An esg risk information driven dynamic tracking portfolio management method and system

Abstract

This paper presents a dynamic tracking portfolio management method and system driven by ESG risk information, belonging to the fields of financial portfolio management and sustainable investment technology. It dynamically updates return and risk parameters using ESG risk as a state variable. Within a tracking portfolio (TP) framework, two types of constrained optimization models are constructed. The system automatically selects and calls one model based on preset operating logic, setting multiple constraints such as minimum portfolio return and maximum volatility to minimize the portfolio's weighted average ESG risk. Empirical testing based on S&P 100 index constituents demonstrates that this method outperforms other methods across multiple indicators. It addresses the technical problems of static model parameters and difficulties in data fusion in traditional models, enabling quantitative control of ESG risk while maintaining index tracking accuracy. The system boasts a high degree of automation and is suitable for index-tracking sustainable investment management scenarios.

Description

Technical Field

[0001] This invention belongs to the field of financial portfolio management and sustainable investment technology, specifically relating to an ESG risk information-driven dynamic tracking portfolio management method and system, which is particularly suitable for the dynamic management of ESG risks in index tracking products. Background Technology

[0002] The fundamental research in portfolio management can be traced back to the mean-variance model proposed by Markowitz (1952). With the United Nations establishing the Sustainable Development Goals in 2015, investment approaches based on Environmental, Social and Governance (ESG) are rapidly becoming an important frontier issue in investment decision-making. Market participants are paying increasing attention to investment strategies that balance returns with social responsibility and sustainable development characteristics [Ling, A., Li, J., Wen, L., & Zhang, Y. (2023). When trackers are aware of ESG: Do ESG ratings matter to tracking error portfolio performance Econ. Model., 125, 106346.].

[0003] Over the past decade, research on the relationship between ESG factors and portfolio performance has undergone significant evolution, gradually shifting from proof-of-concept to systematic model integration. Within a well-structured investment framework, ESG factors do not require sacrificing risk-adjusted returns. Current research has constructed an ESG efficient frontier framework, incorporating ESG performance into the Sharpe ratio maximization objective, bridging the gap between sustainable preferences and portfolio efficiency. Subsequently, ESG factors have been more widely introduced into mean-variance models [Buckle, D. (2023). The futility of measuring relative performance of ESG portfolios if ESG investing improves the market performance. J. Asset Manag., 24(7)]. [601–607.]; Cesarone et al. (2022) found through a multi-objective optimization method that aggressive ESG objectives help identify portfolios with better financial performance (at least in the US context); to this end, they further incorporated downside risk into the ESG efficient portfolio method and found that ESG rating integration helps reduce the negative skewness of return distribution and reduce transaction costs; at the asset level, green features have been shown to have diversification advantages under specific market conditions, and impact investing also shows significant hedging characteristics in portfolio construction [Akhtaruzzaman, M., Banerjee, AK, Le, V., Moussa, F. (2024). Hedging precious metals with impact investing. Int. Rev. Econ. Finance, 89, 651–664.].

[0004] Effectively integrating ESG factors into portfolio optimization faces two main challenges in practice. First, significant differences in the quality of ESG ratings among different institutions exist, with objective rating discrepancies and incomplete data coverage continuously troubling investors [Caprioli, S., Foschi, J., Crupi, R., & Sabatino, A. (2025). Denoising ESG: Uncertainty-aware scoring through probabilistic imputation of missing data. Quant. Finance, 1–10.]. Avramov et al. (2022) found an inverse relationship between ESG uncertainty and market premium, and Yang et al. (2025) further revealed that ESG rating premiums have non-linear characteristics. Second, existing research is mostly conducted within a static framework, with insufficient attention paid to how ESG factors affect portfolio decisions under dynamic market conditions [Soupe, F., & Kovarcik, G. (2024). Impact of ESG objectives on a portfolio. J. Portf. Manag., [50(6),102–121.]; How to systematically manage ESG risks within a dynamic portfolio framework that maintains tracking objectives and financial performance remains an unsolved problem; Chinese authorized patent CN115907975B discloses a stock portfolio recommendation method based on multi-source information fusion of complex networks, proposing a deep learning model based on multi-source data fusion of gated recurrent units and graph convolution to improve the accuracy of stock prediction.

[0005] The tracking portfolio (TP) approach offers a potential solution to the aforementioned problems, but related research is still in its early stages. By incorporating downside risk control into index tracking models, it was found that combining TP strategies with ESG uncertainty can improve risk-adjusted returns. Furthermore, risk-adjusted performance can be improved within tracking error limits by constructing tracking portfolios targeting specific ESG dimensions (while controlling industry and regional weights). From a utility maximization perspective, it was found that portfolios incorporating ESG risk optimization exhibit stronger robustness under various market scenarios, further demonstrating that ESG-related factors capture the common changes in stock returns across periods, providing empirical support for viewing ESG as a systematic risk factor.

