# Research on the Prediction of Nonbreakeven Financial Products’ Yield of Commercial Banks Based on Machine Learning

Authors: Xiaoli Tong; Jiangjiao Duan
Journal: Mobile Information Systems
 (2022)

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## Abstract

Bank wealth management solutions have now become one of the most important components of the financial industry after nearly two decades of continuous development. However, there are still problems such as an imperfect pricing model and an ambiguous pricing mechanism. In this paper, we use machine learning to predict the yield of nonguaranteed financial products, and after model training and prediction, both the random forest model and the LightGBM model have high applicability; that is, machine learning can be effectively used in the yield forecasting process.


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## Body

## 1. Introduction

2018 was a significant turning point for bank wealth management business. With the release of the “New Asset Management Regulations,” bank wealth management products have shown a trend of nonguaranteed and net worth in line with policy requirements. Yueqiu and Bo believe that capital-guaranteed wealth management will gradually withdraw from the market and the main task of commercial banks in the future is to actively transform products according to policies and to transparently disclose daily net worth. In fact, nonguaranteed wealth management products are off-balance sheet businesses of banks and can be classified as shadow banking. Due to its high risk and rapid development trend in recent years, shadow banking has attracted great attention from supervisory authorities and scholars [1].The availability of huge data and the development of a large number of scientific computing tools have fostered the use of machine learning in recent years, as computer science and technology have advanced. Although machine learning has problems, it is still a relatively new topic in asset pricing. However, it is undeniable that in a rapidly changing financial market with a huge amount of data, it is difficult to find the relationship between variables quickly and accurately with traditional forecasting models. Therefore, based on the method of machine learning, we will analyze the rate of return of wealth management products of Chinese commercial banks and predict the rate of return according to its influencing factors.The rest of the study is organized as follows: Section2 overviews the background. Section 3 discusses the theoretical analysis of the proposed concepts. Section 4 discusses the model, and in section 5, we explore the training and prediction of the suggested work. Section 6 concludes the article.


## 2. Background

With the development of bank wealth management products, scholars have begun to pay attention to the influencing variables of product yield. Pelster and Schertler [2] proposed that the most critical impact indicator is the way of capital operation. Acharya et al. [3] made an empirical analysis of wealth management products issued by 25 banks in the past seven years and proposed that the number of wealth management products due this year and the number of new issuance will have an impact on the yield. After empirical model testing, Warne and Sharma [4] determined that investors’ investing patterns and investment goals will have a role, with income being the most important element. Furthermore, freshly produced wealth management products are increasingly popular among investors. Based on the perspective of regulatory policy changes, Na [5] concluded that the introduction of regulatory policies will have a short-term inhibitory effect on the return of wealth management products, and the product term and market interest rate are the decisive factors for the return of wealth management products. Shiyang et al. [6] believe that, on the one hand, commercial banks are subject to strict loan-to-deposit ratio control, and on the other hand, due to their poor ability to absorb deposits, they cannot obtain sufficient funds to expand their business scale and usually need to issue wealth management products as a substitute for deposits. . Therefore, commercial banks with poor deposit-taking ability will tend to formulate higher expected product returns.Some scholars have also conducted research on the prediction of the yield. Some scholars have also conducted research on the prediction of the rate of return. Ronghua et al. [7] classified financial products according to their risk levels according to the nature of bank financial products and then used a semiparametric model with random effects to construct and analyze the yield curve of financial products. Chunling et al. [8] summarized the research progress on the predictability of capital market returns and found that a machine learning method is a research hotspot in recent years.Gan et al. [9] suggested a deep learning-based strategy for option pricing that can produce more accurate results at a faster rate. Li et al. [10] generated the stock technical index value using the stock’s daily frequency price and trading volume data and then utilized the derived technical index value as an input variable to anticipate the stock price rise or decline in a few days. Pan et al. [11] used neural networks to predict the stock return rate to capture the nonlinear relationship between the three factors of the market portfolio return rate, book-to-market value ratio, and market value. Chen [12] conducted a series of studies on the pricing of catastrophe bond risk spreads and compared the effects of machine learning models and traditional regression models.Furthermore, machine learning can be applied in fields such as risk prediction. Fang and Luo [13] built a risk indicator alarm mechanism using the random forest algorithm to separate the risk alarm indicator variables into two categories: enterprise characteristics and business conduct.Some scholars have also compared the application of various algorithms. Breiman [14] believes that the random forest algorithm has obvious superiority. Due to the theorem of large numbers, using this algorithm will not overfit the model. Kampichler et al. [15] compared the practical results of five machine learning algorithms: decision tree, random forest, artificial neural network, support vector machine, and rule-based fuzzy model and finally proposed that the prediction effect of the random forest is the best.


