WO2020000718A1 - Investment portfolio generation method and apparatus, and computer-readable storage medium - Google Patents

Abstract

Provided are an investment portfolio generation method and apparatus, and a computer-readable storage medium. The method comprises: generating a sample matrix according to transaction data of constituent stocks of a target market index in a plurality of consecutive historical trading days (S10); calculating a first sample covariance matrix according to the sample matrix (S20); calculating an eigenvalue of the first sample covariance matrix and an eigenvector corresponding to the eigenvalue (S30); calculating the theoretical maximum eigenvalue of the first sample covariance matrix based on the M-P law, and denoising an eigenvalue diagonal matrix of the first sample covariance matrix according to the theoretical maximum eigenvalue (S40); calculating a second sample covariance matrix according to the denoised eigenvalue diagonal matrix and a matrix composed of eigenvectors (S50); and calculating the investment proportion of each constituent stock according to the second sample covariance matrix, and generating an investment portfolio (S60). By means of the method, the denoising processing of a sample covariance matrix is realized, and the risk of an investment portfolio is reduced.

Description

Method, device and computer-readable storage medium for generating portfolio

This application is based on the Paris Convention claiming the priority of a Chinese patent application filed on June 29, 2018 with the application number 201810697668.4 and the name "Portfolio generation method, device and computer-readable storage medium", the entire Chinese patent application The contents are incorporated herein by reference.

Technical field

The present application relates to the field of information processing technology, and in particular, to a method, a device, and a computer-readable storage medium for generating a portfolio.

Background technique

Markowitz's portfolio boundary theory has opened up the field of modern mathematical finance. For the first time, mathematical tools have been introduced to financial analysis, which has provided a more reliable mathematical analysis foundation for investment theory. In practice, investors describe the correlation between assets using an empirical covariance matrix instead of a theoretical covariance matrix, that is, using historical data to calculate the covariance between assets, and using sample covariance instead of the overall covariance. . However, due to the weak effectiveness of the Chinese stock market, there is a large amount of white noise data in the obtained earnings data. The existence of white noise makes the sample covariance matrix a biased estimate of the theoretical covariance matrix, and the sample covariance between stocks. The matrix is an important parameter in the calculation of the optimal portfolio of asset allocation. The white noise of high-dimensional data will seriously distort the sample covariance matrix, which will distort the calculation of the optimal portfolio and lead to a higher investment risk in the created asset portfolio. .

Summary of the invention

This application provides a method, device, and computer-readable storage medium for generating a portfolio, the main purpose of which is to implement denoising processing on the sample covariance matrix and reduce the risk of the portfolio.

In order to achieve the above purpose, this application also provides a method for generating a portfolio, which method includes:

Determining a target market index, and generating a sample matrix based on the transaction data of the constituent stocks of the target market index over successive historical trading days;

Calculating a first sample covariance matrix of the constituent stocks of the target market index according to the sample matrix;

Calculating a eigenvalue of the first sample covariance matrix and a eigenvector corresponding to the eigenvalue;

Calculating a theoretical maximum eigenvalue of the first sample covariance matrix based on M-P law, and performing a denoising process on the eigenvalues of the first sample covariance matrix on the angular matrix according to the theoretical maximum eigenvalue

Calculate a second sample covariance matrix according to the eigenvalue diagonal matrix and the matrix formed by the eigenvectors after the denoising process;

Calculate the investment ratio of each constituent stock according to the second sample covariance matrix and the Markowitz mean variance model, and generate an investment portfolio according to the investment ratio.

In addition, in order to achieve the above object, the present application further provides an investment portfolio generation device, which includes a memory and a processor, where the memory stores an investment portfolio generation program that can be run on the processor, and the investment portfolio When the generated program is executed by the processor, the following steps are implemented:

Determining a target market index, and generating a sample matrix based on the transaction data of the constituent stocks of the target market index over successive historical trading days;

Calculating a first sample covariance matrix of the constituent stocks of the target market index according to the sample matrix;

Calculating a eigenvalue of the first sample covariance matrix and a eigenvector corresponding to the eigenvalue;

Calculating a theoretical maximum eigenvalue of the first sample covariance matrix based on the M-P law, and performing denoising processing on the eigenvalues of the first sample covariance matrix on the angular matrix according to the theoretical maximum eigenvalue;

Calculate a second sample covariance matrix according to the eigenvalue diagonal matrix and the matrix formed by the eigenvectors after the denoising process;

Calculate the investment ratio of each constituent stock according to the second sample covariance matrix and the Markowitz mean variance model, and generate an investment portfolio according to the investment ratio.

In addition, in order to achieve the above object, the present application further provides a computer-readable storage medium, where the computer-readable storage medium stores a portfolio generation program, and the portfolio generation program can be executed by one or more processors. To achieve the following steps:

Determining a target market index, and generating a sample matrix based on the transaction data of the constituent stocks of the target market index over successive historical trading days;

Calculating a first sample covariance matrix of the constituent stocks of the target market index according to the sample matrix;

Calculating a eigenvalue of the first sample covariance matrix and a eigenvector corresponding to the eigenvalue;

Calculating a theoretical maximum eigenvalue of the first sample covariance matrix based on M-P law, and performing denoising processing on the eigenvalues of the first sample covariance matrix on the angular matrix according to the theoretical maximum eigenvalue;

Calculate a second sample covariance matrix according to the eigenvalue diagonal matrix and the matrix formed by the eigenvectors after the denoising process;

Calculate the investment ratio of each constituent stock according to the second sample covariance matrix and the Markowitz mean variance model, and generate an investment portfolio according to the investment ratio.

