A multi-factor orthogonalization and weighted regression asset risk exposure evaluation method
By employing multi-factor orthogonalization and weighted regression methods, the problems of insufficient factor correlation and standardization adaptability in existing technologies are solved, thereby achieving stability and automation in risk assessment and supporting unified risk assessment and benchmark comparison analysis for multiple accounts and multiple sub-portfolios.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NANJING NEW GENERATION ARTIFICIAL INTELLIGENCE RES INST CO LTD
- Filing Date
- 2026-04-10
- Publication Date
- 2026-07-21
AI Technical Summary
Existing multi-factor risk assessment methods have shortcomings in terms of factor correlation control, standardization adaptability, and unified assessment at the portfolio level. These shortcomings lead to unstable risk contribution assessment, inaccurate factor exposure, lack of automated assessment mechanisms, and difficulty in supporting unified risk assessment and benchmark comparison analysis for multiple accounts and multiple sub-portfolios.
Using multi-factor orthogonalization and weighted regression, a complete risk exposure assessment system is formed through structural standardization, composite factor construction, orthogonalization to eliminate collinearity, automatic screening by weighted regression, and unified assessment at the portfolio level. This system includes steps such as data preprocessing, risk factor preprocessing, composite factor construction, orthogonalization, weighted regression, and portfolio-level assessment.
It improves the stability and reliability of risk assessment, realizes the unified structured standardization of risk factors across markets, reduces the redundancy of the number of factors, improves the automation level of factor contribution assessment, and supports unified risk assessment and benchmark comparison analysis for multiple accounts and multiple sub-portfolios.
Smart Images
Figure CN122434531A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the fields of data processing and financial risk analysis technology, and is applicable to core business scenarios such as portfolio risk analysis, real-time risk monitoring, risk structure decomposition, and benchmark comparison assessment for institutional investors such as public funds, private funds, and securities asset management companies. It can provide comprehensive data support for investment decision-making, portfolio optimization, and risk management, and in particular, it relates to an asset risk exposure assessment method based on multi-factor orthogonalization and weighted regression. Background Technology
[0002] Asset risk exposure assessment is a core and fundamental task in the field of financial investment. Its core objective is to accurately identify the exposure levels of assets or portfolios across different risk dimensions, providing a basis for risk management and investment decisions. Existing multi-factor risk assessment methods typically construct multiple risk factors and quantify the impact of each factor on asset risk based on regression analysis. While this type of method has been widely adopted in practice, it still has shortcomings in areas such as factor correlation control, standardization adaptability, and unified assessment at the portfolio level.
[0003] [Existing Core Technical Issues] 1. Strong correlations among risk factors affect the stability of assessments. Most risk factors exhibit significant correlations during their construction. Directly using them for regression analysis or risk exposure calculations can easily lead to multicollinearity, resulting in unstable risk contribution assessments and insufficient interpretability. Size factors and nonlinear size factors, as well as volatility factors and Beta factors, often have high correlation coefficients; direct use of these factors can lead to inaccurate regression coefficient estimates.
[0004] 2. Factor standardization methods neglect asset structure characteristics. Existing methods often employ simple mean-variance standardization, failing to adequately consider differences in asset size or weight structure. This makes risk assessment results susceptible to extreme samples or variations in size distribution. Large-cap and small-cap stocks exhibit systematic differences in factor exposure; simple standardization may lead to an underestimation of the factor exposure of large-cap stocks.
[0005] 3. Lack of a systematic approach to constructing composite risk factors. Core risk dimensions such as volatility, liquidity, and leverage have multi-dimensional characteristics, and a single indicator cannot fully reflect the true level of risk. Existing technologies lack a systematic approach for unified combination and modeling of multiple indicators, resulting in blind spots in risk characterization.
[0006] 4. Factor contribution assessment relies heavily on empirical rules and lacks automation. In multi-factor environments, factor selection and contribution assessment often depend on manual experience or fixed rules, lacking data-driven automated assessment mechanisms. This can lead to the inclusion of noisy factors in the model, affecting the accuracy of risk analysis.
[0007] 5. Lack of a unified framework for portfolio-level risk exposure assessment. Existing technologies often analyze single assets or portfolios, making it difficult to support unified risk assessment and comparative analysis of multiple accounts and sub-portfolios. The lack of comparative analysis capabilities with benchmark indices prevents the provision of comprehensive risk references for investment decisions.