[0006] Existing publicly available patents and academic research can only achieve basic stock portfolio recommendations and simple ESG data fusion. They generally suffer from technical defects such as static model parameters, insufficient ability to fuse multi-source heterogeneous data, and inability to dynamically respond to changes in external data. They have not designed a dynamic ESG risk control framework for index tracking scenarios, and the integration of tracking portfolio strategies with ESG risk management systems is low. Based on the above-mentioned defects in existing technologies, developing a dynamic tracking portfolio management method and system driven by ESG risk information has become a technical problem that the industry urgently needs to solve. Summary of the Invention

[0007] The purpose of this invention is to overcome the technical shortcomings of existing index-tracking investment systems, such as static and fixed parameters, difficulty in integrating heterogeneous ESG data, inability of models to dynamically respond to market and risk changes, and reliance on manual operation. It provides an ESG risk information-driven dynamic tracking portfolio management method and system. Through computer data processing and dedicated optimization algorithms, it achieves dynamic parameter updates, adaptive model switching, and fully automated operation, ensuring system stability and computational efficiency while adapting to the business needs of sustainable investment.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] An ESG risk information-driven dynamic tracking portfolio management method, with the following specific steps:

[0010] Step 1: Build a data acquisition module based on the Python programming environment. This module captures market data for relevant securities via an internet interface, covering core indicators such as stock prices and daily trading volume, and simultaneously obtains ESG risk score data from Wharton Research Data Service (RepRisk). This data acquisition module runs on general-purpose computer hardware and can be built by those skilled in the art using conventional programming methods, without the need for specialized equipment or systems. RepRisk uses an event-driven methodology to continuously capture ESG disputes and adverse event records from public channels, which can be used for quantitative modeling of ESG-related downside risks in dynamic market environments. Its risk score range is set from 0 to 100, with 0 representing the optimal state and 100 representing the worst state. The lower the score, the better the company's overall performance in corporate responsibility fulfillment, risk management, and sustainable development practices.

[0011] Step 2: Construct a portfolio optimization model, assuming the entire investment period is T, and the investor manages a portfolio of M assets during this period; let... Let be the proportion of investment allocated to asset i in period t. Let $t$ be the corresponding rate of return on investment; correspondingly, the investment weight vector and return vector of all assets in period $t$ are denoted as $t$, ... and ;Utilizing ESG risk vectors The conditional expected return vector and the conditional variance-covariance matrix are as follows: and ;

[0012] The combined weighted average ESG risk score is defined as follows:

[0013] (1)

[0014] in A vector representing the ESG risk score of an asset; This represents the transpose of the investment weight vector in period t;

[0015] Step 3: Roll (1992) defined tracking error as an indicator of relative risk, with a weight of _____. The tracking portfolio and weight vector are The difference in returns between the benchmark portfolio (MV method); the weight vector of the tracking portfolio can be represented as:

[0016] (2)

[0017] in To adjust the weight vector; Let be the weight vector of the benchmark portfolio in period t; after incorporating ESG information, the objective is to minimize the adjusted weighted average ESG risk score. This refers to the ESG risk deviation relative to the benchmark portfolio; the minimum ESG risk TP optimization problem (P1) is formulated under the following five constraints:

[0018] (3)

[0019] in, For the ESG risk minimization tracking optimization model, the portfolio weight vector in period t is used. To optimize variables, the objective function This represents minimizing the weighted average ESG risk deviation of the tracking portfolio relative to the benchmark portfolio. Let be the weight vector of the benchmark portfolio in period t. The ESG risk score vector for the asset; Let be the conditional expected excess return vector for period t. It is an ESG state variable; Let be the conditional variance-covariance matrix for period t; It is a vector consisting entirely of 1s; Represents the maximum comprehensive ESG risk score; and These constraints represent the minimum excess return and maximum excess variance (risk) of the portfolio, respectively. Constraint (a) ensures that both expected return and risk estimates are conditioned on corporate ESG risk. Constraints (b) and (c) satisfy the requirements of completeness and non-negativity of weights. In addition, constraint (d) limits the downside of the adjusted excess portfolio return, while constraint (e) sets an upper limit on the adjusted excess portfolio risk, thereby ensuring that the difference between investment performance and the benchmark index is within a controllable range. These constraints work together to make the optimal portfolio approach the benchmark index in terms of return deviation and risk exposure, while reducing the ESG risk relative to the benchmark allocation.

[0020] The problem (P1) is solved using the Lagrange multiplier method, where the multipliers are respectively... , ,and The expression for the Lagrange function is as follows:

[0021] (4)

[0022] Here, the Lagrange multiplier , and This reflects the inherent trade-offs in the optimization process: Shadow prices that reflect overall investment constraints; This reflects the marginal benefit of relaxing the minimum excess return requirement in reducing ESG risks; This indicates the marginal cost of tightening excess variance constraints on ESG risk;

[0023] Step 4: Extend the portfolio optimization model by adopting a mean-variance (MV) optimization problem that considers ESG risk constraints; the objective is to maximize the MV objective function under the constraint that the ESG risk score does not exceed the maximum ESG risk score threshold; the MV optimization problem (P2) is formulated as follows:

[0024] (5)