The investment portfolio generation method, device and computer-readable storage medium proposed in this application determine the target market index, and generate a sample matrix based on the transaction data of the constituent stocks of the target market index over multiple consecutive historical trading days; calculate the target based on the sample matrix The first sample covariance matrix of the constituent stocks of the market index; calculates the eigenvalues of the first sample covariance matrix and the eigenvectors corresponding to the eigenvalues; calculates the theoretical maximum eigenvalue of the first sample covariance matrix based on MP's law , Performing a denoising process on the eigenvalues of the first sample covariance matrix based on the eigenvalues and the theoretical maximum eigenvalues; calculating the second based on the eigenvalues diagonal matrix and the matrix composed of eigenvectors after denoising Sample covariance matrix; calculate the investment proportion of each constituent stock based on the second sample covariance matrix and the Markowitz mean variance model, and generate an investment portfolio based on the investment proportion. This solution is based on MP's law to denoise the sample covariance matrix of the market index and filter out the random data, so that the data in the recalculated second sample covariance matrix is a relatively reliable correlation coefficient, which makes investment The portfolio is optimized to reduce investment risks.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic flowchart of an investment portfolio generation method according to an embodiment of the present application;

FIG. 2 is a schematic diagram of an internal structure of an investment portfolio generating device according to an embodiment of the present application; FIG.

FIG. 3 is a schematic diagram of a module of a portfolio generation program in a portfolio generation device provided by an embodiment of the present application.

The implementation, functional characteristics and advantages of the purpose of this application will be further described with reference to the embodiments and the drawings.

detailed description

It should be understood that the specific embodiments described herein are only used to explain the application, and are not used to limit the application.

This application provides a method for generating a portfolio. Referring to FIG. 1, a schematic flowchart of a method for generating a portfolio provided by an embodiment of the present application is shown. The method may be performed by a device, which may be implemented by software and / or hardware.

In this embodiment, the method for generating a portfolio includes:

In step S10, a target market index is determined, and a sample matrix is generated according to the transaction data of the constituent stocks of the target market index over multiple consecutive historical trading days.

Step S20: Calculate a first sample covariance matrix of the constituent stocks of the target market index according to the sample matrix.

The target market index in this application may be a market index such as the Shanghai Composite Index, Shanghai and Shenzhen 300. In the following embodiments, the method of this application will be described using the Shanghai and Shenzhen 300 as an example. Obtain the closing price data of the 300 constituent stocks in the CSI 300 from the database for each trading day in the past ten years. Specifically, step S10 includes the following detailed steps:

The target market index is determined, and transaction data of constituent stocks of the target market index within multiple consecutive historical trading days is obtained; the acquired transaction data is standardized; and the sample matrix is constructed according to the standardized processed transaction data.

In addition, because the closing price data is used as financial time series data, it has the characteristics of peaks and fat tails. In order to eliminate this feature, the log closing data of the stock is first processed:

among them,

Is the logarithmic yield of stock i at the end of period t,

Is the closing price of stock i at the end of period t. Assuming that there have been data of closing prices for T trading days in the past ten years, the logarithmic return at the end of period t is the closing price data for the tth trading day in T consecutive trading days.

In addition, in order to eliminate the influence of the dimension, the logarithmic rate of return is standardized. For the component stock i, the standardized treatment method is as follows:

among them,

T is the total number of trading days,

δ _i is the standard deviation of the logarithmic yield of stock i.

The number of component bonds in the target market index is N. For Shanghai and Shenzhen 300, N = 300, and the number of trading days is T. All the logarithmic return data after normalization process form a N × T matrix. The logarithmic yield of a constituent stock can be regarded as a random variable, and the logarithmic yield of all constituent stocks in T trading days constitutes a sample logarithmic yield matrix. The logarithmic return sequence matrix of all constituent stocks after normalization is as follows:

Get the first sample covariance matrix according to the following formula:

Since the covariance between the random variables is calculated, the first sample covariance matrix obtained is an N × N matrix.

Step S30: Calculate a feature value of the first sample covariance matrix and a feature vector corresponding to the feature value.

Step S40: Calculate the theoretical maximum eigenvalue of the first sample covariance matrix based on the M-P law, and perform denoising processing on the angular matrix of the eigenvalues of the first sample covariance matrix based on the theoretical maximum eigenvalue.

Step S50: Calculate a second sample covariance matrix according to the eigenvalue diagonal matrix and the matrix composed of the eigenvectors after the denoising process.

Step S60: Calculate the investment ratio of each constituent stock according to the second sample covariance matrix and the Markowitz mean variance model, and generate an investment portfolio according to the investment ratio.

Step S40 may include the following detailed steps: calculating a theoretical maximum eigenvalue of the first sample covariance matrix based on MP law; arranging the eigenvalues in ascending order to generate a diagonal matrix of eigenvalues; from The eigenvalues of the first sample covariance matrix that are greater than the theoretical maximum eigenvalue and whose previous eigenvalue is less than the theoretical maximum eigenvalue are found as the intercept point eigenvalues; the eigenvalue pairs are deleted Eigenvalues in the angular matrix that are smaller than the eigenvalues of the intercept points are used to denoise the angular matrix on the characteristic values.