## 3. Theoretical Analysis

The yield of wealth management products should be impacted heavily by the nature of the product itself. The longer the money is invested, the greater the uncertainty investors bear and the higher the liquidity risk they face. In addition, the risk effect and the threshold effect will also have an impact on the time value of capital, capital liquidity, and investment risk of investment, which are reflected in the product’s yield.There are also some variations between banks. State-owned commercial banks are controlled directly by state-owned capital and are subject to greater regulation. Although wealth management-issued products are not legally guaranteed, they are actually implicitly guaranteed by state credit to investors, and banks will be more cautious when pricing assets.In addition, smaller banks often need to broaden their funding sources to expand their business scale. The release of wealth management products in asset management business is a form. Therefore, in order to improve operational efficiency and also to absorb funds, formulating higher yields may become a way for commercial banks to increase the scale of wealth management business.Macroeconomic changes can have a large and far-reaching impact on the financial industry. The position in other marketplaces should also be considered. The interbank market position represents the liquidity of funds in the interbank market and, thus, indirectly reflects the bank’s funding channels. In addition, a considerable part of funds raised after the issuance of wealth management products will actually be invested in the fund pool for operation and management, and part of the fund pool involves the stock market.Therefore, we discuss the independent variables that affect the yield of wealth management products from four aspects: issuing banks, product design, macroeconomics, and other markets. The variables are shown in Table1.Table 1
Independent variables.
VariableFeatureLength of the commission periodPeriodRiskRiskThresholdThresholdBank natureBankAsset sizeSizeNumber of wealth management products issued in the previous yearQuantityCapital adequacy ratioCrDeposit ratioLdLiquidity ratioLrProvision coveragePcGross national productGDPBroad money supplym2National consumptionCPIFintech indexFintechInterbank marketShiStock marketPrice


## 4. Model

### 4.1. Multiple Linear Regression Model

The multiple linear regression model is usually used to study the relationship between a dependent variable and multiple independent variables, which is represented by a matrix.We first use the multiple linear regression model to make regression predictions on the two sample sets and set up model 1 based on the analysis of influencing factors:(1)rate_maxi=α+β1periodi+β2riski+β3thresholdi+β4banki+β5sizei+β6quantityi+β7cri+β8lri+β9ldi+β10pci+β11gdpi+β12m2i+β13cpii+β14fintechi+β15shii+β16pricei.Model 2 is as follows:(2)rate_mini=α+β1periodi+β2riski+β3thresholdi+β4banki+β5sizei+β6quantityi+β7cri+β8lri+β9ldi+β10pci+β11gdpi+β12m2i+β13cpii+β14fintechi+β15shii+β16pricei.


