it表示所述初始投资组合中第i只股票对应的对数收益率序列中第t时刻该股票的对数收益率,P it表示t时刻第i只股票的收盘价,t表示在优化初始投资组合之前的某时刻。 Where RS it represents the logarithmic rate of return of the stock at the t-th time in the logarithmic rate of return corresponding to the i-th stock in the initial portfolio, Pit represents the closing price of the i-th stock at time t, and t represents Optimize a moment before the initial portfolio.
  7. 根据权利要求6所述的投资组合优化方法,其特征在于,所述各股票对应的残差序列的计算公式为:The portfolio optimization method according to claim 6, wherein the calculation formula of the residual sequence corresponding to each stock is:
    e it=RM t-(α ii*RS it) e it =RM t -(α ii *RS it )
    其中,RM t表示市场对应的对数收益率序列中第t时刻市场的对数收益率,RS it表示所述初始投资组合中第i只股票对应的对数收益率序列中第t时刻该股票的对数收益率,α=[α 123,…,α n],β=[β 123,…,β n],e it表示所述初始投资组合中第i只股票对应残差序列,e it=[e 1i,e 2i,e 3i,…,e Ti]。 Where RM t represents the logarithmic rate of return of the market at the t-th time in the logarithmic rate of return sequence corresponding to the market, and RS it represents the stock at the t-th time in the logarithmic rate of return sequence corresponding to the i-th stock in the initial portfolio Logarithmic rate of return, α = [α 1 , α 2 , α 3 , ..., α n ], β = [β 1 , β 2 , β 3 , ..., β n ], e it represents the initial portfolio The i-th stock corresponds to the residual sequence, e it =[e 1i , e 2i , e 3i ,..., e Ti ].
  8. 根据权利要求7所述的投资组合优化方法,其特征在于,所述初始投资组合对应的协方差矩阵中各股票之间的协方差加权和最小的解的计算公式为:The portfolio optimization method according to claim 7, wherein the calculation formula of the covariance weighted sum minimum between the stocks in the covariance matrix corresponding to the initial portfolio is:
    min W T∑W Min W T ∑W
    s.t∑ iw 0i*RS i=R St∑ i w 0i *RS i =R
    e TW=1 e T W=1
    其中,W为待求解,W=[w 1,w 2,…,w n],表示每只个股应该对应的权重,∑表示所述初始投资组合对应的协方差矩阵,RS i表示优化投资组合前一时刻各股票对应的对数收益率,w 0i表示初始投资组合中各股票对应的初始权重,RS表示优化投资组合前一时刻初始投资组合对应的总对数收益率,e TW=1表示W中各股票对应的权重总和为1。 Where W is to be solved, W=[w 1 ,w 2 ,...,w n ], indicating the weight corresponding to each stock, ∑ represents the covariance matrix corresponding to the initial portfolio, and RS i represents the optimized portfolio The logarithmic rate of return corresponding to each stock in the previous moment, w 0i represents the initial weight corresponding to each stock in the initial portfolio, and RS represents the total logarithmic yield corresponding to the initial portfolio of the optimized investment portfolio, e T W=1 Indicates that the sum of the weights corresponding to each stock in W is 1.
  9. 一种电子装置,其特征在于,该电子装置包括:存储器、处理器,所述存储器上存储有投资组合优化程序,所述投资组合优化程序被所述处理器执行时实现如下步骤:An electronic device, comprising: a memory, a processor, and a portfolio optimization program stored on the memory, where the portfolio optimization program is executed by the processor to implement the following steps:
    接收输入的待优化的初始投资组合中的股票、初始投资组合中各股票对应的初始权重,获取各股票对应的市场及该初始投资组合中各股票在第一预设时间内的历史数据;Receiving the initial weights of the stocks in the initial portfolio to be optimized and the stocks in the initial portfolio, and obtaining the historical data of the market corresponding to each stock and the stocks in the initial investment portfolio in the first preset time;
    根据所述历史数据及预设的第一分析规则,计算得到所述初始投资组合中的各股票之间的相关性最小时,各股票应对应的权重,并对初始投资组合中的各股票对应的权重进行调整,确定初步优化后的第一投资组合;及Calculating, according to the historical data and the preset first analysis rule, a weight corresponding to each stock when the correlation between the stocks in the initial investment portfolio is minimum, and corresponding to each stock in the initial investment portfolio The weights are adjusted to determine the first optimized investment portfolio; and
    获取所述第一投资组合中的各股票在第二预设时间内的历史数据,构建各股票的特征向量,并输入各股票对应的预先训练好的未来收益率预测模型中,预测所述第一投资组合中的各股票的未来对数收益率,根据预设的第二分析规则对所述第一投资组合中的各股票对应的权重进行调整,确定第二投资组合。Obtaining historical data of each stock in the first investment portfolio in a second preset time, constructing a feature vector of each stock, and inputting a pre-trained future profit rate prediction model corresponding to each stock, predicting the first The future logarithmic yield of each stock in a portfolio is adjusted according to a preset second analysis rule for the weight corresponding to each stock in the first portfolio, and the second portfolio is determined.