Specifically, the eigenvalues λ _{(i) of the} first sample covariance matrix are solved, and the eigenvalues are sorted in ascending order of the eigenvalues λ ₍₁₎ <λ ₍₂₎ <... λ _(N) . These characteristics The values form the eigenvalue diagonal matrix Λ:

Calculate the eigenvector corresponding to the eigenvalue.

u _(i) is a feature vector corresponding to λ _(i) , the feature vector is a column vector, and all the feature vectors form a matrix U = (u ₍₁₎ , u ₍₂₎ , ..., u _(N) ).

Remember

Then according to the MP law (Marchenko-Pastur LAW, referred to as MP law), if the elements in the matrix are independent and identically distributed, the theoretical maximum eigenvalue of the matrix can be calculated according to Q, The specific calculation formula is as follows:

After calculating the theoretical maximum eigenvalue of the first sample covariance matrix according to MP's law, the intercept point eigenvalues are found. Specifically, the eigenvalues λ ₍₁₎ , λ ₍₂₎ , ... are arranged in ascending order. In λ _(N) , the k-th largest eigenvalue λ _{(k) is found} so that it meets the following conditions:

λ _(k) > λ _max ≥λ _(k-1)

λ _(k-1) is the eigenvalue ranked one ahead of λ _(k) . Let λ _(k) be the eigenvalue of the intercept point, and replace all eigenvalues whose eigenvalues in the eigenvalue diagonal matrix are smaller than the eigenvalue of the intercept point with 0.

Because the premise of MP law assumes that the elements in the matrix are independent and identically distributed, that is, assuming that the elements in the first sample covariance matrix are independent and identically distributed, the theoretical maximum eigenvalues are consistent with

If the eigenvalues calculated based on actual data are greater than the theoretical maximum eigenvalues, it means that some elements in the matrix are not independent and identically distributed, but have a certain correlation. The eigenvalues that conform to MP's law are deleted, and the second covariance matrix recalculated from the diagonal matrix based on the new eigenvalues excludes random data, and the remaining data is relatively reliable related data.

What needs to be explained here is that the theoretical minimum eigenvalue of the first sample covariance matrix can also be calculated according to MP's law, and for eigenvalues smaller than the theoretical characteristic minimum, the absolute value is generally close to 0 and can be ignored Neglect, and the smaller the eigenvalue, the lower its importance, which can be ignored. Therefore, in the solution of this embodiment, all the eigenvalues smaller than the theoretical maximum eigenvalue are deleted from the diagonal matrix of eigenvalues. The eigenvalues also include those that do not conform to MP's law and are smaller than the theoretical minimum eigenvalue.

Alternatively, in other embodiments, step S40 may include the following thinning steps: calculating a theoretical maximum eigenvalue of the first sample covariance matrix based on MP law; arranging the eigenvalues in ascending order, Generate a eigenvalue diagonal array; delete the eigenvalues from the eigenvalue diagonal array that are smaller than the theoretical maximum eigenvalue to perform denoising processing on the eigenvalue diagonal array.

The diagonal matrix of eigenvalues after denoising is as follows:

According to the eigenvalue diagonal matrix Λ _filtered after the noise reduction process, the covariance matrix is recalculated according to the eigenvalue decomposition formula to obtain the second sample covariance matrix, which has eliminated the influence of the white noise data:

Σ _filtered = UΛ _filtered U ^-1

Where U is a matrix composed of the feature vector, U ^-1 is an inverse matrix of the matrix composed of the feature vector, and Δ _filtered is a diagonal matrix of eigenvalues after denoising processing.

The denoised sample covariance matrix is substituted into the Markowitz mean variance model, the investment proportion of each constituent stock is solved, and the constituent stocks are combined according to the calculated investment proportion to generate an investment portfolio. The sample covariance matrix after denoising is used to calculate in the Markowitz mean variance model, so that the calculated portfolio is optimized and the risk of the portfolio is reduced.

The investment portfolio generation method proposed in this embodiment determines the target market index, and generates a sample matrix based on the transaction data of the constituent stocks of the target market index over multiple consecutive historical trading days; and calculates the first component constituents of the target market index based on the sample matrix. A sample covariance matrix; calculate the eigenvalues of the first sample covariance matrix and the eigenvectors corresponding to the eigenvalues; calculate the theoretical maximum eigenvalue of the first sample covariance matrix based on MP's law, according to the eigenvalues and the theoretical maximum The eigenvalues denoise the diagonal matrix of the eigenvalues of the first sample covariance matrix; calculate the second sample covariance matrix according to the eigenvalue diagonal matrix and the matrix composed of the eigenvectors after denoising; The two-sample covariance matrix and the Markowitz mean variance model calculate the investment proportion of each constituent stock, and generate an investment portfolio based on the investment proportion. This solution is based on MP's law to denoise the sample covariance matrix of the market index and filter out the random data, so that the data in the recalculated second sample covariance matrix is a relatively reliable correlation coefficient, which makes investment The portfolio is optimized to reduce investment risks.

The present application also provides an investment portfolio generation device. Referring to FIG. 2, a schematic diagram of an internal structure of an investment portfolio generation device according to an embodiment of the present application is shown.

In this embodiment, the investment portfolio generation device 1 may be a PC (Personal Computer) or a terminal device such as a smart phone, a tablet computer, or a portable computer. The portfolio generating device 1 includes at least a memory 11, a processor 12, a network interface 13, and a communication bus.