### 4.2. Random Forest Model

The random forest model is constructed based on the bagging ensemble learning method, so the process of training and constructing the random forest model basically follows the basic process of bagging ensemble learning. Specifically, for a data setD containing k samples, we first perform k random self-sampling on D, collect k training sample subsets D1, D2,…, Dk, and then select D1, D2,…, Dk to trainand constructk decision trees, then we can combine these decision trees to obtain a random forest model.Table2 shows the names, descriptions, and settings of important parameters in the random forest model.Table 2
The parameters of the random forest model.
ParametersDescriptions and settingsn_estimatorsThe number of classifiers, also called the number of iterations, is the number of decision trees in the forestCriterionThe standard used for splitting nodes, the default is giniMax_depthMaximum depth of treesMin_samples_splitMinimum number of samples required to split a node inside the tree, defaults to 2Min_samples_leafMinimum number of samples required at leaf nodes, defaults to 1Min_weight_fraction_leafMinimum weighted score in the sum of weights at all leaf nodes, defaults to 0Max_featuresThe number of features to consider when finding the best segmentation, the default is none; that is, all features are consideredMax_leaf_nodesThe maximum number of leaf nodes, which must be an integer, the default is noneMin_impurity_decreaseIf the decrement of the split index is greater than this value, then split, default is 0BootstrapWhether there is a randomly selected sample to put back, the default is trueOob_scoreWhether to use out-of-bag samples to evaluate the quality of the model, set to trueN_jobsThe number of parallel calculations, the default is noneRandom_stateControls the randomness of bootstrap and randomness of the selected samples. In order to facilitate the adjustment of other parameters, this parameter adopts the default valueVerboseControls verbosity when fitting and predicting, default is 0Warm_startWhether to use the trained model and add more base learners to it, set to false


### 4.3. LightGBM Model

The LightGBM model is partially optimized on the traditional boosting algorithm. Since the traditional boosting algorithm needs to scan all the sample points for each feature to select the best segmentation point, it is very time consuming, while the LightGBM algorithm is based on the histogram. The decision tree algorithm greatly reduces the time complexity. The histogram algorithm first performs binning processing on the eigenvalues. For continuous features, binning processing is to discretize continuous data, and then, there is no need to scan each feature as in the traditional algorithm but only need to press the bins that are scanned, which speeds up training.Table3 shows the names, descriptions, and settings of important parameters in the LightGBM model.Table 3
The parameter of the random forest model.
ParametersDescriptions and settingsTaskTrainObjectiveModel training target, which can be selected as a regression model or binary classification modelBoosing_typeBase learner, for gbdtMetricMetrics as a function of evaluating the optimal modelLeaning_rateLearning rate, the default is 0.1, the smaller the value, the more accurate the learningn_estimatorsThe number of iterations in the classifierNum_leavesThe number of leaves in the tree, the indicator should be less than 2 to the power of max_depthMax_depthTree depthFeature_fractionThe feature sampling ratio for building the tree, which ranges from 0 to 1Bagging_fractionThe sample sampling ratio for building the tree, the data range is 0 to 1Max_binThe maximum bin value, generally equal to the number of featuresMin_data_in_leafThe minimum number of samples for each leaf node, when the leaf node is smaller than this value, the tree will no longer be splitMin_gain_to_splitThe tree stops splitting when the leaf node is smaller than this value


## 4.1. Multiple Linear Regression Model

The multiple linear regression model is usually used to study the relationship between a dependent variable and multiple independent variables, which is represented by a matrix.We first use the multiple linear regression model to make regression predictions on the two sample sets and set up model 1 based on the analysis of influencing factors:(1)rate_maxi=α+β1periodi+β2riski+β3thresholdi+β4banki+β5sizei+β6quantityi+β7cri+β8lri+β9ldi+β10pci+β11gdpi+β12m2i+β13cpii+β14fintechi+β15shii+β16pricei.Model 2 is as follows:(2)rate_mini=α+β1periodi+β2riski+β3thresholdi+β4banki+β5sizei+β6quantityi+β7cri+β8lri+β9ldi+β10pci+β11gdpi+β12m2i+β13cpii+β14fintechi+β15shii+β16pricei.


