# Cluster-Based Mutual Fund Classification and Price Prediction Using Machine Learning for Robo-Advisors

Authors: Xiaofei Chen; Shujun Ye; Chao Huang
Journal: Computational Intelligence and Neuroscience
 (2021)

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## Abstract

The rise of FinTech has been meteoric in China. Investing in mutual funds through robo-advisor has become a new innovation in the wealth management industry. In recent years, machine learning, especially deep learning, has been widely used in the financial industry to solve financial problems. This paper aims to improve the accuracy and timeliness of fund classification through the use of machine learning algorithms, that is, Gaussian hybrid clustering algorithm. At the same time, a deep learning-based prediction model is implemented to predict the price movement of fund classes based on the classification results. Fund classification carried out using 3,625 Chinese mutual funds shows both accurate and efficient results. The cluster-based spatiotemporal ensemble deep learning module shows better prediction accuracy than baseline models with only access to limited data samples. The main contribution of this paper is to provide a new approach to fund classification and price movement prediction to support the decision-making of the next generation robo-advisor assisted by artificial intelligence.


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## Body

## 1. Introduction

In recent years, machine learning and deep learning have been widely used in finance to meet financial needs [1–5]. As an application of these novel techniques, robo-advisors are favored by a growing number of fund companies, and thus, the advisors have played an important role in global investments and asset allocations. Since the reform and opening up initiated 40 years ago, China has shown rapid economic growth and has become the second-largest wealth management market in the world. To satisfy residents’ wealth management needs, public funds have gradually become one of the main tools for wealth management, because of their rich investment targets, professional operations, and open and transparent information environment. At the same time, with a timely supplement of technology to the financial market, the participating cost of residents to realize customized financial services has been gradually reduced. In addition, as robo-advisors are affordable to common investors, these advisors have become one of the main tools for financial institutions to carry out wealth management innovation for several advantages, e.g., they can manage long-term asset allocation, applying modern portfolio theory with technologies, such as big data, and implementing cloud computing. They can also automatically provide clients with fund investment suggestions through the Internet, with the consideration of investors’ risk preferences, property status, and financial objectives. Therefore, the application of artificial intelligence technology outperforms traditional investment advisors by optimally dealing with several practical problems encountered by traditional advisors, e.g., cost cutting and customer reach.There are two steps that the robo-advisors need to go through in the process of generating investment plans: fund selection and asset allocation. Fund selection can be further divided into two aspects: fund classification and fund return prediction. In China, current fund classification is generally based on the primary classification (Step1) issued by the China Securities Regulatory Commission (CSRC). There are two main styles of funds categorized by CSRC: stock funds and bond funds. For Step 2 classification, stock funds can further be classified given their market capitalization and the style of their holdings, while bond funds can be classified based on the share of equities held in their position.In terms of fund classification by machine learning, there are two common methods: partition clustering (represented by K-means clustering) and network clustering (represented by SOM). The partition clustering method has the merits of simpler principle, fewer parameters input, and faster convergence speed; however, the shape of circular clustering may be too simple, which would compromise the accuracy of classification results. The network clustering method can effectively deal with multidimensional clustering problems, but it is subject to dimensional disasters and the network model is relatively sensitive to the selection of parameters. In terms of fund movement prediction, ARIMA, artificial neural network (ANN), and backpropagation neural network (BP) are frequently used, while their weakness are that parameters are difficult to estimate and models are subject to overfitting.In order to solve the above problems, we employ the Gaussian mixture clustering method (GMM) in this paper. GMM can effectively solve the problem that the cluster shape is too simple when using a simple parameter. For empirical analysis, we use data from the Chinese market. We continue our analysis using two-step classification to further distinguish the styles and characteristics of stock funds and bond funds of our collected data. Based on the GMM results, we use the spatiotemporal ensemble deep learning model to predict the short-term price movement of each category of funds. We then make full use of the idea of clustering and ensemble learning with the aim to effectively improve the implication and prediction ability of the model, especially when the access to big data is rather limited.To compare the performance of predicting fund net asset values of our model, we compare it with several basic models, that is, residual network (ResNet, hereafter) model, long- and short-term memory network (LSTM, hereafter) model, and one-dimensional convolutional neural network (CNN, hereafter) model. We examine their performance in predicting the short-term returns of the four main classified categories in our results by employing the mean absolute error (MAE) and correlation coefficientR2 as evaluation indicators.Our main findings are as follows. Our two-step GMM method can generate the probabilities that the funds belong to a certain category, according to their risks and returns, and thus outperform the traditional K-means model in classifying funds. Our model also improves the prediction ability, with a reduced prediction error, of fund price movements when compared with other models, i.e., ResNet, LSTM, and CNN models.The main contributions of this paper are as follows: (1) we propose a new two-step GMM model to effectively distinguish the mutual funds in China using simple fund characteristics and (2) we construct an ensemble deep learning model to predict the short-term price movement of different categories of funds.


