IN
DEGREE PROJECT COMPUTER ENGINEERING, FIRST CYCLE, 15 CREDITS
STOCKHOLM SWEDEN 2017,
Trading with Artificial Neural Networks on Large-, Mid- and Small-Cap Stocks
Exploring if Market Cap has an effect on portfolio performance when trading with Artificial Neural Networks trained on historical stock data
LUCIA EDWARDS PATRIK FORSLIND
KTH ROYAL INSTITUTE OF TECHNOLOGY
SCHOOL OF COMPUTER SCIENCE AND COMMUNICATION
Trading with Artificial Neural Networks on Large-, Mid- and Small-Cap Stocks
Exploring if Market Cap has an e↵ect on portfolio performance when trading with Artificial Neural Networks trained on historical stock data
Lucia Edwards and Patrik Forslind
Degree Project in Computer Science, DD143X Supervisor: Jeanette Hellgren Kotaleski
Examiner: ¨Orjan Ekeberg
June 5, 2017
Abstract
In this report one-day ahead stock prediction using artificial neural networks (ANN) is studied on stocks belonging to di↵erent market caps.
Hennes & Mauritz, EnQuest PLC and Rottneros have been selected, rep- resenting large-, mid- and small-cap companies. This report aims to in- vestigate whether a company’s market cap a↵ects the ability to predict stock prices when ANNs are trained using historical stock data.
The study was carried out using feedforward ANNs and trained using the Levenberg-Marquardt backpropogation algorithm. The results from the study show that the large-cap company H&M was easier to predict than the mid- and small-cap companies.
Although the results from this study indicate that a company’s market cap a↵ects the ability to predict stock prices using ANNs, a deeper, more extensive investigation has to be carried out in order to draw any real conclusions.
Keywords: Artificial neural network, stock prediction, backpropoga- tion, market cap
Sammanfattning
I den h¨ar rapporten studeras endags aktieprognoser med hj¨alp av arti- ficiella neurala n¨atverk (ANN) p˚a aktier med olika marknadsv¨arden. Ak- tierna som har valts ¨ar Hennes & Mauritz, EnQuest PLC och Rottneros, som ¨ar exempel p˚a f¨oretag tillh¨orande high-, mid- och low-cap. Syftet med den h¨ar rapporten ¨ar att unders¨oka hurvida ett f¨oretags marknadsv¨arde p˚averkar hur v¨al det g˚ar att f¨orutsp˚a aktiepriser n¨ar ANN tr¨anas p˚a hi- storisk aktiedata.
Studien utf¨ordes med feedforward ANN som tr¨anandes med Levenberg- Marquradt backpropogation algoritm. Resultaten fr˚an studien visar att H&M, som hade h¨ogst marknadsv¨arde, presterade b¨attre ¨an EnQuest PLC och Roternos, som hade l¨agre marknadsv¨arden.
Trots att resultaten fr˚an denna studie indikerar att ett f¨oretags mark- nadsv¨arde p˚averkar f¨orm˚agan att utf¨ora aktieprognoser med ANN s˚a m˚aste en djupare, mer omfattande unders¨okning genomf¨oras f¨or att kunna dra n˚agra riktiga slutsatser.
Nyckelord: Artificiella neurala n¨atverk, aktieprognos, backpropoga- tion, marknadsv¨arde
Contents
1 Introduction 4
1.1 Problem Statement . . . 5
1.2 Scope . . . 5
2 Background 6 2.1 Stock Market . . . 6
2.1.1 Efficient Market Hypothesis . . . 7
2.1.2 Seeking Alpha . . . 7
2.2 Artificial Intelligence . . . 7
2.2.1 Machine Learning . . . 8
2.2.2 Artificial Neural Networks . . . 8
2.2.3 Learning Algorithm . . . 9
2.3 Stock Forecasting Using ANNs . . . 10
2.3.1 Configuration of the Network . . . 10
2.3.2 Other Related Work . . . 10
3 Method 11 3.1 Data Collection . . . 11
3.2 Artificial Neural Network . . . 11
3.3 Performance Measures . . . 12
3.4 Trading Strategy . . . 12
4 Results 13 4.1 Configuring and Training the Networks . . . 13
4.2 Trading Performance . . . 14
4.3 Comparison of Performance . . . 15
5 Discussion 16
6 Conclusion 17
References 18
1 Introduction
The stock market is extremely important for the world’s financial system. Sev- eral driving forces exist behind the stock market, one of the obvious ones is the strive to make money, both for companies and investors. If you look at the general stock market it always seems to go up over time[20]. There will however always be winners and losers, so picking the right stock is an important task for investors.
