We have researched how machine-learning techniques can be applied in software tools for personal investment portfolio planning. This paper contains a brief overview of different types of machine learning algorithms and a description of the mathematical model used to build the optimal investment portfolio. The newly demanded and not implemented feature of Fintech software tools for personal investments (such as Robo-Advisor) is to forecast rates of financial instruments to quickly rebalance the structure of investment portfolio to increase potential income and decrease losses of investors. The price forecasting methods proposed in the paper can be used for this feature. During the experimental part of our research, we implemented a software tool that builds an optimal investment portfolio using price predictions created by LSTM neural network and linear regression method. The results were compared to a portfolio built using only historical data on financial instruments price. The research shows that using LSTM neural network forecasted values allows building better investment portfolios even during the global stock market recession.
Modern methods of machine learning are actively used in many areas of human activity. The most
common use cases are optical character recognition, classification and clustering, time series
forecasting, etc. Machine learning (ML) systems and artificial intelligence (AI) destroy routine jobs and
create new human jobs. These jobs require new skills that have no analogues. Among these jobs are
trainers, explainers and sustainers [
This paper is devoted to a review of the possibilities of using supervised machine learning techniques
for the task of building an optimal investment portfolio for long-run investments of a client. This task
is one of the features of software tools that help people to manage their personalized investment and
insurance portfolios. Such software tools are called Robo-Advisors (RA). In one of our previous works
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2022 Copyright for this paper by its authors.
The purpose of this paper is to develop and implement a software tool for building an optimal investment portfolio using machine-learning techniques for time series of financial instruments’ profitability predictions.
Research objectives include the examination of which machine learning techniques can be applied to financial instruments' price prediction and profitability analysis of a portfolio built using only historical data with portfolios built taking into account price predictions.
The paper is structured as follows: Part 2 addresses the literature review. Part 3 describes the theoretical model behind the optimal investment portfolio generation and the experimental part of the research. Part 4 presents obtained results. Finally, the last part concludes.
Prediction of risk issues can be done using both classical machine learning (ML) and deep learning
(DL) techniques such as random forest, convolutional neural networks (CNNs) and long short-term
memory (LSTM). Although deep learning models (DL) are good prediction systems, it must be
confirmed whether in this field they behave better than other machine learning (ML) techniques.
Classical Python libraries like pandas is used for this pre-processing of food security data [
Other authors [
Robo-Advisors
Robo-Advisors are complex software tools, usually presented as web applications, which provide
all types of services for personal investments [
Linear regression (LR) is a classical machine learning technique that is used for modeling the correspondence between some dependent variable and one or more explanatory (independent) variables. Linear regression also shows which explanatory variables have more impact on the dependent variable value. It could be useful in case if we have a lot of input data and we want to reduce the number of inputs. We also used Long Short Term Memory (LSTM) neural network for predicting future price of different financial instruments. LSTM neural network is a kind of Recurrent Neural Network (RNN) that has special memory neurons, therefore they can store, filter and pass long-run dependencies from one layer to another. Such feature of LSTM neural networks makes them especially good in time series forecasting (e.g., return rates and standard deviations or risks of financial instruments).
Currently, using LSTM neural networks to predict prices for stocks, currency pairs, and other
financial instruments is being actively studied. The study by A. Staffini [
Application of machine learning algorithms to predict return and risk metrics of financial instrument
and corresponding development of backend development of web applications requires powerful
programming language. Python is an open source general purpose programming language. According
to the TIOBE Programming Community index, Python is the most popular programming language [
We used the Markowitz portfolio model for generating optimal investment portfolio. Markowitz
portfolio model is a mathematical framework that solves the optimization problem of assembling a
portfolio where expected return is maximized for a given level of risk (1) or when the level of risk is
minimized for a given level of expected return (2) [
{ { → ≤
≥ 0 ≥ →
≥ 0 1 + 2 + ⋯ + = 1 1 + 2 + ⋯ + = 1 a target function which minimizes the ratio of risk to profit (3). where N is a number of assets, is an expected return of the portfolio, is a level of risk (standard deviation), and is a percentage of asset in portfolio . For a risk neutral investor, we need to define (1) (2) (3)
The experimental part of this research includes comparison of the profitability of three portfolios. The first one is built based on the historical data on Close prices of different financial instruments for two years. We chose the following set of stocks for our experiment: AAPL, GOOG, MSFT, AMZN, INTC, AMD, NVDA, F, TSLA, JPM, MS, VOO. The set includes shares of companies from different sectors of the economy, such as high technology, microelectronics, engineering, banking, and finance. Data on the price history of all the companies listed above can be found in the public domain on the Yahoo Finance service. Close prices include all information after opening of assets trades, so close price is more relevant than open prices, maximal and minimal prices. Another two portfolios are built using additional data with forecasted Close prices for the next month. Predictions of the Close price for the next month were made for each financial instrument using the LSTM neural network and linear regression method. Comparisons of the obtained results are presented in Part 4. We used the Anaconda Data Science Platform for our machine learning tasks. Anaconda is a software distribution of the Python and R programming languages for scientific computing, including development, data processing, and visualization tools. It also aims to simplify package management and deployment on any operational system. The list of libraries that were used during development is presented in Table 2. Experimental part of this research consists of the following stages: • Collecting historical data from open sources. • Initial data processing. Removing rows with missing values and data normalization. • Generate predictions on next month's Close price for each financial instrument using LSTM neural network and Linear Regression. • Building an optimal investment portfolio based only on historical data. Building an optimal investment portfolio based on historical data and next month's predictions. • Comparing the effectiveness of three portfolios.
