Investment portfolio investment risk assessment method and system

Abstract

The present invention relates to the technical field of financial transaction analysis, and disclosed are an investment portfolio investment risk assessment method and system. The method comprises: acquiring a plurality of pieces of asset data; computing logarithmic return rates for a plurality of asset prices; selecting a certain amount of data as samples, computing sample covariances, spectrally correcting each sample covariance matrix into a spiked model form, and adding a regularization parameter to the spectrally-corrected covariance matrix; substituting the spectrally-corrected and regularized covariance into a portfolio weight to obtain a portfolio weight estimation formula, and correspondingly substituting same into a portfolio risk expression to obtain a spectrally-corrected and regularized global minimum variance portfolio risk estimation formula, so as to compute a portfolio risk of each asset in a new period. By referencing the spiked model, the computational complexity of large-dimensional data can be effectively reduced in the method, and parameters that need to be designed are greatly reduced, so that the portfolio risk can be estimated more efficiently, and a more precise risk estimation value of the portfolio can be obtained.

Description

A method and system for assessing asset portfolio investment risk Technical Field

[0001] The present invention relates to the technical field of financial transaction analysis, and in particular to an asset portfolio investment risk assessment method and system. Background Art

[0002] As the operating rules of my country's securities market gradually improve, the question of how to rationally construct an investment portfolio with investors' funds has become a hot topic in applied finance. Markowitz's mean-variance portfolio theory focuses on determining the optimal portfolio weights—the proportion of wealth invested in financially risky assets. It is a key component of capital market theory in addressing financial investment decisions. According to this theory, investors can construct optimal portfolios by globally minimizing the portfolio variance (GMVP) for a given expected return or maximizing the portfolio return for a given portfolio risk. To implement these portfolios in practice, we must estimate the mean and covariance matrix of asset returns.

[0003] Traditionally, sample means and covariance matrices are used as estimates. However, due to estimation errors, the resulting portfolio weights can fluctuate significantly over time. Estimating the mean of asset returns is more difficult than estimating the covariance of asset returns, and estimation errors in the mean are often large. The "problematic" mean of asset returns means that global minimum variance (GMVP) models often perform better than mean-variance models, and thus global minimum variance portfolio models are widely used in portfolio selection problems. The only input required by GMVP is the covariance matrix of the asset returns under consideration. The output of GMVP is a vector of portfolio weights, which tells investors how much wealth to invest in each stock to achieve a portfolio with the minimum amount of variance.

[0004] However, the traditional method involves many parameters when calculating, which increases the complexity of the calculation, resulting in a higher estimation error of the global minimum variance portfolio risk.

[0005] Summary of the Invention

[0006] In view of the disadvantage that the existing technology involves too many parameters during calculation, resulting in a high estimation error of the global minimum variance investment portfolio risk, the present invention proposes an asset portfolio investment risk assessment method and system. The reference of the Spiked model can effectively reduce the computational complexity of large-dimensional data and greatly reduce the parameters that need to be designed, thereby more efficiently estimating the investment portfolio risk and obtaining a more accurate risk estimate value of the investment portfolio, thereby solving the problem that the existing technology involves too many parameters during calculation, resulting in a high estimation error of the global minimum variance investment portfolio risk.

[0007] An asset portfolio investment risk assessment method comprises the following steps:

[0008] Acquire a plurality of different asset data; each of the asset data includes multiple periods of data;

[0009] Divide the closing price of each asset in each period by the closing price of the previous period to obtain the relative price of each asset in each period;

[0010] Set a time window based on the relative price of each asset, and select the sample covariance matrix within the time window corresponding to each asset data;

[0011] The sample covariance matrix is ​​spectrally corrected to the Spiked model form, and the regularization parameter is added to the spectrally corrected covariance matrix to obtain the spectrally corrected covariance matrix and the regularized covariance matrix respectively;

[0012] According to the spectrum correction covariance matrix and the regularization covariance matrix, the spectrum correction and regularization estimation formula of the overall covariance matrix are obtained;

[0013] By inputting multiple different asset data into the spectral correction and regularization estimation formula of the overall covariance matrix, the portfolio weights of different assets and the global minimum variance portfolio risk corresponding to the portfolio weights are calculated;

[0014] Based on the portfolio weight estimation formula of different assets and the global minimum variance portfolio risk estimation formula corresponding to the portfolio weight, the portfolio risk of each asset in the new period is calculated and evaluated.