Automatic trading using computers began as early as the late 1990s and the market has only evolved from there [15]. How much of all trading that is done by computers today is hard to estimate since it is a very secretive world. A report from Morgan Stanley in 2012 stated that 84% of all trades on the US stock exchanges were done by algorithmic trading[23]. The amount of information available to base stock predictions on has been growing in recent years, making it impossible for people to analyze all the available data before making decisions.
The role computers will play in the future of stock trading will only continue to grow. Using various algorithms, it is possible for computers to analyze huge amounts of data and make trades in an instant [24].
Various approaches have been attempted in recent years using algorithms to forecast the stock market based on available data. Some examples of this are analyses of the huge information flow in tweets and other social media platforms, used to determine the general sentiment about companies, this type of analysis is called sentimental analysis [4]. It is also possible to apply more traditional analyses such as technical and fundamental analyses with the help of computers.
Some machine learning algorithms have been proven to perform particularly well at predicting how stocks will move. Examples of these are artificial neural networks and support vector machines [11, 26]. But a lot of research still remains to be done in the field to find the optimal set up for these algorithms.
The use of artificial neural networks to predict stock prices is a well stud- ied field, where many di↵erent approaches have been tried. Some studies have focused on the algorithms used to train the network and the number of lay- ers while others have focused more on the data used as input to the network.
Though no matter the focus, these previous studies have mainly been interested in stock prediction using stocks from established large-cap companies or market indices for example S&P 500 or OMXS30 [1, 25]. A less studied area are the riskier, more volatile mid- and small-cap stocks. In theory being able to predict the short term movements of these stocks could yield greater returns, since they generally have more potential to grow[8].
1.1 Problem Statement
In this study large-, mid- and small-cap stocks have been selected and the aim is to investigate if there’s a di↵erence in how well next day closing prices can be predicted for these stocks when artificial neural networks are used. The question this report will aim to answer is therefore:
Is there a di↵erence in portfolio performance when trading on stocks with artificial neural networks trained on historical data of companies from di↵erent market caps?
1.2 Scope
This study will be restricted by a number of factors including the access to financial data, processing capabilities, prior knowledge and time. Earlier studies of this type have had access to huge data sets not accessible to the general public. The study has been limited to measuring performance of one stock from each market cap. For this reason the study is more exploratory than actually producing definitive results, the aim being simply to give better knowledge and insight into the emerging challenges in a computer-based financial market and introduce a topic which could be interesting to research more thoroughly in future research.
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2 Background
The aim of this section is to provide the reader with background information, which will be needed in order to understand the rest of the report. Firstly the financial aspects of the study will be presented followed by general information about artificial intelligence and machine learning and a deeper description of the algorithm to be used in the study. Later artificial neural networks (ANN) and how they can be applied to stock forecasting will be presented. Finally work which is related to this report is presented.
2.1 Stock Market
A stock market is a place where companies can let investors trade shares of their business in the public domain. The market exists to increase liquidity in the stock and to open up for anyone to buy or sell shares in companies. Often companies o↵er their stock on these markets as a way of generating more money for the company. Stocks are traded based on the price that people are willing to sell and buy them for. The ask and bid price are what people on the market want to sell and buy shares for. When the ask and buy of a stock are matched the trade is executed instantly and therefore the supply and demand for a stock is basically what sets the price and valuation of a company publicly quoted.
These prices are constantly changing, with no one factor determining what kind of change will occur.
Market Index is often used as a measurement of the movements on the market as a whole. In Sweden the 30 most traded stocks on the largest Swedish Stock Exchange (Nasdaq OMX) have an index called OMXS30. This is often used as a benchmark when comparing the performance of your investments.
