Twitter : the modern-day trading floor : a comparative analysis of dierences in returns for trading strategies based on positive and negative sentiment extracted from Twitter

Bachelor Thesis

Twitter: The Modern-Day Trading Floor

sentiment extracted from Twitter

Willem-Jan Kemperink

June 26, 2018

Universiteit van Amsterdam

*E-mail address: willem-jan.kemperink@student.uva.nl. I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it. All omissions and errors are my own. The University of Amsterdam is responsible solely for the supervision of completion of the work, not for the contents.

I study to what extent differences are present in trading returns based on positive and negative sentiment as extracted from Twitter. The Twitter data concerns companies listed on the Dow Jones and the Dow Jones Industrial Average. It is first of all confirmed that Twitter contains statistically significant information regarding changes in the daily open price. Furthermore, a positive relation is present between levels of Twitter sentiment polarity and differences in the daily open price. Three variables axes are considered for investigating differences between both sentiments. The first axes concerns the period of aggregating Twitter information. Positive trades produce the highest profits at a two-day aggregation,

while negative trades produce this at a three-day aggregation. The results also indicate significant

differences are found in favour of the aggregated total of negative returns. The second axes concerns how long a position is held open. The results indicate that positive trades benefit from holding periods from seven-plus days, while the highest profits for negative trades are found at two-to-three days. Significant differences are found in favour of the aggregated total of positive returns. The third and final axis concerns the threshold for sentiment polarity. No significant differences are found.

2 Literature Study 1

2.1 Media and Twitter . . . 1

2.2 Volume versus Sentiment . . . 3

2.2.1 Volume . . . 3

2.2.2 Sentiment . . . 4

2.3 Continuous versus Event-Based Data Analysis . . . 5

2.4 Human Behaviour . . . 6 2.5 Trading Strategies . . . 7 3 Methodology 9 3.1 Data sets . . . 9 3.1.1 Twitter-Data . . . 9 3.1.2 Stock-Data . . . 10 3.1.3 Preliminary Analysis . . . 11 3.2 Trading System . . . 12 3.2.1 Random Strategy . . . 12 3.2.2 Individual Strategy . . . 13 4 Empirical Results 15 4.1 Preliminary Analysis . . . 15 4.2 Trading System . . . 17 4.2.1 Random Strategy . . . 18 4.2.2 Individual Strategy . . . 18 4.2.2.1 Sentiment Aggregation . . . 18

4.2.2.2 Position Holding Period . . . 21

4.2.2.3 Thresholds . . . 23

5 Conclusion 25

4.1 OLS Varying Thresholds . . . 16

4.2 Analysis Stock Prices . . . 17

4.3 Results Twitter Aggregation . . . 20

4.4 Results Holding Period . . . 22

4.5 Results Varying Thresholds . . . 24

A.1 Residual Diagnostics . . . i

A.2 R-Squared and Correlation . . . ii

A.3 Analysis Sentiment Polarity . . . iii

A.4 Mean Returns after SP . . . iv

List of Figures

The technology-sector has seen tremendous growth in the 20th and 21st century, and as a result of this technological revolution, social-media companies have been able to establish themselves as leading tech-companies. The technological revolution gave rise to personal devices such as computers and smart phones, which enabled social-media stalwarts such as Facebook, Twitter and Instagram to provide the personal life of friends and strangers at just the click of a button. The constant awareness of other peoples lives has led some to even coin this the “4th-dimension” in life (Scott, 2015). These social networks generate vast amounts of data on general public behaviour and may therefore provide valuable insights into the sentiment of the public.

Although Facebook, Twitter and Instagram each provide previously unknown glances into the life of friends and strangers, some nuances are present within these platforms as to how they operate. Facebook and Instagram focus more on sharing images and activities that capture the imagination of those following you, while Twitter provides a more basic insight into someone’s daily routines, moods and thoughts through “tweets”. A tweet is a 140-character reflection of a contributor’s mind and emotion at a particular time. Twitter, therefore, may be argued to be a truer reflection of emotion of the general public and consequently, is often used as the medium of choice to proxy public sentiment. (Sprenger, Tumasjan, Sandner, and Welpe, 2014a).

A key area where this information may be of interest is finance. A classical school of thought in finance is the “Efficient Market Hypothesis” (Fama, 1970). It assumes that all pub-licly available information is already accounted for in the stock price and that no advantage can be taken by analysing the past. Price-fluctuations will reflect the availability of new information and since news generally is unpredictable, prices follow a random-walk. This would imply that analysing social-media data cannot provide an investor with new insights about the movement of prices. The hypothesis, however, has often been challenged in academia, where data suggests that prices actually do not follow a random walk (Qian, 2006). Furthermore, it is also suggested that social-media may contain indicators concerning economic trends and may therefore provide insights into how news will affect prices (Bollen, Mao and Zeng, 2010).

There are two dominant approaches for extracting investor sentiment from Twitter. These approaches focus on the question of what the best indicator is to gauge investor sentiment regarding a specific company: is it the volume of tweets or the sentiment within each tweet?

Moat, Curme, Avakian, Dror and Stanley (2013) used the volume of Dow-Jones listed company-pages visited on Wikipedia as an indicator whether the stock of that company would rise or fall and used this as a buy-sell signal. The other approach would be to analyse the sentiment within each tweet. This approach classifies each tweet according to a predetermined set of mood-states. Zhang, Fuehres and Gloor (2011), for example, found that emotional tweets negatively correlated with the Dow-Jones, NASDAQ and S&P 500. Bollen et al. (2010) also opted for sentiment-analysis and used multiple language-processing techniques to analyse tweets. His results indicated that predicting movements of the Dow-Jones could be significantly improved by incorporating certain mood classifications for tweets.

The second point of consideration is the choice of time-frames, which can be applied to four aspects. First, which time-frame regarding Twitter-data and prices is most efficient? Should data be considered on the minute-, daily- or weekly-level? Zheludev, Smith and Aste (2014) investigated changes in the sentiment of tweets and prices on an hourly basis for example, while Bollen et al. (2010) and Sprenger, Sander, Tumusian and Welpe (2014b) used the aggregated daily total of tweets. Second, what is the time-frame to establish a trading signal? Is a one-day divergence sufficient to buy or sell or does one wait for a “confirmation” of a trend? Third, how long will the effect of the signal last on the price? Ranko, Aleksovski, Calderell, Grcar and Mozetic (2015) found for instance that abnormal returns can last for several days after irregular events. This will affect the decision of how long a position should be held open. Fourth and lastly, will the trading strategy be operating continuously or only around certain events (Moat, 2013; Ranko, 2015)?

Assuming that one is able to extract sentiment from Twitter, how should this subse-quently be interpreted? Human behavioural analysis is essential for translating investor senti-ment to actual real-time actions from these same investors. How do investors react to profits and losses on their portfolio? Kahneman and Tversky (1979; 1983) their research points out that an asymmetry is present between the feelings after earning profits or making losses of similar monetary values. This is directly linked to the stock market. How do investors react to profits and loses on their portfolio?

The theories in behavioural economics combined with the new streams of data avail-able through Twitter, raise the question whether investor sentiment on Twitter also leads to asymmetries in returns on the stock market. This leads to the main research question:

To what extent are significant differences present between trading returns based on positive and negative Twitter sentiment?

The remainder of the paper is structured as follows. Chapter 2 discusses current literature regarding the analysis of Twitter-data. The methodology and data set are explained in chapter 3. The results are presented in chapter 4 and subsequently interpreted in chapter 5. Finally, chapter 6 summarises all of the above and ends with some concluding remarks regarding future research.

Literature Study

The main research question will be answered by constructing a sentiment-based trading strategy and subjecting the trading results to statistical analysis. Literature concerning Twitter, human-behaviour and the stock-market have to be discussed before such a trading strategy can be set-up. They will form a basis for the model put forward in chapter 3.

First and foremost, a framework for understanding how news may impact prices and the kind of role Twitter may play in this framework is necessary. Media plays an important part in investor decision-making, since new information may uncover previously unknown and unforeseen difficulties and opportunities of a company. Secondly, the vast amount of data provided by Twitter warrants the question of how tweets can and should be interpreted. Third, different techniques for analysing and aggregating data are discussed. Some authors consider data on a continuous basis, while other authors try to identify special events and only consider the data around these events to be relevant. This is directly linked to a trading strategy: will it operate continuously (i.e., a stock is bought and/or sold every day or week) or only around certain events? The fourth subsection discusses the theories of loss-aversion and prospect theory put forward by Kahneman and Tversky (1983). These theories may explain asymmetries in human decision-making. They will act as a basis for investigating the potential differences between the effects of positive and negative tweets on trading strategies. The fifth and final subsection gives a brief overview of current trading strategies that employ Twitter-based criteria and data. It discusses potential parameters and the time-frequency on which strategies may operate.

2.1

Media and Twitter

The “Efficient Market Hypothesis” (EMH) formulated by Eugene Fama in 1970 pro-poses that all available information is directly incorporated into a stock price and that only the availability of new information pertaining to a stock will lead to changes in the underlying stock price. The market is said to be “efficient”. He argues that news is generally unpredictable and therefore stock prices are as well. According to Fama, investors are theoretically incapable of making abnormal returns if their strategy is based solely on analysing publicly available in-formation or market-timing. Notwithstanding the importance of the general theory formulated

by Fama, assumptions underlying the EMH have been challenged numerous times in literature. This may provide room for abnormal returns.

Firstly, Chan (2003) examined the effect of public news releases on a subset of stocks. He compared the differences in returns for a company when no significant information had been released with the returns after significant news had indeed been released. Chan finds evidence of a drift in stock prices after news-releases, especially after negative information is released. This implies that markets under-react to new information and that news, in contradiction with Fama, is not directly reflected in prices changes. If this is indeed the case, investors stand to benefit by analysing (old) news in order to make a trade-decision.