[0015] Furthermore, the time length of the multiple periods of data is more than 500 weeks.

[0016] Furthermore, the closing price of each asset in each period is divided by the closing price of the previous period to obtain the relative price of each asset in each period. The calculation process is expressed as:

[0017] in, represents the closing price of the i-th asset in period t, represents the closing price of the i-th asset in period t-1, It represents the relative rate of return of the ith asset in period t.

[0018] Furthermore, the time window is a time period with a fixed length of w before the current period.

[0019] Furthermore, a time window is set according to the relative price of each asset, and the time window is obtained by performing a logarithmic operation on the relative prices of multiple periods, which is expressed as: LX = (logx t-1 , logxt-2 ,…,logx t-w )

[0020] Among them, LX is the time window, X is the relative price series of the time window, and t is the current time.

[0021] Furthermore, the optimal regularization parameter is selected through network search, and the optimal regularization parameter is expressed as: γ * =arg min(pσ 2 (γ))

[0022] Among them, σ 2 (γ) is the global minimum variance portfolio risk,

[0023] Furthermore, the spectrum correction and regularization estimation of the overall covariance matrix are obtained according to the spectrum correction covariance matrix and the regularization covariance matrix, which are expressed as:

[0024] in, is the spectral correction and regularization estimate of the population covariance matrix, I p is the p-dimensional unit matrix, λ j is the eigenvalue, u j is its corresponding eigenvector; for u j The transposed vector of ; I1={1,…,r1}, I2={-r2,…,-1}, where r1 and r2 are the number of large Spiked eigenvalues ​​and small Spiked eigenvalues, respectively.

[0025] Furthermore, the investment portfolio weight estimation formula of the different assets is expressed as:

[0026] Among them, 1 p is a p-dimensional vector of all 1s, 1 p Transpose a vector.

[0027] Furthermore, the investment portfolio risk is calculated as follows:

[0028] in, Estimation of portfolio weights The corresponding global minimum variance portfolio risk.

[0029] Furthermore, an asset portfolio investment risk assessment system includes:

[0030] An acquisition module, configured to acquire a plurality of different asset data; each of the asset data includes multiple periods of data;

[0031] The asset return calculation module is used to divide the closing price of each asset in each period by the closing price of the previous period to obtain the relative price of each asset in each period;

[0032] The selection module is used to set a time window based on the relative price of each asset in each period and select the sample covariance matrix within the time window corresponding to each asset data;

[0033] The correction module is used to correct the sample covariance matrix spectrum to the Spiked model form, and add regularization parameters to the spectrally corrected covariance matrix to obtain the spectral correction and regularization estimation formula of the population covariance matrix;

[0034] The calculation module calculates the portfolio weights of different assets and the global minimum variance portfolio risk corresponding to the portfolio weights by inputting multiple different asset data into the spectral correction and regularization estimation formula of the overall covariance matrix;

[0035] The evaluation module is used to calculate and evaluate the portfolio risk of each asset in the new period based on the portfolio weight estimation formula of different assets and the global minimum variance portfolio risk estimation formula corresponding to the portfolio weight.

[0036] The present invention provides an asset portfolio investment risk assessment method and system, which has the following beneficial effects:

[0037] The present invention can effectively reduce the computational complexity of large-dimensional data and greatly reduce the parameters that need to be designed by spectrally correcting the sample covariance matrix into the Spiked model form and adding regularization parameters to the spectrally corrected covariance matrix. At the same time, the portfolio risk of each asset in a new period is calculated and evaluated based on the portfolio weights of different assets and the global minimum variance portfolio risk corresponding to the portfolio weights, thereby more efficiently estimating the portfolio risk and obtaining a more accurate risk estimate for the portfolio. At the same time, multi-period historical data is used, and the data information implicit in the historical data is utilized. Compared with other portfolio risk estimation methods, it provides a more robust investment risk and has achieved relatively excellent performance in both domestic and foreign markets. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] FIG1 is a flow chart of an asset portfolio investment risk assessment method according to the present invention. DETAILED DESCRIPTION