[0008] Therefore, it is necessary to propose a technical solution that can reduce the impact of factor correlation, introduce structural weight information, support composite risk modeling, and realize combined-level risk exposure assessment. Summary of the Invention
[0009] To address the problems existing in the prior art, the purpose of this invention is to provide an asset risk exposure assessment method based on multi-factor orthogonalization and weighted regression, which can be implemented through a corresponding system and storage medium. The core innovation of this invention lies in the organic integration of five major technical means: "structural standardization factors, composite factor construction, orthogonalization to eliminate collinearity, automatic screening via weighted regression, and unified assessment at the portfolio level," forming a complete risk exposure assessment system. 1. Introduce asset size weighting to optimize standardized processes and solve structural adaptability issues; 2. Construct multi-dimensional composite risk factors to achieve a comprehensive characterization of risk; 3. Factor orthogonalization is achieved through OLS regression residuals to eliminate collinearity interference; 4. Based on weighted regression using the forward selection algorithm, automatic evaluation of factor contributions is achieved; 5. Design a unified portfolio-level evaluation framework that supports single portfolio, multi-account aggregation, and benchmark comparison analysis.
[0010] To achieve the above objectives, the technical solution adopted by this invention is: a method for assessing asset risk exposure using multi-factor orthogonalization and weighted regression, comprising the following steps: Step 1: Data Acquisition and Preprocessing. Collect the basic data required for asset risk assessment, and then preprocess the data by replacing positive and negative infinity values with missing values and filling them in, while deleting data from abnormal trading days. Step 2: Risk factor preprocessing and structural standardization. First, missing values are filled and outliers are shrunken in the factor data. Then, market capitalization weights are introduced to achieve weighted decentralization and eliminate the impact of differences in asset size. Finally, standardization is completed based on the weighted standard deviation. Step 3: Construct a composite risk factor. Based on the historical risk explanatory power, determine the weights of sub-factors for the three core risk dimensions of volatility, liquidity, and leverage, and construct the composite factor. After the composite factor is constructed, remove the sub-factors that participate in the portfolio. Step 4: Orthogonalization of risk factors. Select the composite volatility risk factor and the composite liquidity risk factor as the objects to be orthogonalized, and perform orthogonalization using the market risk factor and the size factor as explanatory variables respectively. Step 5: Factor contribution assessment based on weighted regression. First, a weighted least squares regression model with the square root of market capitalization as the weight is adopted. Its weight function is used to enhance the influence of the dominant asset on the regression results. Then, a forward selection algorithm is introduced, using the incremental explanatory power of the model as the screening criterion, to gradually introduce risk factors that have a significant explanatory power for returns, and automatically remove redundant or noisy factors. Step Six: Calculate the risk exposure of assets or asset portfolios, supporting three types of assessment scenarios and constructing a unified portfolio-level assessment framework: single portfolio risk exposure is calculated through portfolio exposure; multi-account aggregated assessment requires first accumulating the holdings of each account to obtain the total holdings, and then calculating according to the single portfolio method; benchmark comparison assessment is calculated through active exposure to quantify the degree of risk deviation of the portfolio relative to the benchmark. Step 7: Results Output and Visualization. Output multi-dimensional results, along with model R², factor IC mean, and information ratio effectiveness evaluation indicators. Then, generate a multi-subplot heatmap to visually display the results.
[0011] As a preferred embodiment of the present invention, in step one, the basic data includes asset price and return data, asset size and weight data, and raw data of multidimensional risk factors covering market risk, size and volatility.
[0012] In a preferred embodiment of the present invention, in step two: Weighted Decentralization: Introducing market capitalization weights to calculate the weighted mean of factors eliminates the impact of asset size differences on factor distribution. Market capitalization weighting calculation: ; Weighted mean: ; Decentralized operation: ; Weighted standardization: Factor normalization is achieved based on weighted standard deviation, as shown in the following formula: Weighted standard deviation: ; Standardization results: .