Like Chan (2003), Antweiler and Frank (2004) also challenged the EMH and wrote one of the first papers that incorporated the new stream of online data. They tested the assumption that news is unpredictable, as formulated by Fama (1970), by exploring potential relationships between online user posts and stock prices. To this end, they investigated the potential effect of user posts on stock prices. More than 1.5 million messages that were posted on Raging Bull and Yahoo! Finance (online message boards) were analysed in order to test whether increased bullishness had any effects on stock prices. Although the economic effects were small due to transaction costs, statistically significant evidence is found that increased volume in posts on message boards predict negative returns the following day.

Bollen, Mao and Counts (2011) also find evidence contradicting the supposed unpre-dictability of the financial markets. They looked at whether online data sets (Google Search queries, Twitter) hold any predictive power regarding market indices and “traditional” investor sentiment trackers such as public surveys. Evidence was found that although news may be unpredictable in itself, social-media may contain indicators regarding certain economic trends. Furthermore, Twitter Investor Sentiment with a lag of up to two days is found to be a statistically significant predictor of daily log returns of the Dow Jones Industrial Average (DJIA).

This is supported by Sprenger et al. (2014a). According to them, stock micro-blogs and Twitter contain valuable information that is yet to be fully reflected by current market indicators. Their approach is able to identify news events that may move the market, based on data-feeds extracted from Twitter. They also argue that Twitter is an appropriate source of information because tweets are generally written from the perspective of investors. Tweets may therefore be a good representation of investor sentiment, which in turn can have an impact on stock market prices. The above literature provides evidence against assumptions made under the EMH. Investors may very well stand to gain from analysing information that is not completely

new. Furthermore, some authors have also demonstrated the validity of Twitter data. This supports the choice of Twitter as an appropriate medium for analysing sentiment-based return differences.

2.2

Volume versus Sentiment

Past literature has primarily focused on sentiment analysis to extract the general mood from online posts. Sentiment analysis tries to extract a particular emotion from each individual post. A simple, non-adapting Lexicon-based approach may be to look at particular words (“love”, “hate”) or advises (“buy”, “short”), while more advanced methods, such as those based on machine-learning, may go a level deeper and find nuances in how positive or negative words are actually formulated (Smailovic, 2014). It is hypothesized that large scale sentiment analysis should be able to give an indication of the Twitter investor sentiment, which would act as a proxy for real investor sentiment. The focus in this paper is on the differences between positive and negative signals as extracted from Twitter and therefore sentiment analysis is an obvious key aspect. The following section will nevertheless briefly discuss how online data volumes may be used for predicting stock market prices. Sentiment analysis is discussed thereafter.

2.2.1

Volume

Volume may be measured by how often a name and/or symbol relevant to a particular listed stock or other financial instrument is mentioned, or how often a page has been visited. Changes in volume may tell something about investor sentiment. This approach formed the basis for the research of Moat et al. (2013). In their research they investigated whether a connection between the stock price and changes in weekly levels of Wikipedia-page visits of a respective company are present. They construct a strategy that buys (sells) a particular stock based on whether the number of weekly page-visits of the respective company has decreased (increased). The results of this strategy are compared to those of a strategy that randomly buys and sells a stock each week. The returns of the “Wikipedia-strategy” are found to be significantly higher than the returns of the random strategy and they therefore concluded that volume may help explain changes in stock prices.

Mao, Wang, Wei, and Liu (2012) also focused on volume as the leading indicator. They considered potential relationships between the volume of tweets mentioning Standard & Poor 500 (S&P 500) stocks and the underlying stock prices. They find a positive relationship between the volume and these indices and furthermore, conclude that forecasting models that include Twitter-based indicators are more accurate for predicting the direction of closing prices.

2.2.2

Sentiment

Neoclassical economic theory dictates that investors are rational actors. They seek to maximise profits (Simon, 1955). This notion of rationality may however be a simplification of reality. Although investors indeed wish to maximise profits, they are not always capable of actually doing so. This is due to the potential obstructing role that emotions play in decision-making (Bollen et al., 2010). Twitter sentiment, in this regard, may act as a proxy for human emotions, indicating what the emotions of the general public may be. Knowing what the overall sentiment is among investors may therefore provide very valuable insights into the direction of the market. This is the reason that researchers are often interested in the sentiment of tweets, rather than the sheer volume of tweets mentioning a specific stock. They try to anticipate changes in the market direction by extracting the underlying meaning of each individual tweet and aggregating them to find the general investor sentiment.

Sentiment analysis lies at the core of research done by Ranco, Aleksovski, Caldarelli, Grcar, and Mozetic (2015). Over 1.5 million financial tweets (from June 1st, 2013 to September 19th, 2014) are subjected to sentiment analysis in order to study the relation between sentiment and stock price returns of the 30 companies in the DJIA. A time-series for each sentiment is built for each respective company and analysed alongside the stock price time-series. Furthermore, they construct a new metric, called “sentiment polarity1 ”, denoted by Pt. This metric gives an

indication of how polarized the opinions are regarding a specific stock. Absolute values close to zero entail higher levels of polarization.

Pt=

tw_t+− tw−_t tw_t++ tw−_t

where the total positive or negative amount on day t is denoted by tw+/−_t .

They find that SP during identified events indicate which direction the market will head.

Zheludev et al. (2014) consider both tweet sentiment and volume. A comparative analysis is conducted between both. They constructed an Information Theory metric, both for tweet sentiment and volume, in order to determine to what degree tweets contain lead-time information about stocks. Their comparative analysis finds sentiment to be more statistically significant in leading-time information than the volume of tweets and conclude that sentiment may be a better indicator than volume.

Sprenger et al. (2014b) support this view and argue that “taking news sentiment into account is essential”. Their results indicate that the sentiment of tweets may be more predictive of the future direction of stock prices than tweet volumes. Zhang et al. (2011) come to a similar conclusion. They find that the emotion in each tweet (“hope” and “fear”) is significantly related the Dow Jones, S&P 500 and NASDAQ.

While the authors above treat emotions more or less as a binary set, Bollen et al. (2010) look at a range of six emotions (“calm”, “alert”, “sure”, “vital”, “kind” and “happy”). They investigate whether public mood measurements extracted from Twitter are correlated and can even predict values of the DJIA. Only “calm” and “happy” are found to have significant predictive power for stock market prices. Overall, however, they conclude that they have found affirmative results that show that public sentiment may indeed be extracted from tweets and be used for prediction. Their results indicate that including Twitter feeds and public mood significantly improve the directional-accuracy of DJIA predictions. An accuracy of 87.6% for predicting the daily up and down is obtained. These results may have been the reason that subsequent research of Twitter sentiment, such as those mentioned earlier, have treated emotions as either positive, neutral or negative.

2.3

Continuous versus Event-Based Data Analysis

Just as there are a multitude of approaches to analyse the sentiment within tweets, many different methods exist for deciding on which time-frame Twitter data should be treated. Two approaches are predominantly found in literature: event-based or continuous analysis.

Ranco et al. (2015) make use of the event-study methodology in order to analyse the effects of Twitter sentiment on stock prices. The event-study method tries to identify special events through ex-post identification and data analysis. This is done in order to eliminate po-tential “noise” stemming from small, insignificant events. In this particular case, the authors tried to identify those days on which abnormal volumes of tweets and sentiment are present. If these volumes exceed a certain threshold they are called “events”. These events are treated as if standing on their own, where a range of data points before and after the event is in-vestigated. Traditional examples of (ex-post identified) events are earning announcements or potential mergers, but every statistically abnormal data point may be identified as an event.

Moat et al. (2013), on the other hand, treat the data differently. As mentioned in section 2.2.1, they used volumes on Wikipedia-visits of companies in the Dow Jones in order to construct a trading strategy. Although aggregating the data on a weekly basis, each week a

decision is made to either buy or sell a stock. They therefore treat data on a continuous level and do not zoom in on particular data points that exhibit large spikes. This method is also chosen by Mao et al. (2012). As mentioned earlier, they correlated S&P 500 daily Twitter data with S&P 500 daily stock prices and related indicators. They construct a linear regression model is used to predict stock market indicators, where Twitter is an exogenous input.

2.4

Human Behaviour

Extracting sentiment from tweets is very valuable, but interpreting and linking this sentiment to human behaviour may be of even greater importance. In two seminal papers in behavioural economics, Kahneman and Tversky (1979; 1983) develop the theory of ”loss-aversion”. This theory is linked to how humans perceive gains and losses. In here they find that if people are given two scenarios with equal economic results, but where the situation is either framed as gaining or losing, people generally make asymmetric decisions. In their study, participants were presented with two scenarios. In the “positive” scenario, participants start with $1,000 and can either win $1,000 or $0 with a 50/50 percent chance (option A) or win $500 with a 100% change (option B). In the “negative” scenario, participants start with $2,000 and they either lose $1,000 or $0 with a 50/50 percent chance or lose $500 with 100%. The majority of participants chose B (secure option) in the positive scenario, while choosing A (risk-taking option) under the negative scenario. They conclude that there is a pronounced difference in how people experience losses and gains. “Losses loom larger than gains” (Kahneman & Tversky, 1979), since the pain of losing is found to be almost twice as large as the gratification experienced by gaining.

These asymmetries in human behaviour form the basis for the research by Moat et al. (2013) mentioned earlier. In this, they theorise that since people care more about avoiding losses than on making gains, they will probably do relatively more research when planning to sell. Therefore, increases in the volume of page visits of a company Wikipedia-page should correspond to a subsequent future decline in the stock price of that particular company. They construct a trading strategy based on this assumption and find that this strategy performs statistically better than a random strategy of buying and selling.

