Asset investment portfolio method and device, computer equipment and storage medium
By optimizing the parameterized inverse covariance matrix using the Spiked model and expected utility maximization theory, the problem of inaccurate covariance matrix estimation in high-dimensional environments is solved, resulting in more accurate and stable portfolio allocation and improving the robustness and reliability of the portfolio.
Patent Information
- Application Number
- CN202511789825.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-01
- Publication Date
- 2026-03-31
AI Technical Summary
In high-dimensional environments, the estimation of the covariance matrix in existing technologies is inaccurate, leading to a severe degradation in portfolio selection performance. There is an urgent need for a more stable and reliable portfolio allocation strategy.
A parameterized inverse covariance matrix estimator is constructed using the Spiked model. Combining expected utility maximization theory and numerical optimization algorithms, the modifiable parameters are optimized to generate the portfolio weight vector. Through iterative optimization using gradient descent, the optimal portfolio weights are finally calculated.
It significantly improves the accuracy and robustness of high-dimensional covariance structure estimation, suppresses noise interference, captures key risk factors, and forms a portfolio allocation strategy that performs more stably and reliably under different market conditions.
Smart Images
Figure CN121767102A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of financial transaction analysis technology, specifically relating to an asset portfolio method, apparatus, computer equipment, and storage medium. Background Technology
[0002] The optimal portfolio selection problem has always been at the core of portfolio theory research. It studies the optimal allocation of assets in uncertain environments to achieve an equilibrium between maximizing investor returns and minimizing risk under different objective functions. The Expected Utility Portfolio (EUP) can simultaneously achieve the investment objectives of maximizing expected returns and minimizing risk, and plays a crucial role in the optimal portfolio selection problem.
[0003] In existing technologies, historical data is directly selected to generate sample variance for estimation. When the ratio of the number of training samples to the number of features is large enough, it does not affect the estimation effect. However, in high-dimensional environments, the estimation of the covariance matrix is highly inaccurate, which leads to a serious degradation of portfolio selection performance. Therefore, there is an urgent need for a strategy that can provide more stable and reliable portfolio allocation. Summary of the Invention
[0004] To address the aforementioned problems, the present invention provides an asset portfolio method, apparatus, computer device, and storage medium.
[0005] To achieve the above objectives, the present invention provides the following technical solution: An asset portfolio approach, the approach comprising: Obtain historical price data for multiple assets as samples and calculate the multi-period returns for each asset; The sample covariance matrix is calculated based on the multi-period returns, and a parameterized inverse covariance matrix estimator is constructed based on the Spiked model and the sample covariance matrix, wherein the spectrum of the inverse covariance matrix is set as a set of modifiable parameters. Based on the expected utility maximization theory, a parameterized portfolio weight vector is determined using the parameterized inverse covariance matrix estimator. Based on the parameterized portfolio weight vector, a portfolio expected utility objective function is constructed with the correctable parameter as a variable; Based on the objective function of maximizing the expected utility of the portfolio, the correctable parameter is optimized using a numerical optimization algorithm to obtain the optimal value of the correctable parameter; Based on the optimal correctable parameters, the final portfolio weights are calculated using the parameterized inverse covariance matrix estimator as the asset allocation scheme.
[0006] Optionally, the Spiked model simulates the covariance structure of high-dimensional financial data of multiple assets by decomposing the sample covariance matrix into two parts, wherein the first part is a multiple of the identity matrix representing global background noise, and the second part is a low-rank matrix driven by multiple significant principal components and their corresponding eigenvalues.
[0007] Optionally, constructing a parameterized inverse covariance matrix estimator based on the sample covariance matrix includes: Obtain the eigenvalues of the significant principal components and their corresponding eigenvectors in the sample covariance matrix; assign an independent, modifiable parameter to each significant eigenvector to adjust its contribution in the inverse matrix; Assign a shared scaling parameter to the remaining insignificant components, which applies to the identity matrix; The independent, modifiable parameters and scaling parameters are used to suppress noise in sample estimation and enhance the true sample covariance matrix signal.
[0008] Optionally, determining a parameterized portfolio weight vector using the parameterized inverse covariance matrix estimator includes: Multiplying the parameterized inverse covariance matrix estimator by the asset's expected return vector yields a weight direction; The weight directions are normalized to generate a parameterized portfolio weight vector.