Here is a brief overview of the experimental part of our research. Listings 1 through 4 correspond to the first four steps of the workflow. We have used historical data on twelve stocks monthly close prices for ten years to train our ML models. After that, we got a prediction on next month's close price for each ticker. All data is retrieved using yfinance library which returns values as pandas dataframe object. After all data is loaded, it should be filtered from null values and scaled to values from 0 to 1. On the next code snippet, you can see the main function that accepts a dataframe object and a ticker name. This function splits data to train and test datasets, creates an LSTM model, trains in on train dataset and evaluates root mean squared error (RMSE), and returns prediction on next month Close price for a given ticker. The dataset was divided into training and test parts in a ratio of 3 to 1.
To determine the final prediction, we used the average of three independent LSTM model predictions. Each iteration has random initial weights; network is trained for 100 epochs. The result of each prediction may vary due to the stochastic nature of the algorithms used during the training process of the neural network. We have also defined a separate function for building a prediction using linear regression approach. Here we have no need to run training process more than once, because this algorithm has no randomized parameters. Previous month close price was determined as explanatory variable. The source code of the function is presented in listing 4. The last listing shows the usage of pypfopt library, that generates an optimal (in terms of min volatility) investment portfolio based on monthly Close price data for two years plus one value with prediction on next month Close price, which we’ve generated by LSTM network or LR model. All source code is available on GitHub via the link https://github.com/serhii1savchenko/invest-portfolio-generator.
Table 3 presents the results of the accuracy assessment of the LSTM and LR models on the test dataset by the RMSE score. Fourth and sixth columns show the ratio of the RMSE score to the value of the last known Close price. The most minor deviations for LSTM Close price predictions were obtained for tickers VOO, GOOG, and MSFT. The lowest deviations for LR predictions also were obtained for the same tickers. In two-thirds of the cases, the LR method gave better prediction results, however, the difference is not very high. Therefore, we have built investment portfolios using both LSTM and LR predictions.
Listing 4: Next month close price prediction using linear regression.
. The distribution of the shares of financial instruments in the portfolio built exclusively on historical data (Portfolio 1), the portfolio where the LSTM forecast for the next month was used (Portfolio 2), and the portfolio where the LR forecast was used (Portfolio 3) is presented in Table 4. All portfolios are built for risk-neutral investors. This is achieved by introducing a condition for minimizing the level of allowable volatility (listing 5, line 13). Based on these weights we calculated the dynamics of changes in the value of each of the portfolios during the first half of 2022. The initial balance of each portfolio is USD 100,000.
As we can see, all three portfolios lost in price, but the portfolio made taking into account LSTM price predictions shows better dynamics (less loss). Also this portfolio has the smallest difference between the expected and real value of 6-month income. Portfolio 1 (which was built only on historical dataset) has the biggest difference between the expected and real return. Figure 2 is a graph showing the percentage difference in the loss of the first portfolio relative to the second. For example, as of February 2022, Portfolio 1 lost USD 9653.74 while Portfolio 2 lost USD 9432.89. Thus, the portfolio made taking into account the forecast received a loss of 2.29% less than the base portfolio.
Thus, the paper contains a brief overview of different machine learning approaches which can be used in the scope of personal finance software tools. During the experimental part of our research, we developed a Linear Regression model and LSTM neural network that generate a prediction on next month's close price of defined financial instrument. The predictions are based on historical data of the financial instrument. We have also demonstrated that an investment portfolio that is build used not only historical data but also one-month prediction shows better results even during the global recession period. The paper doesn’t cover more sophisticated deep learning approaches for time series predictions. We are going to expand current research on using more complex LSTM models, which includes the windows method, multivariate time series forecasting, and using other methodologies for an investment portfolio building, such as Black-Litterman portfolio optimization model.