Ranco et al. (2015) also find differences in the effects of positive and negative events. Their event-study supports the notion that negative emotions may be more pronounced than positive emotions. The cumulative abnormal returns for negative events are almost twice as large (circa two percent) as those for positive events (circa one percent). This suggests that negative investor sentiment may have a larger impact on stock prices than positive sentiment.

2.5

Trading Strategies

Although the body of research on relationships between Twitter and stock markets is ever increasing, not much of it has been dedicated to implementing past research into an actual trading strategy. This may very well be because authors are simply not willing to share profitable trading strategies. This section will discuss some of the trading strategies publicly available that implement sentiment extracted from Twitter and other media.

First of all, Moat et al. (2013) use changes in weekly volume of Wikipedia page-visits of DJIA companies as a basis for a trading strategy. The trading strategy operates on a continuous, weekly basis where stocks are either bought or sold. The basis for this decision is the assumed inverse relation between page-visits and price changes. Increases in weekly page-visits for week t constitute a sell-signal, while a decrease constitutes a buy-signal. The specific stock is subsequently bought or sold in week t + 1. The results are then compared to a random strategy, which buys and sells a particular stock each week with a 50/50 percent chance. Significant positive returns of 0.5 percent are found for the “Wikipedia” strategy.

Zhang and Skiena (2010) focused on Twitter as a key input for making trading deci-sions. They constructed a market-neutral trading strategy to demonstrate the predictive power of news data. Their strategy first ranks all companies in the data set according to the daily sentiment for each respective company. According to their ranking, equal amounts of capital are deployed to buy (sell) a predetermined amount of companies who had positive (negative) sentiment.

Four variable parameters are chosen:

1. N: number of stocks in the portfolio, divided equally over buy/sell orders

2. S: sentiment analysis window size

3. H: how long stocks are held

4. C(l) and C(u): lower and upper bounds for market caps

They varied each of these parameters, while holding the others fixed. The results indicated that an investor “should hold small numbers of selected stocks, use short sentiment-calculation and stock holding periods, and avoid holding medium-sized firms”.

While Moat et al. (2013) and Zhang et al. (2010) deploy continuous trading strategies, Goel and Mittal (2011) use a non-continuous trading strategy. A predictive model, implementing

an earlier performed sentiment analysis based on Twitter data, forecasts the closing DJIA values one day in advance. They additionally calculate the running standard deviation and average of all stocks for the previous k days. A buy (sell) signal is established if the predicted stock value for the next day is n (m) standard deviations from the current mean. The optimal parameters are found to be: n = m = 1 and k = 7 or 15.

Methodology

Chapter 2 has shown that there is a considerable amount of statistical evidence that Twitter contains useful information about the stock market. These results are taken into account in order to construct a trading strategy to investigate to what extent there are differences in trading returns for positive and negative Twitter sentiment present.

The data set, obtained from Ranco et al. (2015), which contains stock prices and Twitter sentiment data on the 30 stocks listed on the Down Jones, is first discussed. The pre-liminary investigation of the data is discussed secondly. This analysis will establish a connection between the financial data and Twitter, and will act, alongside the discussed literature, as a basis for the trading strategies. Furthermore, a quick analysis of the stock market for the period covering the data set is given. Third and lastly are the principles of the trading strategies. These trading strategies are deployed to investigate whether any real-world significant differences are present between positive- and negative-induced sentiment trading.

3.1

Data sets

3.1.1

Twitter-Data

Ranco et al. (2015) collected over 1.5 million tweets for the period spanning from June 1st, 2013 to September 18th, 2014. Tweets are short messages that generally contain the expressions and feelings of the user. Tweets regarding stocks generally include a “cash-tag” with the ticker of the stock, for example “$AAPL” for Apple. Search-queries with cash-tags for the tickers of DJIA-listed companies were used to filter the tweets. They constructed a Support Vector Machine (SVM) classification model to extract the sentiment from each tweet. The possible sentiments in a tweet are: positive, negative and neutral. Before an SVM model can actually extract the sentiment, it first has to “learn” from a data set where tweets are already classified as a certain sentiment. To this end, ten financial experts labelled over 100,000 tweets according to the above mentioned three sentiments and this data set was fed to the SVM model. The underlying method of extraction is not within the scope from this paper and will thus not be discussed. Five time series are created for each DJIA-listed company, based on

sentiment-classified tweets. These are:

1. Tweet volume, T Wt: total number of tweets on day t

2. Positive Tweets, tw+_t : number of positive tweets on day t

3. Neutral Tweets, two_t: number of neutral tweets on day t

4. Negative Tweets, tw_t−: number of negative tweets on day t

5. Sentiment Polarity, Pt: metric, ranging from -1 to 1, which gives an indication whether

sentiment is positive (Pt> 0) or negative (Pt < 0) on day t, given by:

Pt=

tw_t+− tw−_t tw_t++ tw−_t

The data set shows that on some days, no positive and negative tweets are present. This would obviously mean that the SP metric is impossible to calculate due to having zero in the denominator. I subsequently re-value this metric to zero in order to correct for this problem. This practice is in line with Sprenger et al. (2014b) and Antweiler and Frank (2004).

3.1.2

Stock-Data

The fact that the Twitter data set of Ranco et al. (2015) is used, makes that the choice of financial data is limited to those companies for which the sentiment Twitter data is available. This limitation is fortunately not too restrictive, since data still covers thirty companies listed on the Down Jones, which are some of the largest and most wide-known brand in the world.

For these companies, four daily prices are retrieved from Yahoo! Finance: high, low, open and close. A fifth time-series, the log market return, is further created and will act as the dependent variable. The log market return1, rather than the actual price by one of the four indicators listed above, is taken in order to correct for the obvious auto-correlation between prices of today and the immediate past. The return on day t for company i is given by:

Ri,t = log(OP ENi,t− OP ENi,t−1)

The opening price of a stock, rather than the closing prices, is taken to measure price changes. This is due to the fact that the Twitter data supplied by Ranco et al. (2015) is aggregated on a daily level. This limits the comparison of Twitter data on day t with stock data

on the same day (f.e., the closing price), since Tweets might have been sent after the market had closed. It is therefore natural to only consider Twitter data that has been sent before day t as to not distort the information that was actually available. It is more sensible to consider the opening price, since this is a truer reflection of the start of a new day.

While the Twitter dataset provides data on a daily level, stock data is confined to just weekdays. The data does not contain prices for the weekends and for public holidays due to the fact that exchanges are then closed. Missing values are replaced through linear interpolation. The interpolation method approximates the missing value (Pt) based on the previous non-missing

value (Pt−1) and the next non-missing value (Pt+1). To account for the fact that sometimes more

than one value is missing between (Pt), Pt+1), the variable (λ) is used to indicate the relative

position of the missing value (Eviews). The formula is given by:

Pt= (1 − λ)Pt−1+ λPt+1

3.1.3

Preliminary Analysis

A trading strategy is built upon certain principles that guide trading decisions. These building blocks need to have a basis in the data. The preliminary analysis will try to establish and validate connections between SP and daily changes in the opening prices. The first step is to set-up an autoregressive AR(1) model to estimate differences in daily changes in the opening price (∆OP ENt) by looking at lagged values of (∆OP ENt). The first model for company i is

therefore given by:

∆OP ENt,i = αi+ β1,i∆OP ENt−1,i+ εi,t

This model will then be extended to by adding SP (∆P OLt,k) aggregated over k days,

for k = {1, 2, . . . , 7}. The model will consider lagged values up to seven days, due to the fact that information generally is disseminated quite quickly (Fama, 1970). The second model for company i is given by:

∆OP ENt,i= αi+ β1,i∆OP ENt−1,i+ β2,i∆P OLt−1,k+ εt, for k = {1, 2, , 7}

Supplementary to these two regression models are a correlation analysis and an analysis of the mean returns following increases and decreases in sentiment polarity. The models will enable a comparison and subsequent interpretation of the relevance of Twitter for the stock prices. The additional correlation analysis will shed further light on the direction of a possible

relation. The information that results from these regressions and tests are, along with previous literature, implemented in the trading strategy.

A final analysis will focus on the market conditions found in our dataset. This analysis investigates whether possible biases in returns are to be expected due to the fact that the stock market predominantly rose or declined during June 1st, 2013 to September 18th, 2014.

3.2

Trading System

The aim of this paper is not to find the best model to predict how stock prices change based on Twitter sentiment data. This paper takes a rather practical view and tries answer to what extent trading returns based on positive and negative sentiment differ. It is obviously necessary to first set-up a trading strategy that produces trades based on both sentiments. These trades subsequently provide information on the possible magnitude of the differences between positive and negative sentiment.

The proposed strategy will be quite simple, as to ensure that other possible aspects of a trading strategy do not blur and complicate the interpretation of the results. The SP for stock i will determine whether a stock will be bought or sold. This is the basis of the trading strategy. How the level of the SP should be interpreted will be determined by the preliminary analysis.

3.2.1

Random Strategy

In order to present a true reflection of the average percentual returns over all companies and the whole time-period, 100 simulations will be run. It should theoretically make no profits (or losses) as trading decisions are made on a randomised basis. Returns with a mean around zero give weight to the fact that in order to make profits with the proposed strategy, “skill” is required and not just sheer luck.

The total returns will first be subjected to a Jarque-Bera test. The null-hypothesis under this test is that the returns come from a normally distributed distribution or not. Either a Student’s t-test or a two-tailed, one-sample Wilcoxon signed-rank test will be run in order to test whether the returns indeed are not significantly better or worse than zero. The null hypothesis under this test is that the sample comes from a distribution centered around zero against the alternative hypothesis that it is not. The advantage of the Wilcoxon signed-rank test is that it does not require that the samples are normally distributed, unlike the Student’s t-test.