## 2. Literature Review

### 2.1. Literature on Fund Classification

Fund classification is the basis of fund evaluation. Different types of funds need different analysis methods and evaluation dimensions due to their distinct characteristics such as risk and return. Thus, fund classification ensures the effectiveness and comparability of fund evaluation. There are two methods of fund classification: ex ante classification and ex post classification. The ex ante classification method determines the fund category according to its investment objectives and strategies, which are specified in the fund issuance announcement. However, in the actual operation, the specified information frequently deviates from the original agreements. Dibartolomeo et al. [6] find that after regressing the net value of the fund using the William Sharp’s attribution method, more than 40% of the stock funds have misclassification, and they argue that the main reasons for the misclassification are the imprecision of the ex ante classification method and the ex post deviating manipulation by fund managers due to peer pressure. Luo et al. [7] classify 54 funds listed in China through factor and cluster analyses, and they find that nearly 40% of the funds are inconsistent with the investment style described in their prospectus. In contrast, ex post classification method specifies fund types according to their performance after fund operation and their characteristics specified in the issuance announcement. As an improvement to this classification method, Brown et al. [8] use a factor model to capture the nonlinear characteristics of fund returns and map them into the mainstream of investment managers’ style to classify funds. Kim et al. [9] choose more market characteristics, through principal component analysis (PCA), and classify funds based on these newly identified variables. However, the ex post classification method also has limitations, for example, the collinearity of factors in multiple regressions.Fortunately, the introduction of machine learning mitigates the limitations of the traditional fund classification methodology because of its ability to capture nonlinear features and its independence of data characteristics, for example, sample size, under unsupervised learning. Marathon et al. [10] classify funds by K-means clustering to find that 43% of the fund samples were inconsistent with the investment types the funds were originally described. They also find that many fund categories under traditional classification methods show very similar risk and return characteristics, thus suggesting that the introduction of classification analysis reduces the complexity of fund management. Lajbcygier et al. [11] maintain that the boundaries of funds with different styles should be continuous rather than strictly being divided. Thus, they use a flexible clustering method of fuzzy C-means and find that this method can obtain better classification results. Menardi et al. [12] employ a two-step clustering method, and the first step of which is to reduce the dimensionality of 24 fund characteristics using PCA, and the second step is to classify 1436 public funds into those 24 categories of characteristics using hierarchical clustering. For the extraction of nonlinear characteristics, Moreno et al. [13] classify 1,592 funds from the Spanish market by using self-organizing mapping neural network (SOM) and find that compared with K-means clustering, SOM can effectively reduce misclassification.


### 2.2. Literature on Fund Return Prediction

Yaser et al. (1996) argue that financial time series itself is noisy and is a nonstationary process, which means the historical information is not enough to explain the relationship between past and future returns. They also argue that the financial market is not completely unpredictable due to the existence of the price trend effect. Cao et al. (2001) maintain that financial time series can be predicted by both univariate and multivariate analyses. They argue that the input of the univariate analysis model is the time series itself, which is predicted by the autoregressive integral moving average (ARIMA) model. However, ARIMA’s performance is not satisfactory, mainly because (1) it requires the parameters to be estimated ex ante and (2) it assumes that the time series is stable and linear, which violates reality. Concerning multivariate analysis, artificial neural network (ANN) is one of the main prediction methods due to its ability in accommodating more available information and its outstanding performance in handling nonstationary processes. Schneburg [14] uses several methods, such as MADALINE and BP models, to predict stock returns of three listed companies in the German market and reveals that the accuracy of prediction reaches 90%. Schneburg [14] also finds that the BP model performs better than other methods considered, which confirms the effectiveness of neural networks in predicting fund returns. Kimoto [15] uses a modular neural network to develop a trading strategy for Tokyo Stock Exchange and find that the modular neural network can connect more basic neural networks and help generate a more accurate prediction. For improvement, Vapnik et al. (1996) propose a new method based on the support vector machine (SVM) to improve the generalization of neural networks by solving nonlinear regression problems. In addition, Cao et al. (2001) argue that artificial neural network has overfitting problems, and extra care is needed for parameter estimations and training to get satisfactory results. Khashei et al. [16] maintain that to produce accurate results a large amount of historical data is needed, while the financial market is full of uncertainty and changes rapidly. Accordingly, a new hybrid method, which combines the advantages of artificial neural networks and fuzzy regression, is proposed to overcome the limitations of traditional artificial neural networks. Their empirical results then show that this hybrid model is an effective way to improve prediction accuracy. Liu et al. [17] and Li et al. [18] predict stock returns by employing a CNN-LSTM model and find that introducing an attention mechanism could help improve the accuracy of the CNN-LSTM model.


## 2.1. Literature on Fund Classification

Fund classification is the basis of fund evaluation. Different types of funds need different analysis methods and evaluation dimensions due to their distinct characteristics such as risk and return. Thus, fund classification ensures the effectiveness and comparability of fund evaluation. There are two methods of fund classification: ex ante classification and ex post classification. The ex ante classification method determines the fund category according to its investment objectives and strategies, which are specified in the fund issuance announcement. However, in the actual operation, the specified information frequently deviates from the original agreements. Dibartolomeo et al. [6] find that after regressing the net value of the fund using the William Sharp’s attribution method, more than 40% of the stock funds have misclassification, and they argue that the main reasons for the misclassification are the imprecision of the ex ante classification method and the ex post deviating manipulation by fund managers due to peer pressure. Luo et al. [7] classify 54 funds listed in China through factor and cluster analyses, and they find that nearly 40% of the funds are inconsistent with the investment style described in their prospectus. In contrast, ex post classification method specifies fund types according to their performance after fund operation and their characteristics specified in the issuance announcement. As an improvement to this classification method, Brown et al. [8] use a factor model to capture the nonlinear characteristics of fund returns and map them into the mainstream of investment managers’ style to classify funds. Kim et al. [9] choose more market characteristics, through principal component analysis (PCA), and classify funds based on these newly identified variables. However, the ex post classification method also has limitations, for example, the collinearity of factors in multiple regressions.Fortunately, the introduction of machine learning mitigates the limitations of the traditional fund classification methodology because of its ability to capture nonlinear features and its independence of data characteristics, for example, sample size, under unsupervised learning. Marathon et al. [10] classify funds by K-means clustering to find that 43% of the fund samples were inconsistent with the investment types the funds were originally described. They also find that many fund categories under traditional classification methods show very similar risk and return characteristics, thus suggesting that the introduction of classification analysis reduces the complexity of fund management. Lajbcygier et al. [11] maintain that the boundaries of funds with different styles should be continuous rather than strictly being divided. Thus, they use a flexible clustering method of fuzzy C-means and find that this method can obtain better classification results. Menardi et al. [12] employ a two-step clustering method, and the first step of which is to reduce the dimensionality of 24 fund characteristics using PCA, and the second step is to classify 1436 public funds into those 24 categories of characteristics using hierarchical clustering. For the extraction of nonlinear characteristics, Moreno et al. [13] classify 1,592 funds from the Spanish market by using self-organizing mapping neural network (SOM) and find that compared with K-means clustering, SOM can effectively reduce misclassification.