[0013] Where i represents the i-th asset in the sample. This represents the market value of the i-th asset during the observation period; The market capitalization weight of asset i is defined as the proportion of that asset's market capitalization to the total market capitalization of the sample. This represents the original factor exposure of asset i to the corresponding risk factor; Indicates market capitalization weight The calculated weighted average of the risk factors; This represents the factor exposure value of asset i after weighted decentralization, where centered indicates the state after decentralization. It represents the weighted standard deviation of the risk factor calculated under market capitalization weighting, used to characterize the contribution of the dominant asset to the overall factor volatility; This indicates that the standardized factor exposure results obtained after weighted standardization have consistent dimensions and can be used as input features for subsequent orthogonalization and regression analysis.
[0014] In a preferred embodiment of the present invention, in step three, the composite factor includes a composite volatility risk factor, a composite liquidity risk factor, and a composite leverage risk factor. A composite volatility risk factor that integrates short-term and medium-term volatility characteristics: ; Wherein, Dastd: standard deviation of daily returns, Cmra: range of cumulative returns, and Hsigma: idiosyncratic volatility; A composite liquidity risk factor covering short-, medium-, and long-term turnover rates: ; Where Stom: monthly turnover rate, Stoq: quarterly turnover rate, and Stoa: annual turnover rate; Composite leverage risk factor, integrating market leverage and book leverage: ; Where Mlev is market leverage, Dtoa is the debt-to-equity ratio, and Blev is book leverage.
[0015] As a preferred embodiment of the present invention, in step four, the following regression model is constructed to perform hierarchical decoupling processing on the composite risk factors: ; in, This represents the composite risk factor exposure of asset i. This represents the corresponding explanatory variables, including market risk factors or size factors. For the intercept term, For regression coefficients, For the regression residual term, the regression residual It is defined as the risk factor exposure value after orthogonalization.
[0016] As a preferred embodiment of the present invention, in step five, the square root of market value is used as the regression weight, effective factors are screened according to the R² increment of the model, and then weighted regression is performed with stock return rate as the dependent variable and effective factors as independent variables. Formula for regression weights The model is ; in Let i be the rate of return of stock i. Let i be the exposure of stock i to the k-th efficient factor. This represents the factor return, i.e., the contribution of a factor to the return.
[0017] In a preferred embodiment of the present invention, the specific formula in step six is as follows: Amount weighting calculation: ; Combined factor exposure: , The standardized factor exposure of stock i reflects the portfolio's sensitivity to that factor; Position aggregation: The total position is obtained by repeatedly reading the position data of each account and summing them up. , This represents the holdings data for the i-th account; Exposure calculation: Based on the total aggregated holdings, the overall risk exposure of multiple accounts is obtained by using a single portfolio exposure calculation method; Active exposure calculation: This reflects the degree of risk deviation of the portfolio relative to the benchmark.
[0018] In a preferred embodiment of the present invention, in step seven, the multi-dimensional results include factor long-short portfolio returns, factor returns, current and previous period risk exposures of the portfolio, benchmark exposure, and factor information coefficients.
[0019] As a preferred embodiment of the present invention, in step seven, the information ratio formula... .
[0020] Compared with the prior art, the main advantages of the present invention are: 1. A unified risk factor structured standardization method adapted to multiple market environments is proposed. By introducing asset structure weights in the factor preprocessing stage, risk factors are subjected to weighted decentralization and weighted standardization, enabling risk factors to have unified dimensions and statistical characteristics under different markets, asset size distributions, and time intervals, significantly improving the comparability and stability of cross-market risk exposure assessment results.
[0021] 2. Construct a multi-dimensional risk factor combination mechanism for characterizing complex risks. For core risk dimensions such as volatility, liquidity, and leverage, a composite risk factor is formed by weighted fusion of multiple sub-factors. This avoids the inadequacy of a single indicator while effectively reducing the redundancy of factors, providing a more intensive and effective risk representation for subsequent orthogonalization processing and factor contribution assessment.
[0022] 3. A hierarchical orthogonalization method is proposed, aiming at decoupling risk sources. Based on the economic meaning and statistical characteristics of risk factors, orthogonalization is selectively applied to composite risk factors and basic systemic factors. This process removes the systemic risk components implicit in composite factors, avoids the problem of overlapping factor meanings, and improves the stability and interpretability of risk exposure assessment.