[0009] Optionally, the objective function for the expected utility of the portfolio is constructed as a trade-off function between the expected return of the portfolio and its variance; the function value of the trade-off function is the expected return minus a variance term weighted by a risk aversion coefficient, thereby quantifying the portfolio's return and risk into an optimizable scalar value.
[0010] Optionally, before optimizing the correctable parameters using a numerical optimization algorithm, the terms involving the population matrix in the objective function of the portfolio's expected utility are replaced with an asymptotic approximation expression that depends on the sample statistics and the correctable parameters, based on the theory of large-dimensional random matrices; the optimization of the correctable parameters using a numerical optimization algorithm includes: Initialize the initial values of the correctable parameters and the algorithm hyperparameters; The gradient descent method is used for iteration. In each iteration, the gradient of the objective function of the portfolio's expected utility with respect to each modifiable parameter is calculated. Based on the gradient and the step size, the values of all parameters are updated. Repeat the above process until the norm of the parameter update is less than the preset tolerance, and output the optimal parameter combination.
[0011] An asset portfolio device, the device comprising: The acquisition module is used to acquire historical price data of multiple assets as samples and calculate the multi-period returns of each asset. A construction module is used to calculate the sample covariance matrix based on the multi-period returns, and to construct a parameterized inverse covariance matrix estimator based on the Spiked model and the sample covariance matrix, wherein the spectrum of the inverse covariance matrix is set as a set of adjustable parameters; based on the expected utility maximization theory, a parameterized portfolio weight vector is determined using the parameterized inverse covariance matrix estimator; and based on the parameterized portfolio weight vector, a portfolio expected utility objective function with the adjustable parameters as variables is constructed. An optimization module is used to optimize the correctable parameters based on the objective function of maximizing the expected utility of the portfolio, using a numerical optimization algorithm, thereby obtaining the optimal value of the correctable parameters; The configuration module is used to calculate the final portfolio weights as an asset allocation scheme based on the optimal and modifiable parameters through the parameterized inverse covariance matrix estimator.
[0012] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned asset portfolio method.
[0013] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the aforementioned asset portfolio method.
[0014] The asset portfolio method provided by this invention has the following beneficial effects: This invention constructs a parameterized inverse covariance matrix estimator using the Spiked model structure and actual sample data, transforming the model's key spectral features into a set of optimizable parameters. Based on this, the parameterized estimator is integrated into an expected utility maximization framework, forming an objective function with spectral parameters as variables, and numerical optimization techniques are used to automatically search for the optimal parameter combination. This approach significantly improves the accuracy and robustness of estimating high-dimensional covariance structures, resulting in investment weights that better reflect the true risk-return relationships between assets. Compared to traditional direct estimation methods of sample covariance, this invention can more effectively suppress noise interference and capture key risk factors in scenarios with a large number of assets and high data dimensionality, thereby helping investors form more stable and reliable portfolio allocation strategies under different market conditions, achieving a quality improvement from data to decision. Attached Figure Description
[0015] To more clearly illustrate the embodiments and design schemes of the present invention, the accompanying drawings required for this embodiment will be briefly described below. The drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0016] Figure 1 This is a flowchart illustrating an asset portfolio method according to an exemplary embodiment of the present invention.
[0017] Figure 2 This is a block diagram of an asset portfolio device provided by the present invention according to an exemplary embodiment. Detailed Implementation
[0018] To enable those skilled in the art to better understand and implement the technical solutions of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and should not be construed as limiting the scope of protection of the present invention.
[0019] The technical solutions provided by the various embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
[0020] First, this invention provides an asset portfolio method, specifically as follows: Figure 1 As shown, it includes the following steps: S101. Obtain historical price data of multiple assets as samples and calculate the multi-period returns of each asset.
[0021] In this step, the multi-period yield of each asset can be calculated one by one based on the historical trading prices of multiple randomly selected assets.
[0022] S102. Calculate the sample covariance matrix based on the multi-period return, and construct a parameterized inverse covariance matrix estimator based on the Spiked model and the sample covariance matrix.
[0023] The spectrum of the inverse covariance matrix is set with a set of modifiable parameters.
[0024] In this step, it is assumed that the overall covariance matrix follows the Spiked model. The sample covariance matrix is decomposed into two parts by the Spiked model to simulate the covariance structure of high-dimensional financial data of multiple assets. The first part is a multiple of the identity matrix representing global background noise, and the second part is a low-rank matrix driven by multiple significant principal components and their corresponding eigenvalues.