[0039] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0040] The present invention proposes a spectral correction and regularized global minimum variance investment portfolio method based on the Spiked model, which obtains multiple asset data; calculates the logarithmic returns of multiple asset prices; selects a certain amount of data as samples, calculates the sample covariance, and spectrally corrects the sample covariance matrix to the Spiked model form under the assumption that the overall covariance matrix follows the Spiked model; adds a regularization parameter to the spectrally corrected covariance matrix and uses grid search to tune it; substitutes the spectral correction and regularized covariance into the investment portfolio weight to obtain an investment portfolio weight estimation formula, and correspondingly substitutes the spectral correction and regularized global minimum variance investment portfolio risk estimation formula into the investment portfolio risk expression; and calculates the investment portfolio risk of each asset in the new period based on the current investment portfolio, as shown in Figure 1. The method specifically includes the following steps:

[0041] Step 1: Acquire multiple different asset data, each of which includes multiple periods of data. The time length of the multiple periods of data is more than 500 weeks and months.

[0042] In this embodiment, the asset data is stock data. The present invention selects 150 random stock data from the Shanghai and Shenzhen A-share markets for simulation, with a time period of January 1, 2010, to December 31, 2021.

[0043] Step 2: Calculate the relative price of each asset in each period.

[0044] Divide the closing price of each period's asset by the closing price of the previous period to obtain the relative price of each period's asset. The calculation formula is as follows.

[0045] Where, represents the closing price of the i-th asset in period t, represents the closing price of the i-th asset in period t-1, It represents the relative rate of return of the ith asset in period t.

[0046] Step 3: Perform logarithmic operations on relative prices over multiple periods.

[0047] The time window is a time window with a fixed length of w before the current period. The time window is a time period of w before the current period.

[0048] The time window is as follows: LX = (logx t-1 , logx t-2 ,…,logx t-w )

[0049] Where LX is the time window, X is the relative price sequence of the time window, and t is the current time.

[0050] Step 4: Calculate the sample covariance matrix by selecting samples of the corresponding time window, and modify the sample covariance matrix spectrum to the Spiked model form, add regularization parameters, and select the optimal regularization parameters through grid search. The optimal regularization parameter is expressed by the following formula: γ * =arg min(pσ 2 (γ))

[0051] In the formula σ 2 (γ) is the global minimum variance portfolio risk,

[0052] Step 5: Get the spectral correction and regularization estimate of the overall covariance matrix as follows:

[0053] In the formula is the spectral correction and regularization estimate of the population covariance matrix, I p is the p-dimensional unit matrix, λ j is the eigenvalue, u j is its corresponding eigenvector; for u j The transposed vector of ; I1={1,…,r1}, I2={-r2,…,-1}, where r1 and r2 are the number of large Spiked eigenvalues ​​and small Spiked eigenvalues, respectively.

[0054] The portfolio weights of different assets are calculated using the following formula:

[0055] The portfolio risk is calculated based on the following formula:

[0056] Where, Estimation of portfolio weights The corresponding global minimum variance portfolio risk.

[0057] Based on the same inventive concept, the present invention proposes an asset portfolio investment risk assessment system, comprising:

[0058] The acquisition module is used to acquire a plurality of different asset data; each asset data includes multiple periods of data.

[0059] The asset return calculation module is used to divide the closing price of each asset in each period by the closing price of the previous period to obtain the relative price of each asset in each period.

[0060] The selection module is used to set a time window according to the relative price of each asset in each period and select the sample covariance matrix within the time window corresponding to each asset data.

[0061] The correction module is used to correct the sample covariance matrix spectrum to the Spiked model form, and add regularization parameters to the spectrally corrected covariance matrix to obtain the spectral correction and regularization estimation formula of the population covariance matrix.

[0062] The calculation module calculates the portfolio weights of different assets and the global minimum variance portfolio risk corresponding to the portfolio weights by inputting multiple different asset data into the spectral correction and regularization estimation formula of the overall covariance matrix.

[0063] The evaluation module is used to calculate and evaluate the portfolio risk of each asset in the new period based on the portfolio weights of different assets and the global minimum variance portfolio risk corresponding to the portfolio weights.

[0064] The present invention estimates the unknown population covariance matrix based on the spectral correction of the Spiked model and the regularized sample covariance matrix, effectively predicting the true correlation between stocks, while reducing the number of parameters we need to predict, greatly improving computational efficiency and reducing computational complexity.

[0065] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solution and inventive concept of the present invention, should be covered by the scope of protection of the present invention.