[0023] 4. Design an adaptive weighted regression factor contribution evaluation mechanism. By introducing structural weights and combining them with a stepwise screening strategy, the mechanism enables automatic identification and contribution quantification of effective risk factors in a multi-factor environment, reducing reliance on human experience and improving the objectivity and automation of factor screening and risk contribution assessment.
[0024] 5. A modular and configurable overall framework for asset risk exposure assessment is established. By modularizing key steps such as risk factor preprocessing, orthogonalization, regression assessment, and portfolio-level calculation, the method of this invention can flexibly adapt to different market environments, business needs, and data conditions, possessing good scalability, engineering implementation flexibility, and long-term application value. Attached Figure Description
[0025] Figure 1 This is a schematic diagram of the asset risk exposure assessment method based on multi-factor orthogonalization and weighted regression in this embodiment. Detailed Implementation
[0026] To better understand the present invention, the technical solution of the present invention will be further explained below with reference to the accompanying drawings and specific embodiments.
[0027] like Figure 1 As shown, this embodiment proposes an asset risk exposure assessment method based on multi-factor orthogonalization and weighted regression. Through seven core steps—data acquisition, factor preprocessing, composite factor construction, orthogonalization, factor contribution assessment, risk exposure calculation, and result output—it achieves accurate quantification and multi-dimensional analysis of risk exposure. Each module functions independently yet works collaboratively to form a complete end-to-end technical solution.
[0028] The specific implementation process is as follows: Step 1: Basic Data Acquisition and Preprocessing The core of this step is to collect the basic data required for asset risk assessment, including asset price and return data, asset size and weight data, and raw data of multidimensional risk factors covering six major categories such as market risk, size, and volatility. After data collection, preprocessing is required to replace positive and negative infinity values with missing values and fill them in, while deleting data from abnormal trading days to ensure data integrity and usability.
[0029] Step 2: Risk Factor Preprocessing and Structural Standardization This approach addresses the shortcomings of traditional factor standardization in terms of adaptability through a three-step process: first, missing value imputation and outlier reduction are performed on the factor data; second, market capitalization weights are introduced to achieve weighted decentralization, eliminating the impact of differences in asset size; and finally, standardization is completed based on the weighted standard deviation. Using market capitalization-weighted standard deviation ensures that the standardization process aligns with the actual risk exposure structure of the portfolio. By introducing market capitalization weights, the weighted standard deviation more accurately reflects the contribution of the dominant asset to the overall factor volatility, thus avoiding the unreasonable amplification of the standardization results by extreme values of small-cap or low-weight assets, and improving the overall reliability and practicality of the risk assessment results. The specific formula is as follows: (1) Weighted Decentralization: Market capitalization weights are introduced to calculate the weighted mean of the factors, eliminating the impact of differences in asset size on the factor distribution. 1) Market capitalization weight calculation: ; 2) Weighted mean: ; 3) Decentralized operation: .
[0030] (2) Weighted standardization: Factor normalization is achieved based on weighted standard deviation, as shown in the following formula: 1) Weighted standard deviation: ; 2) Standardization results: .
[0031] Where i represents the i-th asset (stock) in the sample. This represents the market value of the i-th asset during the observation period; The market capitalization weight of asset i is defined as the proportion of that asset's market capitalization to the total market capitalization of the sample. This represents the original factor exposure of asset i to the corresponding risk factor; Indicates market capitalization weight The calculated weighted average of the risk factors.
[0032] This represents the factor exposure value of asset i after weighted decentralization, where the subscript c indicates "centered", that is, the state after decentralization. It represents the weighted standard deviation of the risk factor calculated under market capitalization weighting, used to characterize the contribution of the dominant asset to the overall factor volatility; This indicates that the standardized factor exposure results obtained after weighted standardization have consistent dimensions and can be used as input features for subsequent orthogonalization and regression analysis.