## 2.2. Literature on Fund Return Prediction

Yaser et al. (1996) argue that financial time series itself is noisy and is a nonstationary process, which means the historical information is not enough to explain the relationship between past and future returns. They also argue that the financial market is not completely unpredictable due to the existence of the price trend effect. Cao et al. (2001) maintain that financial time series can be predicted by both univariate and multivariate analyses. They argue that the input of the univariate analysis model is the time series itself, which is predicted by the autoregressive integral moving average (ARIMA) model. However, ARIMA’s performance is not satisfactory, mainly because (1) it requires the parameters to be estimated ex ante and (2) it assumes that the time series is stable and linear, which violates reality. Concerning multivariate analysis, artificial neural network (ANN) is one of the main prediction methods due to its ability in accommodating more available information and its outstanding performance in handling nonstationary processes. Schneburg [14] uses several methods, such as MADALINE and BP models, to predict stock returns of three listed companies in the German market and reveals that the accuracy of prediction reaches 90%. Schneburg [14] also finds that the BP model performs better than other methods considered, which confirms the effectiveness of neural networks in predicting fund returns. Kimoto [15] uses a modular neural network to develop a trading strategy for Tokyo Stock Exchange and find that the modular neural network can connect more basic neural networks and help generate a more accurate prediction. For improvement, Vapnik et al. (1996) propose a new method based on the support vector machine (SVM) to improve the generalization of neural networks by solving nonlinear regression problems. In addition, Cao et al. (2001) argue that artificial neural network has overfitting problems, and extra care is needed for parameter estimations and training to get satisfactory results. Khashei et al. [16] maintain that to produce accurate results a large amount of historical data is needed, while the financial market is full of uncertainty and changes rapidly. Accordingly, a new hybrid method, which combines the advantages of artificial neural networks and fuzzy regression, is proposed to overcome the limitations of traditional artificial neural networks. Their empirical results then show that this hybrid model is an effective way to improve prediction accuracy. Liu et al. [17] and Li et al. [18] predict stock returns by employing a CNN-LSTM model and find that introducing an attention mechanism could help improve the accuracy of the CNN-LSTM model.


## 3. Data

The data used in this paper are mainly from the WIND database. The collected data are the full samples of stock funds, hybrid funds, and bond funds under the classification caliber of CSRC. QDII funds, closed-end funds, alternative funds, and monetary funds are not included in the analysis due to their peculiarity to our chosen funds. The date of April 30, 2021, is taken as the cut-off date. The funds that have been established more than two years before the cut-off date, with a total asset value of above 50 million RMB, and have not undergone type conversion during their operation period are selected. This selection process leads to a total number of 3,625 funds.The fund fee normally includes the daily subscription fee, daily redemption fee, management fee, and custody fee. The fund fee used in this paper is the sum of the management fee and custody fee. The value of the fee is adopted as of April 30, 2021. For fund returns, we focus on their rolling rate of return, which is defined as the ratio of the funds’ compound net value on that day to the funds’ compound net valueN days ago, where N = 1, 5, 20, 60, 120, and 250 days as rolling windows. The number of fundholders, shares per capita, shares that are held by institutions and individual holders, shares purchased and redeemed by the fund managers, and ratios of the market value of stocks and bonds to funds’ total value are collected from their quarterly reports. Since the publication time of the quarterly reports varies across funds, we take the last trading day in January, April, July, and October of each year as the observation date to obtain the latest published data before that date. If no new data is published in the latest quarter, the value of the previous quarter will be used. Table 1 summarizes the data used in this paper.Table 1
Summary statistics.
ItemObservationsFrequencyStep of clusteringRate of return in the past 1 day237 × 3,604DailyFirstRate of return in the past 5 days237 × 3,604DailyFirstRate of return in the past 20 days237 × 3,604DailyFirstRate of return in the past 60 days237 × 3,604DailyFirstRate of return in the past 120 days237 × 3,604DailyFirstRate of return in the past 250 days237 × 3,604DailyFirstRate of fund fee36 × 4 × 1As of April 30, 2021SecondNumber of fund holders10 × 3,604QuarterlySecondShares per capita10 × 3,604QuarterlySecondShares held by institutions (%)10 × 3,604QuarterlySecondShares held by individuals (%)10 × 3,604QuarterlySecondShares purchased by fund managers10 × 3,604QuarterlySecondShares redeemed by fund managers10 × 3,604QuarterlySecondRatios of stocks to total assets (%)10 × 3,604QuarterlySecondRatios of bonds to total assets (%)10 × 3,604QuarterlySecond


## 4. The Model

In this section, we develop the model framework, including the clustering model and the prediction model, as shown in Figure1. First, we cluster the fund via GMM using fund features described in the previous section, from which the dimension of the fund features is reduced using the PCA method. Then, we develop a deep learning-based prediction model to predict the fund trend based on the clustering results. Therefore, we will briefly introduce the PCA and GMM at first. The deep learning-based model is then presented in detail.Figure 1
Model framework.


### 4.1. Clustering Models

This paper uses two models for analysis, that is, principal component analysis (PCA) and the Gaussian mixture model (GMM). In this paper, we employ PCA to reduce the dimension of the rolling yield data of funds with different maturities used in the first step of classification.


#### 4.1.1. PCA

Principal components analysis (PCA) is a dimension reduction method, namely, transfers the original feature space into a brand-new feature space. It is generally used for data preprocessing. For example, assume that there aren fund samples, with each fund sample contains 2,000 features. Among these features, there exists the vast amount of noises or useless information. Therefore, PCA can be conducted to reduce noises and save computational resources. Table 2 shows the number of eigenvalues used and the reducibility using PCA. One can notice that the PCA method has a high degree of reducibility, and the higher the reducibility, the more rolling days are selected, keeping the number of eigenvalues constant. A detailed description of PCA is shown in Appendix A.Table 2
PCA result for data used in classification.
DataNumber of eigenvaluesReducibility (%)Rate of return in the past 1 day10094.89Rate of return in the past 5 days10099.19Rate of return in the past 20 days10099.81Rate of return in the past 60 days10099.94Rate of return in the past 120 days10099.97Rate of return in the past 250 days10099.98


#### 4.1.2. GMM

GMM clustering is the main classification model, which can give the probability that the sample belongs to a certain category. The so-called Gaussian mixture model is the combination of multiple Gaussian distributions, and it uses the likelihood function as the objective function for parameter estimation. Although a larger sample size could help improve the accuracy of the model, the increased sample size will add the complexity of the model and could thus cause overfitting problem. Therefore, we rely on Akaike information criterion (AIC) and Bayesian information criterion (BIC) to assess the quality of classification. A detailed description of GMM is presented in Appendix B.


