ETF Portfolio Construction via Neural Network trained on Financial Statement Data

The key idea of our method is based on the fact that an ETF is simply an aggregation of its components. Therefore, the future performance of an ETF may be predictable if a machine learning model is capable of predicting the future performance of its components. The overall procedure of our method, which is illustrated in Fig 1, is designed to achieve this purpose and is described as follows.

The first step is to train our neural network to predict the future performance of individual stocks based on financial statement data. Our neural network takes the past 2 years, or 8 quarters, of financial statement data consisting of balance sheets, income statements, and cashflow statements of stock c as input and outputs $o_{t}^{c}$ at each time t. Our neural network is trained to predict the 3-month ahead performance (the price change from t to t+1) of the stock c. This procedure is depicted at the left side of Fig 1.

After training, scores are assigned to the individual stocks and the ETFs at the test stage. As depicted in the right side of Fig 1, our trained neural network assigns a score to each of the component of $ETF_{t}^{1}$ based on its financial statement data. Note that the four neural networks at the right side of Fig 1, are actually the same network with the same parameters. The purpose of the illustration is to emphasize that our neural network does not take the aggregated input of multiple stocks at once, it takes the input of the individual stocks independently.

After assigning scores to all components of $ETF_{t}^{1}$, the score of $ETF_{t}^{1}$, which is $S_{t}^{1}$, is calculated based on the scores of individual stocks. By using the values ($o_{t}^{1}$, $o_{t}^{2}$, $o_{t}^{3}$, and $o_{t}^{4}$) from our neural network and the weights provided in PDF of $ETF_{t}^{1}$, score $S_{t}^{1}$ can be calculated in a quantitative manner. In other words, score $S_{t}^{1}$ is calculated by averaging the multiple of the score and weight of the individual stocks composing $ETF_{t}^{1}$.

After the scores are calculated for all of the ETFs in the investment universe at time t, the portfolio of ETFs at t is constructed based on the scores of ETFs.

First, approximately 1200 of the top liquid stocks (based on data from Jan. 2021) listed on the US stock market are considered as the data for our experiments. To eliminate noise, at each time step, the suspended stocks and the stocks with no trading volume are eliminated. More specifically, the stocks that are not traded for longer than 5 days over the 3-month timespan are eliminated. Thus, the number of valid stocks that are used in our training and experiment changes over time.

After the stocks were chosen, the financial statement data¹¹1The type of financial statement data used in our method is listed in the appendix. and daily closing price data were collected for these stocks. In the US, financial statement data are usually released quarterly. These releases occur approximately 2 to 12 weeks after the last business day of the previous quarter. In other words, financial statement data for the first quarter are generally released between the last day of March and June. Therefore, to prevent using not released data as an input, the financial statement data for the first quarter are not used as an input feature until the last business day of June.

Closing price data are used to generate labels on training stage, and evaluate the performance on test stage. Since our neural network is trained as a binary classification problem, the label is generated based on the 3-month ahead percent change of each stock. To avoid the long bias issue, the training data are neutralized by assigning ”up” to the top 50% of the companies and ”down” to the bottom 50% of the companies based on the 3-month ahead percent changes at each time t. Considering the release period of financial statement data and operating issues, our neural network is trained on a quarterly basis.

The data of individual stocks are collected over 22 years (Jan. 2000 - Apr. 2022) and divided into training and test sets. The first 10 years (Mar. 2002 - Mar. 2012) of data are used as training data, and the last 10 years (Mar. 2012 - Apr. 2022) of data are used as test data. Approximately 70% of the training data are used for training our neural network, and the other 30% of the data are used for optimizing the hyperparameters. All of the financial statement and closing price data are collected from Morningstar.

Similar to individual stocks, only the ETFs that are listed on the US stock market are considered as our investment universe. In addition, since individual stocks that are listed on the US stock market are used for training our neural network, ETFs that consist of individual stocks that are not listed in the US stock market are also excluded.

Two groups of ETFs are selected for our investment universe²²2The description of our investment universe is provided in the appendix. . First, 11 ETFs that track the 11 Global Industry Classification Standard (GICS) sectors in the US stock market are selected as the classic group. The ETF data in this group are collected over 10 years (Mar. 2012 - Apr. 2022), which is the same period as the test data from individual companies. Next, 26 ETFs with an inception date after 2017 are selected as the exotic group. The ETFs in the exotic group are selected based on their inception date and net asset value (NAV). The ETF data in the exotic group are collected starting from the inception date of each ETF to Apr. 2022.

After the ETFs are chosen, the daily closing price data and PDF of each ETF are collected. The daily closing price is used to evaluate the performance of our method. The PDF provides the historical weight of each component (i.e., individual stocks) of the corresponding ETF. Entire PDFs and the closing price data of ETFs are also collected from Morningstar.

In this subsection, the shape of the input and the architecture of our neural network are provided. Among various choices of the network architecture, we attempted to keep the network architecture as simple as possible, since proposing a novel network architecture is not one of our main research contributions. The overall architecture of our neural networks is illustrated in Fig 2.