[0033] Step 3: Construction of Composite Risk Factors For the three core risk dimensions of volatility, liquidity, and leverage, the weights of sub-factors are determined based on the explanatory power of historical risk, and composite factors are constructed to achieve a comprehensive risk profile. The core formulas include the calculation of composite volatility risk factor, composite liquidity risk factor, and composite leverage risk factor. After constructing the composite factors, sub-factors participating in the portfolio are removed to avoid redundancy. The calculation formulas for the three types of core composite factors are as follows: (1) Composite volatility risk factor (combining short-term and medium-term volatility characteristics):
[0034] (Dastd: Standard deviation of daily returns, Cmra: range of cumulative returns, Hsigma: idiosyncratic volatility) (2) Composite liquidity risk factor (covering short-, medium-, and long-term turnover rates):
[0035] (Stom: monthly turnover rate, Stoq: quarterly turnover rate, Stoa: annual turnover rate) (3) Composite leverage risk factor (integrating market leverage and book leverage):
[0036] (Mlev: Market leverage, Dtoa: Debt-to-equity ratio, Blev: Book leverage) Step 4: Orthogonalization of risk factors This step is one of the core innovations of this invention, proposing a "hierarchical orthogonalization method for risk source decoupling". Based on the economic meaning of risk factors, this method achieves structural decoupling between composite risk factors and basic systemic factors through targeted orthogonalization operations, thereby improving the stability and interpretability of risk exposure assessment.
[0037] Specifically, this invention selects composite volatility risk factors and composite liquidity risk factors as the objects to be orthogonalized, and performs orthogonalization using market risk factors and size factors as explanatory variables, respectively. The reason for this is that market risk factors mainly reflect the overall systemic volatility level, while size factors are highly correlated with liquidity characteristics in the actual market; both often significantly interfere with composite risk factors. If composite factors are used directly without distinction, the underlying systemic risk component will be mixed into their risk exposure, weakening the composite factors' ability to characterize specific risk dimensions.
[0038] This invention employs a hierarchical decoupling process for composite risk factors by constructing the following regression model: , in, This represents the composite risk factor exposure of asset i. This represents the corresponding explanatory variable (market risk factor or size factor). For the intercept term, For regression coefficients, This refers to the regression residual term. The regression residual... It is defined as the risk factor exposure value after orthogonalization.
[0039] Through the above processing, the orthogonalized composite risk factor is statistically completely uncorrelated with the explanatory variables, thus achieving effective extraction of the "non-systematic risk component." This method avoids the problems of overlapping factor meanings and mixed risk sources in traditional multi-factor models, providing purer and more stable input features for subsequent factor contribution assessment.
[0040] Step 5: Evaluation of Factor Contributions Based on Weighted Regression This step proposes an "adaptive factor contribution evaluation method for portfolio structure," which automatically identifies and quantifies factor effectiveness in a multi-factor environment by introducing structural weights and a stepwise screening mechanism. First, a weighted least squares regression model with the square root of market capitalization as the weight is employed. Its weight function enhances the influence of the dominant asset on the regression results, thus making the factor contribution evaluation results closer to the actual portfolio risk structure. Based on this, a forward selection algorithm is introduced, using the model's explanatory power increment as the screening criterion to gradually introduce risk factors that significantly explain returns while automatically eliminating redundant or noisy factors.
[0041] Specifically, the square root of market capitalization is used as the regression weight (formula). The effective factors are selected incrementally according to the R² of the model, and then a weighted regression is performed with stock returns as the dependent variable and the effective factors as the independent variables. The model is as follows: ,in Let i be the rate of return of stock i. Let i be the exposure of stock i to the k-th efficient factor. This refers to the factor return (i.e., the contribution of the factor to the return).
[0042] Compared to traditional equal-weighted regression or manual experience screening, this method can improve the objectivity and automation of factor contribution assessment while ensuring model stability. It is particularly suitable for real-world business scenarios with a large number of factors and complex asset structures.
[0043] Step Six: Calculation of Risk Exposures of Assets or Portfolios This step supports three assessment scenarios, constructing a unified portfolio-level assessment framework: single portfolio risk exposure is calculated through portfolio exposure; multi-account aggregated assessment requires first summing the holdings of each account to obtain the total holdings, and then calculating using the single portfolio method; benchmark comparison assessment is calculated through active exposure to quantify the portfolio's risk deviation relative to the benchmark. The specific formulas are as follows: (1) Calculation of monetary weights: ; (2) Combined factor exposure: ( (Standardized factor exposure of stock i) reflects the portfolio's sensitivity to that factor.
[0044] (3) Position Aggregation: The total position is obtained by reading the position data of each account in a loop and summing them up. ( (This refers to the holdings data of the i-th account). (4) Exposure calculation: Based on the total holdings after aggregation, the overall risk exposure of multiple accounts after aggregation is obtained by using the single portfolio exposure calculation method.
