DEGREE PROJECT IN TECHNOLOGY, FIRST CYCLE, 15 CREDITS STOCKHOLM, SWEDEN 2018

How Google Search Trends Can Be Used as Technical Indicators for the S&P500-Index

A Time Series Analysis Using Granger’s Causality Test

ALBIN GRANELL

FILIP CARLSSON

KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ENGINEERING SCIENCES

How Google Search Trends Can Be Used as Technical Indicators for the S&P500-Index

A Time Series Analysis Using Granger’s Causality Test

ALBIN GRANELL FILIP CARLSSON

Degree Projects in Applied Mathematics and Industrial Economics Degree Programme in Industrial Engineering and Management KTH Royal Institute of Technology year 2018 Supervisors at KTH: Jörgen Säve-Söderbergh, Julia Liljegren Examiner at KTH: Henrik Hult

TRITA-SCI-GRU 2018:182 MAT-K 2018:01

Royal Institute of Technology School of Engineering Sciences KTH SCI SE-100 44 Stockholm, Sweden URL: www.kth.se/sci

Abstract This thesis studies whether Google search trends can be used as indicators for movements in the S&P500 index. Using Granger’s causality test, the level of causality between movements in the S&P500 index and Google search volumes for certain keywords is analyzed. The result of the analysis is used to form an investment strategy entirely based on Google search volumes, which is then backtested over a five year period using historic data. The causality tests show that 8 of 30 words indicate causality at a 10% level of significance, where one word, mortgage, indicates causality at a 1% level of significance. Several investment strategies based on search volumes yield higher returns than the index itself over the considered five year period, where the best performing strategy beats the index with over 60 percentage units.

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Hur Google-s¨oktrenderkan anv¨andassom tekniska indikatorer f¨or SP500-indexet: en tidsserieanalys med hj¨alpav Grangers kausalitetstest

Sammanfattning Denna uppsats studerar huruvida Google-s¨oktrenderkan anv¨andas som indikatorer f¨orr¨orelseri S&P500-indexet. Genom Grangers kausalitet- stest studeras kausalitetsniv˚anmellan r¨orelseri S&P500 och Google- s¨okvolymer f¨ors¨arskilltutvalda nyckelord. Resultaten i denna analys anv¨ands i sin tur f¨oratt utforma en investeringsstrategi enbart baserad p˚aGoogle-s¨okvolymer, som med hj¨alpav historisk data pr¨ovas ¨over en fem˚arsperiod. Resultaten av kausalitetstestet visar att 8 av 30 ord in- dikerar en kausalitet p˚aen 10%-ig signifikansniv˚a,varav ett av orden, mortgage, p˚avisarkausalitet p˚aen 1%-ig signifikansniv˚a.Flera invester- ingsstrategier baserade p˚as¨okvolymer genererar h¨ogreavkastning ¨anin- dexet sj¨alvt¨over den pr¨ovade fem˚arsperioden, d¨arden b¨astastrategin sl˚ar index med ¨over 60 procentenheter.

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Acknowledgements We would like to thank our supervisors at the Royal Institute of Tech- nology (KTH), P¨arJ¨orgenS¨ave-S¨oderbergh and Julia Liljegren for their support before and throughout the study.

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Contents

1 Introduction 9 1.1 Background ...... 9 1.2 Objective ...... 9 1.3 Problem Statement ...... 10 1.4 Limitations ...... 10 1.5 Previous Research ...... 10

2 Theoretical Framework 12 2.1 Technical Indicators ...... 12 2.2 Financial Theory ...... 12 2.2.1 Efficient Market Hypothesis (EMH) ...... 12 2.2.2 Behavioural Finance ...... 13 2.3 Mathematical Framework ...... 13 2.3.1 Vector Autoregression (VAR) ...... 13 2.3.2 VAR Order Selection ...... 14 2.3.3 Stable VAR process ...... 15 2.3.4 Stationarity ...... 16 2.3.5 Augmented Dickey-Fuller Test ...... 16 2.3.6 OLS Estimation of VAR Parameters ...... 16 2.3.7 Breusch-Godfrey test ...... 17 2.3.8 Granger-Causality ...... 17 2.3.9 F-Statistics for Granger-Causality ...... 18

3 Method 19 3.1 Word selection ...... 19 3.2 Data collection ...... 21 3.2.1 Search data ...... 21 3.2.2 S&P500-Index ...... 22 3.3 Investment Strategies ...... 22 3.4 Outline ...... 24

4 Results 26 4.1 Transformation of Data ...... 26 4.2 Selection of lag order ...... 26 4.3 Model Validation ...... 27 4.4 Granger-Causality Tests ...... 28 4.5 Backtesting Investment Strategies ...... 29 4.5.1 Strategy 1 ...... 29 4.5.2 Strategy 2 ...... 30 4.5.3 Strategy 3 ...... 31

5 Discussion 32 5.1 Interpretation of Results ...... 32 5.1.1 Granger-Causality Test ...... 32 5.1.2 Investment Strategies ...... 33 5.1.3 Comparison to Previous Findings ...... 34 5.1.4 Financial Implications ...... 35 5.2 Sources of Errors ...... 36

7 5.2.1 Mathematical Sources of Errors ...... 36 5.2.2 Errors From Data Collection ...... 36 5.2.3 Nature of the Financial Market ...... 37 5.3 Further Research ...... 37 5.4 Conclusion ...... 38

References 40

A Appendix 41 A.1 Augmented Dickey-Fuller test ...... 41 A.2 Strategy 1 Returns ...... 43 A.3 Strategy 2 Returns ...... 44 A.4 Strategy 3 Returns ...... 45

8 1 Introduction 1.1 Background In the beginning of the 21st century, papers, books, tv broadcasting and radio were the main sources of information. Today, this has changed as the Internet has developed and changed our way of living. Nowadays, top news are shown as a pop-up notification in smartphones only minutes, sometimes even seconds after the occurrence and information is never more than an online search away. Simultaneously with this rapid change Google has become the number one search engine worldwide with trillions of searches every year and a 91% online search market share by February 2018.[1]

In 2010 Google’s Executive Chairman Eric Schmidt claimed that the information gathered over two days, equals the accumulated amount from the dawn of mankind up to 2003.[2] The new era of big data creates new possibilities and several businesses see it as the holy grail for finally being able to predict who, where and when customers will buy their products.[3] Despite the emergence of big data, the increase of information used does not compare as only about one percent of the data collected is analyzed.[4] Thus, there is a lot of unexplored possibilities in the new era of big data.

Today’s most commonly used technical trading indicators have not been influenced by the increase in big data, as they are still mainly based on momentum calculated from trading volumes, volatility and historical returns of the considered asset.[5] Such indicators are used by investors in order to analyze price charts of financial assets to be able to, for example, predict future stock price movements. Unlike fundamental analysis, in which investors try to determine whether a company is under- or overvalued, technical analysis does not consider the fundamental value of the stock. Instead indicators are used to identify patterns and in that way predict short term movements in the price of the considered asset.[6]

1.2 Objective The thesis investigates whether there exists a causal relationship between online search activity and the overall performance of the stock market. Today, many investors base their trading on technical indicators or key performance indicators, such as price-earnings ratios, earnings per shares, historic returns etc. However, as a result of the Internet’s, Google’s in particular, increasing influence on peoples day-to-day life it is reasonable to believe that data from online activity potentially could reflect the overall state of the economy.

As further discussed in section 1.6, there is no prevailing consensus on the topic, as previous studies come to different conclusions using various methods. The objective of the thesis is to find mathematically substantiated evidence, through Granger-causality tests, that Google search volumes can be used as a technical indicator for movements on the S&P500 index. Furthermore, based on the results of the causality tests, the thesis aims to find a trading algorithm using Google search volumes that, using a backtest strategy, can be

9 shown to give a higher return than the index itself over a 5-year period.

1.3 Problem Statement The problem statement is broken down into two general questions underlying the thesis: • Can Google search volumes be used as a technical indicator for the S&P500 index? • Can a successful investment strategy be based on these potential findings?

1.4 Limitations The thesis only considers the S&P500 index and 30 selected keywords. Search volumes and index prices are limited to the period of March 24th 2013 to March 24th 2018. As the stock markets and overall economy in different countries may vary it is not reasonable to assume that there is an overall global trend in the economy, in the sense of cause-effect mechanisms from Google searches. Thus, in order for the search data to best represent the trend of the American stock market (i.e. the S&P500 index), the search data is geographically limited to within the United States.

1.5 Previous Research Previous research on Google search trends and their predictive ability on the financial market has been conducted in different scale, using various approaches, leading to different conclusions. This section presents a selection of the studies, the tests conducted and their findings.