### 4.2. Deep Learning Model

Applying the idea of ensemble learning to the field of financial studies, we build a spatiotemporal ensemble deep learning model for fund price prediction. The rationale of this model is summarized in three steps. Given the layout and the article length, the descriptions of the components of this model are presented in Appendix C. First, encode the data that are used (i.e., historical value of the fund) to obtain the semantic information of the data. Second, insert the encoded data into three basic models, that is, residual network (ResNet), long- and short-term memory network (LSTM), and one-dimensional convolutional neural network (CNN), to train the model and obtain the output from these three models. The detailed mechanism of ResNet, LSTM, and CNN is shown in Appendixes C.1, C.2, and C.3, respectively. Third, calculate final output; model weights are optimized by the attention mechanism, the rationale of which is shown in Appendix C.4. Those three models are employed to extract complex nonlinear correlations (ResNet), capture time correlations (LSTM), and calculate spatial correlations (CNN). In this paper, we compare the performance of our model with these three benchmark models, and the results are shown in Section5. The detailed spatiotemporal ensemble deep learning model and the inner structure are shown in Figure 2.Figure 2
Diagram of spatial-temporal ensemble learning.


## 4.1. Clustering Models

This paper uses two models for analysis, that is, principal component analysis (PCA) and the Gaussian mixture model (GMM). In this paper, we employ PCA to reduce the dimension of the rolling yield data of funds with different maturities used in the first step of classification.


### 4.1.1. PCA

Principal components analysis (PCA) is a dimension reduction method, namely, transfers the original feature space into a brand-new feature space. It is generally used for data preprocessing. For example, assume that there aren fund samples, with each fund sample contains 2,000 features. Among these features, there exists the vast amount of noises or useless information. Therefore, PCA can be conducted to reduce noises and save computational resources. Table 2 shows the number of eigenvalues used and the reducibility using PCA. One can notice that the PCA method has a high degree of reducibility, and the higher the reducibility, the more rolling days are selected, keeping the number of eigenvalues constant. A detailed description of PCA is shown in Appendix A.Table 2
PCA result for data used in classification.
DataNumber of eigenvaluesReducibility (%)Rate of return in the past 1 day10094.89Rate of return in the past 5 days10099.19Rate of return in the past 20 days10099.81Rate of return in the past 60 days10099.94Rate of return in the past 120 days10099.97Rate of return in the past 250 days10099.98


### 4.1.2. GMM

GMM clustering is the main classification model, which can give the probability that the sample belongs to a certain category. The so-called Gaussian mixture model is the combination of multiple Gaussian distributions, and it uses the likelihood function as the objective function for parameter estimation. Although a larger sample size could help improve the accuracy of the model, the increased sample size will add the complexity of the model and could thus cause overfitting problem. Therefore, we rely on Akaike information criterion (AIC) and Bayesian information criterion (BIC) to assess the quality of classification. A detailed description of GMM is presented in Appendix B.


## 4.1.1. PCA

Principal components analysis (PCA) is a dimension reduction method, namely, transfers the original feature space into a brand-new feature space. It is generally used for data preprocessing. For example, assume that there aren fund samples, with each fund sample contains 2,000 features. Among these features, there exists the vast amount of noises or useless information. Therefore, PCA can be conducted to reduce noises and save computational resources. Table 2 shows the number of eigenvalues used and the reducibility using PCA. One can notice that the PCA method has a high degree of reducibility, and the higher the reducibility, the more rolling days are selected, keeping the number of eigenvalues constant. A detailed description of PCA is shown in Appendix A.Table 2
PCA result for data used in classification.
DataNumber of eigenvaluesReducibility (%)Rate of return in the past 1 day10094.89Rate of return in the past 5 days10099.19Rate of return in the past 20 days10099.81Rate of return in the past 60 days10099.94Rate of return in the past 120 days10099.97Rate of return in the past 250 days10099.98


## 4.1.2. GMM

GMM clustering is the main classification model, which can give the probability that the sample belongs to a certain category. The so-called Gaussian mixture model is the combination of multiple Gaussian distributions, and it uses the likelihood function as the objective function for parameter estimation. Although a larger sample size could help improve the accuracy of the model, the increased sample size will add the complexity of the model and could thus cause overfitting problem. Therefore, we rely on Akaike information criterion (AIC) and Bayesian information criterion (BIC) to assess the quality of classification. A detailed description of GMM is presented in Appendix B.


## 4.2. Deep Learning Model

Applying the idea of ensemble learning to the field of financial studies, we build a spatiotemporal ensemble deep learning model for fund price prediction. The rationale of this model is summarized in three steps. Given the layout and the article length, the descriptions of the components of this model are presented in Appendix C. First, encode the data that are used (i.e., historical value of the fund) to obtain the semantic information of the data. Second, insert the encoded data into three basic models, that is, residual network (ResNet), long- and short-term memory network (LSTM), and one-dimensional convolutional neural network (CNN), to train the model and obtain the output from these three models. The detailed mechanism of ResNet, LSTM, and CNN is shown in Appendixes C.1, C.2, and C.3, respectively. Third, calculate final output; model weights are optimized by the attention mechanism, the rationale of which is shown in Appendix C.4. Those three models are employed to extract complex nonlinear correlations (ResNet), capture time correlations (LSTM), and calculate spatial correlations (CNN). In this paper, we compare the performance of our model with these three benchmark models, and the results are shown in Section5. The detailed spatiotemporal ensemble deep learning model and the inner structure are shown in Figure 2.Figure 2
Diagram of spatial-temporal ensemble learning.