[0025] in, Let be the portfolio weight vector for period t; Let be the weight vector of the benchmark portfolio in period t; Let be the conditional expected excess return vector for period t; Let be the conditional variance-covariance matrix for period t; It is a vector consisting entirely of 1s; The ESG risk score vector for the asset; Risk aversion factor ( >0), This represents the maximum comprehensive ESG risk score; given ESG information, investors can first select stocks with lower ESG risk scores for investment, and then optimize the asset weight vector in period t. To maximize the objective function;

[0026] Similarly, the Lagrange multiplier method is used to solve the problem (P2), where multipliers are used. and Thus, the Lagrange function is obtained:

[0027] (6)

[0028] in, It is a Lagrange function; Let be the portfolio weight vector for period t; Let be the weight vector of the benchmark portfolio in period t; Let be the conditional expected excess return vector for period t; Risk aversion factor ( >0); Let be the conditional variance-covariance matrix for period t; It is a vector consisting entirely of 1s; This is the ESG risk score vector for an asset. Represents the maximum comprehensive ESG risk score; Represents the shadow price under full investment constraints. The marginal cost of ESG risk constraints is relatively high. This indicates that investors need to sacrifice higher expected returns to achieve marginal improvements in ESG risk reduction, reflecting the trade-off between financial performance and sustainability goals;

[0029] Step 5: Optimization Model Selection Determination: During the initialization phase, the system pre-configures judgment logic for two types of operating modes. The system automatically calls the corresponding optimization model based on preset identifiers. There are two types of operating modes: one is the ESG risk minimization mode, which is suitable for scenarios where the core objective is to reduce the sustainable risk exposure of the portfolio while meeting the lower limit constraint of returns. The system automatically calls the first optimization model P1. The other is the return maximization mode, which is suitable for scenarios where the optimal risk-adjusted return is pursued under the premise that the comprehensive ESG score does not exceed a predetermined threshold. The system automatically calls the second optimization model P2. The above two types of models run mutually exclusively, are called individually, and are not activated in parallel.

[0030] Step 6: Automated Portfolio Adjustment: The system reads the optimal asset weight vector output by the model, calls the built-in portfolio rebalancing algorithm, collects the current actual portfolio weights at fixed intervals, compares the weight deviations through preset calculation formulas and calculates the rebalancing quantities of various assets, automatically generates trading instructions to update the portfolio allocation of various assets, and completes the dynamic adjustment of the portfolio.

[0031] This invention provides an ESG risk information-driven dynamic tracking portfolio management system, which is mounted on a general-purpose computer hardware platform. The hardware includes a processor, memory, network interface, and persistent storage media. Each functional module runs on the aforementioned hardware, with the processor as the computing core, and data transfer between modules is accomplished via an internal bus. The system consists of the following six functional modules:

[0032] The data acquisition module, located at the system input end, uses a network interface to retrieve daily market transaction data and ESG risk score data of the target assets from an external database. After data cleaning and standardization preprocessing, the structured data is unidirectionally transmitted to the dynamic parameter correction module.

[0033] The dynamic parameter correction module receives the structured data from the data acquisition module, uses the asset ESG risk score as the state variable, calculates the conditional expected return vector and the conditional variance covariance matrix, and outputs the above conditional parameters to the dual-model optimization solution module.

[0034] The dual-model optimization and solution module is the core computing unit of the system. It receives the conditional parameters from the dynamic parameter correction module and has built-in ESG risk minimization tracking optimization model and ESG threshold constraint mean variance optimization model. It calls the corresponding model according to the type of investment objective and uses the Lagrange multiplier method to solve for the optimal asset weight vector. The solution results are synchronously transmitted to the performance evaluation module and the data storage and interaction module.

[0035] The robustness verification module maintains a bidirectional connection with the data acquisition module and the dual-model optimization and solution module. By switching the ESG data source and adjusting the sample period, it drives the data to be re-input, triggering the dual-model optimization and solution module to recalculate and complete the policy robustness verification across data sources and sample periods.

[0036] The performance evaluation module receives the optimal weight vector and historical return data from the dual-model optimization solution module, calculates quantitative indicators such as cumulative portfolio value, annualized return, annualized volatility, Sharpe ratio, maximum drawdown, information ratio, Sortino ratio, and 95% conditional value at risk, and transmits the performance analysis results to the data storage and interaction module.

[0037] The data storage and interaction module, as the system's data hub, is connected to all the above modules, collects and stores historical transaction data, ESG score data, and calculation results from each module, and provides data retrieval and visualization output interfaces to user terminals.

[0038] The position adjustment module has a built-in position rebalancing algorithm, which compares the actual position with the target weight, calculates the adjustment amount, and automatically completes the position update.