Several studies have managed to prove the predictable properties of Google search volumes on different economic and social indicators. Varian et al. showed how Google trends can be used to forecast near term economic indicators such as automobile sales, travel destinations, and unemployment rates.[7] Four years later L. Kristoufek et al. used an autoregressive approach to show that Google search volumes also significantly increases the accuracy of the prediction of suicide rates in the UK, compared to only using historical rates for forecasting.[8]

In 2013 Moat, Preis et al. empirically studied the relationship between Google search trends and the financial market with a quantifying approach. By analyzing the search volumes the study identified patterns that could be interpreted as “early warning signs” of upcoming stock market moves. This was done using a hypothetical trading algorithm “Google Trends Strategy”, determining the type of investment action (buy/sell) based on whether a week’s search volume of a certain word is higher or lower than the average volume of the past three weeks. The strategy was implemented theoretically on the Dow Jones Industrial Average (DJIA) over the time period 2011-2014, using numerous keywords (98 in total). The results indicates that certain words might serve as technical indicators. The strategy for the word “debt” yielded a return of 326 %, compared with the buy-and-hold strategy which yielded only 16 %.[9]

10 Perlin et al. modeled Google search volumes together with volatility, log-returns on market indices and trade volume respectively as bivariate vector autoregression models. In addition to the modelling, two-way Granger-Causality tests were also performed on the models. The study was performed on four different markets, using the most frequently occuring, financially related, words in four economic textbooks. The findings stated that a causality for some words and the stock market had been identified. The keyword “stock” was claimed to have the most significant overall impact on the market, where an increase in search volumes caused volatility to increase and the weekly returns to decrease.[10]

Challet et al. were not able to show whether Google search volumes better predicts future returns than historic returns themselves. Using non-linear machine learning methods and backtesting strategies their final conclusion was that search volumes and historical returns indeed do share many properties and Google trends data could sometimes even be equivalent to returns themselves. However, they were not able to show any predictable properties of the Google trends data.[11]

11 2 Theoretical Framework 2.1 Technical Indicators In order to determine whether Google search volumes can be used as a technical indicator for the S&P500 index, the definition of a technical indicator has to be introduced. A technical indicator is a tool for predicting short term movements in asset prices using historical trading data. A technical indicator is described as follows: The essence of technical indicators is a mathematical transformation of a financial symbol price aimed at forecasting future price changes. This provides an opportunity to identify various characteristics and patterns in price dynamics which are invisible to the naked eye.[12]

Thus, in order to be valid as a technical indicator, the data has to have predictive properties on the considered asset. As there are no stated rules or definitions of how these predictive properties are measured, it will throughout this thesis be measured by causality, where high levels of causality implies good predictive properties.

2.2 Financial Theory There are several theories behind the mechanics of the financial markets. This section presents some of the most well known theories, in order to give further insight to what causes market movements according to conventional financial theory.

2.2.1 Efficient Market Hypothesis (EMH) The efficient market hypothesis (EMH) states that at any given time, in any liquid market, the prices of securities reflect all available information. Eugene Fama presents EMH in three different degrees depending on the information set that is of interest: weak, semi-strong and strong form.[13]

The weak form of EMH has its foundation in the historical price data, available on the securities market, and claims that previous information of the stock price is not sufficient for determining future direction of security prices. Returns in the stock market are instead modelled as a “fair game”. In other words, the prices of securities follow a random walk and its expected return conditioned on today’s information is zero.

By including all publically available information on securities in the information subset the semi-strong form of EMH is obtained. The model states that stock prices adjust rapidly after release of new public information. As a consequence the current stock prices are reflections of the information subset and a fundamental analysis cannot achieve excess returns.

The strong form of EMH assumes that all available information, both public and private, are factored in the securities price. An additional assumption for this model is, however, that no investor or group have monopolistic access to

12 certain information.

The main implication of Fama’s theory is that there is no systematic way (e.g. stock picking using fundamental analysis) for investors to outperform the financial market in the long run. This is a consequence of the prevailing competition on the market, adjusting the prices instantly after new information is made available.

2.2.2 Behavioural Finance Since the development of the EMH, new theoretical models have emerged which in some cases contradict the fundamentals of the EMH. Behavioural finance is a relatively new field that, with a combination of psychology and conventional economics, attempts to explain why investors act irrationally. R.J. Schiller’s paper “Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?” is commonly cited as the beginning of behavioural finance as he demonstrated that stocks fluctuate too much to be justified by rational theory of stock valuation.[14] After the release of his paper, much more research on the subject has been done and the psychological aspect of the economy has been recognized as an important influence in the aftermath of several financial crises, as investors psychology has tended to deepen the crisis.[15]

In 1986, Fisher Black introduced the concept of noise, a contradiction to information, which in its sense of a large numbers of small events often is considered as a causal factor much more powerful than a small number of large events. Factors such as hype, inaccurate data or inaccurate ideas are the essence of noise. According to Black, the noise is what keeps us from knowing the expected return of a stock or portfolio and thus it is what makes our observations imperfect. Different beliefs must arise from different information, which Black explains as noise often being treated as information. In this way, noise can explain some of the anomalies in the EMH.[16]

2.3 Mathematical Framework This section presents the multiple time series framework used in the mathematical part of the thesis. If nothing else is specified, the theory is collected from the literature written by Helmut L¨uthkepol.[17]

2.3.1 Vector Autoregression (VAR) In order to perform a structural analysis of the respective time series, the concept of a vector autoregressive (VAR) model has to be introduced. In this setting K autoregressive time series are expressed as linear combinations of each other with a predetermined order:

yt = ν + A1yt−1 + ... + Apyt−p + ut, t = 0, ±1, ±2,..., (1)

Here yt = (y1,t, ··· , yK,t) is a (K x 1) vector containing K autoregressive models, A is a (K x K) coefficient matrix, the variable p defines the model’s order (i.e. the number of lags used to model yi,t) and lastly ut represents a k-dimensional and serially uncorrelated innovation process with expected value

13 zero and non-singular variance.

In order to derive the properties of the VAR model it is convenient to look at the model of order one. Breaking down yt starting at some point, say t = 1, then yields the following:

y1 = ν + A1y0 + u1,

y2 = ν + A1y1 + u2 = ν + A1(ν + A1y0 + u1) + u2 2 = (IK + A1)ν + A1y0 + A1u1 + u2, . . t−1 t−1 t X i yt = (IK + A1 + ··· + A1 )ν + A1y0 + A1ut−1 i=0 . .

2.3.2 VAR Order Selection There are several criteria that can be used for VAR order selection. Two commonly used are presented by L¨utkepohl: the Akaike Information Criterion (AIC) and the Schwarz Criterion (SC). The different properties of these criteria will affect the estimated lag order depending on the properties of the time series on which they are applied.

Akaike Information Criterion Based on the idea to optimize the maximum likelihood estimate while withholding the model parsimony (simplicity), Akaike derived a criterion for model selection.

AIC(m) = ln|Σeu(m)| + 2/T (number of freely estimated parameters) 2 = ln|Σeu(m)| + 2mK /T

Here Σeu represents the maximum likelihood estimate of the white noise covariance matrix, T is the sample size and K is the dimension of the time series. The lag m is selected in order for AIC(m) to be minimized. Hence, there is a trade-off between model variance and number of estimated parameters. In addition, it can be shown that AIC estimates asymptotically overestimates the true lag.

Schwarz Criterion Schwarz derived a slightly different criterion for model selection, that also deals with the trade off between lack-of-fit and number of estimated parameters, but penalizes harder for adding additional lag into the model. As a consequence, the lag order estimated by SC rarely overestimates the true lag.

SC(m) = ln|Σeu(m)| + ln(T )/T (number of freely estimated parameters) 2 = ln|Σeu(m)| + ln(T )mK /T

14 Comparison of Criterion In addition to AIC and SC, there exists other criteria for VAR order selection, such as the Final Prediction Error (FPE) (similar to AIC) and the Hannan- Quinn Criterion (HQ) (similar to SC). Though, as stated by L¨utkepohl, there is no common consensus regarding which criteria to use. However, the criterion do have properties that affect their functionality under different circumstances. When the sample size increases (i.e. T → ∞), the probability of selecting the true lag differs. AIC, as well as FPE, are said to be inconsistent estimators for larger sample sizes, meaning that its asymptotic estimator does not converge with the reality, whereas SC and HQ are strongly consistent. However, since AIC and FPE put larger emphasis on the forecast prediction error, models with order selection based on these criteria often have better predictive capabilities, even though the lag order is not necessarily correct.