## 4.2. Random Forest Model

The random forest model is constructed based on the bagging ensemble learning method, so the process of training and constructing the random forest model basically follows the basic process of bagging ensemble learning. Specifically, for a data setD containing k samples, we first perform k random self-sampling on D, collect k training sample subsets D1, D2,…, Dk, and then select D1, D2,…, Dk to trainand constructk decision trees, then we can combine these decision trees to obtain a random forest model.Table2 shows the names, descriptions, and settings of important parameters in the random forest model.Table 2
The parameters of the random forest model.
ParametersDescriptions and settingsn_estimatorsThe number of classifiers, also called the number of iterations, is the number of decision trees in the forestCriterionThe standard used for splitting nodes, the default is giniMax_depthMaximum depth of treesMin_samples_splitMinimum number of samples required to split a node inside the tree, defaults to 2Min_samples_leafMinimum number of samples required at leaf nodes, defaults to 1Min_weight_fraction_leafMinimum weighted score in the sum of weights at all leaf nodes, defaults to 0Max_featuresThe number of features to consider when finding the best segmentation, the default is none; that is, all features are consideredMax_leaf_nodesThe maximum number of leaf nodes, which must be an integer, the default is noneMin_impurity_decreaseIf the decrement of the split index is greater than this value, then split, default is 0BootstrapWhether there is a randomly selected sample to put back, the default is trueOob_scoreWhether to use out-of-bag samples to evaluate the quality of the model, set to trueN_jobsThe number of parallel calculations, the default is noneRandom_stateControls the randomness of bootstrap and randomness of the selected samples. In order to facilitate the adjustment of other parameters, this parameter adopts the default valueVerboseControls verbosity when fitting and predicting, default is 0Warm_startWhether to use the trained model and add more base learners to it, set to false


## 4.3. LightGBM Model

The LightGBM model is partially optimized on the traditional boosting algorithm. Since the traditional boosting algorithm needs to scan all the sample points for each feature to select the best segmentation point, it is very time consuming, while the LightGBM algorithm is based on the histogram. The decision tree algorithm greatly reduces the time complexity. The histogram algorithm first performs binning processing on the eigenvalues. For continuous features, binning processing is to discretize continuous data, and then, there is no need to scan each feature as in the traditional algorithm but only need to press the bins that are scanned, which speeds up training.Table3 shows the names, descriptions, and settings of important parameters in the LightGBM model.Table 3
The parameter of the random forest model.
ParametersDescriptions and settingsTaskTrainObjectiveModel training target, which can be selected as a regression model or binary classification modelBoosing_typeBase learner, for gbdtMetricMetrics as a function of evaluating the optimal modelLeaning_rateLearning rate, the default is 0.1, the smaller the value, the more accurate the learningn_estimatorsThe number of iterations in the classifierNum_leavesThe number of leaves in the tree, the indicator should be less than 2 to the power of max_depthMax_depthTree depthFeature_fractionThe feature sampling ratio for building the tree, which ranges from 0 to 1Bagging_fractionThe sample sampling ratio for building the tree, the data range is 0 to 1Max_binThe maximum bin value, generally equal to the number of featuresMin_data_in_leafThe minimum number of samples for each leaf node, when the leaf node is smaller than this value, the tree will no longer be splitMin_gain_to_splitThe tree stops splitting when the leaf node is smaller than this value


## 5. Training and Prediction

### 5.1. Data

We collected 201,572 nonguaranteed wealth management products issued by 20 commercial banks (five each of state-owned commercial banks, joint-stock commercial banks, city commercial banks, and agricultural commercial banks) from January 2017 to December 2020. The dependent variable is the upper and lower bounds of the yield set at the time of issuance.At the same time, we collected data such as the minimum purchase threshold amount and the period set in the product description, as well as the asset size of the issuing bank, the number of wealth management products issued, and the nature of the bank. The sample banks were chosen based on their issuance size in recent years, and the data are all obtained from the wind database. In addition, we have gathered the Shibor Index, Fintech Index, and Consumer Price Index in terms of macroeconomic operation. Because of the short publishing cycle, GDP and m2 only have annual data. At the same time, since the 20 banks in the sample are all listed banks, the closing price is taken as one of the factors to be considered in other markets.We take the capped expected yield and the floored expected yield of the financial products in the sample as dependent variables, named rate_max and rate_min.After data preprocessing, we divide samples after removing missing values and extreme values into the training set and the test set. The divided test set ratio is set to 0.2, and the division standard is randomly divided by using software.