[0039] This invention combines a dynamic parameter iteration mechanism, a dual-model constraint optimization algorithm, and an ESG risk quantification data processing mechanism to construct an adaptive portfolio optimization framework suitable for dynamic financial time-series scenarios. This addresses the technical shortcomings of traditional static modeling and single optimization structures, such as poor system adaptability, parameter lag, and lack of risk control. Compared with existing technologies, the main technical effects and advantages of this invention are:

[0040] 1. This invention addresses the technical problems of diverse ESG data sources and insufficient adaptability of static models by treating ESG risk as a dynamic state variable, enabling real-time updates of return vectors and covariance matrices, and improving the model's adaptability to volatile financial data. At the same time, it realizes systematic and quantitative management of ESG risk within the framework of index tracking algorithms, filling the technical gap of tracking models lacking dynamic ESG optimization design.

[0041] 2. This invention constructs two types of differentiated optimization models to achieve the ultimate minimization of ESG risks and the balanced optimization of returns and ESG risks, respectively. The optimal weights are accurately solved by the Lagrange multiplier method. The multiplier parameters can intuitively quantify the constraints and trade-offs between the three types of indicators: returns, risks, and ESG, effectively improving the interpretability of the model's operation logic.

[0042] 3. The optimized portfolio scheme of this invention, while controlling tracking error and ensuring that the calculation results are consistent with the benchmark index, reduces the overall ESG risk index value, reduces output deviation in extreme market environments, and optimizes risk-related calculation indicators, making the model's anti-interference ability significantly better than that of traditional tracking models without ESG constraints.

[0043] 4. This invention verifies the robustness of the method through multiple data sources and different time periods, making the model adaptable to various scenarios such as normal data scenarios and extreme shock data scenarios; the system architecture is simple, the algorithm is highly implementable, and it can be widely used in the sustainable investment-related data processing work of public funds and asset management institutions. Attached Figure Description

[0044] Figure 1 This is a schematic diagram of the overall architecture of the ESG risk-driven dynamic tracking portfolio management system according to an embodiment of the present invention.

[0045] Figure 2This is a comparison chart of the cumulative returns of four portfolio methods. Detailed Implementation

[0046] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. These embodiments are implemented based on the technical solution of the present invention, providing detailed implementation methods and operating procedures; however, the scope of protection of the present invention is not limited to the following embodiments.

[0047] The embodiment of the dynamic tracking portfolio management method considering ESG risks designed in this invention includes the following steps:

[0048] S1. Setting up the financial transaction system environment

[0049] A trading simulation environment of the financial market is built in the portfolio management system. Market information of relevant securities or stocks is input via the Internet (such as the S&P 100 index constituent stock database), including key data such as stock price and daily trading volume, as well as daily frequency RepRiskESG risk score data, covering the sample period from January 2019 to December 2020.

[0050] S2, ESG Conditional Portfolio Optimization Model Construction

[0051] An investment trading environment is constructed within the management system, and the financial market is statistically composed of M types of assets; an ESG condition optimization framework is designed, utilizing ESG risk vectors. Conditional estimation of the expected return vector and covariance matrix, i.e. and This conditional estimation method is consistent with the framework proposed by Merton (1980), which uses ESG risk scores as state variables, allowing the estimates of returns and covariance to be dynamically adjusted as market and sustainability conditions change.

[0052] In the presence of transaction costs, the portfolio return of M assets in period t, as well as the tracking error framework, are established according to the methods described in steps 2 to 4 of the above-described invention.

[0053] S3, ESG risk minimization tracking combination (TP-Min-ESG-Risk)

[0054] Solving the P1 optimization problem: Under the tracking combinatorial framework, with Given the objective function, the optimal weight vector is solved using the Lagrange multiplier method (Equation 4); where, Shadow prices that reflect full investment constraints; This reflects the marginal benefit of relaxing the minimum excess return requirement on reducing ESG risk; This reflects the marginal cost of tightening excess variance constraints on ESG risk. The first-order condition for obtaining the solution is... The formula is derived as follows:

[0055] (7)

[0056] in, This represents the ESG risk score vector of an asset. This represents the expected payoff vector under ESG conditions. This represents the tracking combined weight vector. Represents the benchmark portfolio weight vector. This represents a vector consisting entirely of 1s.

[0057] The optimal portfolio vector can be represented as:

[0058] (8)

[0059] The optimal portfolio vector can be viewed as a benchmark portfolio, adjusted by a correction term that balances ESG risk reduction with return enhancement and variance control; the relative importance of each factor is determined by the Lagrange multiplier. , and Decision; Next, substituting equation (8) into constraint (b) in equation (3), we obtain the following expression:

[0060] (9)

[0061] After expansion, the following expression can be derived:

[0062] (10)

[0063] set up , , Then we have:

[0064] (11)

[0065] The following expression can be further derived:

[0066] (12)

[0067] In the above expression, , and This means that by interpolating the corresponding row vector with... The scalar obtained by performing the inner product; and in equations (15) and (16), , and They respectively represent their relationship with The inner product; similarly, substituting equation (8) into the constraint (d) of equation (3) yields:

[0068] (13)

[0069] After expansion, the following two expressions can be obtained:

[0070] (14)

[0071] (15)

[0072] Substituting equation (12) into equation (15), we obtain the following expression:

[0073] (16)

[0074] Rearrange the terms in equation (16) and include the terms involved. The items are categorized on the left. The lower bound can be represented as:

[0075] (17)

[0076] Similarly, substituting equation (8) into the constraint (e) in equation (3) yields:

[0077] (18)

[0078] Expand to get information about and The inequality; then, substituting equation (12) back into the inequality, we get about The inequalities can be determined by solving these equations and inequalities based on equations (12), (17) and (18). The range of values ​​for which can be determined, and thus the range of values ​​for which can be determined. and The value of .