3.2.2

Individual Strategy

The principles guiding the buying or selling short of a company under the random strategy will also hold for the individual strategy. The individual strategy, however, takes an approach similar to Zhang et al. (2010) in section 2.5, by considering several variable axes. These are: horizon to aggregate sentiment polarity, number of days a position is held open and different thresholds of the SP. The first two axes stem directly from the questions raised in section 2.3, while the third axes is a natural point of consideration. The horizon for aggregating SP and for holding a position open will be varied from one to seven days. The threshold for positive-induced trades will be differed from 0 to 0.5 in steps of 0.1, while similar, but negative, thresholds will be considered for trades induced by negative sentiment.

To enhance the interpretability of the results, only one of the three axes will be subject to change at a time. The other two axes will be set to a default value. The default values are:

1. Time horizon for aggregating Twitter sentiment: 1 day

2. Position holding period: 1 day

3. Threshold for SP: 0.0

I argue that setting the aggregation and holding periods to one day gives the simplest interpreta-tion of the results, since setting it at, for example three days, further warrants an extra dimension to be interpreted. The threshold of 0.0 is intuitively the natural threshold for seperating positive and negative sentiment.

The strategy will aggregate for each company and for each sentiment, the return that is earned per trade and will subsequently calculate the average. This makes it possible to see how changes in one of the axes affects the average return. Furthermore, this strategy will enable a comparison between returns for positive- and negative-induced trades per company, as well as on a whole per level in the changing axis. The returns are also subjected to two tests. A one-tailed, one-sample Wilcoxon signed-rank test is deployed in order to test whether the mean returns are significantly larger than zero. The second test is a two-tailed, two-sample Wilcoxon rank-sum test for testing whether returns from both sentiments are significantly different from each other. The null-hypothesis for the rank-sum test is that the two samples come from a continuous distribution with a shared median, against the alternative hypothesis that they are not. Like the Wilcoxon signed-rank test, the Wilcoxon rank-sum test does not require normally distributed returns. The test assumes that the two samples are independent. It is argued that

this indeed holds for the positive- and negative-induced trades, since realised returns do not depend on how well or bad a trade performed in the past.

Throughout both strategies, zero transaction costs are assumed. This assumption weighs more heavily for some strategies and combinations and others, but as per Moat el al. (2013), “this assumption does not have consequences for conclusions about the possible rela-tionship”.

Empirical Results

This section presents show the results of the preliminary analysis as laid out in the previous chapter. The preliminary results will be incorporated into the trading strategy, whose results are presented in section 4.2. The interpretation and analysis of the trading strategies will be put forward in chapter 5.

4.1

Preliminary Analysis

Before a trading strategy can be constructed, it is first necessary to investigate whether a statistical connection between the Twitter data and stock prices is present. Results of the analysis are found in Table 4.1. Table A.1 and Table A.2 in the appendix show the residual diagnostics and correlation results. Table 4.1 shows the results of the two regression models: the model with and without Twitter data. The difference in open price on day t will act as the dependent variable, since the object of the preliminary analysis is to investigate whether Twitter has a relation with stock prices. The results indicate that for the first model, the lagged dependent variable is only significant for four companies. Furthermore, the R-squared is almost equal to zero. Predicting the daily open price change by considering the previous daily change is therefore not useful.

The model is then extended by adding SP aggregated for k days, where k = {1, 2, , 7}. The results show that for 26 out of the 31 stocks, SP aggregated over the previous day is statistically significant. The number of stocks for which the aggregated SP is significant declines as the time-horizon increases, and it is only significant for nine stocks when aggregated over the previous seven days. The R-squared values for the second model show increases compared to the first model, but it is still quite low.

Table 4.1: OLS Varying Thresholds

Beta significance AXP BA CAT CSCO CVX DD DIS GE GS HD IBM INTC JNJ JPM KO MCD MMMMRK MSFT NKE PFE PG T TRVUNH UTX V VZ WMT XOMDJIA Significant k = 0Lagged dependent variable0.09 0.23 0.158 0.08 0.045* 0.179 0.382 0.7230.187 0.004**0.583 0.325 0.055 0.813 0.012* 0.865 0.757 0.012* 0.308 0.352 0.395 0.591 0.055 0.7630.122 0.873 0.617 0.598 0.603 0.48 0.23 4 k = 1Lagged dependent variable0.175 0.925 0.502 0.025* 0.129 0.055 0.169 0.7810.767 0.043* 0.069 0.821 0.085 0.891 0.006**0.897 0.93 0.007**0.87 0.203 0.542 0.218 0.047*0.7120.379 0.629 0.134 0.424 0.855 0.1520.719 5 Polarity0.019* 0** 0** 0.007**0.005**0.005**0** 0.0570** 0** 0** 0.001**0.021*0.023*0.002**0.007**0.096 0.059 0** 0** 0.041*0** 0.155 0.59 0.008**0.003**0** 0** 0** 0** 0** 26 k = 2Lagged dependent variable0.251 0.788 0.563 0.017* 0.188 0.101 0.134 0.8340.997 0.053 0.022* 0.535 0.099 0.918 0.007**0.885 0.988 0.011* 0.814 0.165 0.556 0.384 0.036*0.7320.345 0.503 0.118 0.38 0.997 0.0920.684 5 Polarity0.002**0** 0.002**0.001**0.006**0.081 0.003**0.0660** 0.002**0** 0.032* 0.078 0.057 0.027* 0.036* 0.021*0.09 0** 0** 0.05 0.024* 0.12 0.6980.032* 0** 0** 0.007**0.002**0** 0** 23 k = 3Lagged dependent variable0.234 0.518 0.404 0.013* 0.186 0.099 0.174 0.8320.922 0.052 0.036* 0.501 0.087 0.927 0.006**0.963 0.985 0.017* 0.68 0.178 0.48 0.424 0.053 0.8090.303 0.451 0.127 0.467 0.927 0.0750.594 4 Polarity0.017* 0.01* 0.027* 0** 0.005**0.098 0.007**0.0890** 0.017* 0** 0.056 0.119 0.153 0.03* 0.047* 0.082 0.271 0** 0.001**0.216 0.04* 0.345 0.8250.027* 0.001**0** 0.028* 0.01* 0** 0.002** 21 k = 4Lagged dependent variable0.108 0.377 0.3 0.015* 0.167 0.124 0.224 0.7020.703 0.011* 0.083 0.533 0.069 0.934 0.016* 0.868 0.875 0.021* 0.618 0.202 0.354 0.453 0.094 0.8130.282 0.618 0.222 0.743 0.768 0.0940.402 4 Polarity0.096 0.048*0.085 0.001**0.01* 0.184 0.023* 0.1630** 0.063 0** 0.056 0.16 0.129 0.143 0.059 0.17 0.847 0.001**0** 0.249 0.016* 0.796 0.5960.024* 0.007**0** 0.074 0.032* 0** 0.007** 15 k = 5Lagged dependent variable0.093 0.351 0.242 0.019* 0.133 0.12 0.249 0.7440.585 0.008**0.139 0.501 0.053 0.959 0.018* 0.883 0.866 0.022* 0.53 0.208 0.349 0.421 0.1 0.7840.194 0.649 0.324 0.631 0.713 0.0940.355 4 Polarity0.258 0.071 0.267 0.002**0.033* 0.127 0.048* 0.0990** 0.224 0** 0.055 0.559 0.157 0.423 0.226 0.274 0.99 0.003**0.001**0.388 0.007**0.711 0.9230.141 0.008**0.001**0.057 0.056 0** 0.035* 12 k = 6Lagged dependent variable0.082 0.379 0.243 0.022* 0.104 0.14 0.281 0.7460.559 0.006**0.173 0.499 0.05 0.977 0.018* 0.968 0.828 0.023* 0.459 0.238 0.332 0.435 0.099 0.8220.153 0.718 0.41 0.603 0.717 0.1120.331 4 Polarity0.44 0.03* 0.176 0.004**0.116 0.375 0.119 0.2330.001**0.351 0.001**0.057 0.593 0.115 0.338 0.212 0.618 0.777 0.01* 0.005**0.533 0.02* 0.57 0.8580.268 0.025* 0.005**0.046* 0.041* 0** 0.044* 13 k = 7Lagged dependent variable0.071 0.383 0.221 0.024* 0.105 0.13 0.282 0.7360.528 0.006**0.231 0.484 0.051 0.985 0.019* 0.942 0.82 0.022* 0.391 0.243 0.317 0.443 0.097 0.8310.108 0.79 0.488 0.588 0.697 0.1010.331 4 Polarity0.904 0.053 0.33 0.005**0.067 0.198 0.094 0.2850.005**0.314 0.006**0.081 0.482 0.129 0.51 0.414 0.788 0.933 0.032* 0.002**0.836 0.014* 0.622 0.8950.804 0.045* 0.013* 0.066 0.078 0** 0.059 9

The second part of the preliminary analysis covers characteristics and developments of the stock market and the Twitter data. The results can be found in Table 4.2, and Table A.4 and Table A.3 in the Appendix. The Twitter data show a strong bias towards positive SP. The number of days with positive sentiment is 81% on average. This bias is strengthened as Twitter is aggregated over a longer time-horizon. This asymmetry is clearly shown in Figure 4.1. The histograms show a strongly right-skewed distribution in favour of positive SP. The average goes from circa 75% to almost 90% when varying the aggregation period from one to seven days. The average polarity stays relatively equal.