[0045] (5) Active exposure calculation: This reflects the degree of risk deviation of the portfolio relative to the benchmark, providing a basis for active management decisions.
[0046] Step 7: Results Output and Visualization This step outputs multi-dimensional results including factor long-short portfolio returns, factor returns, current and previous period portfolio risk exposure, benchmark exposure, and factor information coefficient, along with effective evaluation metrics such as model R², factor IC mean, and information ratio (information ratio formula). By generating multi-subplot heatmaps, the results are visually presented, providing clear data support for risk management decisions.
[0047] Optional embodiments and extended descriptions: Without departing from the technical solution of this invention, the method of this invention can be extended and implemented in various ways according to different application scenarios. In one optional embodiment, the basic data can be data with different time granularities, including but not limited to minute-level, hour-level, or day-level data. The method of this invention can first calculate the risk factor exposure of each asset at a higher time resolution, and then obtain the risk exposure results at a lower time resolution through time aggregation, thereby improving the stability and applicability of risk exposure estimation.
[0048] Furthermore, during the time aggregation process, assets can be grouped according to the number of assets, asset category, or preset rules, and the risk factor exposure values within each group can be statistically summarized. The statistical methods include, but are not limited to, mean, weighted mean, extreme value, or interval statistical value, to form a combined-level risk exposure indicator.
[0049] In another optional implementation, the types, number, and construction methods of risk factors, the order of orthogonalization of risk factors, the form of the regression model, and the regression weight function can all be adjusted or replaced according to actual application needs. The regression model is not limited to a linear regression model. Furthermore, the output format of the risk exposure assessment results can be tables, graphs, or visualization interfaces, and these results can be used for risk monitoring, risk comparison analysis, or risk structure assessment.
[0050] The above embodiments are only for illustrating the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly. They should not be construed as limiting the scope of protection of the present invention. All equivalent changes or modifications made in accordance with the spirit and essence of the present invention should be covered within the scope of protection of the present invention.
Claims
1. A method for assessing asset risk exposure using multi-factor orthogonalization and weighted regression, characterized in that, Includes the following steps: Step 1: Data Acquisition and Preprocessing. Collect the basic data required for asset risk assessment, and then preprocess the data by replacing positive and negative infinity values with missing values and filling them in, while deleting data from abnormal trading days. Step 2: Risk factor preprocessing and structural standardization, firstly, missing value imputation and outlier reduction are performed on the factor data; Then, market capitalization weight is introduced to achieve weighted decentralization, eliminating the impact of differences in asset size, and finally standardization is completed based on weighted standard deviation; Step 3: Construct a composite risk factor. Based on the historical risk explanatory power, determine the weights of sub-factors for the three core risk dimensions of volatility, liquidity, and leverage, and construct the composite factor. After the composite factor is constructed, remove the sub-factors that participate in the portfolio. Step 4: Orthogonalization of risk factors. Select the composite volatility risk factor and the composite liquidity risk factor as the objects to be orthogonalized, and perform orthogonalization using the market risk factor and the size factor as explanatory variables respectively. Step 5: Factor contribution assessment based on weighted regression. First, a weighted least squares regression model with the square root of market capitalization as the weight is adopted. Its weight function is used to enhance the influence of the dominant asset on the regression results. Then, a forward selection algorithm is introduced, using the incremental explanatory power of the model as the screening criterion, to gradually introduce risk factors that have a significant explanatory power for returns, and automatically remove redundant or noisy factors. Step Six: Calculate the risk exposure of an asset or portfolio, supporting three types of assessment scenarios and constructing a unified portfolio-level assessment framework: the risk exposure of a single portfolio is calculated through portfolio exposure; Multi-account aggregated assessment requires first summing up the holdings of each account to obtain the total holdings, and then calculating using a single portfolio method; benchmark comparison assessment quantifies the risk deviation of the portfolio relative to the benchmark through active exposure calculation. Step 7: Results Output and Visualization. Output multi-dimensional results, along with model R², factor IC mean, and information ratio effectiveness evaluation indicators. Then, generate a multi-subplot heatmap to visually display the results.