[0079] S4, MV tracking combined ESG risk constraints (TP-MV ESG-Risk-Cons) implementation

[0080] To achieve the P2 optimization problem: Under the MV tracking and combination framework, with the goal of maximizing the MV objective function, the constraint is imposed that the ESG risk score does not exceed the maximum threshold. The shadow price represents the price under full investment constraints. The marginal cost reflecting ESG risk constraints is relatively high. This suggests that investors need to sacrifice more expected returns to achieve marginal improvement in ESG risk.

[0081] The primary condition for solving the problem is defined as follows: The following equation can be obtained: The optimal portfolio vector can be represented as:

[0082] (19)

[0083] Solve for the Lagrange multiplier , The method is similar to the steps described for P1.

[0084] S5. Automatic Model Determination and Execution

[0085] The system pre-writes two types of operation identifiers and decision logic during the initialization phase. The entire process is automated by the computer program, handling identification and model invocation. When the system detects that the current operation identifier is ESG risk minimization mode, it automatically calls the aforementioned P1 model to solve for the weights. When the system detects that the current operation identifier is profit maximization mode, it automatically calls the aforementioned P2 model to solve for the weights. The system employs a mutual exclusion mechanism, ensuring that only one model is activated within the same operating cycle; the two models will not operate simultaneously. After the model solves, it outputs the corresponding optimal asset weight vector, providing data for subsequent portfolio adjustments.

[0086] S6. Setting the Benchmark Model

[0087] To verify the effectiveness of the method proposed in this invention, two other portfolio methods were selected as benchmarks, and together with the P1 and P2 models of this invention, a total of four strategies were constructed for horizontal performance comparison.

[0088] 1) TP-Min-ESG-Risk (P1 model of this invention): The tracking portfolio method proposed in this invention is based on minimum ESG risk optimization and has minimum excess return and maximum excess variance constraints (Equation 3).

[0089] 2) TP-MV ESG-Risk-Cons (P2 model of this invention): Applying maximum ESG risk constraints based on the MV method within the TP framework (Equation 5);

[0090] 3) TP-MV ESG-Risk Tilt: A TP method based on MV optimization that tilts portfolio weights through ESG risk scoring;

[0091] 4) TP-MV Non-ESG: MV optimization TP method that does not incorporate any ESG risk score;

[0092] Table 1 provides an overview of the four portfolio management approaches;

[0093] Table 1. Overview of the Four Portfolio Approaches

[0094]

[0095] The invocation of models P1 and P2 is determined based on the investment objective type pre-set by the investor during the initialization phase. When the investment focus is on reducing the portfolio's sustainable risk exposure and strictly controlling negative ESG exposure, model P1 is invoked, with minimizing the weighted average ESG risk score as the primary objective, and the lower limit of return and the upper limit of variance as hard constraints. When the investment focus is on seeking the optimal risk-adjusted return under the premise of controllable ESG risk, model P2 is invoked, with maximizing the mean-variance objective function as the primary objective, and the upper limit of the comprehensive ESG score as a hard constraint. Both models share the same underlying parameter update mechanism, using the ESG risk score as the state variable to perform conditional dynamic estimation of the expected return vector and covariance matrix. In terms of optimization objectives and constraint structure, P1 aims to minimize ESG risk and uses financial indicators as constraints, while P2 aims to maximize financial returns and uses ESG thresholds as constraints. Their objectives and constraints are inversely related, forming a complete dynamic ESG tracking investment strategy system covering different investment preferences. Each model is invoked individually according to its objective type and cannot be used concurrently.

[0096] S7, Robustness Verification and Extension Analysis

[0097] This study utilizes S&P 100 index constituent stock data for daily analysis. A stratified sample approach is employed for testing, using RepRisk ESG risk score data from January 2019 to December 2020 as the base sample. This sample range covers periods of stable market operation and extreme volatility, effectively verifying the model's performance under abnormal market conditions. After completing the basic empirical testing, the sample range is extended to 2024, employing Refinitiv ESG rating scores to conduct a robustness extension analysis across data sources and over a longer period. This validates the robustness of four portfolio strategies, assessing operational consistency under different market conditions. Based on Refinitiv scores, an ESG gap is constructed to re-evaluate the four portfolio strategies, verifying the operational stability and consistency of the dual-model optimization framework and the core objective of ESG risk minimization under different ESG data sources, market institutions, and long-term samples.