The companies listed on the stock market are categorized into three groups based on their market capitalization (market cap). The value of a company’s market cap is calculated by multiplying the current market price of the com- pany’s stock with the total number of shares a company has. This value then places each company into one of three categories; large-cap, mid-cap or small- cap companies, which is used instead of sales or asset figures to determine the size of a company. The market cap value will take other factors into account, such as risk, which is relevant to investors. Large-cap companies tend to be well known companies that act in large industries and therefore do not carry a lot of risk, where profit is seen in the long run. Mid-cap companies are often well known companies which operate in growing industries, they carry higher risk than large-cap companies but are more likely to give a profit over shorter periods of time. Small-cap companies are associated with the highest risk, often because of their age, size and the industry in which they operate. Because of these factors small-cap companies are often more susceptible to changes in the market [6].
Stock dividends and splits are two actions that a↵ect the value of a com- pany’s shares. A stock dividend is when a company pays shareholders in the form of more shares as opposed to a cash payout. This occurs when the com-
pany does not have sufficient funds to pay out in cash or when there are plans to invest [9]. Stock split is when a company divides shareholders existing stocks into more stocks. This a↵ects the price of the individual share but not the value of the shareholders shares as a whole [10].
There are several strategies by which to trade on the stock market. Buying stocks that you think are going to go up and selling them for a profit is probably the most obvious one. You can also bet against a stock that you think will decrease in value by taking something called a short position. Shorting a stock is when an investor pays to borrow stocks from a broker to sell it on the open market. The aim is to buy it back at a lower price and return it to the broker having made a profit[7].
2.1.1 Efficient Market Hypothesis
The Efficient Market Hypothesis (EMH) states that the market price always reflects all the factors known to the public which makes it impossible to “beat the market”, unless riskier investments are made. In financial theory the hypothesis is widely debated. In more recent years many critics of the theory have arisen.
These critics believe that stock prices can, at least in part, be predicted based on past patterns and other values and it could therefore be possible to outperform the market [5, 18].
2.1.2 Seeking Alpha
Alpha is a financial term for a measurement of investments generating returns that exceed the market index. Despite the EMH there exist several approaches in trying to forecast stocks and the stock market. Two of the most common ways to value a stock is technical analysis and fundamental analysis. Fundamental analysis focuses on financial factors such as a company’s balance sheet, market positions, credit value etc. and uses these to make an estimate of the com- pany’s intrinsic value. Technical analysis on the other hand bases its estimates purely on historical data such as the stock price and di↵erent key indicators.
A somewhat less common way of valuing a company or stock is by performing a sentimental analysis. This reflects the sentiment of investors who invest in a specific company or market.
2.2 Artificial Intelligence
In computer science Artificial Intelligence (AI) is a term which describes the development of software, where the aim is to simulate human intelligence. This includes, but is not limited to; learning, reasoning, recognition and self improv- ing software. There is no clear definition of what intelligence is and it is not possible to give a yes or no answer to the question “Is this machine intelli- gent?”[17].
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2.2.1 Machine Learning
Machine Learning (ML) is a field within AI focused on constructing algorithms which learn based on past experience, i.e that have not been explicitly told how to behave by the programmer. ML is a combination of computer science and statistics. The ML algorithms learn how to behave based on learning problems with sample data, through which they can build data models to base future decisions on [12].
Within ML there are mainly two types of techniques used when training the model, supervised and unsupervised learning. In supervised learning the goal is to develop a predictive model based on both input and output data. When doing unsupervised training only input data is used and this technique is mostly used for clustering of data. This paper will focus on supervised learning, more specifically, regression with Artificial Neural Networks.
2.2.2 Artificial Neural Networks
An artificial neural network (ANN) is an algorithm within machine learning that simulates the workings of the human brain. The synapses in the brain di↵er largely from the computational methods of a computer and outperform computers in many areas, for example pattern recognition and motor control.
That is why scientists have been attempting to construct computational models of the human brain since the 50’s, in hope that it will advance the field of machine learning [13, 19].