Claims

1. A method for evaluating the risk of portfolio investment, characterized in that, Comprising the following steps: Obtain a plurality of different asset data; each said asset data includes multiple periods of data; Divide the closing price of each period of each asset data by the closing price of the previous period to obtain the relative price of each period of the asset; Set a time window according to the relative price of each period of the asset, and select the sample covariance matrix within the corresponding time window of each asset data; Spectral correct the sample covariance matrix into the form of a Spiked model, and add a regularization parameter to the spectrally corrected covariance matrix, thereby obtaining the spectral correction and regularization estimation formula of the overall covariance matrix; By respectively inputting a plurality of different asset data into the spectral correction and regularization estimation formula of the overall covariance matrix, calculate the portfolio weights of different assets and the global minimum variance portfolio risk corresponding to the portfolio weights; Calculate and evaluate the portfolio risk of each asset in a new period according to the portfolio weights of different assets and the global minimum variance portfolio risk corresponding to the portfolio weights.

2. The method for evaluating the investment risk of an asset portfolio according to claim 1, wherein The time length of the said multiple periods of data is more than 500 weeks.

3. The method for evaluating the risk of portfolio investment according to claim 1, wherein Dividing the closing price of each asset in each period by the closing price of the previous period to obtain the relative price of each period of the asset, the calculation process is expressed as: Among them, Denote the closing price of the i-th asset in the t-th period, Denote the closing price of the i-th asset in the (t - 1)-th period, Denote the relative return rate of the i-th asset in the t-th period.

4. The asset portfolio investment risk assessment method according to claim 1, characterized in that The said time window is a time period with a fixed length of w before the current period.

5. The method for evaluating the risk of portfolio investment according to claim 4, wherein A time window is set according to the relative price of each period of assets. By performing logarithmic operations on the relative prices of multiple periods, the time window is obtained, which is expressed as: LX = (logx t-1 , logx t-2 , …, logx t-w ) Wherein, LX is the time window, X is the relative price sequence of the time window, and t is the current time.

6. The method for evaluating the risk of portfolio investment according to claim 1, wherein, Select the optimal regularization parameter through network search, and the optimal regularization parameter is expressed as: γ * = arg min(pσ 2 (γ)) where, σ 2 (γ) is the risk of the global minimum variance portfolio, p is the dimension of the stock data, 7. The risk assessment method for portfolio investment according to claim 1, characterized in that The spectral correction and regularization estimation of the overall covariance matrix are obtained from the spectral correction covariance matrix and the regularization covariance matrix, expressed as: Among them, For the spectral correction and regularization estimation of the overall covariance matrix, I p is the p-dimensional identity matrix, λ j is the eigenvalue, u j is its corresponding eigenvector; is the transposed vector of u j ; I1 = {1, …, r1}, I2 = {-r2, …, -1}, where r1 and r2 are the numbers of large and small spiked eigenvalues respectively, and γ1 and γ2 represent regularization parameters.

8. A method for evaluating the risk of portfolio investment according to claim 7, characterized in that The portfolio weight estimation formula for the different assets is expressed as: where 1 p is a p-dimensional vector of all 1s, is 1 p Transposed vector.

9. The method for evaluating the risk of portfolio investment according to claim 8, characterized in that, The calculation formula for the risk of the portfolio is as follows: Among them, For portfolio weight estimation The corresponding global minimum variance portfolio risk.

10. A portfolio investment risk assessment system, characterized in that, Including: An obtaining module, used to obtain a plurality of different asset data; Each said asset data includes multiple periods of data; An asset return calculation module, used to divide the closing price of each period of each asset data by the closing price of the previous period to obtain the relative price of each period of the asset; A selection module, used to set a time window according to the relative price of each period of the asset, and select the sample covariance matrix within the corresponding time window of each asset data; A correction module, used to spectral correct the sample covariance matrix into the form of a Spiked model, and add a regularization parameter to the spectrally corrected covariance matrix, thereby obtaining the spectral correction and regularization estimation formula of the overall covariance matrix; A calculation module, by respectively inputting a plurality of different asset data into the spectral correction and regularization estimation formula of the overall covariance matrix, calculates the portfolio weights of different assets and the global minimum variance portfolio risk corresponding to the portfolio weights; An evaluation module, used to calculate and evaluate the portfolio risk of each asset in a new period according to the portfolio weights of different assets and the global minimum variance portfolio risk corresponding to the portfolio weights.

Images