## 5. Results

### 5.1. Clustering Analysis

The rolling returns of the fund in the past 1, 5, 20, 60, 120, and 250 days are used as the input of the first step GMM, in which we rely on AIC to determine the optimal number of categories. As shown in Figure3, when the number of categories (clusters) is greater than 10, the AIC value begins to rise, which means the optimal number of classifications is 10.Figure 3
Number of main classes.We then measure our classification results of the first step GMM from multiple dimensions; the results are shown in Table3. We start by examining the average ratio of the market value of funds’ holdings of stocks and bonds to funds’ total value (disclosed in their 2020 annual report) for each category. We define that for each fund when its market value of stocks accounts for less than 60% of its total value, this fund does not belong to stock funds. Thus, one can see that categories 1 and 10 are not classified as stock categories, while others are classified as stock categories. In addition, the average stock holding of category 10 is higher than that of category 1. Therefore, we define category 1 as pure bond funds while category 10 as bond-like funds. Notice that funds in category 1 have an average ratio of bonds to fund value that is greater than 100%; this is a special characteristic of bond funds that utilize leverage through repurchase agreement (repo); a similar phenomenon also occurs in Table 4. Due to a large number of funds within these two categories (more than 500 funds), we will conduct a secondary classification for these two categories, the results of which will be shown in Table 4.Table 3
Funds category for the first step of GMM.
CategoryNumber of fundsRatio of stocks to fund value (%)Ratio of bonds to fund value (%)Classifications19513108Bond2402883Stock3181892Stock4106891Stock593911Stock6233788Stock7125842Stock8454768Stock9482883Stock105772968Bond-likeTable 4
Classification result of subclasses in categories 1 and 10.
CategorySubcategoryShare of stocks (%)Share of bond (%)Number of holdersRatio of institutional investors (%)Style1161053368965Primary bond20110401997Pure bond301218100Institution customized bond10123801474490Secondary bond278117146238Low dividend stock323761441171New stockRegarding the other eight categories classified as stock funds, we further define their styles according to the following criterion: a fund is defined as an industry-themed fund if more than 30% of its investments are in a certain industry or if above 50% of its holdings go to less than three specific industries. If a category of funds contains at least 50% of funds within the same industry or above 50% shares of this category is industry-themed funds, this category is defined as an industry category. Take category 4 as an example, the largest industry invested by this category is pharmaceuticals, and 91% of funds (96 out of 106) within this category invest more than 30% of their shares in the pharmaceuticals industry. Therefore, this category is defined as the pharmaceuticals-themed (industry) category. The classification results of the categories are shown in Table5.Table 5
Classification of categories.
CategoryNumber of fundsShare of the largest industry (%)Share of largest three industries (%)IndustryShare of the themed industry (%)Style31813863Food and beverage74Industry41067080Pharmaceuticals91Industry5932957Energy and power69Industry71255170Technology48IndustryFor other categories, that is, categories 2, 6, 8, and 9, belonging to the category of stock but found not falling into the style of industry-themed ones, we conduct a separate classification. For category 2, its fund holdings are rather dispersed, that is, there is no representing industry. Therefore, this category is classified as a market category. Category 6 contains a large portion of funds investing in small and medium enterprises (SME), and their holdings are also relatively dispersed across industries. Therefore, category 6 is classified as an SME market category. Most funds within category 8 invest in large blue-chip industries such as banking, nonbanking finance, and food and beverage. Therefore, category 8 is classified as a large-cap style. Category 9 is found to have similar characteristics to those of category 6, while the top three industries invested by category 9’s funds are pharmaceuticals, electronics, and science and technology, which are growing industries in the Chinese market. Therefore, category 9 is classified as SME growth style. The classification results of these categories are summarized in Table6.Table 6
Classification result for other stock categories.
CategoryNumber of fundsShare of the largest industry (%)Share of largest three industries (%)IndustryShare of the themed industry (%)Style24021941Pharmaceuticals12All markets62331937Pharmaceuticals45SME-market84541737Food and beverage30Large-cap value94822349Pharmaceuticals26SME-growthWe continue our analysis by conducting the second step of classification for categories 1 and 10, the results of which are shown in Figure4. According to AIC, the optimal number of clusters for each category exceeds 10, which is not practical in real-world scenarios. Bond funds are hard to be distinguished by pure quantitative measures due to their low volatility, and thus, we choose to make the minor adjustment by combining classification results with our practical experience. We can see that AIC decreases significantly when cluster number reaches 3, and bond funds are usually separated by the involvement of equity assets. As a result, we set the number of subcategories of these two categories as three to distinguish among pure bond funds, bond funded with equity, and special-purpose bond funds.Figure 4
Number of subcategories of categories 1 and 10.Subcategory 1 of category 1 has no excessive leverage ratio, and its share in stocks is less than 10%, which implies that subcategory 1 belongs to the primary bond category. Subcategory 2 has no positions in stocks, and its ratio of the market value of the bond to its total value is higher than that of subcategory 1. Thus, subcategory 2 can be classified as a pure bond. Subcategory 3 is classified as an institutional-customized bond category as its market value of term bonds accounts for a high proportion of its total value and its average number of holders is in single digit, implying that these funds are mainly held by several institutional investors.Regarding category 10, the holdings of stocks of subcategory 1 accounts for more than 20%, and there is no excessive leverage. Accordingly, subcategory 1 is classified secondary bond. Subcategory 2 is classified as low dividend stock as most of its funds invest in low dividend stocks. Subcategory 3 has a very similar feature to subcategory 1 in terms of shares of stock and bond holdings. However, further investigation shows that the average market value of the funds within subcategory 3 is less than 1 billion RMB (while the figure for subcategory 1 is 1.9 billion RMB), and there is a relatively high proportion of hybrid funds within this subcategory. This indicates that subcategory 3 is mainly made up of fixed income and new funds established for the issuance of new stocks in the primary market. Thereby, subcategory 3 is classified as a new stock category. The secondary classification results for categories 1 and 10 are shown in Table6.To test the creditability of our classification results, we average the daily rate of return of the funds in each category and employ several industry style indexes (in which we select CITIC class I industry classification index as the industry index and we employ Juchao index as style index) as reference. We conduct our test by calculating the correlation coefficient between the calculated return in each category and the reference index. The results are shown in Table7. One can see from Table 7 that category 3 has the highest correlation with CITIC food and beverage index, reaching 94%. The correlation between the return in category 4 and the CITIC pharmaceuticals index is high at 97%. The correlation between the rate of return of category 5 and the CITIC power and new energy index is 94%. The rate of return of category 7 has a high correlation coefficient with CITIC power and new energy, computers, electronics, and military industry indexes.Table 7
Correlation categories and benchmark sector index (CITIC)
CITIC indexCategory 3 (%)Category 4 (%)Category 5 (%)Category 7 (%)Food and beverage94746558Pharmaceuticals82977267Power and new energy74679485Computers64627792Communications57576880Electronics64578193Military56526984Table8 summarizes the correlation between fund returns and Juchao style index for categories 2, 6, 8, and 9, which are not classified as industry-themed categories, as in Table 6. (Thus, industry indexes, such as CITIC indexes, are inappropriate to evaluate its industry classification results, while style index, for example, Juchao index, are more suitable for the evaluation of their style classifications.) From Table 8, we can see that our classification method has high accuracy in identifying the styles of these categories. To be specific, category 2 has a higher correlation with market style indexes defined by the Juchao style index; category 6 is closer to SME market; category 8 is similar to market value, and category 9 alike SME growth. (In recent years, fund managers pay more attention to funds that are growing while less attention is paid to value investing. Thus, the classification result of category 8 is less pronounced WIND database: https://www.wind.com.cn/en/edb.html.)Table 8
Correlation result of other stock categories (Juchao style index).
Juchao indexCategory 2 (%)Category 6 (%)Category 8 (%)Category 9 (%)Small value82908875Small growth90978890Medium value83889175Medium growth96979296Large value73708861Large growth95879292