A simple reconstruction of the brain consists of billions of neurons that are interconnected via synapses. An ANN is constructed in a similar fashion and can easily be represented by a graph, where the nodes represent neurons and edges represent the synapses [13].
The artificial neuron is built up of three essential elements; a number of inputs, xi , each with a weight, wji, an adder which sums the weighted inputs and an activation function which computes the output, limiting the amplitude so small changes in input weight only cause small changes in output, giving the artificial neuron the desired functionality. A bias is added to the sum of the weighted inputs, this serves as a threshold value [13, 19].
ANNs can be single or multilayered which, as the names imply, either have a single layer of neurons or several layers that are interconnected, with the outputs of one layer being the inputs of the next. The layers that are neither the first input layer nor the final output layer are called hidden layers. Networks can be dealt into one of two groups, feedforward or recurrent depending on their interconnections. In a feedforward network there are no loops, one layer of neurons passes input to the next, whereas in a recurrent network there are loops which form circular paths. Although both types serve a purpose, the multilayered, feedforward network is most popular [13].
Figure 1: Neural network with two input nodes, one hidden layer with four nodes and an output layer with two output nodes
2.2.3 Learning Algorithm
Instead of having a programmer explicitly form a model of the real world based on observations an ANN receives real world data and is able to form its own model. The process through which this model is created is called the networks learning algorithm. For supervised learning the learning algorithm adjusts the inputs’ weights, wjiand bias value, so the network’s output corresponds with the desired value, i.e. the real world result. Given a set of training data the ANN will iteratively grow closer to being a correct model, this process stops when the ANN reaches its stopping criteria. The stopping criteria can be one or a collection of parameters, for example the number of iterations. In order to iteratively grow closer to the desired result the network sends the calculated error back to the start of the network, the mean squared error is used to calculate the error in this study. This form of learning algorithm is called backpropogation and for this study the Levenberg-Marquardt (LM) algorithm will be used. The LM algorithm is a combination of the steepest descent (SD) method and the Gauss- Newton (GN) method. Combining these methods results in an algorithm with the fast calculation ability of the GN method while maintaining the stability of the SD method. Given the calculated error the LM algorithm is used to re-adjust the nodes’ weights [13, 27].
During the learning process it is possible for overfitting to occur. Overfit- ting is when the error on the data used to train the network is small but when new data is introduced it gives a large error. This is due to the network sim- ply memorizing the training data as opposed to actually learning to generalise
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from it, as intended. In order to avoid overfitting steps can be taken, smaller data sets require less advanced functions, which lessens the risk of overfitting, regularisation and early stopping can also be used to avoid overfitting [16].
The ratio between the amounts of data used for training, validation and testing a↵ects the performance of the network. The training data is used so the network can update the node weights, validation data is used to determine how well the network is generalizing and stop training when generalization is no longer improving and the test data is used to measure how well the network performs during and after training.
2.3 Stock Forecasting Using ANNs
Many studies similar to the one in this report have been carried out, applying machine learning techniques to the stock market has been a popular field of study for the past decades. ANNs can be used to perform a technical analysis of the stock market. Using historical stock data as input it is possible to pick up on trends and predict future stock values. The ability ANNs have to generalize on nonlinear data makes them an ideal choice to model the volatile stock market by [22]. Feedforward ANNs are most commonly used when dealing with stock predictions, with several previous studies finding them to be superior to other ANNs. Backpropagation algorithms have also been shown to outperform other forms of training where stock predictions are concerned [25]. Market Cap has been Identified as one of the important datapoints for analyzing stock data using ANNs [21].
2.3.1 Configuration of the Network
As mentioned earlier there are multiple ways of configuring ANNs. Choosing the number of nodes in the hidden layer(s), selecting the best data points, dividing the training data and testing data etc are all examples of factors which a↵ect the network. In earlier research there have been many di↵erent ratios used for testing and training networks with historical stock data. For this study 70%
was used for training, 15% for validation and 15% for testing, which has been found to be sufficient in other research about ANNs and stock forecasting[14].