The input of our neural network at time t is the past 8 quarters of financial statement data. The size of the input vector is 8 $\times$ f, where f is the number of financial statement features.

The architecture of our neural network consists of 5 fully connected layers followed by 1 softmax layer. Five fully connected layers consist of 8 $\times$ f $\times$ 64, 64 $\times$ 32, 32 $\times$ 16, 16 $\times$ 8 and 8 $\times$ 2 parameters. The first four fully connected layers contain a batch normalization (Ioffe and Szegedy, 2015) layer followed by ReLU. Xavier initialization (Glorot and Bengio, 2010) is used for initializing the parameters in the network.

In the first stage of our method, our neural network is trained to predict the performance of the next quarter of individual stocks based on financial statement data.

When the training process using individual stocks is complete, scoring ETFs using this trained neural network is quite straightforward. Fig 3 provides an illustration of the overall process for scoring ETFs, which is described as follows.

First, for each $ETF_{t}^{e}$, our trained neural network assigns a score to the components of $ETF_{t}^{e}$, as follows.

Next, the score of $ETF_{t}^{e}$ is calculated based on the score and weight of its components.

To evaluate the performance of our method, we conduct an experiment on our test period with two groups of ETFs. Since the performance of our trained neural network on individual stocks is crucial for the performance on ETFs, we also conduct an experiment on individual stocks. The test period is from Mar. 2012 to Apr. 2022 for experiments on both individual stocks and the classic ETF group and from June 2020 to Apr. 2022 for the exotic ETF group. We select the starting date of the experiment on the exotic ETF group based on the number of valid ETFs⁴⁴4See appendix for the list of inception dates. . From June 2020, the number of ETFs in the exotic group exceeded 10.

In our experiments, we assume that the rebalancing interval is 3 months and conduct rebalancing on the last business days of March, June, September, and December. As described in the Individual Stocks Data Description section, only accessible financial statement data at each rebalancing time are used as input for our trained neural network. There are two main reasons why we fixed our rebalancing interval as 3 months. The first reason is that our neural network is trained based on financial statement data of individual stocks, and the release period of the financial statement data is 3 months. Another reason is that an excessively high turnover ratio may result in high trading costs and difficulty in operation, especially when managing large amount of asset.

For our experiments, a portfolio is constructed based on the score described in the previous section as follows. First, the ETFs (or individual stocks) in the investment universe for each experiment are sorted based on their scores at each time t. Here, only valid ETFs or individual stocks are considered. Next, top scoring ETFs (or individual stocks) are selected and invested for the next 3 months.

As mentioned in the Methods section, our method of scoring ETFs is based on the softmax output of our trained neural network. Therefore, before conducting experiments on ETFs, validating whether the stocks with higher softmax output values outperform the stocks with lower softmax output values is necessary.

The portfolio is constructed as follows. At each rebalancing time t, all the valid stocks at time t are sorted based on their score $s_{t}^{c}$, assigned by the output of our trained neural network. Then, the top K % of the valid stocks are selected and invested until time t+1, which is the next rebalancing time. An equal weight is assigned to each of the selected stocks. Our experimental period is approximately 10 years (Mar. 2012 - Apr. 2022), and the average number of valid stocks is 1017. Note that the number of valid stocks changes over time.

Table 1 provides a summary of the experimental results on individual stocks. Each row represents a portfolio. For example, Top 80$\%$ refers to the portfolio consisting of the top 80% of all valid stocks with the highest score. We compare our annualized return with two baselines, the S&P 500 index and equal weight portfolio, which is exactly the same as the Top 100$\%$ portfolio.

The results clearly show that when the portfolio assigns more of its asset to the companies with higher scores, the annual return is increased.

In this section, the experimental results on two different groups of ETFs are provided. As mentioned in the ETF Data Description section, these two groups are the classic group and the exotic group. The purpose of conducting experiments on two different groups is as follows.

First, the ETFs in the classic group have a relatively long history and track 11 GICS sectors in the US stock market. Additionally, the components of these 11 ETFs are mutually exclusive and cover a large portion of the major stocks in the US stock market. Therefore, we reason that this group is more appropriate for evaluating the general performance of our method for a long period of time. In contrast, the ETFs in the exotic group usually consist of more thematic stocks, and the length of the historical data for these stocks is short. Thus, naively applying advanced machine learning methods, such as neural networks, to this group of ETFs is literally impossible.

By conducting experiments on two different types of ETFs, we attempted to show that our method generally outperforms the baselines over a long period of time, and unlike most of the previous works that use the same types of data on training and test stages, our method can be deployed for constructing portfolios of ETFs that have an extremely short period of historical time series for training neural networks. For this reason, we have not compared our method with previous works. Since most of the existing studies require a certain amount of data for training the proposed machine learning model, applying those studies to our dataset is not feasible.

The construction of portfolios of ETFs is very similar to that for portfolios of individual stocks. First, at each rebalancing time t, all valid ETFs are sorted based on their score $S_{t}^{c}$, and the top K % of valid ETFs or top K valid ETFs are selected and invested for the next 3 months. The equal weight is assigned to the selected ETFs.