[0025] Obtain the eigenvalues and corresponding eigenvectors of the significant principal components in the sample covariance matrix; assign an independent adjustable parameter to each significant eigenvector to adjust its contribution in the inverse matrix; assign a shared scaling parameter to the remaining insignificant components, which acts on the identity matrix; based on the independent adjustable parameter and the scaling parameter, suppress noise in the sample estimation and enhance the signal of the true sample covariance matrix.
[0026] S103. Based on the expected utility maximization theory, a parameterized portfolio weight vector is determined using the parameterized inverse covariance matrix estimator.
[0027] In this step, the parameterized inverse covariance matrix estimator is multiplied by the asset's expected return vector to obtain a weight direction; this weight direction is then normalized to generate a parameterized portfolio weight vector.
[0028] S104. Based on the parameterized portfolio weight vector, construct a portfolio expected utility objective function with the modifiable parameter as the variable.
[0029] The objective function for the expected utility of the portfolio is constructed as a trade-off function between the expected return and the variance of the portfolio. The value of this trade-off function is the expected return minus a variance term weighted by a risk aversion coefficient, thereby quantifying the portfolio's return and risk into an optimizable scalar value.
[0030] S105. Based on the objective function of maximizing the expected utility of the portfolio, the correctable parameter is optimized by a numerical optimization algorithm to obtain the optimal value of the correctable parameter.
[0031] Before optimizing the correctable parameter using a numerical optimization algorithm, the terms involving the population matrix in the objective function of the portfolio's expected utility are replaced with an asymptotic approximation expression that depends on the sample statistics and the correctable parameter, based on the theory of large-dimensional random matrices.
[0032] In this step, when optimizing the correctable parameter, the initial value of the correctable parameter and the algorithm hyperparameters are first initialized; then, the gradient descent method is used for iteration. In each iteration, the gradient of the expected utility objective function of the portfolio with respect to each correctable parameter is calculated; based on the gradient and step size, the values of all parameters are updated; finally, the above process is repeated until the norm of the parameter update is less than the preset tolerance, and the optimal parameter combination is output.
[0033] S106. Based on the optimal value of the correctable parameter, the final portfolio weights are calculated as the asset allocation scheme through the parameterized inverse covariance matrix estimator.
[0034] Using the above method, a parameterized inverse covariance matrix estimator is constructed through the Spiked model structure and actual sample data, transforming the key spectral features of the model into a set of optimizable parameters. Based on this, the parameterized estimator is integrated into the expected utility maximization framework, forming an objective function with spectral parameters as variables, and numerical optimization techniques are used to automatically search for the optimal parameter combination. This technical approach significantly improves the accuracy and robustness of estimating high-dimensional covariance structures, thus enabling the final calculated investment weights to better reflect the true risk-return relationship between assets. Compared with traditional direct estimation methods of sample covariance, this invention can more effectively suppress noise interference and capture key risk factors in scenarios with a large number of assets and high data dimensionality, thereby helping investors form more stable and reliable portfolio allocation strategies under different market conditions, achieving a quality improvement from data to decision.
[0035] Based on the above steps, this invention provides an embodiment of an asset portfolio method based on the Spiked model.
[0036] Step 1: Obtain closing price data for multiple stocks, and calculate the multi-period returns for each stock based on the closing price data.
[0037] This invention randomly selects data from 100 stocks for simulation, with a trading period of 3688 days.
[0038] Then, the period return for each stock is calculated using the following formula: ; in, Indicates the first Stock returns Indicate the first Only one stock in the first The closing price of the period, Indicates the first Only one stock in the first The closing price of the period.
[0039] Step 2: Select a certain amount of data as a sample, calculate the sample covariance, and give the inverse covariance matrix under the Spiked model under the assumption that the population covariance matrix follows the Spiked model.
[0040] First, we assume the overall covariance matrix to be in the following form: ; in ,and The covariance matrices are mutually orthogonal, and this form of covariance matrix is the Spiked model. In practical applications, we can estimate the parameters using various algorithms from relevant literature. Therefore, we can assume the parameters... as well as All of these are completely known.
[0041] Based on the information of the overall covariance, the inverse of the covariance matrix can be represented in the following form: ; in, , The sample covariance matrix is the first The eigenvectors corresponding to large eigenvalues For any parameter that needs optimization and All to satisfy It is positive.