2.3.3 Stable VAR process It can be shown that, in order for the VAR process to be well defined (stable), the eigenvalues of A1 need to have absolute values less than one. This condition can then be generalized for the V AR(p) model using the fact that it can be expressed as a V AR(1) model by making yi,t a Kp-dimensional vector. The corresponding V AR(1) can be defined as:

Yt = ν + AYt−1 + Ut (2) where,   yt  yt−1  Y :=   t  .   .  y t−p−1 (Kp × 1)

ν 0 ν :=    .   .  0 (Kp × 1)

  A1 A2 ··· Ap−1 Ap IK 0 ··· 0 0     0 IK ··· 0 0  A :=    ......   . . . . .  0 0 ··· I 0 K (Kp × Kp)

  ut  0  U :=   t  .   .  0 (Kp × 1)

15 In the generalized form, the model is said to be stable if:

det(IKp − Az) 6= 0, for z ≤ 1 (3)

2.3.4 Stationarity L¨utkepohl proposition 2.1 states that if a VAR process is stable, then it is also stationary. Hence, the stability condition is often referred to as the stationary condition. The reverse relationship, however, is not always necessarily true. As a consequence stationarity in the subprocesses of a VAR model is a necessary condition for the model’s stability.

In order for a process to be stationary its mean and autocorrelation should be time invariant. Thus, the following two equations must hold:

E[yt] = µ (4)

0 E[(yt − µ)(yt−h − µ) ] = Γt(h) (5)

2.3.5 Augmented Dickey-Fuller Test A way to analyze whether a time series is stationary or not is by evaluating the possible presence of a unit root. The presence of a unit root implies that the time series is integrated of order one, meaning that its first difference will be stationary. A unit root for a process yt is said to exist if its characteristic function has a root equal to unity, z = 1. That is:

yt = v + a1yt−1 + a2yt−2 + ... + apyt−p + t (6) with the corresponding characteristic function,

2 p 1 − α1z − α2z − ... − αpz = 0 (7)

A way for evaluating the presence of unit roots is by performing an Augmented Dickey-Fuller test. The test evaluates the null hypothesis of a unit root present by first modelling the time series as:

p X ∆yt = γyt−1 + as∆yt−s + t (8) s=1

The test statistic (tau statistic) is then defined as DTτ =γ/SE ˆ (ˆγ), and follows a Dickey-Fuller distribution which critical values can be collected from a Dickey-Fuller table.[18]

2.3.6 OLS Estimation of VAR Parameters

The least squares estimators B = [νi,Ai,1, ··· ,Ai,t−p] can be obtained with several approaches where one is to use a multivariate approach and solve for all yi,t simultaneously. However, the approach can also be rewritten so that

16 the coefficients can be obtained using ordinary least-squares on each equation individually. First, the LS-estimator is rewritten in a vectorized form as per below:

0 0 −1 0 ˆb = vec(Bˆ ) = (IK ⊗ (ZZ ) Z)vec(Y ) (9)

0 Let bK be the k-th row of B, implicating that bk contains all parameters of the k-th equation. With y(k) defined as the time series available for the k-th variable, i.e y(k) = [yk1, ··· , ykT ], the following expression for the OLS 0 estimator of the model y(k) = Z bk + u(k) is received:

ˆ 0 −1 bk = (ZZ ) Zy(k) (10)

0 where u(k) = [uk1, ··· , ukT ] .

2.3.7 Breusch-Godfrey test The Breusch-Godfrey test is used to test for residual autocorrelation, which may have a negative impact on the VAR model. To construct the test a VAR model for the error vector is assumed, i.e ut = D1ut−1 + ··· + Dhut−h + vt, where vt is white noise. Then, in order to test for autocorrelation a null hypothesis stating no autocorrelation in the residuals is set. This is expressed as:

H0 : D1 = ··· = Dh = 0

H1 : Dj 6= 0, for some j = (1, 2, ··· , h)

Using the Lagrange multiplier principle, L¨uthkepol Proposition 4.8 states that under the null hypothesis the following asymptotic distribution for the residual autocorrelation holds:

d 2 2 λLM (h) −→ χ (hK ) (11)

This property is used to calculate the probability p of faulty rejecting the null 2 2 hypothesis. If p, defined as Pr[X > λLM (h)] where X follows a χ (hK ) distribution, is greater than α, the null hypothesis of no autocorrelation cannot be rejected at a α level. Simultaneously, if Pr[X > λLM (h)] is less than α, there may be autocorrelation between regressors at a α confidence level.

2.3.8 Granger-Causality Granger-causality is a concept of causality defined by Clive WJ Granger.[19] It formally explains and gives a mathematical definition of causality, which under suitable conditions works well with the VAR-framework. Let Ωt denote the information set containing all relevant information available up to time t. Furthermore, let zt(h|Ωt) denote the MSE-minimizing h-step predictor of the process zt at time t, based on the information given by Ωt. Thus, the

17 corresponding MSE-forecast is denoted as Σz(h|Ωt). According to Granger’s definition of causality, xt is said to cause zt if it can be shown that:

Σz(h|Ωt) < Σz(h|Ωt\{xs|s < t}), for at least one h = 1, 2, 3 ... (12)

A practical problem with the implementation of this definition is the choice of Ωt. Usually all relevant information up to time t is not available and thus Ωt is replaced by {zs, xs|s ≤ t}, which is all past and present information in the considered process.

2.3.9 F-Statistics for Granger-Causality In time series analysis the F-statistics is used to test the null hypothesis that there is no Granger causality. Formally, this hypothesis can be expressed using the VAR-coefficients as:

H0 : α12,j = 0, for i = (1, 2, ..., P )

H1 : α12,j 6= 0, for some j = (1, 2, ..., P )

The F-statistic for the test can be derived from the distribution of the Wald statistic, given as Proposition 3.5 in L¨utkepohl:

ˆ 0 0 −1 0 −1 ˆ d 2 λW = (Cβ − c) [C((ZZ ) ⊗ Σˆ u)C ] (Cβ − c) −→ χ (N) (13)

Here C represents a (N x (K2p + K))-matrix, consisting of ones and zeros such that C corresponds to the coefficients that causality is tested for. From the 2 properties of χ , the distribution of λW can be expressed in terms of a F random variable by noting the following relationship between the two distributions:

NF (N,T ) −−−−→d χ2 (14) T →∞

Here N is given by the lag order times K (number of time series) and T represents the sample size. Thus, for a large sample size the the variable λF = λw/N will be approximately F-distributed. Just like in the F-statistics for regression with non stochastic regressors the denominator degrees of freedom are set equal to the sample size minus the number of estimated parameters. Hence, the approximate distribution becomes as per below:

2 λF ≈ F (N,KT − K p − K) (15)

The null hypothesis is rejected at a significance level of α if λf > F (α/2,N,KT − K2p − K). This can be described with the p-value, which is defined as the probability of faulty rejecting the null hypothesis.

18 3 Method 3.1 Word selection There is a limited amount of previous research made on the predictive properties of Google search data against stock markets. Thus, there is no natural way or stated theory on how to choose words for analyzing causalities. Without previous evidence based selection criteria there are many words that potentially could have predictive properties on the index. Thus, an aim to cover a diverse set of words is applied where the selection is based on common financial words supported by a set of intuitively chosen words.

To cover some of the most basic and common financial terms, 20 words listed as 20 English Words for Finance You Simply Must Know by FluentU will be tested. The words, with FluentU’s definitions, are presented below [20]: • Debt - Debt refers to any kind of borrowing such as loans, mortgages, etc. Debts are a way for you or your company to borrow money (usually for large purchases) and repay it at a later date with interest.

• Interest rate - Interest is the amount the bank (or other moneylender, which is any person or organization that gives you money) will charge you or your company for the money you borrow from them. That amount, or interest rate, is expressed as a percentage of the loan. • Investment - The noun investment refers to money that you put into your business, property, stock, etc., in order to make a profit or earn interest. • Capital - Capital refers to your money or assets. • Cash outflow - Cash outflow refers to the money that your company spends on its expenses and other business activities.

• Revenue - Your revenue is the amount of money your company makes from the sale of goods and services. • Profit - Profit describes the amount of revenue your company gains after excluding expenses, costs, taxes, etc. The goal of every business is to make profit.

• Loss - In finance, we often hear the phrase profit and loss. Loss is when you lose money. It’s the opposite of profit, and it’s a word that no one in finance ever wants to hear. Still, it’s something that can happen when a company makes less money than it spends. • Bull market - A bull market is a financial market situation where stock prices are up (just like the bull’s horns) as a result of investor confidence and the expectations of a strong market. • Bear market - A bear market is the opposite of a bull market. In a bear market, stock prices are falling and the financial market is down—the bear’s paws are facing downwards, and coming down on its enemies.

19 • Rally - As you know, stock markets go up and down. A stock market rally is when a large amount of money is entering the market and pushing stock prices up.

• Stocks - The word stocks is a general term used to describe the ownership certificates of any company. The holder of a company’s stocks is a stock- holder. As a stockholder, you’re entitled to a share of the company’s profit based on the number of stocks you hold.

• Shares - Some companies divide their capital into shares and offer them for sale to create more capital for the company. • Overdraft - An overdraft is when you spend more money than you have in your bank account. The bank will often make you pay an overdraft fee if you do this.