Table 4.2: Analysis Stock Prices

Market Conditions AXP BA CAT CSCO CVX DD DIS GE GS HD IBM INTC JNJ JPM KO MCD MMM MRK MSFT NKE PFE PG T TRV UNH UTX V VZWMT XOM DJIAAverageDistribution Price: begin$ 75.89 $ 99.36 $ 85.91$ 24.23$ 122.35$ 55.84$ 63.05$ 23.37$ 161.51$ 78.68$ 208.40$ 24.89 $ 84.27$ 54.60$ 39.95$ 96.77$ 110.51$ 48.93$ 34.93$ 61.83$ 27.29$ 76.87$ 34.99$ 83.78$ 62.78 $ 95.18$ 178.75$ 48.42$ 75.06$ 90.53$ 15,123.55 -

-Price: end$ 90.68$ 129.27$ 104.85$ 25.21$ 125.21$ 69.78$ 90.80$ 26.35$ 188.26$ 92.85$ 194.54$ 35.05$ 107.89$ 61.74$ 41.98$ 93.95$ 147.42$ 60.75$ 46.81$ 81.85$ 30.76$ 84.52$ 35.35$ 95.33$ 88.51$ 109.10$ 215.57$ 50.04$ 76.45$ 97.08$ 17,267.21 - -Gain % 19.5% 30.1% 22.0% 4.0% 2.3% 25.0% 44.0% 12.8% 16.6% 18.0% -6.7% 40.8% 28.0% 13.1% 5.1% -2.9% 33.4% 24.2% 34.0% 32.4% 12.7% 10.0% 1.0% 13.8% 41.0% 14.6% 20.6% 3.3% 1.9% 7.2% 14.2% 17.3% -Number of days with increases in price 262 255 276 246 246 256 288 241 254 258 225 250 262 249 228 238 284 255 258 258 238 255 231 256 265 268 267 236 251 240 272 253.81 54.3% Number of days with decreases in price 207 213 193 221 222 211 184 218 213 207 245 202 203 220 233 230 188 213 214 213 229 208 238 210 204 201 205 234 215 226 201 213.58 45.7% One-day positive SP % 81% 88% 64% 87% 80% 81% 94% 94% 66% 82% 79% 90% 81% 47% 84% 57% 88% 87% 89% 91% 85% 78% 90% 70% 80% 88% 86% 90% 57% 81% 93% 81.0%

-The DJIA and it’s listed companies enjoyed considerable growth for the period span-ning the dataset. Table 4.2 shows that 28 out of 30 companies experienced increases in stock prices, with an average growth of 17.3%. Furthermore, only one company had more days with decreases in the daily opening price than increases. This shows that the market was in a overall upward trend. The results on the mean return in Table A.4 of each stock following an increase or decrease in SP, highlight that differences are present between the one-day returns for both sentiments. The returns in stock prices after positive sentiment compared to those after nega-tive sentiment are higher in circa 90% of the cases. Furthermore, the returns are almost always positive for each stock after periods of positive sentiment, while stock returns are also positive after negative sentiment. This results in negative trading returns if that stock has been sold due to negative sentiment. At the one-day aggregation of SP, negative trades experience positive returns for sixteen stocks. Increasing the aggregation of SP over a longer time-frame, however, decreases the amount of profitable mean returns to (almost) zero. This is confirmed by the Wilcoxon signed-rank test. The null-hypothesis of the test is whether the returns are larger than zero. We see that the this is generally true after positive sentiment, as well as for after negative sentiment if the SP aggregation period is longer than one day.

4.2

Trading System

The trading results are presented in the current section. The results from section 4.1 show that Twitter data is indeed statistically significant in predicting how the opening price will behave. The results also indicate that there is a positive relationship present between the magnitude of the SP and the daily changes in the open, which means that stocks are bought if the SP is positive and sold short if the SP is negative. This section will cover the results of three variable axes as metioned in section 3.2.2.

4.2.1

Random Strategy

The random strategy buys and sells stocks based on randomised one-day SP. The 100 simulations each produce returns for all 473 days and 31 stocks. Figure 4.2 below displays the distribution of returns for both sentiments combined. The figure’s results are in line with the intuitive results: the mean of the returns is circa zero. A Jarque-Bera test for normal distribution is performed to test the null hypothesis that the returns are normally distributed against the alternative hypothesis that it is not. The p-value of 0.000 indicates that we should reject the null-hypothesis of a normal distribution and therefore conclude that there is not enough statistical evidence to conclude that the returns are normally distributed. This means that a Student’s t-test is not valid for testing whether the returns are not significantly different from zero. The two-tailed, one-sample Wilcoxon signed-rank test is therefore used. The results of the test (p-value = 0.312, signed-rank = 2.5255e+13, alpha = 0.05) indicate that the null-hypothesis of zero mean is not rejected. The random-strategy acts as theorised: it has neither positive nor significantly negative returns.

Figure 4.2: Distribution Random Total Trades

4.2.2

Individual Strategy

4.2.2.1 Sentiment Aggregation

The results for changing the sentiment aggregation axis are shown in Table 4.3. This table shows the mean return for each stock per aggregation level, as well as the p-values of the Wilcoxon ranksum test.

circa 55% of the time. The average return per aggregation lag lies around 0.08%, with the average number of trades slightly below 400. Increasing the aggregation period for SP increases the number of periods with positive sentiment, as was shown in the preliminary analysis. Lastly, we see that the median aggregation-lag with the highest average profit is for one-day aggregation, with an average of 2.1 days. The Wilcoxon signed rank test further shows that at all levels returns are significantly higher than 0%.

The negative-induced trades show slightly different results. The number of profitable trades is also circa 55%, but the average return is around 0.24%. The number of trades is considerably lower compared to the number of positive trades, ranging from 59 to 83. The index at which the highest mean returns can be found is slightly higher: a median of three days and an average of 3.3 days. The Wilcoxon signed rank test again shows that the aggregated total of all returns based on negative trades per aggregation level is significantly higher than 0%.

A Wilcoxon ranksum test is performed for each company in order to test whether the returns for positive and negative trades for each respective stock differ significantly. The related p-values are found in the third part of Table 4.3. The results indicate that for each aggregation level, only a small number of companies demonstrate significant differences in returns from positive and negative trades. The Wilcoxon ranksum test is also employed to test whether all positive and all negative trades as a whole are significantly different from each other. The results indicate that for a two-to-six day aggregation lag significant differences are indeed present. Whatsmore, for lags of one to six, the rank-sum test finds at a 5% significance level that negative-induced trades outperform positive-negative-induced trades.

