## 4.1 Methods of financial performance evaluation

There are many methods of financial performance evaluation, from the original DuPont analysis method to the balanced scorecard method, economic value-added method and factor analysis method and the analytic hierarchy process of statistical method measurement, which gradually adapt to the current market situation and the requirements of the times. The DuPont analysis method focuses on a company's return on equity (ROE). Emphasizing the intrinsic relationship between the various financial indicators, followed by a more in-depth analysis, focusing on long-term and short-term debt solvency, profitability and overall operating conditions, the basic formula is:

$$\text{"Roe"= "Sales margin"}\left(\text{N}\text{P}\text{M}\right)\times \text{ "Asset Turnover" }\left(\text{A}\text{U}\right)\times \text{ "Equity Multiplier"(EM)}$$

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The economic value added is the minimum return for the enterprise manager to make the same amount of investment in the enterprise and obtain the net profit under the same operational risk level, which can represent the difference between the total profit after tax and the total capital of the enterprise. It also includes the cost of equity capital and the cost of debt capital. The specific calculation formula is as follows:

$$\text{E}\text{V}\text{A}=\text{O}\text{p}\text{e}\text{r}\text{a}\text{t}\text{i}\text{n}\text{g} \text{n}\text{e}\text{t} \text{p}\text{r}\text{o}\text{f}\text{i}\text{t} \text{a}\text{f}\text{t}\text{e}\text{r} \text{t}\text{a}\text{x}-\text{t}\text{o}\text{t}\text{a}\text{l} \text{c}\text{o}\text{s}\text{t} \text{o}\text{f} \text{c}\text{a}\text{p}\text{i}\text{t}\text{a}\text{l}；\text{w}\text{h}\text{i}\text{c}\text{h} \text{i}\text{s}：\text{E}\text{V}\text{A}=\text{N}\text{O}\text{P}\text{A}\text{T}-\text{C}\text{a}\text{p}\text{i}\text{t}\text{a}\text{l} \text{C}\text{h}\text{a}\text{r}\text{g}\text{e}$$

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Economic value added is the embodiment of the ability to create value for shareholders and the ability to operate capital, and EVA, or final value, is the result of financial performance. Compared with the balanced scorecard method, economic value-added is stricter in decision-making, and it also avoids decision-makers from misinterpreting performance indicators. For example, enterprise managers may pay more attention to products with lower production costs to reduce average costs; in order to expand reproduction, blindly seeking greater financial leverage and other situations that have a negative impact on company operations, managers can avoid shortsightedness. This method is more intuitive and scientific, and can change the vision of managers from a purely paper-based vision to actively realize the long-term investment return of the enterprise.

## 4.2 Screening methods of financial risk indicators

For the screening of financial risk indicators, this paper chooses the regression analysis method of risk measurement method, and chooses the relatively simple but high precision least square regression method in the regression analysis method.

The least squares regression model is defined as follows:

$$\text{y}=\text{X}{\beta }+{\epsilon }$$

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Define S(β) as the mean squared error of the linear model:

$$\text{S}\left({\beta }\right)=\sum _{\text{i}=1}^{\text{n}} ={{\epsilon }}_{\text{i}}^{2}=(\text{Y}-\text{X}{\beta }{)}^{{\prime }}(\text{Y}-\text{X}{\beta })$$

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Since S(β) is a convex function, there must be a minimum value for S(β). Write S(β) as follows:

$$\text{S}\left({\beta }\right)={\text{Y}}^{{\prime }}\text{Y}+{\beta }{\text{X}}^{{\prime }}\text{X}{\beta }-2{{\beta }}^{{\prime }}{\text{X}}^{{\prime }}\text{Y}$$

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And take its partial derivative with respect to β, we have:

$$\begin{array}{c}\frac{\partial \text{S}\left({\beta }\right)}{\partial {\beta }}=2{\text{X}}^{{\prime }}X\beta -2XY\\ \end{array}$$

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$$\frac{{\partial }^{2}\text{S}\left({\beta }\right)}{\partial {{\beta }}^{2}}=2{\text{X}}^{{\prime }}\text{X}$$