• Credit rating - The credit rating of a person or company is either a formal evaluation or an estimate of their credit history, and it indicates their potential ability to repay any new loans. • Long term loan - Sometimes businesses need to buy assets, equipment, inventory and other things. Banks offer long term loans for businesses that need to borrow a large amount of money for a longer period of time. • Short term loan - As a business or individual, you can borrow money from the bank for short periods of time. A short-term loan is usually repaid in less than five years.

• Mortgage - A mortgage is a loan in which your property—most commonly your house—will be held by a bank or other moneylender as collateral. You’ll receive a loan for the value of the property. This means the mon- eylender will hold your property until your loan has been fully repaid. • Collateral - Collateral is something valuable, such as a property you own, that you pledge (temporarily give to) a bank, financial company or other moneylender as a guarantee of your loan repayment. • Recession - When we talk about a recession, we’re referring to a period of significant (major) decline in a country’s economy that usually lasts months or years.

Furthermore, there are words, not included in the 20 already chosen, that intuitively are considered interesting to investigate. These are described and motivated below: • Crisis - Searches for crisis, in financial terms, could reflect an overall con- cern for the near future of the stock market and might reflect a constrained behaviour among investors • S&P500 - S&P500 is a stock index containing 500 American stocks and is the index that this thesis tests causality against. It is believed that increased searches on this index potentially could signal an increased appetite for investments.

20 • SPX - SPX is the market ticker for the S&P500-index. It serves as an abbreviated unique identifier for the index, used for getting real time in- formation on the security

• Amazon - One of the biggest companies in the world, that as well constitue a significant part of the S&P500-index. Its online search volumes could also reflect consumer behaviour in the economy due to its businesses within e-commerce

• Restaurants - It is believed that in an economy doing well, people tend to go out to eat to greater extent. • Risk - Risk and reward often goes hand in hand. A sudden change in its search volumes for risk could reflect either a change of appetite for risk, or a bigger concern for future fluctuations in the economy.

• Dividend - It is believed that if people are willing to investment more, then it is intuitive to assume that more investors will research certain stocks and their dividend policies. • Gold - A sudden change in the demand for gold could either symbolize an increased demand for investments in general, or the opposite, an increased demand for fixed assets. • Taxes - The tax system is a relatively complex system, both concerning taxes and returns on investments. An increased interest in these details could reflect an higher returns on the market

• Inflation - The inflation prognoses are often seen as indicators of the future state of the economy. Hence, searches for inflation could potentially reflect investors’ view on the future of the market. For the words selected by choice, the category under which the search data will be collected from Google differ. Some of the words are obviously finance related and their search data will thus be collected using the ”Finance” category. This will prevent searches including other topics, e.g. risk that your food gets burnt in the oven, to be falsely included. However, Amazon, Restaurants and Gold will be collected from unbiased searches.

3.2 Data collection The analysis will consider two types of data which are Google search volumes and historical prices of the S&P500 index. Below, the data collection method and sources of data are presented.

3.2.1 Search data The search volume data will be obtained from the open source tool Google Trends which provides historical Google search volumes for different words. Those can be segmented using several criteria such as location or category. In order to make comparison between different terms easier, Google normalizes the search volumes on a scale from 1-100 by dividing each data point by the total search volume of the specified time period and geographical area.

21 The presented data from Google Trends is an unbiased sample of Google search data and only a percentage of the total search volumes is used to compile the trend data. The non real time data can be collected from 2004 up to 36 hour prior the search and weekly data is presented each Sunday. Google trends does not provide a tool for gathering weekly search data on a time period longer than five years, as for longer time periods the data is presented on a monthly basis. In the period of March 24th 2013 to March 24th 2018, 260 data points are provided which will be considered enough to get reliable results in the causality test. Thus, the data used in the analysis will be from the period of March 24th 2013 to March 24th 2018.

Search volumes for words with a small amount of searches will not be available and in case of multiple searches from the same person, for the same word, during a short time period, the algorithm is built to only account for the first search. However, the search does not need to be only for the specific word as the algorithm also accounts for searches with the word included in a sentence.[21]

3.2.2 S&P500-Index The S&P500 index consists of 500 American stocks and is widely considered to be the best single gauge of large cap in the U.S.[22] The index is capitalization-weighted, meaning that the proportion of the stocks are weighted by their respective market value of outstanding shares. It is designed to measure the performance of the broad domestic economy through changes in the stock market and contains stocks from all industries with a market capitalization of at least $6.1 billions.[23] The index expresses the total market value of the shares against a base level of 10 set in the base period of 1941-1943. It opened 2018 at 2,683.73 the 2nd of January.[24]

The historical prices of S&P500 will be collected from Yahoo Finance for the same period as the search volume data. The index is only open during business days and therefore the close price of the last business day before Sunday will be used in order to match the search volumes, which are presented per Sundays.

3.3 Investment Strategies This section describes three different investment strategies that will be backtested using historic data. In order to perform the desired backtests a simplification is made by ignoring transaction fees. This is believed to have a minor impact on the actual returns as the fees are usually small in comparison to invested capital.

To simplify the descriptions of the investment strategies, the following

22 four notations used in this section are introduced. p(i) Price of S&P500 index week i n(i) Google search volume week i v(i) Value of portfolio week i R(i) Return of investment made week i

Strategy 1 As stated in section 1.6, Preis et al. claimed that it was possible to yield a 326% return over a three year period, by selling and buying the DIJA index according to changes in Google search volumes. To verify whether it is possible to achieve the same returns on the S&P500 index, the same strategy will be tested on the best performing words in the causality tests.

Preis et al. used a strategy where they week i invested in the index at price p(i) and sold one week later at price p(i + 1), if n(i) > n(i − 1). Simultaneously, if n(i) < n(i − 1), they used the possibility of shorting, i.e selling week i at price p(i) and buying it back at price p(i + 1) one week later. Thus, depending on whether a long or short investment is made, the corresponding return is given by R(i) = 1 + [p(i + 1) − p(i)]/p(i) if long, or R(i) = 1 + [p(i) − p(i + 1)]/p(i) if short. Hence, v(i + 1) = v(i) ∗ R(i).

This strategy description has assumed a positive causality, i.e that higher search volumes indicate a rising price of the S&P500 index. However, this may not be the case as some words may have a negative causality implicating that higher search volumes cause a decrease in price. Thus, before the strategy is tested the coefficient from the corresponding VAR-model will be analyzed. If it is negative, the method described in the previous section will be changed to buying the index if n(i) < n(i−1) and taking a short position if n(i) > n(i−1).

Strategy 2 The second strategy will use a three week moving average of the Google search volume in order to better capture the trend in the search activity. Thus, if n(i) is greater than the three week moving average (i.e [n(i−3)+n(i−2)+n(i−1)]/3) an investment will be made at p(i) and sold one week later at p(i + 1). Simultaneously, if n(i) < [n(i − 3) + n(i − 2) + n(i − 1)]/3 a short position will be taken, selling the index at p(i) and buying it back one week later at p(i + 1).

Just like in Strategy 1 it has to be taken into consideration whether the considered search volume has a positive or negative causality. In the case of a negative causality, the same changes as in Strategy 1 will be made.

Strategy 3 In the third strategy combinations of technical indicators (i.e search trends) will be used. The idea of this algorithm will be to stay fully invested at all times and when both search trends indicates a negative movement of the index take a short positions. Thus, for positively causal search trends we have that if n1(i) < n1(i − 1) and n2(i) < n2(i − 1) a negative indication is given and a short position is taken. The return the following week

23 is hence R(i) = 1+[p(i)−p(i+1)]/p(i), otherwise R(i) = 1+[p(i+1)−p(i)]/p(i).

The idea of this algorithm is to have a return that at most times mimics the index and then identify opportunities where a short position would yield positive returns. However, since all possible combinations of the search trends are large in number, a limitation to only test this strategy for pairwise combinations of the five best performing search trends from the causality test will be made.

3.4 Outline When testing for Granger-Causality certain key assumptions regarding the characteristics of the underlying data (see section 2.3) will have to be ensured for valid results. Hence, the testing in this thesis will be divided into six phases based on the Box-Jenkins method: stationary-check of the data, transformation of non-stationary data, selection of the appropriate lag-order for each VAR process, estimation of model parameters, model checking (i.e. resudual analysis) and the Granger-Causality test itself.

Generally, historic data from stock prices show clear trends and is thus not considered as a stationary process. However, a stable process can normally be obtained by taking the first order difference of these prices. Thus, the tests performed towards the stock market throughout this thesis will reference to the weekly returns of the S&P500-index.

To ensure stationarity of the Google search trends data, individual Augmented Dickey-Fuller (ADF) tests will be performed on each time series. The ADF test will try the null hypothesis of the presence of a unit root, equivalent to that the process is non-stationary, and reject the hypothesis if the time series is stationary. If the hypothesis is not rejected at a significance level of 5 % or better, the data will be considered non-stationary and a need for further transformation will be declared.