T able 4.3: Results Twitter Aggregation P ositiv e AXP BA CA T CSCO CVX DD DIS GE GS HD IBM INTC JNJ JPM K O MCD MMM MRK MSFT NKE PFE PG T TR V UNH UTX V VZ WMT X OM DJIA Mean return Mean n um b er of trades Profitable trades Signed-rank p-v alues 1-da y 0.10% 0.10% 0.15% 0.07% 0.05% 0.12% 0.11% 0.03% 0.21% 0.13% 0.10% 0.13% 0.08% 0.12% 0.03% 0.05% 0.09% 0.09% 0.13% 0.11% 0.04% 0.09% 0.03% 0.01% 0.15% 0.08% 0.11% 0.07% 0.11% 0.05% 0.04% 0.09% 355 56.2% 0* 2-da y 0.10% 0.09% 0.19% 0.08% 0.05% 0.12% 0.11% 0.03% 0.17% 0.13% 0.08% 0.12% 0.08% 0.17% 0.01% 0.05% 0.09% 0.07% 0.12% 0.08% 0.06% 0.08% 0.01% 0.08% 0.19% 0.10% 0.11% 0.02% 0.09% 0.05% 0.03% 0.09% 383 56.1% 0* 3-da y 0.09% 0.09% 0.18% 0.07% 0.05% 0.09% 0.10% 0.03% 0.16% 0.10% 0.07% 0.11% 0.07% 0.19% 0.01% 0.05% 0.09% 0.07% 0.11% 0.07% 0.06% 0.05% 0.01% 0.07% 0.16% 0.10% 0.10% 0.01% 0.10% 0.05% 0.03% 0.08% 394 55.6% 0* 4-da y 0.06% 0.09% 0.19% 0.06% 0.05% 0.09% 0.08% 0.03% 0.15% 0.09% 0.07% 0.10% 0.07% 0.19% 0.02% 0.05% 0.09% 0.06% 0.10% 0.07% 0.06% 0.05% 0.00% 0.07% 0.14% 0.08% 0.08% 0.01% 0.08% 0.06% 0.02% 0.08% 399 55.3% 0* 5-da y 0.07% 0.09% 0.18% 0.06% 0.05% 0.08% 0.08% 0.03% 0.13% 0.08% 0.07% 0.09% 0.07% 0.16% 0.01% 0.05% 0.09% 0.07% 0.10% 0.06% 0.04% 0.04% 0.00% 0.04% 0.13% 0.07% 0.06% 0.01% 0.09% 0.05% 0.03% 0.07% 401 55.0% 0* 6-da y 0.06% 0.08% 0.17% 0.06% 0.04% 0.08% 0.08% 0.03% 0.13% 0.06% 0.06% 0.09% 0.07% 0.20% 0.01% 0.04% 0.09% 0.07% 0.11% 0.06% 0.03% 0.05% 0.00% 0.04% 0.11% 0.06% 0.06% 0.01% 0.08% 0.04% 0.02% 0.07% 403 54.8% 0* 7-da y 0.06% 0.08% 0.15% 0.05% 0.03% 0.07% 0.08% 0.03% 0.11% 0.05% 0.04% 0.08% 0.07% 0.23% 0.00% 0.04% 0.09% 0.06% 0.10% 0.05% 0.04% 0.04% 0.00% 0.05% 0.12% 0.05% 0.06% 0.01% 0.09% 0.04% 0.03% 0.06% 405 54.6% 0* Highest profit at lag 2 1 4 2 3 2 2 1 1 1 1 1 2 7 1 5 7 1 1 1 3 1 1 2 2 2 1 1 1 4 1 0.08% 391 55.4% Median lag 1 Av erage lag 2.1 Negativ e AXP BA CA T CSCO CVX DD DIS GE GS HD IBM INTC JNJ JPM K O MCD MMM MRK MSFT NKE PFE PG T TR V UNH UTX V VZ WMT X OM DJIA Mean return Mean n um b er of trades Profitable trades Signed-rank p-v alues 1-da y 0.19% 0.21% 0.17% 0.32% 0.13% 0.12% 0.12% 0.01% 0.27% 0.34% 0.43% 0.40% 0.07% 0.04% 0.13% 0.08% 0.07% 0.09% 0.49% 0.29% 0.14% 0.18% 0.14% -0.05% 0.21% 0.26% 0.28% 0.53% 0.13% 0.12% 0.19% 0.20% 83 54.9% 0* 2-da y 0.23% 0.18% 0.21% 0.51% 0.26% 0.36% 0.60% 0.05% 0.27% 0.45% 0.44% 0.46% 0.13% 0.09% 0.09% 0.09% 0.08% 0.08% 0.61% 0.10% 0.16% 0.16% 0.02% 0.13% 0.41% 0.58% 0.45% 0.24% 0.09% 0.22% 0.05% 0.25% 75 57.4% 0* 3-da y 0.26% 0.34% 0.19% 0.65% 0.28% 0.29% 0.37% 0.20% 0.27% 0.40% 0.41% 0.58% 0.14% 0.10% 0.07% 0.09% 0.21% 0.08% 0.51% 0.03% 0.26% 0.14% 0.30% 0.13% 0.28% 0.53% 0.48% 0.10% 0.13% 0.25% -0.03% 0.26% 70 56.5% 0* 4-da y 0.18% 0.31% 0.20% 0.58% 0.26% 0.31% 0.50% 0.21% 0.31% 0.42% 0.41% 0.73% 0.17% 0.09% 0.10% 0.10% 0.28% 0.27% 0.44% -0.12% 0.28% 0.14% 0.42% 0 .09% 0.29% 0.48% 0. 43% 0.16% 0.10% 0.29% -0.03% 0.27% 65 54.9% 0* 5-da y 0.33% 0.21% 0.20% 0.55% 0.22% 0.28% 0.27% 0.27% 0.27% 0.35% 0.36% 0.51% 0.15% 0.07% 0.05% 0.09% 0.37% 0.52% 0.43% -0.10% 0.20% 0.11% 0.46% 0.05% 0.40% 0.44% 0.17% 0.33% 0.10% 0.28% 0.03% 0.26% 64 53.7% 0* 6-da y 0.31% 0.20% 0.20% 0.45% 0.21% 0.25% -0.20% 0.35% 0.29% 0.22% 0.32% 0.52% 0.16% 0.09% -0.01% 0 .09% 0.29% 0.47% 0.59% -0.14% 0.13% 0.13 % 0.79% 0.06% 0.23% 0.37% 0.08% 0.29% 0.11% 0.27% -0.01% 0.23% 61 53.5% 0* 7-da y 0.25% 0.16% 0.16% 0.41% 0.19% 0.22% 0.17% 0.35% 0.19% 0.17% 0.24% 0.13% 0.17% 0.09% 0.02% 0.08% 0.43% 0.38% 0.48% -0.35% 0.19% 0.15% 0.28% 0.08% 0.32% 0.44% 0.16% 0.29% 0.12% 0.29% 0.20% 0.21% 59 51.9% 0* Highest profit at lag 5 3 2 3 3 2 2 7 4 2 2 4 7 3 1 4 7 5 2 1 4 1 6 3 2 2 3 1 1 4 7 0.24% 68 54.7% Median lag 3 Av erage lag 3.3 Rank-sum p-v alues AXP BA CA T CSCO CVX DD DIS GE GS HD IBM INTC JNJ JPM K O MCD MMM MRK MSFT NKE PFE PG T TR V UNH UTX V VZ WMT X OM DJIA Significan t Negativ e = P ositiv e Negativ e > P ositiv e p-v alue 1-da y 0.815 0.312 0.394 0.584 0.480 0.964 0.784 0.710 0.611 0.315 0.004* 0.151 0.423 0.159 0.272 0.913 0.071 0.567 0.118 0.204 0.426 0.468 0.178 0.116 0.696 0.409 0.303 0* 0.923 0.309 0.179 2 0.060 0.03* 2-da y 0.879 0.383 0.372 0.508 0.055 0.044* 0.002* 0.717 0.534 0.031* 0.005* 0.055 0.671 0.173 0.411 0.611 0.079 0.490 0.0 94 0.822 0.482 0.763 0.197 0.659 0.468 0.006* 0.050 0.145 0.687 0.053 0.415 6 0* 0* 3-da y 0.628 0.017* 0.263 0.132 0.031* 0.294 0.135 0.429 0.486 0.077 0.018* 0.012* 0.932 0.147 0.807 0.647 0.806 0.586 0.883 0.918 0.115 0.993 0.057 0.529 0.657 0.061 0.034* 0.830 0.779 0.014* 0.812 6 0* 0* 4-da y 0.927 0.042* 0.195 0.831 0.080 0.336 0.127 0. 463 0.234 0.221 0.032* 0.029* 0.991 0.12 0 0.428 0 .684 0.899 0.033* 0.9 26 0.217 0.089 0.895 0.096 0.366 0.668 0.052 0.171 0.750 0.910 0.003* 0.826 5 0* 0* 5-da y 0.423 0.158 0.296 0.962 0.162 0.480 0.620 0.375 0.366 0.619 0.051 0.382 0.756 0.126 0.912 0.709 0.362 0* 0.897 0.245 0.261 0.807 0.114 0.193 0.831 0.082 0.975 0.706 0.992 0.007* 0.790 2 0.008* 0.004* 6-da y 0.611 0.214 0.216 0.613 0.290 0.676 0.964 0.276 0.163 0.793 0.074 0.308 0.944 0.101 0.507 0.479 0. 372 0* 0.334 0.195 0.590 0.864 0.090 0.225 0.603 0.111 0. 533 0.993 0.927 0.017* 0.981 2 0.026* 0.013* 7-da y 0.894 0.376 0.133 0.645 0.403 0.845 0.467 0.277 0.639 0.527 0.384 0.782 0.931 0.052 0.369 0.664 0.111 0.01* 0.553 0.014* 0.353 0.863 0.418 0.517 0.789 0.039* 0.778 0.984 0.799 0.021* 0.261 4 0.160 0.080

4.2.2.2 Position Holding Period

The second variable axis is the amount of days a position is held open. Table 4.4 shows the results for varying the holding period of a position between one to seven days. The results for the positive-induced trades show an increasing accuracy in profitable trades from 56.7% to 58.0%, with an average of 57.5%. The average return per holding period is 0.21%. Furthermore, the median holding period for which the highest return is found is at seven days, with an average of 6.1. The Wilcoxon signed-rank test further shows that at all levels, the returns are significantly higher than 0%.

This is in contrast with the results for the negative-induced trades. These show a decreasing accuracy from 54.4% to 48.4%, with an average of 50.3%. The average return per holding period level is 0.14%. While the positive trades find higher returns for longer holding periods, negative trades find these at shorter holding periods. The median holding period is three days, with an average at 3.2. Lastly, the Wilcoxon signed-rank test indicates that while negative trades returns are significantly higher than 0% for holding periods of one to three days, they are not for holding periods longer than three days.

The Wilcoxon ranksum test results are displayed in the third part of Table 4.4. The results indicate that for higher holding periods, more significant differences are found within the 31 stocks. It rises from only three (for one-day holding period) to 11 (seven-day holding period). This process is mirrored by the aggregated totals of positive and negative returns, where only for a one-day holding period no significant differences are present.