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Set the above equation equal to 0 to get the rule equation:

$${\text{X}}^{{\prime }}\text{X}\text{b}={\text{X}}^{{\prime }}\text{Y}$$

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If X is a full rank matrix of column vectors, then X'X must be positive definite and must have a unique solution, that is:

$$\text{b}={\left({\text{X}}^{{\prime }}\text{X}\right)}^{-1}{\text{X}}^{{\prime }}\text{Y}$$

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The least squares estimate of β can be expressed as

$${\widehat{{\beta }}}^{\text{L}\text{S}\text{E}}=\text{a}\text{r}\text{g}\text{m}\text{i}\text{n}\sum _{\text{i}=1}^{\text{n}} {\left({\text{y}}_{\text{i}}-\sum _{\text{j}=1}^{\text{p}} {\text{x}}_{\text{j}}{{\beta }}_{\text{j}}\right)}^{2}={\left({\text{x}}^{\text{T}}\text{x}\right)}^{-1}{\text{X}}^{\text{T}}\text{y}$$

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The above formula is to find the beta coefficient that minimizes RSS. In a typical form, the mean squared error of the parameter estimates for the βLSE coefficients is:

$$\text{M}\text{S}\text{E}\left(\widehat{{\beta }}\right)={{\sigma }}^{2}\sum _{\text{i}=1}^{\text{p}} \frac{1}{{{\lambda }}_{\text{i}}}$$

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The basis of SVM is to find the optimal hyperplane classification method under linear disjoint conditions. First give a set of variables:

$$\text{S}=\left\{{\left({\text{x}}_{\text{i}}\cdot {\text{y}}_{\text{i}}\right)}_{\text{i}=1}^{\text{n}}\mid {\text{x}}_{\text{i}}\in {\text{R}}^{\text{d}},{\text{y}}_{\text{i}}\in \{+1,-1\},\text{i}=\text{1,2},\cdots ,\text{n}\right\}$$

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Where: xi is the data; yi is the category to which the data belongs.

If the hyperplane equation wx + b = 0 achieves optimal plane classification (selecting samples when the classification separation is the largest), then the idea of optimal plane classification can be replaced by the following equations and inequalities, we call the following goals respectively objective function and constraints:

$$\left\{\begin{array}{c}min\left(\frac{1}{2}\parallel \text{w}{\parallel }^{2}\right)\\ \text{ }\text{s}\text{.}\text{t}\text{.}\text{ }{\text{y}}_{\text{i}}\left(\text{w}{\text{x}}_{\text{i}}+\text{b}\right)\ge 1(i=\text{1,2},\cdots n)\end{array}\right.$$

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Where: w represents the weight that determines the direction of the split plane; b represents the offset value that makes the plane linearly separable.

In many cases, some samples are often not classified correctly. In order to ensure the classification accuracy, a relaxation factor ξi ≥ 0 is introduced here, i = 1, 2, n, and the optimization problem can be expressed as:

$$\left\{\begin{array}{c}min\left(\frac{1}{2}\parallel \text{w}{\parallel }^{2}\right)+C\sum _{\text{i}=1}^{\text{n}} {{\xi }}_{\text{i}}\left({{\xi }}_{\text{i}}\ge 0\right)\\ \text{ }\text{s}\text{.}\text{t}\text{.}\text{ }{\text{y}}_{\text{i}}\left\{\begin{array}{c}{\text{y}}_{\text{i}}\left(\text{w}{\text{x}}_{\text{i}}+\text{b}\right)\ge 1-{{\xi }}_{\text{i}}\\ C\ge 0\end{array}(\text{i}=\text{1,2},\cdots \text{n})\right.\end{array}\right.$$

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where: c(cost) is the penalty factor.

There is a natural conflict between the hyperplane classification accuracy of the model calculation method and the complexity of the hyperplane calculation, and it is difficult to reconcile, so we need to find a coefficient that balances the two. Therefore, a penalty factor c(cost) is created. The above function can easily be considered as the solution of quadratic programming, and the optimal solution to the problem is obtained by solving the Lagrangian function.