[0042] Step 3: Set the spectrum of the inverse covariance matrix as an adjustable parameter and substitute it into the corresponding objective function.
[0043] The investment weights of multiple assets are calculated using the following formula: ; in, , Represents the weight vector. Describe the inverse matrix of the covariance. Represents a matrix. This represents a set where all elements are 1. 3D column vector, This represents the risk aversion coefficient.
[0044] Substituting the above weight expression into the target expression, it can be expressed as: ; in, , It is defined as A quadratic function.
[0045] Step 4: Use gradient descent to find the optimal parameters based on maximizing expected utility.
[0046] For parameters in the objective expression that cannot be directly derived, an approximate asymptotic expression can be obtained using the relevant properties of large-dimensional random matrices. Then, an optimization algorithm can be used to find the approximate optimal parameters. Based on the relevant properties of large-dimensional random matrices, we can obtain: ; in, ; ; ; ; ; ; ; and, .
[0047] The parameters are obtained using the gradient descent method. The specific steps are as follows: S1: Set initial parameter values and, the step size of parameter updates in each iteration. and tolerance .
[0048] S2: Calculate the objective function using partial derivatives. The gradient of each parameter.
[0049] S3: According to the formula Update the value of each parameter.
[0050] S4: Add constraints to ensure that each parameter after each update satisfies the constraints in this paper. .
[0051] S5: Determine if the convergence condition has been met by checking the norm of the gradient. Convergence occurs when the norm of the gradient is less than a given tolerance. When the convergence condition is met, the iteration stops and the optimal values of the parameters are output. .
[0052] Step 5: After substituting the optimal parameters, recalculate the investment weights of different assets. Based on the current portfolio, calculate the expected utility of the portfolio in the later period for each asset. This can be represented by the following steps: S1: Divide the total data into training datasets. With the test dataset .
[0053] S2: According to the dataset Obtain the optimal parameters And substitute into the weight formula Obtain the weights corresponding to different stocks .
[0054] S3: Weighting of 100 stocks Input into the dataset The rate of return of the test data is obtained and the expected utility of the stock is calculated.
[0055] This invention provides a novel approach to portfolio covariance estimation by setting up a parameterized inverse covariance matrix estimator. It combines a large-dimensional random matrix with the gradient descent algorithm and introduces easily understandable optimization steps, which simplifies the calculation process to a certain extent. This enhances the scalability of the method and provides new methodological support for high-dimensional financial data analysis. It significantly improves the accuracy and precision of portfolio covariance matrix estimation, thereby providing investors with better investment solutions.
[0056] Secondly, the present invention also provides an asset portfolio device, such as Figure 2 As shown, it includes: 201. Acquisition module, used to acquire historical price data of multiple assets as samples and calculate the multi-period returns of each asset.
[0057] 202. A construction module is used to calculate the sample covariance matrix based on the multi-period returns, and to construct a parameterized inverse covariance matrix estimator based on the Spiked model and the sample covariance matrix, wherein the spectrum of the inverse covariance matrix is set as a set of adjustable parameters; based on the expected utility maximization theory, a parameterized portfolio weight vector is determined using the parameterized inverse covariance matrix estimator; based on the parameterized portfolio weight vector, a portfolio expected utility objective function with the adjustable parameters as variables is constructed.
[0058] 203. Optimization module, used to optimize the correctable parameter based on the objective function of maximizing the expected utility of the portfolio, through a numerical optimization algorithm, thereby obtaining the optimal value of the correctable parameter.
[0059] 204. Configuration module, used to calculate the final portfolio weights as an asset allocation scheme based on the optimal value of the correctable parameters and the parameterized inverse covariance matrix estimator.
[0060] The present invention also provides a computer-readable storage medium storing a computer program that can be used to execute the above-described... Figure 1 The steps of the provided asset portfolio method.
[0061] This invention also provides a computer device. At the hardware level, the computer device includes a processor, an internal bus, a network interface, memory, and non-volatile memory, and may also include other hardware required for various operations. The processor reads the corresponding computer program from the non-volatile memory into memory and then executes it to achieve the above-mentioned functions. Figure 1 The steps of the provided asset portfolio method.
[0062] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.
[0063] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.
[0064] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.
[0065] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.
[0066] It should be noted that the specific embodiments described above enable those skilled in the art to more fully understand the present invention, but do not limit the present invention in any way. Therefore, although the present invention has been described in detail in this specification, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the present invention; and all technical solutions and improvements that do not depart from the spirit and scope of the present invention are covered within the protection scope of the patent of the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.