[0098] S8, Portfolio Performance Evaluation

[0099] The system uses a comprehensive set of performance metrics to evaluate each portfolio approach, including cumulative portfolio value (APV), annualized return, annualized volatility, Sharpe ratio, maximum drawdown (MDD), ESG risk score and information ratio, as well as Sortino ratio and 95% conditional value at risk (CVaR), and employs the Ledoit-Wolf bootstrapping test to assess the statistical significance of differences in Sharpe ratios.

[0100] (1) Accumulated Portfolio Value (APV): It reflects the increase in portfolio value over time and is a measure of investment return.

[0101] (20)

[0102] in, The initial portfolio value is typically set to 1; T represents the total number of periods. This represents the transpose of the weight vector. This represents the rate of return vector.

[0103] (2) Annualized rate of return: Based on the cumulative portfolio value, it is discounted over time to measure the annual return and appreciation level of the portfolio. It is the core quantitative indicator for evaluating the long-term performance of the portfolio.

[0104] (twenty one)

[0105] Where N is the number of investment periods within the year, which is usually set to 252 trading days.

[0106] (3) Annualized volatility: It is obtained by annualizing the standard deviation of daily returns combined with the number of trading days in a year, and is used to characterize the volatility of portfolio returns and the overall risk level.

[0107] (twenty two)

[0108] In the formula: Indicates the daily rate of return. This represents the average rate of return.

[0109] (4) Annualized Sharpe ratio: It can effectively measure the excess investment return corresponding to a unit of risk and is used to comprehensively evaluate the quality of the portfolio's risk-adjusted returns.

[0110] (twenty three)

[0111] in, This indicates the annualized Sharpe ratio. This represents the annualized return. Indicates annualized volatility. This is the risk-free interest rate.

[0112] (5) Maximum drawdown (MDD): This measures the maximum value loss a portfolio may experience over its entire lifespan, i.e., the maximum potential loss a portfolio may suffer.

[0113] (twenty four)

[0114] in, This represents the portfolio value at period t. This represents the portfolio value in period j. and They represent the first The total value of the portfolio at any given time; generally, the higher the MDD value, the more volatile and risky the investment.

[0115] (6) Annualized Information Ratio: Reflects the ability of an investment to generate excess returns relative to a benchmark and the stability of these excess returns; it is the final portfolio indicator.

[0116] (25)

[0117] in, This represents the annualized return of the portfolio. This is the annualized benchmark return. The standard deviation of excess returns.

[0118] (7) Sortino Ratio: Adjusts returns to reflect downside risk by penalizing negative bias and excluding upside volatility;

[0119] (26)

[0120] in, This represents the annualized downward standard deviation based on negative return observations.

[0121] (8) 95% Conditional Value at Risk (CVaR): Used to measure expected daily loss above the 5th percentile of the return distribution;

[0122] (27)

[0123] in, This refers to the set of trading days whose returns are below the 5th percentile threshold. This indicates the daily rate of return.

[0124] S9. Position Rebalancing and Automatic Rebalancing Execution

[0125] The system incorporates a standardized position rebalancing algorithm, employing a timed triggering mechanism based on trading days. It first collects the current account's total assets and the actual weights of each asset class, then reads the optimal target weight vector output by the model. Finally, it calculates the asset rebalancing quantity for each asset class according to the following formula:

[0126] (28)

[0127] in, Total assets in the account. Let i be the target weight. The actual weight of asset i; when At that time, a buy order is generated; At that time, a buy order is generated; If no adjustments are made, the system will automatically distinguish between buy and sell operations based on the calculation results and generate standardized trading instructions. After the instructions are sent to the trading interface, the system will complete the update of the holdings of all asset classes. After the holdings are updated, the system will automatically store the latest holdings data and enter the next round of data collection, parameter update and model calculation cycle to realize dynamic and automated management of the entire investment portfolio.

[0128] This invention provides an embodiment of an ESG risk information-driven dynamic tracking portfolio management system, wherein each functional module is configured as follows: Figure 1 The connections shown operate in a coordinated manner.

[0129] The system uses market information and ESG information as external inputs. The market information includes stock prices, number of stocks, and trading data. The data acquisition module captures daily market data and ESG score data from external data sources, and after cleaning and preprocessing, the structured data is passed to the dynamic parameter correction module.

[0130] The dynamic parameter correction module uses the ESG risk score as the state variable, iteratively updates the conditional expected return vector and the conditional variance-covariance matrix, and inputs the conditional parameters into the dual-model optimization solution module. The dual-model optimization solution module calls either the ESG risk minimization tracking optimization model or the ESG threshold constraint mean-variance optimization model according to the investment objective type. Under the dual constraints of minimum return and maximum volatility, it constructs an adaptive investment model, uses the Lagrange multiplier method to solve for the optimal asset weight vector, and the solution results are synchronously transmitted to the performance evaluation module and the data storage and interaction module.

[0131] The robustness verification module switches the data source and sample period, driving the data acquisition module and the dual-model optimization solution module to recalculate and complete the strategy verification; the performance evaluation module calculates various quantitative indicators and then transmits the results to the data storage and interaction module; the data storage and interaction module collects all the running data and outputs the visualized analysis results to the user terminal.

