The impact of Trump's tweets on the volatility of the American stock market

Master’s Thesis

The impact of Trump’s tweets on the

volatility of the American stock market

Rick Poel

Student number: 10772200 Date of final version: August 6, 2018 Master’s programme: Econometrics

Specialisation: Free track

Supervisor: Prof. dr. F. R. Kleibergen Second reader: dr. K. A. Lasak

Faculty of Economics and Business

Faculty of Economics and Business

Amsterdam School of Economics

Requirements thesis MSc in Econometrics.

1. The thesis should have the nature of a scientic paper. Consequently the thesis is divided up into a number of sections and contains references. An outline can be something like (this is an example for an empirical thesis, for a theoretical thesis have a look at a relevant paper from the literature):

(a) Front page (requirements see below)

(b) Statement of originality (compulsary, separate page) (c) Introduction (d) Theoretical background (e) Model (f) Data (g) Empirical Analysis (h) Conclusions

(i) References (compulsary)

If preferred you can change the number and order of the sections (but the order you use should be logical) and the heading of the sections. You have a free choice how to list your references but be consistent. References in the text should contain the names of the authors and the year of publication. E.g. Heckman and McFadden (2013). In the case of three or more authors: list all names and year of publication in case of the rst reference and use the rst name and et al and year of publication for the other references. Provide page numbers.

2. As a guideline, the thesis usually contains 25-40 pages using a normal page format. All that actually matters is that your supervisor agrees with your thesis.

3. The front page should contain:

(a) The logo of the UvA, a reference to the Amsterdam School of Economics and the Faculty as in the heading of this document. This combination is provided on Blackboard (in MSc Econometrics Theses & Presentations).

(b) The title of the thesis

(c) Your name and student number (d) Date of submission nal version

(e) MSc in Econometrics

Abstract

This thesis examines the impact of Trump’s tweet on the volatility of the Dow Jones. Regressions of the difference in realised volatility are done on the categories of the tweets of Trump. The realised variances are calculated with minute-date of the Dow Jones index. Tweets which are about trade barriers have a rising impact on the volatility. Because of the possible executive orders Trump can make on this subject, investors seem to care about Trump’s tweets about this subject.

Statement of Originality

This document is written by Rick Poel who declares to take full responsibility for the contents of this document.

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. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

Contents

1

Introduction

On the day Trump was elected as the president of the United States American Stock markets immediately fell over 4%. This was the beginning of a colourful presidency of President Trump. Trump became president after a hectic election campaign. While almost all of the traditional media reported that Hilary Clinton was going to win the elections, Trump eventually won by a minor difference. This was the beginning of a stiff relationship between the president and the press. This relationship led to a different way of communicating with the people of the USA. Where former presidents communicated via traditional media, Trump’s main communication platform is Twitter. Besides using Twitter as a platform to communicate with people, he also practises politics via Twitter. He is not afraid to publicly attack another politician on Twitter. One example of this is Trump calling Kim Jung Un ”Little Rocket man” in one of his tweets. He also does not hesitate to put pressure on the democrats in the senate. The tweets of the president are very popular. With around 21.000 retweets on a single tweet and over 52 million followers, he has a big audience. Not only republicans or people with political interests follow his Twitter closely, but also stockbrokers. Tweets about certain subjects can effect the stock price of companies that have to do with this subject. There is even a trading bot called BOTUS. BOTUS is an abbreviation for Bot of the United States. This bot reads the tweets of Donald Trump and uses this information to trade stocks. Because of all this, it is likely that tweets of the president of the United States have an impact on the stock market. An example of having an effect on the markets is found in March 2017 when Trump tweeted the following about the Pharmaceutical industry:

“I am working on a new system where there will be competition in the Drug Industry. Pricing for the American people will come way down!”

Because of the uncertainty in the drug industry, the S&P Pharmaceutical index directly dropped 1.4%. This is just one example of a tweet that caused movement on the stock market. Trump does several of these kind of announcements on his Twitter. Since Trump’s inauguration Trump tweeted, excluding retweets, the massive amount of 3078 tweets. Of course not all tweets will have an impact on the stock market, but announcements about certain policies and other po-litical tweets could possibly have an effect on the stock market. Because tweets not necessarily cause the stock market to go down or to go up, volatility is the way to measure the effect of the tweets. Tweets may have an effect of uncertainty under investors, which is why in this thesis the effect of Trump’s tweets on the volatility of the American stock market is investigated.