The memory 11 includes at least one type of readable storage medium. The readable storage medium includes a flash memory, a hard disk, a multimedia card, a card-type memory (for example, SD or DX memory, etc.), a magnetic memory, a magnetic disk, an optical disk, and the like. The memory 11 may be an internal storage unit of the portfolio generation device 1 in some embodiments, such as a hard disk of the portfolio generation device 1. The memory 11 may also be an external storage device of the portfolio generation device 1 in other embodiments, for example, a plug-in hard disk, a Smart Media Card (SMC), and a secure digital (Secure) Digital, SD) card, Flash card, etc. Further, the memory 11 may further include both an internal storage unit of the portfolio generation device 1 and an external storage device. The memory 11 can be used not only to store application software installed in the portfolio generation device 1 and various types of data, such as the code of the portfolio generation program 01, but also to temporarily store data that has been or will be output.

The processor 12 may be a central processing unit (CPU), a controller, a microcontroller, a microprocessor, or other data processing chip in some embodiments, and is configured to run program codes or processes stored in the memory 11 Data, such as execution of portfolio creation program 01.

The network interface 13 may optionally include a standard wired interface, a wireless interface (such as a WI-FI interface), and is generally used to establish a communication connection between the device 1 and other electronic devices.

The communication bus is used to implement connection communication between these components.

Optionally, the device 1 may further include a user interface. 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. Optionally, in some embodiments, the display may be an LED display, a liquid crystal display, a touch-type liquid crystal display, an OLED (Organic Light-Emitting Diode, organic light emitting diode) touch device, or the like. The display may also be appropriately referred to as a display screen or a display unit for displaying information processed in the portfolio generating device 1 and a user interface for displaying visualization.

FIG. 2 only shows a portfolio generation device 1 having components 11-13 and a portfolio generation program 01. Those skilled in the art can understand that the structure shown in FIG. 1 does not constitute a limitation on the portfolio generation device 1 , Can include fewer or more components than shown, or combine certain components, or different component arrangements.

In the embodiment of the apparatus 1 shown in FIG. 2, the investment portfolio generation program 01 is stored in the memory 11; when the processor 12 executes the investment portfolio generation program 01 stored in the memory 11, the following steps are implemented:

The target market index is determined, and a sample matrix is generated based on the transaction data of the constituent stocks of the target market index over consecutive consecutive historical trading days.

A first sample covariance matrix of the constituent stocks of the target market index is calculated according to the sample matrix.

Calculate a eigenvalue and a eigenvector corresponding to the eigenvalue of the first sample covariance matrix.

The theoretical maximum eigenvalue of the first sample covariance matrix is calculated based on the M-P law, and the eigenvalues of the first sample covariance matrix are denoised to the angular matrix according to the theoretical maximum eigenvalue.

Calculate a second sample covariance matrix according to the eigenvalue diagonal matrix and the matrix composed of the eigenvectors after the denoising process.

Calculate the investment ratio of each constituent stock according to the second sample covariance matrix and the Markowitz mean variance model, and generate an investment portfolio according to the investment ratio.

The target market index in this application may be a market index such as the Shanghai Composite Index, Shanghai and Shenzhen 300. In the following embodiments, the method of this application will be described using the Shanghai and Shenzhen 300 as an example. Obtain the closing price data of the 300 constituent stocks in the CSI 300 from the database for each trading day in the past ten years. The step of determining a target market index, and generating a sample matrix based on the transaction data of the constituent stocks of the target market index over multiple consecutive historical trading days specifically includes the following detailed steps: determining the target market index, and obtaining the target The transaction data of the constituent stocks of the market index within a plurality of consecutive historical trading days; the acquired transaction data is standardized; and the sample matrix is constructed according to the standardized processed transaction data.

In addition, because the closing price data is used as financial time series data, it has the characteristics of peaks and fat tails. In order to eliminate this feature, the log closing data of the stock is first processed:

among them,

Is the logarithmic yield of stock i at the end of period t,

Is the closing price of stock i at the end of period t. Assuming that there have been data of closing prices for T trading days in the past ten years, the logarithmic return at the end of period t is the closing price data for the tth trading day in T consecutive trading days.

In addition, in order to eliminate the influence of the dimension, the logarithmic rate of return is standardized. For the component stock i, the standardized treatment method is as follows:

among them,

T is the total number of trading days,

δ _i is the standard deviation of the logarithmic yield of stock i.

The number of component bonds in the target market index is N. For Shanghai and Shenzhen 300, N = 300, and the number of trading days is T. All the logarithmic return data after normalization process form a N × T matrix. The logarithmic yield of a constituent stock can be regarded as a random variable, and the logarithmic yield of all constituent stocks in T trading days constitutes a sample logarithmic yield matrix. The logarithmic return sequence matrix of all constituent stocks after normalization is as follows:

Get the first sample covariance matrix according to the following formula:

Since the covariance between the random variables is calculated, the first sample covariance matrix obtained is an N × N matrix.