[0132] In the above process, the portfolio tracking subsystem undertakes the task of benchmark index tracking, the ESG risk minimization investment system subsystem completes the ESG conditional optimization solution, and the portfolio strategy evaluation, recommendation and management subsystem is responsible for performance quantification and dynamic portfolio adjustment. The three subsystems operate collaboratively and are connected in sequence. Each module is deployed on a general-purpose computer hardware platform, with the processor as the computing core. Data transmission between modules is completed through an internal bus, and the network interface is responsible for the real-time access of external market data and ESG score data. Ultimately, dynamic portfolio management that balances tracking accuracy, financial returns and ESG risk control is achieved.

[0133] Figure 2 This is a graph showing the cumulative portfolio returns of the method described in this invention and various comparative methods on the S&P 100 index constituent stocks. This experiment uses daily market data and ESG risk score data from January 2019 to January 2021. The comparison objects include the tracking minimum ESG risk portfolio proposed in this invention, the tracking portfolio under ESG risk constraints, the tracking minimum ESG risk allocation portfolio, and the tracking portfolio that does not consider ESG risk. The horizontal axis is time, and the vertical axis is cumulative return. The experiment fully covers the stable market operation stage, the extreme volatility stage, and the valuation repair stage. In terms of cumulative returns at the end of the period, TP-Min-ESG-Risk has a return of approximately 2.12, an annualized return of 44.60%, and a Sharpe ratio of 1.30, ranking first among the four methods. TP-MV-ESG-risk-cons has a cumulative return of approximately 2.01, an annualized return of 41.44%, which is about 5.5% lower than TP-MV-Non-ESG. TP-MV-Non-ESG has a cumulative return of approximately 1.45, which is about 46.2% lower than TP-MV-ESG-risk-tilt. TP-MV-ESG-risk-tilt has a cumulative return of approximately 1.35, which is about 57.0% lower than TP-MV-ESG-risk-tilt. As shown in Table 2, in terms of downside risk, during the extreme market volatility at the beginning of 2020, the maximum drawdown of TP-Min-ESG-Risk was 28.61%, lower than TP-MV-ESG-risk-cons' 34.02%, TP-MV-ESG-risk-tilt's 32.47%, and TP-MV-Non-ESG's 32.41%. Regarding sustainable risk management, the ESG risk score of TP-Min-ESG-Risk is 14.05, lower than TP-MV-ESG-risk-tilt's 29.59 and TP-MV-Non-ESG's 31.73, indicating that this invention is significantly effective in reducing ESG risk exposure. During the valuation repair phase, TP-Min-ESG-Risk recovered the fastest, being the first to return to the level of the stable market phase and continuously widening the return gap with other portfolios. In terms of overall performance, TP-Min-ESG-Risk has the highest annualized return and information ratio among the four methods, and its Sortino ratio of 1.67 is also higher than the other three methods. The Sharpe ratio of TP-MV-ESG-risk-cons (1.36) is slightly higher than that of TP-Min-ESG-Risk (1.30), but its annualized return, information ratio, and ESG risk management effect are all weaker than the latter, and its overall performance is not as good as this invention, thus verifying the actual effectiveness of the dual-model framework.

[0134] Table 2. Comparison of Performance Metrics for Four Portfolio Approaches

[0135]

[0136] This invention embeds the goal of minimizing ESG risk into a dynamic optimization framework for tracking investment portfolios. Through time-varying estimation of ESG conditional returns and covariance, dual constraints of minimum return and maximum volatility, and collaborative optimization of dual models, it achieves a unified approach to tracking benchmarks, financial returns, risk control, and ESG sustainability goals. Simultaneously, this invention introduces user interaction and visualization modules, transforming complex model results into intuitive interactive interfaces and explanatory information, addressing the issues of high technicality and poor interpretability in traditional financial models. The main technical challenge of this invention lies in how to integrate non-financial ESG risk quantification into a multi-constraint optimization model while maintaining controllable tracking error, and ensuring the stability and efficiency of portfolio weights under conditions of severe market volatility and uncertainty in ESG data. Furthermore, it transforms the complex underlying model logic into user-understandable and interactive visualizations, improving the usability and acceptance of the solution. This invention addresses these challenges through dynamic conditional estimation, analytical solution using the Lagrange multiplier method, and interactive visualization design, enabling the portfolio to maintain robust return performance and risk control capabilities even in extreme market environments, while significantly improving user experience and the scalability of the solution.