T able 4.4: Results Holding P erio d P ositiv e AXP BA CA T CSCO CVX DD DIS GE GS HD IBM INTC JNJ JPM K O MCD MMM MRK MSFT NKE PFE PG T TR V UNH UTX V VZ WMT X OM DJIA Mean return Mean n um b er of trades Pr ofitable trades Signed-r ank p-v alues 1-da y 0.13% 0.11% 0.15% 0.08% 0.06% 0.22% 0.11% 0.04% 0.27% 0.16% 0.12% 0.15% 0.09% 0.19% 0.04% 0.05% 0.11% 0.10% 0.13% 0.12% 0.07% 0.10% 0.04% 0.06% 0.16% 0.08% 0.12% 0.10% 0.11% 0.05% 0.06% 0.11% 355 56.7% 0* 2-da y 0.22% 0.16% 0.21% 0.10% 0.11% 0.27% 0.19% 0.07% 0.34% 0.21% 0.14% 0.22% 0.13% 0.25% 0.02% 0.07% 0.20% 0.14% 0.22% 0.20% 0.11% 0.11% 0.04% 0 .10% 0.23% 0.14% 0 .15% 0.11% 0.11% 0.08% 0.10% 0.15% 354 56.8% 0* 3-da y 0.25% 0.20% 0.25% 0.11% 0.11% 0.33% 0.28% 0.10% 0.40% 0.21% 0.11% 0.29% 0.19% 0.29% 0.04% 0.07% 0.24% 0.18% 0.28% 0.29% 0.10% 0.12% 0.04% 0.15% 0.33% 0.18% 0.22% 0.08% 0.15% 0.11% 0.13% 0.19% 353 57.7% 0* 4-da y 0.25% 0.26% 0.28% 0.12% 0.11% 0.35% 0.32% 0.11% 0.40% 0.26% 0.08% 0.36% 0.24% 0.36% 0.02% 0.05% 0.30% 0.24% 0.37% 0.36% 0.08% 0.15% 0.04% 0 .20% 0.41% 0.22% 0 .26% 0.05% 0.16% 0.17% 0.15% 0.22% 352 57.8% 0* 5-da y 0.25% 0.33% 0.30% 0.15% 0.10% 0.38% 0.40% 0.13% 0.44% 0.27% 0.08% 0.46% 0.27% 0.32% 0.00% 0.01% 0.33% 0.30% 0.48% 0.42% 0.11% 0.17% 0.02% 0.19% 0.45% 0.25% 0.31% 0.07% 0.17% 0.19% 0.18% 0.24% 351 57.7% 0* 6-da y 0.26% 0.39% 0.38% 0.17% 0.10% 0.46% 0.47% 0.15% 0.50% 0.30% 0.07% 0.52% 0.33% 0.30% 0.04% 0.02% 0.38% 0.34% 0.52% 0.48% 0.12% 0.16% 0.00% 0 .21% 0.51% 0.26% 0 .37% 0.07% 0.20% 0.22% 0.20% 0.27% 351 57.6% 0* 7-da y 0.30% 0.44% 0.46% 0.18% 0.11% 0.49% 0.55% 0.16% 0.53% 0.34% 0.05% 0.60% 0.40% 0.31% 0.04% 0.01% 0.45% 0.42% 0.61% 0.54% 0.09% 0.19% 0.00% 0.21% 0.55% 0.25% 0.41% 0.06% 0.22% 0.26% 0.24% 0.31% 350 58.0% 0* Highest profit at lag 7 7 7 7 3 7 7 7 7 7 2 7 7 4 7 3 7 7 7 7 6 7 3 7 7 6 7 2 7 7 7 0.21% 352 57.5% Median lag 7 Av erage lag 6.1 Negativ e AXP BA CA T CSCO CVX DD DIS GE GS HD IBM INTC JNJ JPM K O MCD MMM MRK MSFT NKE PFE PG T TR V UNH UTX V VZ WMT X OM DJIA Mean return Mean n um b er of trades Pr ofitable trades Signed-r ank p-v alues 1-da y 0.19% 0.21% 0.18% 0.30% 0.13% 0.12% 0.12% -0.05% 0.27% 0.29% 0.43% 0.40% -0.06% 0.04% 0.13% 0.08% 0.04% 0.07% 0.49% 0.29% 0.02% 0.17% 0.14% -0.05% 0.21% 0.26% 0.28% 0.53% 0.13% 0.11% 0.19% 0.18% 83 54.4% 0* 2-da y 0.35% 0.13% 0.15% 0.39% 0.21% 0.08% -0.03% -0.15% 0.28% 0.13% 0.50% 0.29 % -0.21% 0.04% 0.12 % 0.09% 0.00% 0.06% 0. 56% 0.31% 0.14% 0.16% 0.23% -0.09% 0.11% 0.53% 0.25% 0.66% 0.12 % 0.10% 0.23% 0.19% 83 5 1.4% 0* 3-da y 0.31% 0.04% 0.05% 0.47% 0.16% -0.11% -0.10% -0.01% 0.30% 0.09% 0.43% 0.15% -0.16% 0.02% 0.21% 0.08% -0.19% 0.03% 0.47% 0.45% 0.11% 0.11% 0.19% -0.12% 0.16% 0.56% 0.38% 0.44% 0.17% 0.16% 0.27% 0.17% 82 50.3% 0* 4-da y 0.30% 0.07% -0.02% 0.41% 0.22% -0.17 % -0.42% 0.03% 0.31 % 0.00% 0.42% 0.01% -0.14% 0.06% 0.13% 0.08% -0.24% 0.02% 0.59% 0.65% 0.05% 0.12% 0.27% -0.08% 0.09% 0.61% 0.39% 0.40% 0.18% 0.36% 0. 24% 0.16% 82 4 9.9% 0.002* 5-da y 0.21% 0.05% -0.05% 0.45% 0.16% -0.21% -0.47% 0.09% 0.32% -0.30% 0.45% -0.02% -0.27% -0.03% 0.10% 0.04% -0.43% 0.03% 0.86% 0.82% 0.10% 0.17% 0.11% -0.14% -0.01% 0.64% 0.51% 0.63% 0.16% 0.34% 0.23% 0.15% 82 48.7% 0.053 6-da y 0.10% 0.10% -0.03% 0.46% 0.11% -0.30 % -0.64% -0.03% 0.39% -0.53% 0.49% -0.15% -0.26% -0.09% 0.16 % 0.07% -0.52% -0.09% 0.57% 0.65% 0.07% 0.13% 0.04% -0.13% -0.08% 0.54% 0.59% 0.69% 0.18% 0.38% 0.18% 0.10% 82 4 8.9% 0.12 7-da y -0.08% 0.07% -0.04% 0.38% 0.14% -0.28% -0.59% 0.07% 0.36% -0.61% 0.51% -0.22% -0.22% -0.13% 0.07% 0.06% -0.63% 0.02% 0.60% 0.66% 0.01% 0.13% 0.04% -0.16% -0.22% 0.36% 0.61% 0.65% 0.17% 0.44% 0.22% 0.08% 82 48.4% 0.296 Highest profit at lag 2 1 1 3 4 1 1 5 6 1 7 1 0 4 3 2 1 1 5 5 2 5 4 0 1 5 7 6 6 7 3 0.14% 82 50.3% Median lag 3 Av erage lag 3.2 Rank sum p-v alues AXP BA CA T CSCO CVX DD DIS GE GS HD IBM INTC JNJ JPM K O MCD MMM MRK MSFT NKE PFE PG T TR V UNH UTX V VZ WMT X OM DJIA Significan t T otal P ositiv e > Negativ e 1-da y 0.681 0.355 0.359 0.515 0.526 0.906 0.759 0.674 0.403 0.417 0.007* 0.189 0.346 0.060 0.299 0.999 0.050 0.660 0.120 0.206 0.530 0.597 0.231 0.060 0.627 0.425 0.322 0* 0.814 0.382 0.227 3 0.269 0.866 2-da y 0.714 0.994 0.044* 0.791 0.475 0.255 0.191 0.478 0.239 0.549 0 .095 0.887 0.011* 0.036* 0.56 7 0.941 0.038* 0.61 1 0. 458 0.743 0.499 0.887 0.460 0.031* 0.114 0.336 0.619 0.001* 0.391 0.975 0.706 6 0.036* 0.018* 3-da y 0.860 0.333 0.006* 0.465 0.973 0.023* 0.121 0.867 0.111 0.475 0.293 0.848 0.02* 0.023* 0.421 0.926 0.002* 0.307 0.998 0.563 0.689 0.673 0.582 0.005* 0.110 0.563 0.834 0.048* 0.650 0.964 0.950 7 0* 0* 4-da y 0.987 0.230 0.006* 0.809 0.839 0.005* 0.019* 0.936 0.105 0.250 0.273 0.429 0.023* 0.022* 0.734 0.875 0.001* 0.108 0.950 0.217 0.887 0.543 0.359 0 .004* 0.085 0.642 0.911 0.081 0.605 0.604 0.651 7 0* 0* 5-da y 0.633 0.076 0.009* 0.800 0.987 0.006* 0.015* 0.563 0.131 0.046* 0.277 0.347 0.003* 0.026* 0.953 0.940 0* 0.054 0.802 0.129 0.686 0.657 0.628 0.004* 0.064 0.586 0.969 0.019* 0.616 0.999 0.578 9 0* 0* 6-da y 0.352 0.090 0.011* 0.917 0.733 0.007* 0.007* 0.783 0.176 0.006* 0.199 0.199 0.006* 0 .026* 0.983 0.894 0* 0.009* 0.733 0.566 0.573 0.469 0.686 0.008* 0.048* 0.663 0.806 0.008* 0.65 0 0.964 0.429 11 0* 0* 7-da y 0.122 0.057 0.008* 0.670 0.753 0.011* 0.012* 0.600 0.117 0.003* 0.144 0.142 0.004* 0.027* 0.627 0.883 0* 0.025* 0.401 0.609 0.344 0.461 0.779 0.006* 0.013* 0.976 0.863 0.029* 0.482 0.962 0.443 11 0* 0*

4.2.2.3 Thresholds

The third and final axis is the threshold of the SP. The results are show in Table 4.5. The percentage of profitable returns rises from 56.2% to 59.4% for positive trades, with an average of 57.6%. The average return also rises with increases in threshold values, from 0.09% to 0.15%. The number of trades decreases from 355 to 214. The increase in average profits is supported by the fact that the median threshold with the highest mean percentual return is six (threshold -0.5), with an average of 5.3 (which corresponds to a threshold of 0.44). The Wilcoxon signed-rank test indicates that the aggregated percentual returns are significantly higher than 0% for all threshold levels.

The percentage of profitable returns for trades based on negative sentiment stays relatively stable around 54%. The average return is 0.22%. The (average) number of trades is considerably lower than those of the positive trades, ranging from 27 to 83, with an average of 55. The NaN values for the DJIA indicate that no trades were made and thus that no SP were found to be below -0.4. The negative trades exhibit the same pattern of increasing returns for increasing absolute levels of thresholds, with a median of five (threshold -0.4) and an average of 4.1 (which corresponds to a threshold of -0.34). The Wilcoxon signed-rank test also concludes that the aggregated total of negative-induced trade returns is significantly higher than 0% for all threshold levels.

The Wilcoxon ranksum test in the third part of Table 4.5 demonstrates that there are generally no significant differences between both sentiments, with a max of four stocks for which there are significant differences. The p-values for the test based on the aggregated totals also indicate that there are no significant differences present between the two sentiments.