Volatility modelling began with Arch and Garch like models (Engle (1982)). These models where highly model-dependent. A shock into the model slowly faded away, what may not be the case in real-life. When years passed by high frequency data became available. With the availability of high frequency data, a lot has changed. Merton (1980) already noted that the

volatility could be measured by using a number of sub-periods and called it realised volatility. With the availability of high frequency data this method could be used to estimate volatility over a very short period. Later on several methods are proposed to improve the estimation of volatility using high-frequency data (e.g. Zhang et al.(2005)).

In order to investigate the impact of Trump’s tweets, the realised variance is used to esti-mate the volatility. The difference of the volatility after a tweet and the volatility before a tweet is the dependent variable. The difference is explained by several variables of the tweets. Data of the Dow Jones index are used to measure the impact.

This thesis is organised as follows. First the realised variance is discussed. Secondly the used data are discussed. Thirdly the methodology is discussed whereafter the results are stated in section 5. In section 6, the conclusion is made with a wrap up of this whole thesis.

2

Realised variance

High-frequency data became more and more available since online trading came up in the be-ginning of the current century. This has led to a change in modelling volatility. With all the data available, calculating volatilities has become less dependent on the model you choose for modelling the volatility (e.g. Garch). In the early days daily data was used to estimate monthly volatility, but with upcoming computers it became possible to estimate volatility on a daily basis. At the beginning this was only used in the literature of exchange rates because this data was relatively easily available. Later on these methods have been applied to stock market data. In this section, ways to estimate volatility are discussed. The realised variance is the base to measure the effect of Trump’s Tweets. The realised variance is explained carefully using a simulation study to support the stated results.

In the literature on stock pricing and volatility, a Brownian motion process is widely accepted as a model for the distribution of log prices: following e.g. A¨ıt-Sahalia et al.(2011), a Brownian motion process for the efficient log-prices Xt:

dXt= µtdt + σtdWt, (1)

where µt is a drift at time t, σt the volatility at time t and Wt a Brownian motion process. A

Brownian motion is described by a Wiener process which has the following property Wt− Ws ∼ N (0, t − s) (0 ≤ s ≤ t).

Note the subscript of σt which let the volatility be able to change over time. σt is of great

interest in this thesis. By letting this to change over time, indicated by the subscript t, we can measure the difference in volatility before and after a tweet of Donald Trump. When simulating this Brownian motion process of (1) with a constant µtof 0 a constant σ2t of 0.01 and a dt of 1

second this results in a plot like the one beneath:

This is a so called random walk. When comparing this to a random trading day we see the same sort of patterns. The plot beneath shows the log prices of a trading day at the Dow Jones index on the 22nd of May 2018.

Figure 2: Log prices of the Dow Jones index 22 May 2018

In this thesis the volatility over a certain time period is of particular interest, namely the time period before a tweet is posted and the time period after a tweet is posted. There is a need to have a theoretical measure of the volatility in order to estimate the volatility over a certain time period. Following Andersen et al.(2001), this is captured by the integrated variance. The integrated variance is defined as follows:

IV (t, k) = Z t

t−k

σ2(s)ds, (2)

which is the integral of the true variance over the interval [t − k, t]. It is a way to measure the volatility over a given time period which is of great importance in this thesis. A way to estimate the integrated variance is using the sum of squared returns. In this way the variance is estimated over certain intervals with equal length (assuming a zero mean), by adding these estimates a proper estimate for the integrated variance is obtained. By decreasing the length of the intervals and so increasing the number of intervals the Realised Variance converges to the Integrated Variance. The intuition behind this is described in Merton (1980). When estimating first moments it does not help to increase the frequency only increasing total time will increase precision. This is not the case when using the second moment. Using the second moment, the precision will increase as the frequency increases. When approximating the integrated variance using realised variance, which is the sum of squared returns, using infinitely small intervals does, however, not give a consistent estimator of the integrated variance. The reason for this inconsistency is micro-structure noise (Campbell, Lo, and MacKinlay (1997)). The main reason of the micro-structure noise is the spread between bid and ask prices. In seconds, the price can oscillate between the bid and ask price, but the true efficient price does not change. To have a proper estimate of the integrated variance according to e.g. Zhang et al. (2005) time intervals between 5 and 30 minutes should be used in order to get unbiased estimates. There are some

methods that take the micro-structure noise into account while using all available data, but to measure the effect of president Trump’s tweet this is not needed.