  10. 根据权利要求9所述的电子装置,其特征在于,所述“根据所述历史数据及预设的第一分析规则,计算得到所述初始投资组合中的各股票之间的相关性最小时,所述初始投资组合中各股票应对应的权重”的步骤包括:The electronic device according to claim 9, wherein said "based on said historical data and a preset first analysis rule, when the correlation between the stocks in said initial portfolio is calculated to be minimal, The steps of the weights of the stocks in the initial portfolio should correspond to:
    分别计算第一预设时间内所述市场及所述初始投资组合中各股票对应的对数收益率序列;Calculating a logarithmic rate of return sequence corresponding to each stock in the market and the initial investment portfolio in a first preset time period;
    将所述初始投资组合中各股票对应的对数收益序列分别与所述市场的对数收益序列进行回归,分别计算所述初始投资组合中各股票对应的残差序列,并求得所述初始投资组合对应的协方差矩阵;及Regressing the logarithmic income sequence corresponding to each stock in the initial portfolio with the logarithmic yield sequence of the market, respectively calculating a residual sequence corresponding to each stock in the initial portfolio, and obtaining the initial The covariance matrix corresponding to the portfolio; and
    计算所述初始投资组合对应的协方差矩阵中各股票之间的协方差加权和最小的解,根据计算结果确定所述初始投资组合中各股票应对应的权重。Calculating a minimum solution of the covariance weighted sum between the stocks in the covariance matrix corresponding to the initial portfolio, and determining a weight corresponding to each stock in the initial portfolio according to the calculation result.
  11. 如权利要求10所述的电子装置,其特征在于,所述“根据预设的第二分析规则对所述第一投资组合中的各股票对应的权重进行调整”的步骤包括:The electronic device according to claim 10, wherein the step of "adjusting the weight corresponding to each stock in the first portfolio according to a preset second analysis rule" comprises:
    分别计算各股票对应的未来综合对数收益率,按照各股票的未来综合对数收益率的高低顺序,对所述第一投资组合中的各股票进行排序;Calculating the future comprehensive logarithmic rate of return corresponding to each stock, and sorting the stocks in the first portfolio according to the order of the future comprehensive logarithmic returns of each stock;
    对于未来综合对数收益率大于或等于第一预设阈值的第一类股票,将该类股票对应的权重上调;For the first type of stocks whose future comprehensive logarithmic rate of return is greater than or equal to the first preset threshold, the weight corresponding to the stocks is raised;
    对于未来综合对数收益率小于或等于第二预设阈值的第二类股票,将该类股票对应的权重调整为第三预设阈值;及For the second type of stocks whose future comprehensive logarithmic rate of return is less than or equal to the second predetermined threshold, the weight corresponding to the stocks is adjusted to a third preset threshold;
    对于预设比例的排序靠后的第三类股票,将该类股票对应的权重下调。For the third type of stocks that are sorted by the preset ratio, the weights corresponding to the stocks are lowered.
  12. 如权利要求9至11中任意一项所述的电子装置,其特征在于,所述预先训练好的未来收益率预测模型为长短期记忆网络(Long Short-Term Memory,LSTM)。The electronic device according to any one of claims 9 to 11, wherein the pre-trained future rate of return prediction model is a Long Short-Term Memory (LSTM).
  13. 根据权利要求12所述的电子装置,其特征在于,所述市场对应的对数收益率序列的计算公式为:The electronic device according to claim 12, wherein the calculation formula of the logarithmic rate of return corresponding to the market is:
    RM t=lnPM t-lnPM t-1 RM t =lnPM t -lnPM t-1
    其中,RM t表示市场对应的对数收益率序列中第t时刻市场的对数收益率,PM t表示t时刻市场的收盘价,t表示在优化初始投资组合之前的某时刻。 Where RM t represents the logarithmic rate of return of the market at time t in the logarithmic rate of return corresponding to the market, PM t represents the closing price of the market at time t, and t represents a certain time before the optimization of the initial investment portfolio.