As described, some search data will be considered non-stationary, which would imply uncertainties into the VAR model. Hence, for the data where the null hypothesis is not rejected in the ADF test, transformations of the data sets will be necessary. As for the clearly non-stationary S&P500 data, a transformation by taking the first order difference will be made on the search data that do not pass the ADF test.

Vector autoregression and statistical analysis is conveniently performed in R, by installing the ’VARS’ package. As stated, in advance of estimating the VAR model, an appropriate lag for the model has to be determined. This will be done with the package’s built in VARselect function, which provides the lag estimates from the four different criterias, AIC, HQ, SC and FPE, briefly defined in section 2.3.2. The lag order will be decided from the Schwarz criteria (SC) since it penalizes the most for introducing more lag in the model. The motivation is based on the following three aspects:

• It is believed that too much lag will introduce more disturbance from noise

24 in the model (i.e. other factors affecting the index price) • The tests are based on weekly data. Hence, allowing too much lag in the model and the actual delayed effects it implies might grow up to the size of months • AIC (and FPE), that allows more lag, often yield inconsistent estimates for larger datasets When the VAR order has been selected, the model parameters will be estimated. This will be done using ordinary least squares as described in section 2.3.5 with the VAR function.

In order to validate the selected model and to ensure that the model suitably describes the data, residual analyses will be performed. These analyses will evaluate the whiteness of the residuals from the fitted model using the Lagrange Multiplier test, which tests the null hypothesis of uncorrelated residuals. If the test rejects the null hypothesis of uncorrelated error terms at a significance level of 5 % or better, the model will have to be reevaluated with a higher lag order.

Finally, the test for causality will be performed. A VAR model with the appropriate lag order, determined in the previous stage, will be estimated for every search trend data together with the weekly returns of the S&P500-index. This will be done using the package’s VAR function, modelling each respective pair of time series as described in equation (1) and (2). Finally, for each VAR model, the Granger-Causality will be evaluated using the package’s built in function causality.

The steps are summarized as follows: 1. Make sure that the each time series are stationary. If not, transform the data by taking first order difference

2. Select appropriate VAR order using Schwarz criterion 3. Fit the VAR model with the determined lag order from step two 4. Analyze the whiteness of the residuals from each model. If errors are serially correlated, go back to step two and increase the lag until the issue is resolved 5. Perform Granger-Causality tests on the resulting models

25 4 Results 4.1 Transformation of Data As stated, an initial test of the stationarity of the data was performed. An overview of the tests are shown below, however the detailed test statistics are found in Appendix A.1. The tests showed that most search data were non-stationary and hence required a transformation by taking the first order difference. For four keywords, however, the hypothesis of a unit root was rejected at the desired level. These words were cash outflow, bear market, long term loan and taxes. Thus, no transformation was made for the search volumes of those words.

Table 1: Test summary: Stationarity

Search Word Differenced Data (Yes/No) Debt Yes Interest Rate Yes Investment Yes Capital Yes Cahs Outflow No Revenue Yes Profit Yes Loss Yes Bear Market No Bull Market Yes Rally Yes Stocks Yes Shares Yes Overdraft Yes Credit Rating Yes Long Term Loan No Short Term Loan Yes Mortgage Yes Collateral Yes Recession Yes Crisis Yes S&P500 Yes SPX Yes Amazon Yes Restaurants Yes Risk Yes Dividend Yes Gold Yes Taxes No Inflation Yes

4.2 Selection of lag order As stated in section 3.4, the selection of lag order was based on the Schwarz criteria (SC). However, the received lag orders were preliminary, as they may had to be changed due to systematic model errors found in the model validation. The results from the SC selection are presented in Table 2 (a).

26 4.3 Model Validation After selecting the appropriate VAR order using the Schwarz criterion, each model was fit using least-squares. Subsequently, the models had to be validated to ensure that there were no systematic errors in the fitted models. This was done by analyzing the whiteness of the residuals using a Lagrange Multiplier test, more specifically the Breusch-Godfrey LM test. The results are shown below; where the left table displays the initial tests where the VAR order was determined using SC and the right table displays the models that did not pass the initial test and had to be re-fitted using a higher order of lag.

Table 2: Test Summary: Whiteness of Residuals

(b) Re-fitted models with smallest (a) Test of primary models approved lag order

Search Word Lag Chi-Squared P-value Search Word New Lag Chi-Squared P-value Debt 1 8.2712 0.08214 Investment 3 20.987 0.05057 Interest Rate 1 6.9889 0.1365 Profit 3 9.6057 0.6505 Investment 2 20.779 *** 0.00776 Loss 2 9.9324 0.2698 Capital 4 20.952 0.05108 Bull Market 3 18.987 0.08885 Cash Outflow 1 6.0312 0.1968 Rally 4 20.324 0.206 Revenue 1 5.9297 0.2045 Shares 3 12.963 0.3717 Profit 1 10.658 ** 0.03069 Overdraft 3 15.66 0.2073 Loss 1 9.5166 ** 0.04941 Credit Rating 3 15.403 0.2201 Bear Market 1 9.2606 0.05491 Collateral 3 10.982 0.5305 Bull Market 2 23.795 *** 0.002481 S&P500 4 23.403 0.1034 Rally 2 10.267 ** 0.03617 SPX 4 19.964 0.2218 Stocks 2 3.2734 0.916 Restaurants 7 24.605 0.6492 Shares 2 15.86 ** 0.04442 Risk 3 19.218 0.08339 Overdraft 1 18.156*** 0.00115 Dividend 3 12.839 0.3809 Credit Rating 2 22.317 *** 0.004362 Gold 2 14.147 0.07802 Long Term Loan 1 3.4674 0.4829 Inflation 2 10.295 0.2449 Short Term Loan 3 14.265 0.2841 Mortgage 1 4.3012 0.3668 Collateral 2 15.519 ** 0.04981 Recession 3 15.799 0.2006 Crisis 2 15.456 0.05086 S&P500 2 17.164 ** 0.02844 SPX 2 24.047 *** 0.00225 Amazon 1 2.5649 0.633 Restaurants 2 16.773 ** 0.03256 Risk 1 14.107 *** 0.006961 Dividend 1 9.7634 ** 0.04461 Gold 1 13.316 *** 0.009829 Taxes 1 9.1184 0.05821 Inflation 1 12.676 ** 0.01297 Significance codes: ’***’ 1 %, ’**’ 5 %, ’*’ 10 %

27 4.4 Granger-Causality Tests When all models had been fitted correctly the tests for Granger-Causality could be performed. Eight out of the 30 search words tested indicated a causal ability on the index price. For three words, stocks, mortgage and restaurants, the hypothesis of a non-causal behaviour could be rejected at a level of five percent or better. The summarized test result containing the F-statistics and the corresponding p-values are shown below, together with properties of the final models.

Table 3: Test summary: Granger-Causality

Search Word Order of Difference Lag-Order Causality F-statistic P-value Debt 1 1 1.7599 0.1852 Interest Rate 1 1 1.3425 0.2471 Investment 1 3 3.1188* 0.09111 Capital 1 3 1.5677 0.1963 Cahs Outflow 0 1 0.36579 0.5456 Revenue 1 1 0.72322 0.3955 Profit 1 3 0.39771 0.7547 Loss 1 2 0.83172 0.4359 Bear Market 0 1 2.2307 0.1359 Bull Market 1 3 0.83109 0.4772 Rally 1 4 0.47143 0.7567 Stocks 1 2 3.5698** 0.02888 Shares 1 3 1.6444 0.1782 Overdraft 1 3 1.8456 0.1379 Credit Rating 1 3 1.7837 0.1493 Long Term Loan 0 1 0.10893 0.7415 Short Term Loan 1 3 2.1005* 0.09927 Mortgage 1 1 7.4454*** 0.00658 Collateral 1 3 0.54829 0.6495 Recession 1 3 2.3391* 0.0727 Crisis 1 2 3.0007* 0.05064 S&P500 1 4 2.0484* 0.0865 SPX 1 4 0.53746 0.7083 Amazon 1 1 1.4008 0.2371 Restaurants 1 7 2.0753** 0.04477 Risk 1 3 1.4277 0.2338 Dividend 1 3 1.7055 0.1649 Gold 1 2 0.21574 0.806 Taxes 0 1 0.058257 0.8094 Inflation 1 2 0.59977 0.5493 Significance codes: ’***’ 1 %, ’**’ 5 %, ’*’ 10 %

28 4.5 Backtesting Investment Strategies This section presents the results of the three investment strategies defined in section 3.3.