### 5.2. Importance of Features

The random forest algorithm can measure the relative importance of each feature value for prediction, that is, the average contribution of each feature to each tree in the random forest model. An evaluation index is used to calculate the mistake rate. The difference value of out-of-bag data is calculated by randomly adding noise interference to a feature value. We utilize the random forest approach to examine and rank the importance of the sixteen eigenvalues in the sample after processing characteristics one by one, as shown in Figures1 and 2.Figure 1
Eigenvalue importance of yield cap samples.Figure 2
Eigenvalue importance of yield floor samples.According to the eigenvalue importance ranking results output by the machine learning algorithm, in both samples, the period of entrust is the most important eigenvalue, and the importance of risks and thresholds are also in the upstream position. It can be seen that the design of the wealth management product has a crucial impact on the progress of predicting.However, whether or not it is a state-owned bank has little bearing. In the two samples, bank assets and the number of issuances in the preceding year have diametrically opposed importance and influence.Among the macroeconomic operating variables, the gross national product and m2 in the two sample sets are both factors that will have a greater impact on the expected yield.For other markets, the stock market affects yields more than the interbank market. On the one hand, the stock market situation of listed commercial banks represents the bank’s reputation and the investor’s confidence, and on the other hand, the funds obtained by banks through the issuance of wealth management products will also enter the stock market.


### 5.3. Prediction

The prediction results of the multiple linear regression model are shown in Figure3. Due to the large sample size, only the results of 100 pieces of data are shown in the graph. The horizontal axis is the serial number of the test set, the vertical axis is the expected return value, and the two lines are the true value and the predicted value obtained by the multiple linear regression model. It can be seen from Figure 3 that the two lines do not fit, and the prediction made by the multiple linear regression model does not coincide with the real value.Figure 3
The result of the multiple linear regression model.We use the mean absolute error (MAE) index, root mean square error (RMSE) index, and R-square to score and analyze the model regression results.The mean absolute error is used to measure the mean absolute error between the predicted value and the true value. The smaller the MAE, the better the model. It is defined as follows:(3)MAE=1n∑i=1nyi−yi∗.The root mean square error is also used to indicate the error that the model will produce in prediction. The smaller the indicator is, the better the model is. It is defined as follows:(4)RMSE=1n∑i=1nyi−yi∗2.R-square represents the fit of the model. The closer the value to 1, the better the model. It is defined as follows:(5)R2=1−∑i=1nyi−yi∗2∑i=1nyi−yi¯2.In the random forest, n_estimators is the maximum number of iterations of the weak learners of the random forest model, also known as the maximum number of weak learners in the random forest. We set the range of this parameter from 1 to 200, and other parameters are temporarily set to default values; then, we use the grid search command to adjust the parameters for the upper and lower limits of the expected rate of return of sample financial products.In the random forest model, max depth is the maximum depth of the tree. If it is not altered, the default value is none, which means that the decision tree will not limit the depth of the subtree when it is built. When the sample size is small, this parameter will not have an excessive impact on the regression process. Our sample size is relatively large, so we adjust the maximum depth parameter for the two sample sets, respectively, and set the max_depth parameter range from 1 to 100. After adjustment, the results of the parameters are shown in Table4.Table 4
Random forest model-adjusted parameter results.
ParametersYield cap samplesYield floor samplesn_estimators120110Max_depth5150After applying the adjusted parameters to the regression prediction model, the specific prediction results are shown in Figure4, and only 100 results are displayed. It can be seen from Figure 4 that although some points of the two discounts do not overlap, the trends are basically the same.Figure 4
The result of the random Forest model.We used the grid search approach to optimise the parameters of the LightGBM model as we did for the random forest model and continuously changed the interval and step size until we achieved the ideal parameter values, which are displayed in Table5. Among them, Num_leaves is the number of leaves in each tree, and this parameter has an important influence on the complexity of the model tree.Table 5
LightGBM model-adjusted parameter results.
ParameterYield cap samplesYield floor samplesn_estimators5790Max_depth3279We apply the optimized parameters to the regression model to obtain the prediction result graph. Due to the large sample size, only 100 results are shown in the graph. As shown in Figure5, the two polylines have a high degree of fit and have the same trend.Figure 5
The result of the random forest model.