[0137] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention; any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A dynamic tracking portfolio management method driven by ESG risk information, executed by computer equipment, characterized in that, Includes the following steps: S1. Multi-source data acquisition: Daily market data and ESG risk score data of the target asset are acquired through the network. The market data includes at least stock price and daily trading volume. The ESG risk score data is an event-driven risk score with a score range of 0-100. The lower the score, the lower the sustainable risk of the asset. S2. ESG Conditional Data Processing: Using the asset's ESG risk score as the state variable, an ESG risk vector is constructed. Based on the ESG risk vector, the conditional expected return vector and conditional variance covariance matrix are obtained, so that the return and risk parameters are dynamically updated with the market environment and ESG risk. S3. Constructing an ESG risk minimization tracking optimization model P1: Based on the tracking portfolio framework, five types of constraints are set: minimum excess return, maximum excess variance, non-negative asset weights, full asset investment, and downside control of excess returns. The first optimization model P1 is constructed with the goal of minimizing the asset-weighted average ESG risk score. The Lagrange multiplier method is used to solve the first optimization model to obtain the optimal asset weight vector. S4. Constructing an ESG threshold-constrained mean-variance optimization model P2: Based on the tracking portfolio framework, a maximum comprehensive ESG risk score threshold is set, and a second optimization model P2 is constructed with the goal of maximizing risk-adjusted returns. The optimal asset weight vector under the constraints is obtained by using the Lagrange multiplier method. S5. Optimization Model Selection Determination: The system automatically matches and calls the corresponding model based on the running identifier; there are two running modes: ESG risk minimization mode calls the first optimization model P1; profit maximization mode calls the second optimization model P2; the two types of models are called separately and are not enabled in parallel. S6. Automated portfolio adjustment: Based on the optimal asset weight vector obtained by solving, the preset portfolio rebalancing algorithm is called to compare the actual portfolio weights, calculate the adjustment quantity, and automatically update the asset portfolio allocation to achieve dynamic portfolio management.

2. The method of claim 1, wherein, In step S2, the formula for calculating the asset-weighted average ESG risk score is as follows: ,in, Let be the asset weight vector for period t. This represents the ESG risk score vector of an asset.

3. The method according to claim 1, characterized in that, In step S3, the objective function of the first optimization model is: in, For the ESG risk minimization tracking optimization model, the portfolio weight vector in period t is used. To optimize variables, the objective function This represents minimizing the weighted average ESG risk deviation of the tracking portfolio relative to the benchmark portfolio. Let be the weight vector of the benchmark portfolio in period t. The ESG risk score vector for the asset; Let be the conditional expected excess return vector for period t. It is an ESG state variable; Let be the conditional variance-covariance matrix for period t; It is a vector consisting entirely of 1s; and These are the minimum excess returns for the investment portfolio; The constraints include: (a) return and risk parameters are estimated with ESG risk as a condition; (b) the sum of asset weights is 1; (c) the weight of each individual asset is greater than or equal to 0; (d) a lower limit constraint on excess portfolio returns; and (e) an upper limit constraint on excess portfolio variance.

4. The method according to claim 1, characterized in that, In step S3, the first optimization model is solved by constructing the Lagrange function. The Lagrange function includes the shadow price under full investment constraints, the minimum excess return marginal benefit parameter, and the excess variance constraint marginal cost parameter. Each parameter participates in the calculation and solution of the optimal solution of the model.

5. The method according to claim 1, characterized in that, In step S4, the objective function of the second optimization model is: in, Let be the portfolio weight vector for period t; Let be the weight vector of the benchmark portfolio in period t; Risk aversion factor ( >0), Let be the conditional expected excess return vector for period t; Let be the conditional variance-covariance matrix for period t; It is a vector consisting entirely of 1s; This is the ESG risk score vector for an asset. This represents the maximum comprehensive ESG risk score.

6. A dynamic tracking portfolio management system driven by ESG risk information, characterized in that, For performing the management method according to any one of claims 1-5, comprising: The data acquisition module is used to collect daily market transaction data and ESG risk score data of the underlying assets, and to complete data cleaning and standardization preprocessing. The dynamic parameter correction module is used to dynamically calculate the conditional expected return vector and conditional variance-covariance matrix with the asset's ESG risk score as the state variable. The dual-model optimization solution module includes an ESG risk minimization tracking optimization model and an ESG threshold constraint mean-variance optimization model, which solves for the optimal asset weight vector using the Lagrange multiplier method. The robustness verification module interacts bidirectionally with the data acquisition module and the dual-model optimization and solution module. By switching different ESG data sources and adjusting the sample period to re-import data, it triggers the dual-model optimization and solution module to repeat the calculation and complete the robustness test of the model strategy. The performance evaluation module is used to receive the optimal weight vector and historical return data, calculate multi-dimensional quantitative evaluation indicators, and output analysis results. The data storage and interaction module is used to store historical transaction data, ESG score data, and model calculation results, enabling real-time data retrieval and visualization output. The position adjustment module has a built-in position rebalancing algorithm, which compares the actual position with the target weight, calculates the adjustment amount, and automatically completes the position update.

7. The system of claim 6, wherein, The dual-model optimization solution module has a built-in weight correction algorithm that decomposes the optimal portfolio vector into a benchmark portfolio vector and an ESG risk correction vector, and dynamically adjusts the asset allocation weights through the correction vector.

8. The system of claim 6, wherein, The performance evaluation module has built-in indicator calculation formulas, including the cumulative portfolio value formula, annualized return formula, and 95% conditional value at risk formula. It also integrates a downside risk calculation algorithm and outputs the Sortino ratio and maximum drawdown data.

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