4.5.1 Strategy 1 In the below plot an overview of resulting 5-year returns from Strategy 1 are displayed for each keyword that had a significance of 10 % or better in the Granger-causality test. It is seen that the search data for mortgage, which had the highest level of Granger-causality, aslo yielded the highest return, over-performing the S&P500-index with 30 percentage units. On the remaining search trends Strategy 1 performed significantly worse. For some keywords the strategy resulted in negative returns despite that the index increased with 80 % over the testing period.

A full list of all returns from Strategy 1 is found in Appendix A.2.

Figure 1: Investments based on weekly differences

29 4.5.2 Strategy 2 The results from applying Strategy 2 (i.e. basing the trading decisions on the three week’s moving average of the search volumes) are displayed in the plot below. The overall trend is similar to the result of Strategy 1 where investing based on the search volumes of mortgage was the only strategy that could beat the buy-and-hold strategy of the index. Though, now this strategy outperformed the index with 42 percentage units. The general return of the strategy applied on the remaining search trends was also slightly improved.

A full list of all returns from Strategy 2 is found in Appendix A.3.

Figure 2: Investments based on three weeks’ moving average

30 4.5.3 Strategy 3 In Strategy 3 an attempt to yield excess return was made using combinations of the search trends. The overall result of this strategy was significantly better than the previous two investment strategies and is displayed in the plot below. The best performing combination was mortgage and recession which out-performed the index with over 60 percentage units. The second best and the third best strategies are also combinations of mortgage, with stocks and crisis respectively.

The detailed returns from Strategy 3 are found in Appendix A.4.

Figure 3: Pairwise combination of top-five search trends

31 5 Discussion

In this section the results from Section 4 are explained, contrasted and evaluated from both a mathematical and financial perspective. This is followed by a recommendation for further research on the subject and lastly the conclusions of the thesis are presented.

5.1 Interpretation of Results Here the results from the causality tests and the following investment strategies are analyzed. The indicated causalities are explained and an attempt is performed in order to explain the either successful or non-successful performance of the investment strategies. A comparison with the previous findings on the topic is also presented. Lastly, implications on current financial theory is discussed.

5.1.1 Granger-Causality Test The interpretation of a Granger-causality test is that it evaluates whether the future value of a time series can be predicted with better precision (smaller prediction error) provided an additional set of data from a second time series. If this is the case, the second time series is said to precede the desired time series, which throughout this thesis is a stock index.

For eight out of the 30 series of search data evaluated, the hypothesis of non-causality of the S&P500-index could be rejected at a significance level of 10 % or better. The keywords related to these search trends were investment, stocks, short term loan, mortgage, recession, crisis, S&P500 and restaurants. Thus, better predictions of the future movements of the index could be made using the historical data from these search trends. For restaurants and stocks, the hypothesis was rejected at a level of 5 % and for mortgage it was rejected at a level of 1 %.

The relationship between certain search trends on Google and the performance of the stock market is not evident and hard to explicitly explain. However, based on the results presented in this thesis, speculations on a general level can me made regarding why individuals perform certain searches at a given time and how this could be reflected in the stock market.

When the subprime mortgage market collapsed in 2007 a series of events followed that eventually led to what is claimed to be the worst financial crisis since the great depression in the 30s. Hence, it is not unrealistic that the search volumes of an emotionally charged word such as mortgage, closely associated with a financial crisis, shows the highest level of causality. The fact that mortgage has a negative causality is also reasonable. Increasing mortgage related searches could be reflected by a more restrictive and pessimistic view on the financial market, where investors worry about the future state of the economy. Furthermore, the search volumes for recession and crisis, words which as well can be associated with negative views on the future economic state, also indicated a negative causal behaviour.

32 S&P500 and investment can both be related to an overall demand on the financial market, from which their positive causal relationship to the stock index could be explained; there is a higher level of investors seeking investments, which creates an increased demand that drives up the general stock prices. With the same reasoning increased searches for short term loans and stocks should also be associated with a higher demand for short term investments. However, the resulting VAR model used for the Granger-test indicated a negative causal relationship for these two words.

The only non-finance related search word for which the null hypothesis could be rejected was restaurants. The logic behind including restaurants in the test was that it was believed that the searches for restaurants would be related to individuals tendency to ”eat out” and that this could reflect an increased willingness to spend and invest money. It should be highlighted that here the model required a lag of seven weeks, which in itself makes sense since the hypothetical relationship is indirect, however it also somewhat complicates the model. Furthermore, the coefficients for different lags were non-consistent and took both positive and negative values, meaning that an increase in search volumes one week could indicate a positive return of the index the next week, but a negative return the second week. This makes this particular result harder to interpret. However, since the summarized coefficients for different lags in the model was positive, search volumes for restaurants were believed to have a positive correlation with the stock index.

In addition to the successful test results, some results were not in line with what one might had expected. For instance, indicated in previous studies was that a causal behaviour of the word debt could be expected. This was not the case, whereas the hypothesis of non-causality could be rejected for short term loan, a financial contract that incurs a debt upon the credit taker. Perhaps the fact that a debt can be a result of many different types of loans etc. makes the correlation more complex and harder to mathematically detect. Looking at the words for which the hypothesis was rejected an embryo of a trend can be found: either the words are directly related to the demand on the stock market or closely related to an economic crisis.

5.1.2 Investment Strategies As presented in section 4.5 there were search volumes, or combinations of search volumes, in all three strategies that yielded greater returns than the 77.17 % return yielded by the index itself. For Strategy 1 and 2, where the investment decisions were based on search volumes from one keyword, only the strategies applied on searches for mortgage yielded greater return than the index itself over the five-year testing period. This is an interesting result, out of the eight words for which the null hypothesis was rejected, only the Granger-causality test for the mortgage-data rejected the hypothesis at a level of 1 %. In addition, mortgage had the only historic search data that yielded excess returns over the testing period. A natural trail of thought is to assume that a certain level of causality (i.e. significance level of 1 %) is necessary in order to be compatible with these two rather naive investment strategies.

33 Furthermore it was seen that the return of both Strategy 1 and 2 applied on the search volumes for mortgage had rather equal returns as the S&P500-index itself over the first two years. Thereafter the investment strategies yielded a higher return, where the strategy based on the past three week’s moving average gave the highest return. This can be seen as an indication of that the causality may shift over time. An additionally interesting aspect worth pointing out is that both strategies performed well when the stock index had larger dives. For example, looking at the graph for Strategy 1 it was seen that the stock index had three bigger dives, two occurring after near three years and one at the very end of year five. During all these the strategy yielded positive returns. If the causality for search volumes of mortgage is true, implied by the test results, it means that the strategy noted that searches for mortgage increased in the week preceding the dive and hence took a short position in the market.

Proceeding to Strategy 3, where investment decisions were based on several search trends, a first observation was that the overall performance of the strategies improved. The best performing strategy, with the combination of mortgage and recession, yielded a return of almost 140 % and second best was the combination of stocks and mortgage with a return of almost 130 %. In addition to this, Strategy 3 for all tested combinations gave positive returns. It thus appears as if search trends served their purpose best in combination with each other.

An additional aspect of the result of the investment strategies was the fact that the highest returns were yielded from words with a negative causality towards the overall market. Possible reasons for this could be numerous, however an interesting parallel can be drawn to the theory of loss aversion, presented by Daniel Kahneman. According to Kahneman people respond more to losses than gains, where losses tend to affect the psyche up to twice as much as gains[25]. Together with the aspect from behavioral finance that noise in a larger scale tends to be interpreted as information incorporated in the prevailing stock prices, ”negative” noise could potentially have larger impact on people’s financial decisions, reflected in subsequent stock prices. Thus, a psychological aspect is that words connected to losses reflects a state of uncertainties in the market, causing a more restrictive behaviour among the investors. This could also help explain why the strategies could predict when to take short positions in the index with such accuracy.

5.1.3 Comparison to Previous Findings The views on to what extent Google search trends could serve as technical indicators are diverse. Opposed to what was presented by Challet et al. this thesis does provide mathematically sustained evidence that search volumes for certain words do have a causal effect, in Granger-sense, on the financial market. The causality was best quantified for mortgage, for which various trading strategies yielded a higher return than the S&P500-index itself; something that could not be produced by Challet et al.

34 The results from this study was in line with several previous studies claiming that a relationship between Google search trends and the financial market do exist. Varian et al. showed that economic indicators could be forecasted using search volumes on Google and Perlin et al. showed that a causality for search trends against both volatility and weekly returns could exist. In addition, their study claimed that stocks had the biggest impact on the overall financial market, which as well converges with the findings presented in this thesis. Stocks rejected the hypothesis at the second best significance level, only mortgage had a better significance level and this word was not tested in Perlin et al.’s study. The VAR model on which the causality test is based also indicated on, as by Perlin et al.’s study did across several markets, a negative correlation between the search volumes of stocks. If search volumes increases, then the stock index tends to decrease.