Calculating a theoretical maximum eigenvalue of the first sample covariance matrix based on the MP law, and performing a step of denoising the angular matrix on the eigenvalues of the first sample covariance matrix according to the theoretical maximum eigenvalue may include: The detailed steps are as follows: the theoretical maximum eigenvalue of the first sample covariance matrix is calculated based on MP law; the eigenvalues are arranged in order from small to large to generate a diagonal matrix of eigenvalues; from the first sample The eigenvalues of the covariance matrix that are greater than the theoretical maximum eigenvalue and whose previous eigenvalue is less than the theoretical maximum eigenvalue are found as the intercept point eigenvalues; delete the eigenvalues that are less than A feature value of the intercept point feature value to perform a denoising process on the feature matrix to the angular matrix.

Specifically, the eigenvalues λ _{(i) of the} first sample covariance matrix are solved, and the eigenvalues are sorted in ascending order of the eigenvalues λ ₍₁₎ <λ ₍₂₎ <... λ _(N) . These characteristics The values form the eigenvalue diagonal matrix Λ:

Calculate the eigenvector corresponding to the eigenvalue.

u _(i) is a feature vector corresponding to λ _(i) , the feature vector is a column vector, and all the feature vectors form a matrix U = (u ₍₁₎ , u ₍₂₎ , ..., u _(N) ).

Remember

According to the MP's law (Marchenko-Pastur's law), if the elements in the matrix are independent and identically distributed, the theoretical maximum eigenvalue of the matrix can be calculated according to Q. The specific calculation formula is as follows:

After calculating the theoretical maximum eigenvalue of the first sample covariance matrix according to MP's law, the intercept point eigenvalues are found. Specifically, the eigenvalues λ ₍₁₎ , λ ₍₂₎ , ... are arranged in ascending order. In λ _(N) , the k-th largest eigenvalue λ _{(k) is found} so that it meets the following conditions:

λ _(k) > λ _max ≥λ _(k-1)

λ _(k-1) is the eigenvalue ranked one ahead of λ _(k) . Let λ _(k) be the eigenvalue of the intercept point, and replace all eigenvalues whose eigenvalues in the eigenvalue diagonal matrix are smaller than the eigenvalue of the intercept point with 0.

Because the premise of MP law assumes that the elements in the matrix are independent and identically distributed, that is, assuming that the elements in the first sample covariance matrix are independent and identically distributed, the theoretical maximum eigenvalues are consistent with

If the eigenvalues calculated based on actual data are greater than the theoretical maximum eigenvalues, it means that some elements in the matrix are not independent and identically distributed, but have a certain correlation. The eigenvalues that conform to MP's law are deleted, and the second covariance matrix recalculated from the diagonal matrix based on the new eigenvalues excludes random data. The remaining data is relatively reliable related data.

What needs to be explained here is that the theoretical minimum eigenvalue of the first sample covariance matrix can also be calculated according to MP's law, and for eigenvalues smaller than the theoretical characteristic minimum, the absolute value is generally close to 0 and can be ignored Neglect, and the smaller the eigenvalue, the lower its importance, which can be ignored. Therefore, in the solution of this embodiment, all the eigenvalues smaller than the theoretical maximum eigenvalue are deleted from the diagonal matrix of eigenvalues. The eigenvalues also include those that do not conform to MP's law and are smaller than the theoretical minimum eigenvalue.

Or, in other embodiments, a theoretical maximum eigenvalue of the first sample covariance matrix is calculated based on MP law, and a diagonal matrix of eigenvalues of the first sample covariance matrix is calculated based on the theoretical maximum eigenvalue. The step of performing the denoising processing may include the following thinning steps: calculating a theoretical maximum eigenvalue of the first sample covariance matrix based on MP law; arranging the eigenvalues in order from small to large to generate eigenvalue pairs An angular matrix; deleting the eigenvalues of the eigenvalue diagonal matrix that are smaller than the theoretical maximum eigenvalue to perform a denoising process on the eigenvalues of the angular matrix.

The diagonal matrix of eigenvalues after denoising is as follows:

According to the eigenvalue diagonal matrix Λ _filtered after the noise reduction process, the covariance matrix is recalculated according to the eigenvalue decomposition formula to obtain the second sample covariance matrix, which has eliminated the influence of the white noise data:

Σ _filtered = UΛ _filtered U ^-1

Where U is a matrix composed of the feature vector, U ^-1 is an inverse matrix of the matrix composed of the feature vector, and Δ _filtered is a diagonal matrix of eigenvalues after denoising processing.

The denoised sample covariance matrix is substituted into the Markowitz mean variance model, the investment proportion of each constituent stock is solved, and the constituent stocks are combined according to the calculated investment proportion to generate an investment portfolio. The sample covariance matrix after denoising is used to calculate in the Markowitz mean variance model, so that the calculated portfolio is optimized and the risk of the portfolio is reduced.

The investment portfolio generation device proposed in this embodiment determines a target market index, and generates a sample matrix based on the transaction data of the component stocks of the target market index over multiple consecutive historical trading days; and calculates the first component constituents of the target market index based on the sample matrix. A sample covariance matrix; calculate the eigenvalues of the first sample covariance matrix and the eigenvectors corresponding to the eigenvalues; calculate the theoretical maximum eigenvalue of the first sample covariance matrix based on MP's law, according to the eigenvalues and the theoretical maximum The eigenvalues denoise the diagonal matrix of the eigenvalues of the first sample covariance matrix; calculate the second sample covariance matrix according to the eigenvalue diagonal matrix and the matrix composed of the eigenvectors after denoising; The two-sample covariance matrix and the Markowitz mean variance model calculate the investment proportion of each constituent stock, and generate an investment portfolio based on the investment proportion. This solution is based on MP's law to denoise the sample covariance matrix of the market index and filter out the random data, so that the data in the recalculated second sample covariance matrix is a relatively reliable correlation coefficient, which makes investment The portfolio is optimized to reduce investment risks.