T able 4.5: Results V ary ing Thresholds P ositiv e AXP BA CA T CSC O CVX DD DIS GE GS HD IBM INTC JNJ JPM K O MCD MMM MRK MSFT NKE PFE PG T TR V UNH UTX V VZ WMT X OM DJIA Mean return Mean n um b er of tr ades Profitable trades Sign ed-rank p-v alues 0 0.10% 0.10% 0.15% 0.07% 0.05% 0.12% 0.11% 0.03% 0.21% 0.13% 0.10% 0.13% 0.08% 0.12% 0.03% 0.05% 0.09% 0.09% 0.13% 0.11% 0.04% 0.09% 0.03% 0.01% 0.15% 0.08% 0.11% 0.07% 0.11% 0.05% 0.04% 0.09% 355 56.2% 0* 0.1 0.09% 0.11% 0.18% 0.08% 0.06% 0.12% 0.10% 0.05% 0.28% 0.14% 0.10% 0.12% 0.09% 0.12% 0.02% 0.06% 0.09% 0.09% 0.13% 0.12% 0.05% 0.10% 0.02% 0.01% 0.16% 0.08% 0.12% 0.07% 0.10% 0.0 5% 0.05% 0.10% 342 56.5% 0* 0.2 0.11% 0.14% 0.19% 0.09% 0.07% 0.15% 0.10% 0.05% 0.30% 0.16% 0.10% 0.14% 0.12% 0.17% 0.04% 0.07% 0.10% 0.09% 0.14% 0.14% 0.07% 0.11% 0.04% 0.00% 0.15% 0.08% 0.18% 0.08% 0.12% 0.11% 0.09% 0.11% 317 57.3% 0* 0.3 0.11% 0.17% 0.16% 0.12% 0.08% 0.14% 0.12% 0.07% 0.35% 0.17% 0.13% 0.14% 0.12% 0.17% 0.07% 0.08% 0.10% 0.08% 0.16% 0.14% 0.07% 0.11% 0.03% 0.00% 0.14% 0.09% 0.21% 0.07% 0.16% 0.1 1% 0.13% 0.12% 293 57.8% 0* 0.4 0.13% 0.22% 0.17% 0.13% 0.09% 0.12% 0.13% 0.07% 0.37% 0.21% 0.12% 0.14% 0.14% 0.13% 0.08% 0.08% 0.10% 0.10% 0.17% 0.17% 0.08% 0.12% 0.02% -0.01% 0.17% 0.09% 0.22% 0.06% 0.14% 0.14% 0.14% 0.13% 256 58.4% 0* 0.5 0.16% 0.25% 0.19% 0.08% 0.08% 0.13% 0.15% 0.09% 0.38% 0.23% 0.13% 0.16% 0.15% 0.16% 0.10% 0.11% 0.11% 0.09% 0.20% 0.20% 0.09% 0.14% 0.01% 0.00% 0.20% 0.09% 0.28% 0.08% 0.19% 0.1 7% 0.22% 0.15% 214 59.4% 0* Highest 6 6 3 5 5 3 6 6 6 6 6 6 6 4 6 6 6 5 6 6 6 6 3 1 6 5 6 3 6 6 6 0.12% 296 57 .6% Median 6 Av erage 5.3 Negativ e AXP BA CA T CSC O CVX DD DIS GE GS HD IBM INTC JNJ JPM K O MCD MMM MRK MSFT NKE PFE PG T TR V UNH UTX V VZ WMT X OM DJIA Mean return Mean n um b er of tr ades Profitable trades Sign ed-rank p-v alues 0 0.19% 0.21% 0.17% 0.32% 0.13% 0.12% 0.12% 0.01% 0.27% 0.34% 0.43% 0.40% 0.07% 0.04% 0.13% 0.08% 0.07% 0.09% 0.49% 0.29% 0.14% 0.18% 0.14% -0.05% 0.21% 0.26% 0.28% 0.53% 0.13% 0.12% 0.19% 0.20% 83 54.9% 0* -0.1 0.13% 0.23% 0.20% 0.21% 0.13% 0.15% 0.14% 0.00% 0.21% 0.31% 0.47% 0.45% 0.09% 0.00% 0.11% 0.08% 0.06% 0.09% 0.58% 0.25% 0.18% 0.22% 0.08% -0.03% 0.21% 0.29% 0.28% 0.42% 0.14% 0.13% 0.21% 0.19% 74 54.7% 0* -0.2 0.18% 0.35% 0.24% 0.36% 0.13% 0.16% 0.09% -0.10% 0.24% 0.34% 0.55% 0.56% 0.07% -0.01% 0.02% 0.09% 0.05% 0.00% 0.76% 0.28% 0.11% 0.10% 0.17% -0.03% 0.17% 0.45% 0.24% 0.49% 0.11% 0.14% 0.26% 0.21% 58 54.1% 0* -0.3 0.18% 0.28% 0.25% 0.03% 0.14% 0.17% -0.01% -0.10% 0.26% 0.32% 0.51% 0.89% 0.09% 0.08% 0.02% 0.08% 0.02% 0.08% 0.78% 0.17% 0.12% 0.10% 0.13% -0.02% 0.24% 0.53% 0.20% 0.36% 0.11% 0.10% 0.07% 0.20% 49 54.1% 0* -0.4 0.24% 0.36% 0.17% 0.17% 0.09% 0.28% -0.20% -0.04% 0.26% 0.31% 0.37% 0.72% 0.04% 0.15% 0.09% 0.10% -0.01% 0.03% 1.15% 0.19% 0.03% 0.12% 0.34% -0.01% 0.26% 0.55% 0.19% 0.55% 0.13% 0.11% NaN 0.23% 36 54.5% 0* -0.5 -0.06% 0.50% 0.15% 0.18% 0.10% 0.30% -0.04% -0.05% 0.21% 0.28% 0.40% 1.67% 0.17% 0.22% 0.08% 0.09% -0.13% 0.13% 1.50% 0.34% 0.06% 0.12% 0.10% 0.01% 0.11% 0.25% 0.44% 0.57% 0.11% 0.04% NaN 0.26% 27 53.3% 0* Highest 5 6 4 3 4 6 2 1 1 3 3 6 6 6 1 5 1 6 6 6 2 2 5 6 5 5 6 6 2 3 3 0.22% 55 54.3% Median 5 Av erage 4.1 Rank-sum p-v alues AXP BA CA T CSC O CVX DD DIS GE GS HD IBM INTC JNJ JPM K O MCD MMM MRK MSFT NKE PFE PG T TR V UNH UTX V VZ WMT X OM DJIA Signific an t T otal 0 0.815 0.312 0.394 0.584 0.480 0.964 0.784 0.710 0.611 0.315 0.004* 0.151 0.423 0.159 0.272 0.913 0.071 0.567 0.118 0.204 0.426 0.468 0.178 0.116 0.696 0.409 0.303 0* 0.923 0.309 0.179 2 0.060 0.1/-0.1 0.668 0.179 0.35 6 0.366 0.348 0.786 0.975 0.643 0.083 0.370 0.006* 0.118 0.570 0.07 6 0.533 0.884 0.059 0.570 0.092 0.499 0.25 5 0.367 0.282 0.221 0.622 0.3 18 0.704 0.008* 0.993 0.251 0.299 2 0.192 0.2/-.2 0.896 0.092 0.568 0.756 0.602 0.892 0.846 0.410 0.121 0.389 0.004* 0.179 0.363 0.02* 0.794 0.776 0.033* 0.698 0.054 0.761 0.950 0.718 0.427 0.295 0.642 0.089 0.957 0.015* 0.553 0.600 0.488 4 0.931 0.3/-0.3 0.788 0.279 0.51 8 0.629 0.763 0.802 0.508 0.374 0.078 0.417 0.024* 0.088 0.473 0.23 1 0.685 0.409 0.039* 0.949 0.222 0.805 0.902 0.632 0. 571 0.345 0.814 0.036* 0.695 0.04* 0.382 0.943 0.848 4 0.657 0.4/-0.4 0.829 0.193 0.192 0.831 0.893 0.364 0.299 0.621 0.067 0.780 0.219 0.372 0.207 0.808 0.884 0.727 0.018* 0.599 0.090 0.674 0.515 0.969 0.219 0.451 0.792 0.021* 0.703 0.006* 0.580 0.862 0* 4 0.556 0.5/-0.5 0.141 0.150 0.06 2 0.582 0.883 0.304 0.357 0.657 0.103 0.945 0.442 0.051 0 .687 0.838 0.665 0.251 0.007* 0.965 0.093 0.895 0.41 0 0.787 0.532 0.626 0.268 0.4 12 0.449 0.063 0.054 0.4 61 0* 2 0.078

Conclusion

This chapter interprets the results of the preliminary analysis and the trading results displayed in the previous chapter. First of all, the regression models including Twitter sentiment in the preliminary analysis show a, albeit small, improvement in the accuracy of the models when compared to the regression model that does not include Twitter sentiment. Furthermore, and perhaps more interesting, we see a declining significance of Twitter sentiment as the aggregation period is lengthened. While the polarity aggregated over one day is significant for 26 out of 31 companies, it is only significant for nine companies when aggregated over the last week. This result is more or less in line with the EMH, since it reaffirms the assumption that information is quickly reflected in the stock price. Sentiment over a longer time-frame does not significantly impact the stock price, perhaps because the stock price already reflects that information. The declining importance over time is also confirmed by the correlation analysis. We see that the correlation generally considerably decreases over time, with the highest correlations often found at the one- and two-day lags.

The second part of the preliminary analysis covers the market conditions, covering both the stock market and Twitter. The analysis shows that there is a slight bias towards daily increases in the open (54.3% of the time) and that stocks experienced an average increase of 17.3% in their price. The DJIA rose 14.2%. Furthermore, mean returns in the stock price after positive sentiment are generally positive, while this is also, albeit less so, the case for returns in the stock price after negative sentiment. This is counter-intuitive: one would expect decreasing stock prices after periods of negative sentiment. The positive-bias is considerably stronger for Twitter data. The one-day average of positive SP is 81% over all companies and this steadily increases as the time-horizon for Twitter aggregation is lengthened. One explanation for this may be the earlier mentioned overall upward trend in the stock market. The increases in the stock prices and subsequently that of the Dow Jones Industrial Average, one of the most important stock market indicators in the world, most likely caused a very positive investor atmosphere. This also explains why the bias towards positive sentiment is higher at longer Twitter aggregation periods. Although daily declines are likely to happen, overall the stock market was performing very well.