### 5.2. Return Prediction Analysis

We use the four industry-themed categories (i.e., categories 3, 4, 5, and 7) for the fund price prediction analysis. The data used is the cumulative return of all funds in these four categories from February 2019 to July 2021, totaling 604 days. The PyTorch deep learning framework is used to build the model; 80% of the data sets are used to train the model, and 20% are used to test the model. The input data is divided into 10 dimensions through embedding. The ResNet model includes 7 layers of fully connected networks, containing 16, 16, 10, 16, 16, 10, and 1 neuron. The LSTM model is made up of 1 layer and 64 neurons. The CNN model consists of three layers, and the number of filters is 8, 8, and 1, with the size of convolution kernel of 3. The batch size of all basic models is 1. The final output is obtained using the weighted summation of outputs of these three benchmark models (i.e., ResNet, LSTM, and CNN). The loss function curve of the model is shown in Figure5, from which one can notice that the loss function training and verification set become stable after the 20th iteration, and the convergence is good.Figure 5
The loss function and times of iteration.We then evaluate the performance of our model and three basic models using four indicators: RMSE, MAE,R2, and WMAPE. The results are shown in Tables 9 and 10 and Figure 6. One can see the prediction ability of ResNet is relatively the best in all categories in question (compared with other benchmark models) based on these indicators. For example, the average value of RMSE is 0.034 for all categories, which is lowest when compared with other benchmark models, and R2 is 0.96, which is the highest among other benchmark models. Although LSTM is one of the most effective models dealing with time series problems, it does not perform well as expected, with the average value of RMSE around 0.040 and R2 around 0.95, owing to limited features available and an insufficient number of samples. The poor performance of CNN, with an average value of RMSE around 0.037 and R2 around 0.95, is due partially to its inability to record historical information. As expected, one can see that our spatiotemporal ensemble deep learning model has a better performance in predicting the fund price, which reduces the mean of RMSE to around 0.026 and improves R2 to nearly 0.98. We can thus conclude that our model greatly improves the predictability, that is, the prediction accuracy, of fund price movement compared with these benchmark models as our model obtains the lowest (mean) values of RMSE, MAE, and WMAPE and the highest (mean) value of R2. The improvements lie in the merits of ensemble learning, which complements the advantages of these three benchmark models.Table 9
Prediction result for categories 3 and 4.
Category 3Category 4RMSEMAER2WMAPERMSEMAER2WMAPEResNet0.02670.02130.98900.01140.02910.02200.98060.0121LSTM0.03310.02660.98320.01430.03330.02600.97460.0143CNN0.03080.02370.98530.01270.03890.03230.96540.0176Spatiotemporal0.02190.01650.99270.00890.02620.02020.98430.0110Table 10
Prediction result for categories 5 and 6.
Category 5Category 7RMSEMAER2WMAPERMSEMAER2WMAPEResNet0.03290.02680.98780.01620.04660.03690.87320.0254LSTM0.04320.03490.97890.02110.04950.04150.85630.0286CNN0.03150.02570.98880.01550.04720.03810.86970.0263Spatiotemporal0.03030.02460.98970.01490.02720.02110.95650.0145Figure 6
Prediction results for different categories.Finally, we show the comparison between the actual values of those funds with our predicted values. The results are shown in Figure7. We can see that the predicted values and actual values show a high degree of similarity. This means our spatiotemporal ensemble deep learning model generates a good prediction for fund price, which suggests our model can provide a proper application for robo-advisors in terms of predicting fund price movements.Figure 7
Comparison between the actual values and predicted values.