### 5.4. Comparison

To forecast the upper and lower bounds of the predicted return rate of the financial products in this sample, we utilize the multiple linear regression approach, random forest, and LightGBM model, respectively. The comparison results of MAE, RMSE, and R-square values of each model are shown in Table6.Table 6
The comparison between three models.
Yield cap samplesMultiple linear regressionRandom forestLightGBMMAE0.240.230.21RMSE0.280.230.26R20.390.460.67Yield floor samplesMultiple linear regressionRandom forestLightGBMMAE0.270.180.17RMSE0.300.180.20R20.510.720.81The MAE and RMSE indicators in the cap sample of the multiple linear regression model are 0.24 and 0.28, respectively and in the floor sample, they are 0.27 and 0.30, respectively, all of which show high errors. However, the error values of the random forest model and the LightGBM model are not much different, and they neither exceed 0.26 in the upper sample set nor 0.20 in the lower sample set.R-square is a fitness index. In the cap sample set, the R-square of the three models are 0.67, 0.46, and 0.39, respectively. In the floor sample set, they are 0.51, 0.72, and 0.81, respectively. It can be seen that the fitting degree of the LightGBM regression model is the best, followed by the random forest model, and finally the multiple regression model. The prediction efficiency of the multiple linear regression model and the other two models is quite different.


## 5.1. Data

We collected 201,572 nonguaranteed wealth management products issued by 20 commercial banks (five each of state-owned commercial banks, joint-stock commercial banks, city commercial banks, and agricultural commercial banks) from January 2017 to December 2020. The dependent variable is the upper and lower bounds of the yield set at the time of issuance.At the same time, we collected data such as the minimum purchase threshold amount and the period set in the product description, as well as the asset size of the issuing bank, the number of wealth management products issued, and the nature of the bank. The sample banks were chosen based on their issuance size in recent years, and the data are all obtained from the wind database. In addition, we have gathered the Shibor Index, Fintech Index, and Consumer Price Index in terms of macroeconomic operation. Because of the short publishing cycle, GDP and m2 only have annual data. At the same time, since the 20 banks in the sample are all listed banks, the closing price is taken as one of the factors to be considered in other markets.We take the capped expected yield and the floored expected yield of the financial products in the sample as dependent variables, named rate_max and rate_min.After data preprocessing, we divide samples after removing missing values and extreme values into the training set and the test set. The divided test set ratio is set to 0.2, and the division standard is randomly divided by using software.


## 5.2. Importance of Features

The random forest algorithm can measure the relative importance of each feature value for prediction, that is, the average contribution of each feature to each tree in the random forest model. An evaluation index is used to calculate the mistake rate. The difference value of out-of-bag data is calculated by randomly adding noise interference to a feature value. We utilize the random forest approach to examine and rank the importance of the sixteen eigenvalues in the sample after processing characteristics one by one, as shown in Figures1 and 2.Figure 1
Eigenvalue importance of yield cap samples.Figure 2
Eigenvalue importance of yield floor samples.According to the eigenvalue importance ranking results output by the machine learning algorithm, in both samples, the period of entrust is the most important eigenvalue, and the importance of risks and thresholds are also in the upstream position. It can be seen that the design of the wealth management product has a crucial impact on the progress of predicting.However, whether or not it is a state-owned bank has little bearing. In the two samples, bank assets and the number of issuances in the preceding year have diametrically opposed importance and influence.Among the macroeconomic operating variables, the gross national product and m2 in the two sample sets are both factors that will have a greater impact on the expected yield.For other markets, the stock market affects yields more than the interbank market. On the one hand, the stock market situation of listed commercial banks represents the bank’s reputation and the investor’s confidence, and on the other hand, the funds obtained by banks through the issuance of wealth management products will also enter the stock market.