Optionally, in other embodiments, the investment portfolio generation program may also be divided into one or more modules, and the one or more modules are stored in the memory 11 and implemented by one or more processors (this embodiment It is executed by the processor 12) to complete the present application. The module referred to in the present application refers to a series of computer program instruction segments capable of performing specific functions, and is used to describe the execution process of the investment portfolio generation program in the investment portfolio generation device.

For example, referring to FIG. 3, a schematic diagram of a program module of a portfolio generation program in an embodiment of the portfolio generation device of the present application. In this embodiment, the portfolio generation program can be divided into a sample generation module 10 and a covariance calculation. The module 20, the feature calculation module 30, the matrix denoising module 40, and the combination generation module 50, for example:

The sample generation module 10 is configured to determine a target market index, and generate a sample matrix according to the transaction data of the constituent stocks of the target market index over multiple consecutive historical trading days;

The covariance calculation module 20 is configured to calculate a first sample covariance matrix of the constituent stocks of the target market index according to the sample matrix;

The feature calculation module 30 is configured to calculate a feature value of the first sample covariance matrix and a feature vector corresponding to the feature value;

The matrix denoising module 40 is configured to calculate a theoretical maximum eigenvalue of the first sample covariance matrix based on the MP law, and diagonally compare the eigenvalues of the first sample covariance matrix based on the theoretical maximum eigenvalue. Denoising

The covariance calculation module 20 is further configured to calculate a second sample covariance matrix according to the eigenvalue diagonal matrix and the matrix formed by the feature vector after the denoising process;

The combination generation module 50 is configured to calculate an investment ratio of each component stock according to the second sample covariance matrix and the Markowitz mean variance model, and generate an investment portfolio according to the investment ratio.

The functions or operation steps implemented when the program modules such as the sample generation module 10, the covariance calculation module 20, the feature calculation module 30, the matrix denoising module 40, and the combination generation module 50 are executed are substantially the same as those in the above embodiments, and are not described here. More details.

In addition, an embodiment of the present application further provides a computer-readable storage medium, where the computer-readable storage medium stores a portfolio generation program, and the portfolio generation program can be executed by one or more processors to achieve the following: operating:

Determining a target market index, and generating a sample matrix based on the transaction data of the constituent stocks of the target market index over successive historical trading days;

Calculating a first sample covariance matrix of the constituent stocks of the target market index according to the sample matrix;

Calculating a eigenvalue of the first sample covariance matrix and a eigenvector corresponding to the eigenvalue;

Calculating a theoretical maximum eigenvalue of the first sample covariance matrix based on the M-P law, and performing denoising processing on the eigenvalues of the first sample covariance matrix on the angular matrix according to the theoretical maximum eigenvalue;

Calculate a second sample covariance matrix according to the eigenvalue diagonal matrix and the matrix formed by the eigenvectors after the denoising process;

Calculate the investment ratio of each constituent stock according to the second sample covariance matrix and the Markowitz mean variance model, and generate an investment portfolio according to the investment ratio. The specific implementation manner of the computer-readable storage medium of the present application is basically the same as each embodiment of the above-mentioned portfolio generation device and method, and is not repeated here.

It should be noted that, the serial numbers of the embodiments of the present application are only for description, and do not represent the advantages and disadvantages of the embodiments. And the terms "including," "including," or any other variation thereof, are intended to cover non-exclusive inclusion, such that a process, device, article, or method that includes a series of elements includes not only those elements, but also The other elements listed, or those that are inherent to such a process, device, article, or method. Without more restrictions, an element limited by the sentence "including a ..." does not exclude that there are other identical elements in the process, device, article, or method that includes the element.

Through the description of the above embodiments, those skilled in the art can clearly understand that the methods in the above embodiments can be implemented by means of software plus a necessary universal hardware platform, and of course, also by hardware, but in many cases the former is better. Implementation. Based on such an understanding, the technical solution of the present application, in essence, or a part that contributes to the existing technology, can be embodied in the form of a software product, which is stored in a storage medium (such as ROM / RAM) as described above. , Magnetic disk, optical disc), including a number of instructions to enable a terminal device (which may be a mobile phone, a computer, a server, or a network device, etc.) to execute the methods described in the embodiments of the present application.

The above are only preferred embodiments of the present application, and thus do not limit the patent scope of the present application. Any equivalent structure or equivalent process transformation made using the contents of the description and drawings of the application, or directly or indirectly used in other related technical fields Are included in the scope of patent protection of this application.