  14. 根据权利要求13所述的电子装置,其特征在于,所述初始投资组合中各股票对应的对数收益率序列的计算公式为:The electronic device according to claim 13, wherein the calculation formula of the logarithmic rate of return corresponding to each stock in the initial portfolio is:
    RS it=lnP it-lnP i(t-1) RS it =lnP it -lnP i(t-1)
    其中,RS it表示所述初始投资组合中第i只股票对应的对数收益率序列中第t时刻该股票的对数收益率,P it表示t时刻第i只股票的收盘价,t表示在优化初始投资组合之前的某时刻。 Where RS it represents the logarithmic rate of return of the stock at the t-th time in the logarithmic rate of return corresponding to the i-th stock in the initial portfolio, Pit represents the closing price of the i-th stock at time t, and t represents Optimize a moment before the initial portfolio.
  15. 根据权利要求14所述的电子装置,其特征在于,所述各股票对应的残差序列的计算公式为:The electronic device according to claim 14, wherein the calculation formula of the residual sequence corresponding to each stock is:
    e it=RM t-(α ii*RS it) e it =RM t -(α ii *RS it )
    其中,RM t表示市场对应的对数收益率序列中第t时刻市场的对数收益率,RS it表示所述初始投资组合中第i只股票对应的对数收益率序列中第t时刻该股票的对数收益率,α=[α 123,…,α n],β=[β 123,…,β n],e it表示所述初始投资组合中第i只股票对应残差序列,e it=[e 1i,e 2i,e 3i,…,e Ti]。 Where RM t represents the logarithmic rate of return of the market at the t-th time in the logarithmic rate of return sequence corresponding to the market, and RS it represents the stock at the t-th time in the logarithmic rate of return sequence corresponding to the i-th stock in the initial portfolio Logarithmic rate of return, α = [α 1 , α 2 , α 3 , ..., α n ], β = [β 1 , β 2 , β 3 , ..., β n ], e it represents the initial portfolio The i-th stock corresponds to the residual sequence, e it =[e 1i , e 2i , e 3i ,..., e Ti ].
  16. 根据权利要求15所述的电子装置,其特征在于,所述初始投资组合 对应的协方差矩阵中各股票之间的协方差加权和最小的解的计算公式为:The electronic device according to claim 15, wherein the formula for calculating the solution of the covariance weighted sum between the stocks in the covariance matrix corresponding to the initial portfolio is:
    min W T∑W Min W T ∑W
    s.t∑ iw 0i*RS i=R St∑ i w 0i *RS i =R
    e TW=1 e T W=1
    其中,W为待求解,W=[w 1,w 2,…,w n],表示每只个股应该对应的权重,∑表示所述初始投资组合对应的协方差矩阵,RS i表示优化投资组合前一时刻各股票对应的对数收益率,w 0i表示初始投资组合中各股票对应的初始权重,RS表示优化投资组合前一时刻初始投资组合对应的总对数收益率,e TW=1表示W中各股票对应的权重总和为1。 Where W is to be solved, W=[w 1 ,w 2 ,...,w n ], indicating the weight corresponding to each stock, ∑ represents the covariance matrix corresponding to the initial portfolio, and RS i represents the optimized portfolio The logarithmic rate of return corresponding to each stock in the previous moment, w 0i represents the initial weight corresponding to each stock in the initial portfolio, and RS represents the total logarithmic yield corresponding to the initial portfolio of the optimized investment portfolio, e T W=1 Indicates that the sum of the weights corresponding to each stock in W is 1.