## 5.3. Prediction

The prediction results of the multiple linear regression model are shown in Figure3. Due to the large sample size, only the results of 100 pieces of data are shown in the graph. The horizontal axis is the serial number of the test set, the vertical axis is the expected return value, and the two lines are the true value and the predicted value obtained by the multiple linear regression model. It can be seen from Figure 3 that the two lines do not fit, and the prediction made by the multiple linear regression model does not coincide with the real value.Figure 3
The result of the multiple linear regression model.We use the mean absolute error (MAE) index, root mean square error (RMSE) index, and R-square to score and analyze the model regression results.The mean absolute error is used to measure the mean absolute error between the predicted value and the true value. The smaller the MAE, the better the model. It is defined as follows:(3)MAE=1n∑i=1nyi−yi∗.The root mean square error is also used to indicate the error that the model will produce in prediction. The smaller the indicator is, the better the model is. It is defined as follows:(4)RMSE=1n∑i=1nyi−yi∗2.R-square represents the fit of the model. The closer the value to 1, the better the model. It is defined as follows:(5)R2=1−∑i=1nyi−yi∗2∑i=1nyi−yi¯2.In the random forest, n_estimators is the maximum number of iterations of the weak learners of the random forest model, also known as the maximum number of weak learners in the random forest. We set the range of this parameter from 1 to 200, and other parameters are temporarily set to default values; then, we use the grid search command to adjust the parameters for the upper and lower limits of the expected rate of return of sample financial products.In the random forest model, max depth is the maximum depth of the tree. If it is not altered, the default value is none, which means that the decision tree will not limit the depth of the subtree when it is built. When the sample size is small, this parameter will not have an excessive impact on the regression process. Our sample size is relatively large, so we adjust the maximum depth parameter for the two sample sets, respectively, and set the max_depth parameter range from 1 to 100. After adjustment, the results of the parameters are shown in Table4.Table 4
Random forest model-adjusted parameter results.
ParametersYield cap samplesYield floor samplesn_estimators120110Max_depth5150After applying the adjusted parameters to the regression prediction model, the specific prediction results are shown in Figure4, and only 100 results are displayed. It can be seen from Figure 4 that although some points of the two discounts do not overlap, the trends are basically the same.Figure 4
The result of the random Forest model.We used the grid search approach to optimise the parameters of the LightGBM model as we did for the random forest model and continuously changed the interval and step size until we achieved the ideal parameter values, which are displayed in Table5. Among them, Num_leaves is the number of leaves in each tree, and this parameter has an important influence on the complexity of the model tree.Table 5
LightGBM model-adjusted parameter results.
ParameterYield cap samplesYield floor samplesn_estimators5790Max_depth3279We apply the optimized parameters to the regression model to obtain the prediction result graph. Due to the large sample size, only 100 results are shown in the graph. As shown in Figure5, the two polylines have a high degree of fit and have the same trend.Figure 5
The result of the random forest model.


## 5.4. Comparison

To forecast the upper and lower bounds of the predicted return rate of the financial products in this sample, we utilize the multiple linear regression approach, random forest, and LightGBM model, respectively. The comparison results of MAE, RMSE, and R-square values of each model are shown in Table6.Table 6
The comparison between three models.
Yield cap samplesMultiple linear regressionRandom forestLightGBMMAE0.240.230.21RMSE0.280.230.26R20.390.460.67Yield floor samplesMultiple linear regressionRandom forestLightGBMMAE0.270.180.17RMSE0.300.180.20R20.510.720.81The MAE and RMSE indicators in the cap sample of the multiple linear regression model are 0.24 and 0.28, respectively and in the floor sample, they are 0.27 and 0.30, respectively, all of which show high errors. However, the error values of the random forest model and the LightGBM model are not much different, and they neither exceed 0.26 in the upper sample set nor 0.20 in the lower sample set.R-square is a fitness index. In the cap sample set, the R-square of the three models are 0.67, 0.46, and 0.39, respectively. In the floor sample set, they are 0.51, 0.72, and 0.81, respectively. It can be seen that the fitting degree of the LightGBM regression model is the best, followed by the random forest model, and finally the multiple regression model. The prediction efficiency of the multiple linear regression model and the other two models is quite different.


## 6. Conclusion

We use the multiple linear regression model, random forest, and LightGBM in ensemble learning to predict the yield of the nonguaranteed wealth management products issued by twenty commercial banks in the past four years.The empirical research on forecasting is typically separated into two components, and the first of which is an examination of eigenvalue importance ranking. Then, based on the importance of the eigenvalues of the two sample sets, we built a machine learning model and made value predictions for returns. Regardless of the sample set, the fitting degree of the LightGBM regression model is the best, followed by the random forest model, and finally the multiple regression model.



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