2.3.2 Other Related Work
Some research focuses mainly on the pre-processing of the input data when doing stock prediction with ANNs. Pre-processing by applying Independent Component Analysis (ICA) and Principal Component Analysis (PCA) have proven to increase prediction performance by reducing noice associated with stock data [3, 2].
Due to limitations mentioned earlier the focus of this report is only to inves- tigate the di↵erence in behaviour when training ANNs on historical stock data from di↵erent market caps.
3 Method
This section aims to give the reader a detailed description of how the study was carried out. Starting with which data was collected and why, how the ANN was initiated and trained and finally how the performance of the network is measured.
3.1 Data Collection
To train the network and simulate the algorithmic trading, historical stock data had to be collected. It was downloaded from Nasdaq OMX Group’s website.
The available data-points were: bid-, ask-, high-, low-, opening-, closing-, mean- , prices and volume, turnover and number of trades on every given date. The data was not directly compatible with our program and had to be converted and pre-processed before imported into our program.
• Reverse the order of the historical data into chronological
• Divide into training data and testing data
• Extract the selected data points for the Network
Due to the exploratory nature of this research a single stock was chosen from each of the market cap lists. The stocks chosen for the study were ENQ (EnQuest PLC), HM-B (Hennes & Mauritz), and RROS (Rottneros). They were chosen based on the fact that they have not changed market cap listing during the time span of the collected data. HM-B is a large-cap company, ENQ is mid-cap and RROS is a small-cap company. Data was collected for the past 7 years, 6 years for training and the final year to simulate trading on.
3.2 Artificial Neural Network
For each of the chosen stocks the ANN was implemented using MATLABs stan- dard library. The networks used were nonlinear autogressive neural networks with external inputs (NARXNET). The opening, high and low prices were used as the external inputs and the closing price as the internal input, resulting in four input nodes. Di↵erent configurations were experimented with in regards to the number of neurons in the hidden layer and number of delays. After exper- imenting with a range of configurations, as will be presented in the results, we used the configuration of 2 delays and one hidden layer with 10 neurons for the networks used in the trading simulation. Each network had one output node, the following days closing price.
For this study 70% of the training data was used for training, 15% for valida- tion and 15% for testing. The Levenberg-Marquardt backpropogation algorithm was used to train the network, which requires more memory than other algo- rithms but is stable and fast.
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3.3 Performance Measures
In order to measure the error the mean squared error (MSE) was calculated.
MSE is a commonly used metric for determining the error between a given value and an already known expected value. It is calculated by squaring the di↵erence between the two values and dividing by the number of values to obtain the average.
M SE = 1 n
Xn i=1
( ˆYi Yi)2
Where ˆYi is a vector of predicted values, Yi is a vector of real values and n is the number of predictions done to obtain ˆYi. A value close to zero represents a small error.
Training was done a number of epochs until the validation using MSE was no longer improving more than a certain threshold between epochs. In order to avoid overfitting the network to the training test data the last state of the network, before the MSE dropped below this limit, was then deployed.
3.4 Trading Strategy
Simulation of the algorithmic trading is also done in MATLAB. The trading strategy used is to buy and hold the stock as long as the next day closing price is predicted to be higher than the current day. If the next day closing price is predicted to be lower a short condition is created and the stock is sold.
In order to make the portfolio’s success rate easier to visualize and compare, an average of the portfolio share values will be plotted against the stock price.
When a new position is taken in the portfolio, it will be at a fixed number of shares at the current trading price.
4 Results
In the section below we present the results from training the networks and outcome of the simulated trading.
4.1 Configuring and Training the Networks
The configuration of the neural networks was done with 10 neurons in the hidden layer and a range of di↵erent delays for the closing price was tested to find the best configuration. The networks were trained two times with the range of one to four days of delay to see which configuration had the best performance. The results of the di↵erent configurations, MSE and R, are presented in tables 4.1- 4.3. MSE is the mean square error of the predicted price in comparison to the actual price and R is the result of the regression analysis.