What could not be mathematically sustained, however, is how Moat, Preis et al. could obtain a return over 300 % with a trading strategy based on the search volumes of debt, whereas the testing performed in this thesis could not indicate any Granger-causality. Potentially this could be due to the difference in time span on which the tests are conducted and the complexity of the field of interest. Neither the search activity for a specific word on Google nor the subsequent causal effect on a financial market does necessarily have to be the same today as they were ten years ago. Interesting is also that the time span used for the study performed by Perlin et al. overlapped with Moat, Preis et al.’s, and they were both in fact able to reject the null hypothesis for debt in the Granger-causality test.

5.1.4 Financial Implications As suggested by the efficient market hypothesis, yielding excess returns consistently should be impossible due to the quick adoption of new information on the market. However, one could question the relevance of this theory as of today due to the large amount of technological progress that has been made since the theory was first presented almost 50 years ago. Not only is the amount of information available larger, but also the number of and types of traders active on the market. Today, private investors are only a few clicks away from a trade while institutional traders are applying their analytic framework on the stock market. Meanwhile there is also algorithmic trading, instantly acting on the release of new information, exploiting market inefficiencies etc. Needless to say, there are asymmetries in the information available both in a time and selective perspective depending on the investor. The implied inefficiencies of the market is reflected in the result of the thesis, where excess return was accomplished using Google search data.

From a behavioural finance perspective, people’s exposure to noise is today greater than ever before and separating accurate from inaccurate information can be difficult (just see what implications fake news had on the 2016 American election). All this gives Fisher Black’s concept of noise even more relevance than when it was first presented in 1986. One way to interpret the result of the thesis is that the search volumes could serve as a measure of the prevailing noise. Search volumes indicates what type of information people are searching

35 for and could thus reflect a certain bias in the information set that they are exposed to.

5.2 Sources of Errors Violations of key assumptions for the models used, as well as methodical complexities could imply errors that affects the reliability of the presented results. An evaluation and discussion of these errors are presented below.

5.2.1 Mathematical Sources of Errors There are two main assumptions necessary for modeling several time series as a vector autoregressive model, the assumptions of stationary data and non-residual autocorrelation. The stationary properties of the VAR model is essential for it to be stable and well defined. If this requirement is not fulfilled a high level of uncertainty is implied in the estimated model, consequently affecting the causality test results. However, prior to the causality-testing it was ensured that the data sets were stationary and hence it is believed that non-stationarity in the data used has minor impact on the results in this thesis. Furthermore, to ensure that there are no systematic errors in the estimated models a Breusch Godfrey test was performed for each model. If an indication was given that there were systematic correlation between the residuals, the models were revised until the property was satisfied. Hence, it is believed that the effects from residual autocorrelation also have minor impact on the presented results.

A limitation in the Granger-causality is its ability to identify indirect causalities. Say, hypothetically, that there is a causal relationship between a process X and Z, as well as between Z and a third process Y, then indirectly X would cause Y. In these situations the Granger-causality tends to fail in rejecting the null hypothesis for the indirect causality, whereas rejecting it for the two direct causalities [26]. Since the underlying search trends analyzed are consequences of several events (e.g. political, financial etc.) affecting peoples Internet activity, either consciously or unconsciously, and where correlation between different searches on Google likely is present, the tests performed probably are exposed to various forms of indirect causalities. However, the actual implications on the presented results do not necessarily have to be that severe. As stated, indirect causalities are hard to detect and can thus be ”missed” in the test, but this does not change the nature of the causalities that were found. Rather than affecting the reliability of the causalities found, this aspect raises questions regarding the nature of the causalities that could not be shown. Perhaps the fact that debt did not indicate a causal relationship whereas mortgage did could be a consequence of this. Further studies including the aspects of interrelationship of several search trends are hence encouraged.

5.2.2 Errors From Data Collection As presented in section 2.3.1, Google trends data is an unbiased sample presented on a normalized scale from 1-100. The algorithm for collecting the sample is not public and thus it is hard to evaluate how well it reflects the

36 actual search volumes. The algorithm is however under constant development and since the first search trends were presented in 2008 several improvements of the algorithm have been done. One could argue that the normalized properties of the search data would affect the reliability of the results. However, it is then important to again point out that the ambition of the Granger-causality test performed in this thesis is not to explicitly predict a future value of the stock index, but to evaluate the existence of a causality. It is thus believed that normalized search data serves this purpose sufficiently.

The S&P500 data was collected from Yahoo finance, which is considered a reliable source. Inspecting the data it can be seen that during the period of March 24th 2013 to March 24th 2018, from which the data was collected, the index had a low volatility with a steady growth. Thus, neither the investment strategies or the causality tests have been tested during more volatile periods with bigger declines in the stock market, which could have had an impact on the results. This must be considered when evaluating the findings.

5.2.3 Nature of the Financial Market The financial market is complex and there are many different factors affecting the movements on the stock market. Financial reports, politic turbulence or natural disasters are just some of them, which on both short and long term may have great impact on the performance of the markets. It is not reasonable to believe that search volumes of singular keywords related to finance would be able to predict sudden events like these and this has to be taken into consideration when using search volumes as an indicator for the stock market.

Replicating the S&P500 index is hard due to the large number of stocks and the capitalization weighting. Thus, to invest in the index it is preferable to invest in one of the exchange traded funds (ETF) built to mimic the index. Trading this type of instrument is associated with certain costs, which have been neglected throughout this thesis. Typically it is commission fees and bid-ask spreads which, depending on broker and size of investment, may vary in size. As an example, an investment of SEK 500, 000 in the SPDR SP 500 ETF Trust on Avanza yields total fees of SEK 149, which is below 0, 03 %.[27] Clearly, the fees would implicate slightly lower returns, but assuming big investments it would not have any significant effect on the overall outcome of the backtests.

5.3 Further Research The opportunities that Big Data has to offer are endless and the area explored in this thesis only scratches the surface on what this information stream has to offer. Recommendations for further studies are presented below.

Firstly, as there were several words where the null hypothesis of no causality was rejected at 10%, 5% or even 1% levels as for mortgage, there is a great probability that Google search trends in some cases actually do precede certain movements in the stock market. However, the scope of this thesis is limited geographically to searches within the United States, to the S&P500-index and

37 to a certain amount of words. A natural next step in the search for a causality would be to replicate the testing on several markets using the same set of words (or equivalents). Furthermore there also exists a possibility to enlarge the set of words tested, searching for more causalities.

Secondly, the tests performed throughout the thesis are rather naive, simply evaluating if future stock index prices are determined with a higher level of certainty or not with the information provided from the Google search trends. Explicit correlations, which could be used for better forecasting, are not discussed due to the presumed complexity of the matter. However, it is an interesting aspect to explore further with more advanced, non-linear, methods. A recommendation for further research is also that on a mathematical basis explore how combinations of several search trends together could have an impact on the financial market, as indicated from the overall better performance of Strategy 3.

Lastly, the causalities evaluated in this thesis are very general. However, if search trends are proven to Granger-cause a large stock index, then it is reasonable to also assume that company specific searches could be related to movements on individual stock prices. Studies similar to this have been performed, however it is still seen as a fairly unexplored area where there is more to see. In addition, Google strives to continuously improve their products. A potential outcome is that search trends become more precise, instead of being based on only a few percentages of the total searches, and hence in the future could help describe the state of the financial market more precisely.

5.4 Conclusion In this report it has been shown that search trends from a selection of words do cause, in Granger-sense, the S&P500-index. However, the result of the search volume based investment strategies indicates that the underlying complexity of the found causalities complicates the ability to benefit financially from them. Interesting though, is that it appears as if combinations of search trends better predicts movements in the financial markets.

Based on the findings of the thesis, which in addition are in line with several previous studies on the area, it is clear that a relationship between search activity on Google and the financial market do exist. To what degree and how this relationship can be exploited require further researches as the relationships most likely are not linear, and not necessarily constant over time. It is however shown that excess return can be obtained using strategies based on search trends, but in advance of implementing these in reality, replications of the tests performed on new markets and with new data are desired.