Claims
1. An asset portfolio management method, characterized in that, The method includes: Obtain historical price data for multiple assets as samples and calculate the multi-period returns for each asset; The sample covariance matrix is calculated based on the multi-period returns, and a parameterized inverse covariance matrix estimator is constructed based on the Spiked model and the sample covariance matrix, wherein the spectrum of the inverse covariance matrix is set as a set of modifiable parameters. Based on the expected utility maximization theory, a parameterized portfolio weight vector is determined using the parameterized inverse covariance matrix estimator. Based on the parameterized portfolio weight vector, a portfolio expected utility objective function is constructed with the correctable parameter as a variable; Based on the objective function of maximizing the expected utility of the portfolio, the correctable parameter is optimized using a numerical optimization algorithm to obtain the optimal value of the correctable parameter; Based on the optimal correctable parameters, the final portfolio weights are calculated using the parameterized inverse covariance matrix estimator as the asset allocation scheme.
2. The method according to claim 1, characterized in that, The Spiked model simulates the covariance structure of high-dimensional financial data for multiple assets by decomposing the sample covariance matrix into two parts. The first part is a multiple of the identity matrix representing global background noise, and the second part is a low-rank matrix driven by multiple significant principal components and their corresponding eigenvalues.
3. The method according to claim 2, characterized in that, Constructing a parameterized inverse covariance matrix estimator based on the sample covariance matrix includes: Obtain the eigenvalues of the significant principal components and their corresponding eigenvectors in the sample covariance matrix; assign an independent, modifiable parameter to each significant eigenvector to adjust its contribution in the inverse matrix; Assign a shared scaling parameter to the remaining insignificant components, which applies to the identity matrix; The independent, modifiable parameters and scaling parameters are used to suppress noise in sample estimation and enhance the true sample covariance matrix signal.
4. The method according to claim 1, characterized in that, Determining a parameterized portfolio weight vector using the parameterized inverse covariance matrix estimator includes: Multiplying the parameterized inverse covariance matrix estimator by the asset's expected return vector yields a weight direction; The weight directions are normalized to generate a parameterized portfolio weight vector.
5. The method according to claim 4, characterized in that, The objective function for the expected utility of the portfolio is constructed as a trade-off function between the expected return of the portfolio and its variance; the value of the trade-off function is the expected return minus a variance term weighted by a risk aversion coefficient, thereby quantifying the portfolio's return and risk into an optimizable scalar value.
6. The method according to claim 5, characterized in that, Before optimizing the correctable parameters using a numerical optimization algorithm, the terms involving the population matrix in the objective function of the portfolio's expected utility are replaced with an asymptotic approximation expression that depends on the sample statistics and the correctable parameters, based on the theory of large-dimensional random matrices. The optimization of the correctable parameters using a numerical optimization algorithm includes: Initialize the initial values of the correctable parameters and the algorithm hyperparameters; The gradient descent method is used for iteration. In each iteration, the gradient of the objective function of the portfolio's expected utility with respect to each modifiable parameter is calculated. Based on the gradient and the step size, the values of all parameters are updated. Repeat the above process until the norm of the parameter update is less than the preset tolerance, and output the optimal parameter combination.
7. An asset portfolio device, characterized in that, The device includes: The acquisition module is used to acquire historical price data of multiple assets as samples and calculate the multi-period returns of each asset. A construction module is used to calculate the sample covariance matrix based on the multi-period returns, and to construct a parameterized inverse covariance matrix estimator based on the Spiked model and the sample covariance matrix, wherein the spectrum of the inverse covariance matrix is set as a set of adjustable parameters; based on the expected utility maximization theory, a parameterized portfolio weight vector is determined using the parameterized inverse covariance matrix estimator; and based on the parameterized portfolio weight vector, a portfolio expected utility objective function with the adjustable parameters as variables is constructed. An optimization module is used to optimize the correctable parameters based on the objective function of maximizing the expected utility of the portfolio, using a numerical optimization algorithm, thereby obtaining the optimal value of the correctable parameters; The configuration module is used to calculate the final portfolio weights as an asset allocation scheme based on the optimal and modifiable parameters through the parameterized inverse covariance matrix estimator.
8. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, implements the method described in any one of claims 1 to 6.
9. A computer device, characterized in that, The method includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method described in any one of claims 1 to 6.