Claims (20)

1. A method for generating a portfolio, characterized in that the method includes:

   Determining a target market index, and generating a sample matrix based on the transaction data of the constituent stocks of the target market index over successive historical trading days;

   Calculating a first sample covariance matrix of the constituent stocks of the target market index according to the sample matrix;

   Calculating a eigenvalue of the first sample covariance matrix and a eigenvector corresponding to the eigenvalue;

   Calculating a theoretical maximum eigenvalue of the first sample covariance matrix based on the M-P law, and performing denoising processing on the eigenvalues of the first sample covariance matrix on the angular matrix according to the theoretical maximum eigenvalue;

   Calculate a second sample covariance matrix according to the eigenvalue diagonal matrix and the matrix formed by the eigenvectors after the denoising process;

   Calculate the investment ratio of each constituent stock according to the second sample covariance matrix and the Markowitz mean variance model, and generate an investment portfolio according to the investment ratio.
2. The method for generating a portfolio according to claim 1, wherein the theoretical maximum eigenvalue of the first sample covariance matrix is calculated based on MP law, and the first The steps of denoising the angular matrix by the eigenvalues of this covariance matrix include:

   Calculating a theoretical maximum eigenvalue of the first sample covariance matrix based on M-P law;

   Arrange the eigenvalues in ascending order to generate a diagonal matrix of eigenvalues;

   Finding a feature value that is greater than the theoretical maximum feature value and whose previous feature value is less than the theoretical maximum feature value from the feature values is used as the intercept point feature value;

   Deleting the eigenvalues smaller than the intercept point eigenvalues in the eigenvalue diagonal matrix to perform denoising processing on the eigenvalues on the angular matrix.
3. The method for generating a portfolio according to claim 1, wherein the step of calculating a second sample covariance matrix according to a diagonal matrix of eigenvalues after denoising processing and a matrix composed of the eigenvectors comprises:

   Calculate the second sample covariance matrix Σ _filtered according to the following formula:

   Σ _filtered = UΛ _filtered U ^-1

   Where U is a matrix composed of the feature vector, U ^-1 is an inverse matrix of the matrix composed of the feature vector, and Δ _filtered is a diagonal matrix of eigenvalues after denoising processing.
4. The method for generating an investment portfolio according to claim 1, wherein the step of determining a target market index and generating a sample matrix based on transaction data of constituent stocks of the target market index over a plurality of consecutive historical trading days includes: :

   Determining a target market index, and acquiring transaction data of the constituent stocks of the target market index within multiple consecutive historical trading days;

   Standardize the acquired transaction data;

   The sample matrix is constructed according to the standardized processed transaction data.
5. The method for generating a portfolio according to claim 2, wherein the step of determining a target market index and generating a sample matrix based on transaction data of constituent stocks of the target market index over a plurality of consecutive historical trading days includes: :

   Determining a target market index, and acquiring transaction data of the constituent stocks of the target market index within multiple consecutive historical trading days;

   Standardize the acquired transaction data;

   The sample matrix is constructed according to the standardized processed transaction data.
6. The method for generating a portfolio according to claim 3, wherein the step of determining a target market index and generating a sample matrix based on the transaction data of the constituent stocks of the target market index over a plurality of consecutive historical trading days includes: :

   Determining a target market index, and acquiring transaction data of the constituent stocks of the target market index within multiple consecutive historical trading days;

   Standardize the acquired transaction data;

   The sample matrix is constructed according to the standardized processed transaction data.
7. The method for generating a portfolio according to claim 4, wherein the transaction data is closing price data, and before the step of standardizing the acquired transaction data, the method further comprises the steps of:

   Converting the closing price data into logarithmic yield data;

   The step of constructing the sample matrix based on the standardized processed transaction data includes:

   The sample matrix is constructed according to the logarithmic rate of return data after the normalization process.
8. A device for generating a portfolio, characterized in that the device includes a memory and a processor, and the memory stores a portfolio generating program that can be run on the processor, and the portfolio generating program is processed by the processor Implement the following steps when the processor executes:

   Determining a target market index, and generating a sample matrix based on the transaction data of the constituent stocks of the target market index over consecutive consecutive historical trading days;

   Calculating a first sample covariance matrix of the constituent stocks of the target market index according to the sample matrix;

   Calculating a eigenvalue of the first sample covariance matrix and a eigenvector corresponding to the eigenvalue;

   Calculating a theoretical maximum eigenvalue of the first sample covariance matrix based on the M-P law, and performing denoising processing on the eigenvalues of the first sample covariance matrix on the angular matrix according to the theoretical maximum eigenvalue;

   Calculate a second sample covariance matrix according to the eigenvalue diagonal matrix and the matrix formed by the eigenvectors after the denoising process;

   Calculate the investment ratio of each constituent stock according to the second sample covariance matrix and the Markowitz mean variance model, and generate an investment portfolio according to the investment ratio.
9. The investment portfolio generating device according to claim 8, wherein the theoretical maximum eigenvalue of the first sample covariance matrix is calculated based on MP law, and the first The steps of denoising the angular matrix by the eigenvalues of this covariance matrix include:

   Calculating a theoretical maximum eigenvalue of the first sample covariance matrix based on M-P law;

   Arrange the eigenvalues in ascending order to generate a diagonal matrix of eigenvalues;

   Finding a feature value that is greater than the theoretical maximum feature value and whose previous feature value is less than the theoretical maximum feature value from the feature values is used as the intercept point feature value;

   Deleting the eigenvalues smaller than the intercept point eigenvalues in the eigenvalue diagonal matrix to perform denoising processing on the eigenvalues on the angular matrix.
10. The device for generating a portfolio according to claim 8, wherein the step of calculating a second sample covariance matrix according to a diagonal matrix of eigenvalues after denoising processing and a matrix composed of the eigenvectors comprises:

    Calculate the second sample covariance matrix Σ _filtered according to the following formula:

    Σ _filtered = UΛ _filtered U ^-1

    Where U is a matrix composed of the feature vector, U ^-1 is an inverse matrix of the matrix composed of the feature vector, and Δ _filtered is a diagonal matrix of eigenvalues after denoising processing.
11. The device for generating a portfolio according to claim 8, wherein the step of determining a target market index and generating a sample matrix based on transaction data of constituent stocks of the target market index over a plurality of consecutive historical trading days comprises: :

    Determining a target market index, and acquiring transaction data of the constituent stocks of the target market index within multiple consecutive historical trading days;

    Standardize the acquired transaction data;

    The sample matrix is constructed according to the standardized processed transaction data.
12. The investment portfolio generation device according to claim 9, wherein the step of determining a target market index and generating a sample matrix based on transaction data of constituent stocks of the target market index over a plurality of consecutive historical trading days includes :

    Determining a target market index, and acquiring transaction data of the constituent stocks of the target market index within multiple consecutive historical trading days;

    Standardize the acquired transaction data;

    The sample matrix is constructed according to the standardized processed transaction data.
13. The device for generating a portfolio according to claim 10, wherein the step of determining a target market index and generating a sample matrix based on the transaction data of the constituent stocks of the target market index over a plurality of consecutive historical trading days comprises: :

    Determining a target market index, and acquiring transaction data of the constituent stocks of the target market index within multiple consecutive historical trading days;

    Standardize the acquired transaction data;

    The sample matrix is constructed according to the standardized processed transaction data.
14. The investment portfolio generation device according to claim 11, wherein the investment portfolio generation program is further executable by the processor, so that the transaction data is closing price data, and the acquired transaction data is standardized. Before the processing steps, the following steps are also implemented:

    Converting the closing price data into logarithmic yield data;

    The step of constructing the sample matrix based on the standardized processed transaction data includes:

    The sample matrix is constructed according to the logarithmic rate of return data after the normalization process.
15. A computer-readable storage medium is characterized in that the computer-readable storage medium stores a portfolio generation program, and the portfolio generation program can be executed by one or more processors to implement the following steps:

    Determining a target market index, and generating a sample matrix based on the transaction data of the constituent stocks of the target market index over successive historical trading days;

    Calculating a first sample covariance matrix of the constituent stocks of the target market index according to the sample matrix;

    Calculating a eigenvalue of the first sample covariance matrix and a eigenvector corresponding to the eigenvalue;

    Calculating a theoretical maximum eigenvalue of the first sample covariance matrix based on the M-P law, and performing denoising processing on the eigenvalues of the first sample covariance matrix on the angular matrix according to the theoretical maximum eigenvalue;

    Calculate a second sample covariance matrix according to the eigenvalue diagonal matrix and the matrix formed by the eigenvectors after the denoising process;

    Calculate the investment ratio of each constituent stock according to the second sample covariance matrix and the Markowitz mean variance model, and generate an investment portfolio according to the investment ratio.
16. The computer-readable storage medium of claim 15, wherein the theoretical maximum eigenvalue of the first sample covariance matrix is calculated based on MP law, and the first maximum eigenvalue of the first sample covariance matrix is calculated based on the theoretical maximum eigenvalue. The steps of denoising the angular matrix by the eigenvalues of the sample covariance matrix include:

    Calculating a theoretical maximum eigenvalue of the first sample covariance matrix based on M-P law;

    Arrange the eigenvalues in ascending order to generate a diagonal matrix of eigenvalues;

    Finding a feature value that is greater than the theoretical maximum feature value and whose previous feature value is less than the theoretical maximum feature value from the feature values is used as the intercept point feature value;

    Deleting the eigenvalues smaller than the intercept point eigenvalues in the eigenvalue diagonal matrix to perform denoising processing on the eigenvalues on the angular matrix.
17. The computer-readable storage medium of claim 15, wherein the step of calculating a second sample covariance matrix according to a diagonal matrix of eigenvalues after denoising processing and a matrix composed of the eigenvectors comprises :

    Calculate the second sample covariance matrix Σ _filtered according to the following formula:

    Σ _filtered = UΛ _filtered U ^-1

    Where U is a matrix composed of the feature vector, U ^-1 is an inverse matrix of the matrix composed of the feature vector, and Δ _filtered is a diagonal matrix of eigenvalues after denoising processing.
18. The computer-readable storage medium of claim 15, wherein the step of determining a target market index, and generating a sample matrix based on transaction data of constituent stocks of the target market index over multiple consecutive historical trading days include:

    Determining a target market index, and acquiring transaction data of the constituent stocks of the target market index within multiple consecutive historical trading days;

    Standardize the acquired transaction data;

    The sample matrix is constructed according to the standardized processed transaction data.
19. The computer-readable storage medium of claim 16, wherein the step of determining a target market index, and generating a sample matrix based on transaction data of constituent stocks of the target market index over a plurality of consecutive historical trading days include:

    Determining a target market index, and acquiring transaction data of the constituent stocks of the target market index within multiple consecutive historical trading days;

    Standardize the acquired transaction data;

    The sample matrix is constructed according to the standardized processed transaction data.
20. The computer-readable storage medium of claim 15, wherein the investment portfolio generation program is further executable by the processor to perform the transaction data as closing price data, and perform the pairing of the acquired transaction data. Before the steps of the standardization process, the following steps are also implemented:

    Converting the closing price data into logarithmic yield data;

    The step of constructing the sample matrix based on the standardized processed transaction data includes:

    The sample matrix is constructed according to the logarithmic rate of return data after the normalization process.

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