  17. 一种计算机可读存储介质,其特征在于,所述计算机可读存储介质上存储有投资组合优化程序,所述投资组合优化程序被处理器执行时实现如下步骤:A computer readable storage medium, wherein the computer readable storage medium stores a portfolio optimization program, and when the portfolio optimization program is executed by the processor, the following steps are implemented:
    接收输入的待优化的初始投资组合中的股票、初始投资组合中各股票对应的初始权重,获取各股票对应的市场及该初始投资组合中各股票在第一预设时间内的历史数据;Receiving the initial weights of the stocks in the initial portfolio to be optimized and the stocks in the initial portfolio, and obtaining the historical data of the market corresponding to each stock and the stocks in the initial investment portfolio in the first preset time;
    根据所述历史数据及预设的第一分析规则,计算得到所述初始投资组合中的各股票之间的相关性最小时,各股票应对应的权重,并对初始投资组合中的各股票对应的权重进行调整,确定初步优化后的第一投资组合;及Calculating, according to the historical data and the preset first analysis rule, a weight corresponding to each stock when the correlation between the stocks in the initial investment portfolio is minimum, and corresponding to each stock in the initial investment portfolio The weights are adjusted to determine the first optimized investment portfolio; and
    获取所述第一投资组合中的各股票在第二预设时间内的历史数据,构建各股票的特征向量,并输入各股票对应的预先训练好的未来收益率预测模型中,预测所述第一投资组合中的各股票的未来对数收益率,根据预设的第二分析规则对所述第一投资组合中的各股票对应的权重进行调整,确定第二投资组合。Obtaining historical data of each stock in the first investment portfolio in a second preset time, constructing a feature vector of each stock, and inputting a pre-trained future profit rate prediction model corresponding to each stock, predicting the first The future logarithmic yield of each stock in a portfolio is adjusted according to a preset second analysis rule for the weight corresponding to each stock in the first portfolio, and the second portfolio is determined.
  18. 根据权利要求17所述的计算机可读存储介质,其特征在于,所述“根据所述历史数据及预设的第一分析规则,计算得到所述初始投资组合中的各股票之间的相关性最小时,所述初始投资组合中各股票应对应的权重”的步骤包括:The computer readable storage medium according to claim 17, wherein said "according to said historical data and a preset first analysis rule, calculating a correlation between each stock in said initial portfolio At the very least, the steps in which the stocks in the initial portfolio should correspond to the weights include:
    分别计算第一预设时间内所述市场及所述初始投资组合中各股票对应的对数收益率序列;Calculating a logarithmic rate of return sequence corresponding to each stock in the market and the initial investment portfolio in a first preset time period;
    将所述初始投资组合中各股票对应的对数收益序列分别与所述市场的对 数收益序列进行回归,分别计算所述初始投资组合中各股票对应的残差序列,并求得所述初始投资组合对应的协方差矩阵;及Regressing the logarithmic income sequence corresponding to each stock in the initial portfolio with the logarithmic yield sequence of the market, respectively calculating a residual sequence corresponding to each stock in the initial portfolio, and obtaining the initial The covariance matrix corresponding to the portfolio; and
    计算所述初始投资组合对应的协方差矩阵中各股票之间的协方差加权和最小的解,根据计算结果确定所述初始投资组合中各股票应对应的权重。Calculating a minimum solution of the covariance weighted sum between the stocks in the covariance matrix corresponding to the initial portfolio, and determining a weight corresponding to each stock in the initial portfolio according to the calculation result.
  19. 如权利要求18所述的计算机可读存储介质,其特征在于,所述“根据预设的第二分析规则对所述第一投资组合中的各股票对应的权重进行调整”的步骤包括:The computer readable storage medium according to claim 18, wherein the step of "adjusting the weight corresponding to each stock in the first portfolio according to a preset second analysis rule" comprises:
    分别计算各股票对应的未来综合对数收益率,按照各股票的未来综合对数收益率的高低顺序,对所述第一投资组合中的各股票进行排序;Calculating the future comprehensive logarithmic rate of return corresponding to each stock, and sorting the stocks in the first portfolio according to the order of the future comprehensive logarithmic returns of each stock;
    对于未来综合对数收益率大于或等于第一预设阈值的第一类股票,将该类股票对应的权重上调;For the first type of stocks whose future comprehensive logarithmic rate of return is greater than or equal to the first preset threshold, the weight corresponding to the stocks is raised;
    对于未来综合对数收益率小于或等于第二预设阈值的第二类股票,将该类股票对应的权重调整为第三预设阈值;及For the second type of stocks whose future comprehensive logarithmic rate of return is less than or equal to the second predetermined threshold, the weight corresponding to the stocks is adjusted to a third preset threshold;
    对于预设比例的排序靠后的第三类股票,将该类股票对应的权重下调。For the third type of stocks that are sorted by the preset ratio, the weights corresponding to the stocks are lowered.
  20. 如权利要求17至19中任意一项所述的计算机可读存储介质,其特征在于,所述预先训练好的未来收益率预测模型为长短期记忆网络(Long Short-Term Memory,LSTM)。The computer readable storage medium according to any one of claims 17 to 19, wherein the pre-trained future rate of return prediction model is a Long Short-Term Memory (LSTM).
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