## 5.1. Clustering Analysis

The rolling returns of the fund in the past 1, 5, 20, 60, 120, and 250 days are used as the input of the first step GMM, in which we rely on AIC to determine the optimal number of categories. As shown in Figure3, when the number of categories (clusters) is greater than 10, the AIC value begins to rise, which means the optimal number of classifications is 10.Figure 3
Number of main classes.We then measure our classification results of the first step GMM from multiple dimensions; the results are shown in Table3. We start by examining the average ratio of the market value of funds’ holdings of stocks and bonds to funds’ total value (disclosed in their 2020 annual report) for each category. We define that for each fund when its market value of stocks accounts for less than 60% of its total value, this fund does not belong to stock funds. Thus, one can see that categories 1 and 10 are not classified as stock categories, while others are classified as stock categories. In addition, the average stock holding of category 10 is higher than that of category 1. Therefore, we define category 1 as pure bond funds while category 10 as bond-like funds. Notice that funds in category 1 have an average ratio of bonds to fund value that is greater than 100%; this is a special characteristic of bond funds that utilize leverage through repurchase agreement (repo); a similar phenomenon also occurs in Table 4. Due to a large number of funds within these two categories (more than 500 funds), we will conduct a secondary classification for these two categories, the results of which will be shown in Table 4.Table 3
Funds category for the first step of GMM.
CategoryNumber of fundsRatio of stocks to fund value (%)Ratio of bonds to fund value (%)Classifications19513108Bond2402883Stock3181892Stock4106891Stock593911Stock6233788Stock7125842Stock8454768Stock9482883Stock105772968Bond-likeTable 4
Classification result of subclasses in categories 1 and 10.
CategorySubcategoryShare of stocks (%)Share of bond (%)Number of holdersRatio of institutional investors (%)Style1161053368965Primary bond20110401997Pure bond301218100Institution customized bond10123801474490Secondary bond278117146238Low dividend stock323761441171New stockRegarding the other eight categories classified as stock funds, we further define their styles according to the following criterion: a fund is defined as an industry-themed fund if more than 30% of its investments are in a certain industry or if above 50% of its holdings go to less than three specific industries. If a category of funds contains at least 50% of funds within the same industry or above 50% shares of this category is industry-themed funds, this category is defined as an industry category. Take category 4 as an example, the largest industry invested by this category is pharmaceuticals, and 91% of funds (96 out of 106) within this category invest more than 30% of their shares in the pharmaceuticals industry. Therefore, this category is defined as the pharmaceuticals-themed (industry) category. The classification results of the categories are shown in Table5.Table 5
Classification of categories.
CategoryNumber of fundsShare of the largest industry (%)Share of largest three industries (%)IndustryShare of the themed industry (%)Style31813863Food and beverage74Industry41067080Pharmaceuticals91Industry5932957Energy and power69Industry71255170Technology48IndustryFor other categories, that is, categories 2, 6, 8, and 9, belonging to the category of stock but found not falling into the style of industry-themed ones, we conduct a separate classification. For category 2, its fund holdings are rather dispersed, that is, there is no representing industry. Therefore, this category is classified as a market category. Category 6 contains a large portion of funds investing in small and medium enterprises (SME), and their holdings are also relatively dispersed across industries. Therefore, category 6 is classified as an SME market category. Most funds within category 8 invest in large blue-chip industries such as banking, nonbanking finance, and food and beverage. Therefore, category 8 is classified as a large-cap style. Category 9 is found to have similar characteristics to those of category 6, while the top three industries invested by category 9’s funds are pharmaceuticals, electronics, and science and technology, which are growing industries in the Chinese market. Therefore, category 9 is classified as SME growth style. The classification results of these categories are summarized in Table6.Table 6
Classification result for other stock categories.
CategoryNumber of fundsShare of the largest industry (%)Share of largest three industries (%)IndustryShare of the themed industry (%)Style24021941Pharmaceuticals12All markets62331937Pharmaceuticals45SME-market84541737Food and beverage30Large-cap value94822349Pharmaceuticals26SME-growthWe continue our analysis by conducting the second step of classification for categories 1 and 10, the results of which are shown in Figure4. According to AIC, the optimal number of clusters for each category exceeds 10, which is not practical in real-world scenarios. Bond funds are hard to be distinguished by pure quantitative measures due to their low volatility, and thus, we choose to make the minor adjustment by combining classification results with our practical experience. We can see that AIC decreases significantly when cluster number reaches 3, and bond funds are usually separated by the involvement of equity assets. As a result, we set the number of subcategories of these two categories as three to distinguish among pure bond funds, bond funded with equity, and special-purpose bond funds.Figure 4
Number of subcategories of categories 1 and 10.Subcategory 1 of category 1 has no excessive leverage ratio, and its share in stocks is less than 10%, which implies that subcategory 1 belongs to the primary bond category. Subcategory 2 has no positions in stocks, and its ratio of the market value of the bond to its total value is higher than that of subcategory 1. Thus, subcategory 2 can be classified as a pure bond. Subcategory 3 is classified as an institutional-customized bond category as its market value of term bonds accounts for a high proportion of its total value and its average number of holders is in single digit, implying that these funds are mainly held by several institutional investors.Regarding category 10, the holdings of stocks of subcategory 1 accounts for more than 20%, and there is no excessive leverage. Accordingly, subcategory 1 is classified secondary bond. Subcategory 2 is classified as low dividend stock as most of its funds invest in low dividend stocks. Subcategory 3 has a very similar feature to subcategory 1 in terms of shares of stock and bond holdings. However, further investigation shows that the average market value of the funds within subcategory 3 is less than 1 billion RMB (while the figure for subcategory 1 is 1.9 billion RMB), and there is a relatively high proportion of hybrid funds within this subcategory. This indicates that subcategory 3 is mainly made up of fixed income and new funds established for the issuance of new stocks in the primary market. Thereby, subcategory 3 is classified as a new stock category. The secondary classification results for categories 1 and 10 are shown in Table6.To test the creditability of our classification results, we average the daily rate of return of the funds in each category and employ several industry style indexes (in which we select CITIC class I industry classification index as the industry index and we employ Juchao index as style index) as reference. We conduct our test by calculating the correlation coefficient between the calculated return in each category and the reference index. The results are shown in Table7. One can see from Table 7 that category 3 has the highest correlation with CITIC food and beverage index, reaching 94%. The correlation between the return in category 4 and the CITIC pharmaceuticals index is high at 97%. The correlation between the rate of return of category 5 and the CITIC power and new energy index is 94%. The rate of return of category 7 has a high correlation coefficient with CITIC power and new energy, computers, electronics, and military industry indexes.Table 7
Correlation categories and benchmark sector index (CITIC)
CITIC indexCategory 3 (%)Category 4 (%)Category 5 (%)Category 7 (%)Food and beverage94746558Pharmaceuticals82977267Power and new energy74679485Computers64627792Communications57576880Electronics64578193Military56526984Table8 summarizes the correlation between fund returns and Juchao style index for categories 2, 6, 8, and 9, which are not classified as industry-themed categories, as in Table 6. (Thus, industry indexes, such as CITIC indexes, are inappropriate to evaluate its industry classification results, while style index, for example, Juchao index, are more suitable for the evaluation of their style classifications.) From Table 8, we can see that our classification method has high accuracy in identifying the styles of these categories. To be specific, category 2 has a higher correlation with market style indexes defined by the Juchao style index; category 6 is closer to SME market; category 8 is similar to market value, and category 9 alike SME growth. (In recent years, fund managers pay more attention to funds that are growing while less attention is paid to value investing. Thus, the classification result of category 8 is less pronounced WIND database: https://www.wind.com.cn/en/edb.html.)Table 8
Correlation result of other stock categories (Juchao style index).
Juchao indexCategory 2 (%)Category 6 (%)Category 8 (%)Category 9 (%)Small value82908875Small growth90978890Medium value83889175Medium growth96979296Large value73708861Large growth95879292