Table 1: HM-B
Delay MSE R
1 15,74756 0,960067 2 14,77481 0,960763 3 16,60682 0,955781 4 17,35213 0,903689
Table 2: ENQ
Delay MSE R
1 2,53176e-2 0,986644 2 2,34032e-2 0,987364 3 2,48115e-2 0,987479 4 2,56882e-2 0,977479
Table 3: RROS
Delay MSE R
1 2,52088e-2 0,980047 2 1,79673e-2 0,989855 3 1,96427e-2 0,977915 4 2,81028e-2 0,977161
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4.2 Trading Performance
Presented below is the performance of the algorithmic trading portfolio in com- parison to the stock.
Figure 2: Hennes & Mauritz
Figure 4.1 shows Hennes Mauritz, which is a large cap company, in compar- ison to the trading algorithm. The graph shows that the algorithm outperforms the stock but is still very volatile.
Figure 3: EnQuest PLC
Figure 4.2 is EnQuest PLC, a mid-cap company, compared to the portfo- lio and you can see that the algorithm performs poorly in the beginning and manages to recover somewhat by the end of the year. The overall performance of the stock is still stronger and the portfolio did not have an alpha over the original stock.
Figure 4: Rottneros
Figure 4.3 shows the performance of the simulated portfolio in comparison to Rottneros stock, which is a small cap company. Here also the portfolio is outperformed by the real stock.
4.3 Comparison of Performance
Studying the results shows that the portfolio that performed best was the one trading on the large-cap stock HM-B. This was the only portfolio never to drop below the value of the traded stock. Below we discuss the outcome of the results and how it answers our problem statement.
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5 Discussion
Arguments can be made that our results indicate that large cap companies are easier to forecast with ANNs. This should not be considered to be a final answer to our problem statement as there are a number of limitations with this study.
Our results could be caused by a number of other factors ranging from network performance to data selection. Regarding the historical prices used to train the models they were adjusted to reflect dividends and eventual splits.
This might have had an impact on the performance of the networks. The data used in the simulation of the trading on the other hand was not adjusted to include eventual dividends. Though none of the stocks have had any splits during the year of data used for the algorithmic trading simulation. In order to truly measure the di↵erences several stocks would need to be selected from each market-cap, in this study other factors that are not market-cap could be causing the di↵erence in performance. By using several stocks from each market-cap the e↵ect of these other factors could be reduced.
One of the main research topics connected to this area is focused on reducing the noise surrounding stock data. This is in order to get better inputs for the neural network and produce better predictions. Due to the limitations of knowledge, time and data we had going into this study the outcome of the report does not conclusively answer the initial problem statement. A few steps that can be taken to further investigate this topic is a wider selection of stocks from each market cap, better pre-processing of the data and filtering can be done before feeding it in to the Neural Network. Focusing more on reducing the noise feeding into the network by for example applying techniques such as ICA or PCA could probably be done to improve the results.
Results from our algorithmic trading show that the network’s predictions were not accurate enough to give a definitive alpha over the traded stock. The method for the simulation of the trading does involve potential measurement er- rors since factors such as buy-ask spread have not been taken into account. Also the fact that eventual brokerage fees have not been calculated when simulating the portfolio, which would have generated less cumulative returns. Di↵erent trading strategies could have been tried to find the optimal one for each stock.
To reduce noise from the generated trading signal you could apply rules, filtering or some sort of threshold which could make the trading less frequent.
As stated in the introduction this report only seeks to explore the subject and was never meant to be a comprehensive study. A number of things can been done to further investigate this topic. Due to the limitations in the proceedings of this subject we refer from drawing any final conclusions.
6 Conclusion
Regarding the Efficient market hypothesis we can derive that our method cannot be used to support the hypothesis. We were not able to successfully use available data to gain alpha over the underlying stocks from di↵erent market caps. The EMH already is and, most likely will, continue to be a future topic of further research.
To decisively answer the problem statement a more comprehensive study would need to be carried out. As mentioned, a wider selection of stocks and better and more simulations would have to be done. Further analyses of the input parameters feeding into the network could also be done. As mentioned earlier a lot of the research surrounding algorithmic trading and stock forecasting with neural network is focused on reducing the noise surrounding stock data, which could be done in investigating this question as well.
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