38 References

[1] GlobalStats. Search Engine Market Share Worldwide. 2018. url: http: / / gs . statcounter . com / search - engine - market - share. (Accessed: 23.12.2018). [2] MG Siegler. Eric Schmidt: Every 2 Days We Create As Much Information As We Did Up To 2003. 2010. url: https://techcrunch.com/2010/08/ 04/schmidt-data/. (Accessed: 23.03.2018). [3] Martin Zwilling. What Can Big Data Ever Tell Us About Human Behav- ior? 2015. url: https://www.forbes.com/sites/martinzwilling/ 2015 / 03 / 24 / what - can - big - data - ever - tell - us - about - human - behavior/#75c834e961f9. (Accessed: 23.03.2018). [4] Ari Libarikian Nicolaus Henke and Bill Wiseman. Straight talk about big data. 2016. url: https://www.mckinsey.com/business- functions/ digital-mckinsey/our-insights/straight-talk-about-big-data. (Accessed: 23.03.2018). [5] Investopedia. 7 Technical Indicators to Build a Trading Toolkit. url: https://www.investopedia.com/slide-show/tools-of-the-trade/. (Accessed: 23.03.2018). [6] Michael Khan. Why Technical Analysis Matters. 2010. url: https://www. forbes.com/2010/04/16/disney-hpq-charting-markets-technical- analysis.html#5239a89d4ee5. (Accessed: 23.03.2018). [7] Hyunyoung Choi and Hal Varian. “Predicting the present with Google Trends”. In: Economic Record 88.s1 (2012), pp. 2–9. [8] Ladislav Kristoufek, Helen Susannah Moat, and Tobias Preis. “Estimating suicide occurrence statistics using Google Trends”. In: EPJ data science 5.1 (2016), p. 32. [9] Tobias Preis, Helen Susannah Moat, and H Eugene Stanley. “Quantifying trading behavior in financial markets using Google Trends”. In: Scientific reports 3 (2013). [10] Marcelo S Perlin et al. “Can We Predict the Financial Markets Based on Google’s Search Queries?” In: Journal of Forecasting 36.4 (2017), pp. 454– 467. [11] Damien Challet and Ahmed Bel Hadj Ayed. “Do Google Trend data contain more predictability than price returns?” In: (2014). [12] MetaTrader5. Technical indicators. 2018. url: https : / / www . metatrader5 . com / en / terminal / help / indicators. (Accessed: 30.03.2018). [13] Eugene F Fama. “Efficient capital markets: A review of theory and empirical work”. In: The journal of Finance 25.2 (1970), pp. 383–417. [14] Robert J Shiller. Do stock prices move too much to be justified by subse- quent changes in dividends? 1980. [15] Werner De Bondt et al. “Behavioral finance: Quo vadis?” In: Journal of Applied Finance 18.2 (2008), p. 7.

39 [16] Fischer Black. “Noise”. In: The journal of finance 41.3 (1986), pp. 528– 543. [17] Helmut L¨utkepohl. New introduction to multiple time series analysis. Springer Science & Business Media, 2005. [18] Statistics How To. ADF — Augmented Dickey Fuller Test. 2018. url: http://www.statisticshowto.com/adf-augmented-dickey-fuller- test/. (Accessed: 08.04.2018). [19] Clive WJ Granger. “Investigating causal relations by econometric models and cross-spectral methods”. In: Econometrica: Journal of the Economet- ric Society (1969), pp. 424–438. [20] FluentU. Bulls and Bears: 20 English Words for Finance You Simply Must Know. 2018. url: https://www.fluentu.com/blog/business-english/ english-for-finance/. (Accessed: 26.03.2018). [21] Google Trends. 2018. url: https : / / trends . google . com / trends/. (Accessed: 27.03.2018). [22] S&P Dow Jones Indices. S&P 500. 2018. url: https://us.spindices. com/indices/equity/sp-500. (Accessed: 23.03.2018). [23] Investopedia. Standard Poor’s 500 Index - SP 500. 2018. url: https: //www.investopedia.com/terms/s/sp500.asp. (Accessed: 26.03.2018). [24] Bloomberg. S&P 500 Index. 2018. url: https://www.bloomberg.com/ quote/SPX:IND. (Accessed: 26.03.2018). [25] Daniel Kahneman. Thinking Fast and Slow. Farrar Straus Giroux, 2011. [26] Mariusz Maziarz. “A review of the Granger-causality fallacy”. In: The journal of philosophical economics: Reflections on economic and social issues 8.2 (2015), pp. 86–105. [27] Avanza. Information om b¨orshandlade fonden SPDR SP 500 ETF Trust. 2018. url: https://www.avanza.se/borshandlade-produkter/etf- torg/om-fonden.html/159932/spdr-s-p-500-etf-trust. (Accessed: 14.04.2018).

40 A Appendix A.1 Augmented Dickey-Fuller test

Debt Profit Shares Lag P-value Lag P-value Lag P-value 0 0.454 0 0.276 0 0.310 1 0.530 1 0.373 1 0.394 2 0.568 2 0.424 2 0.469 3 0.621 3 0.470 3 0.520 4 0.610 4 0.516 4 0.550

Interest Rate Loss Overdraft Lag P-value Lag P-value Lag P-value 0 0.411 0 0.249 0 0.376 1 0.522 1 0.262 1 0.561 2 0.563 2 0.393 2 0.612 3 0.636 3 0.486 3 0.671 4 0.596 4 0.508 4 0.685

Investment Bear Market Credit rating Lag P-value Lag P-value Lag P-value 0 0.380 0 0.0100 0 0.111 1 0.437 1 0.0100 1 0.299 2 0.498 2 0.0136 2 0.380 3 0.534 3 0.0282 3 0.408 4 0.566 4 0.0669 4 0.432

Capital Bull Market Long term loan Lag P-value Lag P-value Lag P-value 0 0.461 0 0.0100 0 0.0100 1 0.501 1 0.0538 1 0.0100 2 0.515 2 0.1660 2 0.0514 3 0.532 3 0.2961 3 0.1319 4 0.527 4 0.3581 4 0.2605

Cash outflow Rally Short term loan Lag P-value Lag P-value Lag P-value 0 0.01 0 0.0100 0 0.0100 1 0.01 1 0.0143 1 0.0968 2 0.01 2 0.0745 2 0.2911 3 0.01 3 0.1408 3 0.3800 4 0.01 4 0.2665 4 0.3902

41 Revenue Stocks Mortgage Lag P-value Lag P-value Lag P-value 0 0.0940 0 0.301 0 0.373 1 0.0665 1 0.456 1 0.421 2 0.0803 2 0.554 2 0.444 3 0.2475 3 0.606 3 0.482 4 0.2692 4 0.616 4 0.426

Collateral Recession Crisis Lag P-value Lag P-value Lag P-value 0 0.127 0 0.0100 0 0.0157 1 0.323 1 0.0282 1 0.0684 2 0.414 2 0.0937 2 0.1298 3 0.472 3 0.2428 3 0.1832 4 0.485 4 0.2816 4 0.2948

S&P500 SPX Amazon Lag P-value Lag P-value Lag P-value 0 0.010 0 0.162 0 0.498 1 0.044 1 0.335 1 0.490 2 0.202 2 0.439 2 0.489 3 0.288 3 0.500 3 0.455 4 0.343 4 0.546 4 0.465

Restaurants Risk Dividend Lag P-value Lag P-value Lag P-value 0 0.487 0 0.270 0 0.387 1 0.549 1 0.309 1 0.449 2 0.616 2 0.379 2 0.516 3 0.639 3 0.421 3 0.520 4 0.680 4 0.422 4 0.539

Gold Taxes Inflation Lag P-value Lag P-value Lag P-value 0 0.389 0 0.0100 0 0.158 1 0.438 1 0.0100 1 0.325 2 0.446 2 0.0100 2 0.401 3 0.525 3 0.0403 3 0.448 4 0.571 4 0.0538 4 0.468

42 A.2 Strategy 1 Returns

Word Return (%) Debt 78.53 Interest Rate 40.56 Investment -20.54 Capital -20.72 Cash Outflow -14.96 Revenue 9.54 Profit 26.76 Loss 9.68 Bear market 154.54 Bull market 108.43 Rally -29.40 Stocks 11.13 Shares -35.06 Overdraft -29.46 Credit rating -8.22 Long term loan -22.46 Short term loan -3.04 Mortage 106.33 Collateral 57.15 Recession 32.47 Crisis 10.49 Inflation 18.66 Taxes 11.67 Risk 40.96 Dividend -38.08 S&P500 24.67 SPX 45.21 Gold -24.58 Amazon -21.34 Restaurants -7.11

43 A.3 Strategy 2 Returns

Word Return (%) Debt 62.27 Interest Rate 24.81 Investment -10.91 Capital -16.92 Cash Outflow -14.70 Revenue 28.82 Profit 35.28 Loss 20.24 Bear market 111.22 Bull market 37.21 Rally -49.98 Stocks 1.13 Shares -21.88 Overdraft -27.43 Credit rating 13.20 Long term loan 20.41 Short term loan 47.57 Mortage 118.87 Collateral 43.23 Recession 37.3 Crisis 37.66 Inflation -21.79 Taxes 24.25 Risk 16.25 Dividend -63.42 S&P500 8.18 SPX 52.59 Gold -8.19 Amazon 17.76 Restaurants 5.97

44 A.4 Strategy 3 Returns

Words Return (%) Stocks + Mortgage 129.74 Stocks + Recession 50.65 Stocks + Crisis 33.83 Stocks + Restaurants 32.03 Mortgage + Recession 137.72 Mortgage + Crisis 92.83 Mortgage + Restaurants 69.56 Recession + Crisis 63.82 Recession + Restaurants 34.28 Crisis + Restaurants 29.00

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