## 5.2. Return Prediction Analysis

We use the four industry-themed categories (i.e., categories 3, 4, 5, and 7) for the fund price prediction analysis. The data used is the cumulative return of all funds in these four categories from February 2019 to July 2021, totaling 604 days. The PyTorch deep learning framework is used to build the model; 80% of the data sets are used to train the model, and 20% are used to test the model. The input data is divided into 10 dimensions through embedding. The ResNet model includes 7 layers of fully connected networks, containing 16, 16, 10, 16, 16, 10, and 1 neuron. The LSTM model is made up of 1 layer and 64 neurons. The CNN model consists of three layers, and the number of filters is 8, 8, and 1, with the size of convolution kernel of 3. The batch size of all basic models is 1. The final output is obtained using the weighted summation of outputs of these three benchmark models (i.e., ResNet, LSTM, and CNN). The loss function curve of the model is shown in Figure5, from which one can notice that the loss function training and verification set become stable after the 20th iteration, and the convergence is good.Figure 5
The loss function and times of iteration.We then evaluate the performance of our model and three basic models using four indicators: RMSE, MAE,R2, and WMAPE. The results are shown in Tables 9 and 10 and Figure 6. One can see the prediction ability of ResNet is relatively the best in all categories in question (compared with other benchmark models) based on these indicators. For example, the average value of RMSE is 0.034 for all categories, which is lowest when compared with other benchmark models, and R2 is 0.96, which is the highest among other benchmark models. Although LSTM is one of the most effective models dealing with time series problems, it does not perform well as expected, with the average value of RMSE around 0.040 and R2 around 0.95, owing to limited features available and an insufficient number of samples. The poor performance of CNN, with an average value of RMSE around 0.037 and R2 around 0.95, is due partially to its inability to record historical information. As expected, one can see that our spatiotemporal ensemble deep learning model has a better performance in predicting the fund price, which reduces the mean of RMSE to around 0.026 and improves R2 to nearly 0.98. We can thus conclude that our model greatly improves the predictability, that is, the prediction accuracy, of fund price movement compared with these benchmark models as our model obtains the lowest (mean) values of RMSE, MAE, and WMAPE and the highest (mean) value of R2. The improvements lie in the merits of ensemble learning, which complements the advantages of these three benchmark models.Table 9
Prediction result for categories 3 and 4.
Category 3Category 4RMSEMAER2WMAPERMSEMAER2WMAPEResNet0.02670.02130.98900.01140.02910.02200.98060.0121LSTM0.03310.02660.98320.01430.03330.02600.97460.0143CNN0.03080.02370.98530.01270.03890.03230.96540.0176Spatiotemporal0.02190.01650.99270.00890.02620.02020.98430.0110Table 10
Prediction result for categories 5 and 6.
Category 5Category 7RMSEMAER2WMAPERMSEMAER2WMAPEResNet0.03290.02680.98780.01620.04660.03690.87320.0254LSTM0.04320.03490.97890.02110.04950.04150.85630.0286CNN0.03150.02570.98880.01550.04720.03810.86970.0263Spatiotemporal0.03030.02460.98970.01490.02720.02110.95650.0145Figure 6
Prediction results for different categories.Finally, we show the comparison between the actual values of those funds with our predicted values. The results are shown in Figure7. We can see that the predicted values and actual values show a high degree of similarity. This means our spatiotemporal ensemble deep learning model generates a good prediction for fund price, which suggests our model can provide a proper application for robo-advisors in terms of predicting fund price movements.Figure 7
Comparison between the actual values and predicted values.


## 6. Conclusion

This paper presents a novel fund price prediction tool, i.e., a spatiotemporal ensemble deep learning model, relying on fund classification, to predict the price of our selected funds, in the Chinese market. In this paper, we propose a two-step GMM to classify the mutual funds into different categories to ensure the funds classified in the same category have similar risk and return characteristics. We then employ our proposed model to predict the short-term price movement of each fund category.The main conclusions of this paper are summarized as follows. (1) Compared with the traditional K-means clustering method and network clustering method, our two-step GMM method can generate the probabilities that the funds belong to a certain category, (2) This paper adopts the idea of ensemble learning to improve the prediction ability of fund price movements of other models, i.e., ResNet, LSTM, and CNN models. (3) We classify funds based on their risk and return, which can effectively mitigate the problems of large fluctuations and disorders in the prediction process and thus improve the generality and application of our model.



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