2. The asset risk exposure assessment method based on multi-factor orthogonalization and weighted regression according to claim 1, characterized in that, In step one, the basic data includes asset price and return data, asset size and weight data, and raw data of multidimensional risk factors covering market risk, size and volatility.
3. The asset risk exposure assessment method based on multi-factor orthogonalization and weighted regression according to claim 1, characterized in that, In step two: Weighted Decentralization: Introducing market capitalization weights to calculate the weighted mean of factors eliminates the impact of asset size differences on factor distribution. Market capitalization weighting calculation: ; Weighted mean: ; Decentralized operation: ; Weighted standardization: Factor normalization is achieved based on weighted standard deviation, as shown in the following formula: Weighted standard deviation: ; Standardization results: ; Where i represents the i-th asset in the sample. This represents the market value of the i-th asset during the observation period; The market capitalization weight of asset i is defined as the proportion of that asset's market capitalization to the total market capitalization of the sample. This represents the original factor exposure of asset i to the corresponding risk factor; Indicates market capitalization weight The calculated weighted average of the risk factors; This represents the factor exposure value of asset i after weighted decentralization, where centered indicates the state after decentralization. It represents the weighted standard deviation of the risk factor calculated under market capitalization weighting, used to characterize the contribution of the dominant asset to the overall factor volatility; This indicates that the standardized factor exposure results obtained after weighted standardization have consistent dimensions and can be used as input features for subsequent orthogonalization and regression analysis.
4. The asset risk exposure assessment method based on multi-factor orthogonalization and weighted regression according to claim 1, characterized in that, In step three, the composite factors include a composite volatility risk factor, a composite liquidity risk factor, and a composite leverage risk factor. A composite volatility risk factor that integrates short-term and medium-term volatility characteristics: ； Wherein, Dastd: standard deviation of daily returns, Cmra: range of cumulative returns, and Hsigma: idiosyncratic volatility; A composite liquidity risk factor covering short-, medium-, and long-term turnover rates: ； Where Stom: monthly turnover rate, Stoq: quarterly turnover rate, and Stoa: annual turnover rate; Composite leverage risk factor, integrating market leverage and book leverage: Where Mlev: market leverage, Dtoa: debt-to-equity ratio, and Blev: book leverage.
5. The asset risk exposure assessment method based on multi-factor orthogonalization and weighted regression according to claim 1, characterized in that, In step four, the following regression model is constructed to perform hierarchical decoupling of the composite risk factors: ;in, This represents the composite risk factor exposure of asset i. This represents the corresponding explanatory variables, including market risk factors or size factors. For the intercept term, For regression coefficients, For the regression residual term, the regression residual It is defined as the risk factor exposure value after orthogonalization.
6. The asset risk exposure assessment method based on multi-factor orthogonalization and weighted regression according to claim 1, characterized in that, In step five, the square root of market capitalization is used as the regression weight, and effective factors are screened according to the model R² increment. Then, weighted regression is performed with stock return as the dependent variable and effective factors as independent variables. Formula for regression weights The model is ; in Let i be the rate of return of stock i. Let i be the exposure of stock i to the k-th efficient factor. This represents the factor return, i.e., the contribution of a factor to the return.
7. The asset risk exposure assessment method based on multi-factor orthogonalization and weighted regression according to claim 1, characterized in that, In step six, the specific formula is as follows: Amount weighting calculation: ; Combined factor exposure: , The standardized factor exposure of stock i reflects the portfolio's sensitivity to that factor; Position aggregation: The total position is obtained by repeatedly reading the position data of each account and summing them up. , This represents the holdings data for the i-th account; Exposure calculation: Based on the total aggregated holdings, the overall risk exposure of multiple accounts is obtained by using a single portfolio exposure calculation method; Active exposure calculation: This reflects the degree of risk deviation of the portfolio relative to the benchmark.
8. The asset risk exposure assessment method based on multi-factor orthogonalization and weighted regression according to claim 1, characterized in that, In step seven, the multi-dimensional results include factor long-short portfolio returns, factor returns, current and previous period risk exposures of the portfolio, benchmark exposure, and factor information coefficients.
9. The asset risk exposure assessment method based on multi-factor orthogonalization and weighted regression according to claim 1, characterized in that, In step seven, the information ratio formula .