The realised variance between time t − k and t is defined by

RV (t, k; n) = n X j=1 r  t − k + j nk, k n 2 (3) where rt − k + _njk,k_n= X_t−k+j nk −X_t−k+j+1 n k

, which is the log return between time t−k +_njk and t−k+j+1_n k. k is the length of the interval and n equals the number of observation within the interval [t − k, t]. When increasing the number of observations (n) and decreasing the length of the interval(k), the realised variance can be used to consistently estimate σ2_t (Foster and Nelson 1996) (ignoring micro-structured noise)

plimn→∞,h→0

 RV (t, k; n) k



= σ2_t. (4)

This result is in practise not very useful. According to Andreou and Ghysels (2002), this result is not robust. So a better measure is to compute the realised variance over a fixed interval. To approximate the integrated variance estimates of σ_t2 are used and together with a Riemann sum a solid estimation is obtained. σ2

t is approximated by

r(t−k_n,k_n)2

k (assuming zero mean).

The approximation of σ2_t is for an interval of length k_n. So the entire integral can be estimated by a Riemann approximation. A single element of the sum equals the previously mentioned estimated value of σ2_t times the length of the interval (k_n) which equals the realised variance as is stated in equation (3). The resulting realised variance is an unbiased estimator of the integrated variance over the same interval

E[RV (t, k; n)] = IV (t, k).

Besides being an unbiased estimator for the integrated variance, the realised variance is asymp-totically normally distributed.

(RV (t, k; n) − IV (t, k)) × 2 3RSV (t, k; n) −1₂ d −−−→ n→∞ N (0, 1) (5) where RSV (t, k; n) =Pn j=1r  t − k +_njk,k_n 4

. Which equals the estimated uncentered fourth moment.

When simulating 1000 trading days using the process described in (1) , with dt = 1 second, a constant 0 mean (µt) and a constant σ2t of 0.001, a histogram of the estimated realised variances

can be obtained. The realised variance are computed for full trading days so k equals 6 hours and 50 minutes. The realised variances are computed with intervals (k_n) of 1 second so n equals 6 × 60 × 60 + 50 × 60 + 1 = 24601 . The black line represents a normal distribution with a mean and standard deviation obtained from the calculated values of the realised variances.

Figure 3: Histogram of simulated Realised Variances

We see a distribution that is very close to the normal distribution. When testing normality with a Jarque-Bera test, a p-value of 0.72 is obtained which implies that H0: Normally

dis-tributed cannot be rejected. The estimated mean equals 24.54. The true integrated variance equals IV = R_9:30:0016:20:000.001ds = 0.001 × (6 × 60 × 60 + 50 × 60 + 1) = 24.601. So the mean of the realised variance is very close to the true value of the integrated variance. Using the same simulations as before, but computing the realised variance with larger intervals for instance intervals of 1 minute (n = 6 × 60 + 51 = 411). The realised variances are no longer normally distributed. The p-value corresponding to the Jarque-Bera test equals 1.135 × 10−7, which means that H0: realised variances are normally distributed should be rejected. The mean of

the realised variance is 24.64 which is still very close to the true value of the integrated variance which is 24.601. The histogram of realised variance with k_n of 1 minute is shown below:

Figure 4: Histogram of simulated Realised Variances

The distribution of the Realised Variances is a bit thicker than the one shown before. The standard deviation of the 1-minute interval estimates equals 1.74 against a standard deviation of 0.23 with the 1-second interval estimates. The estimates with a smaller n still seems unbiased,

3

Data

In this section a description of the data is given. The manipulations performed on the data-set are described.

The data of the Dow Jones index are obtained from a Russian financial services company called Finam. The data-set contains minute-data of trading days from the day that president Trump was inaugurated (20th of January 2017) untill the first of June 2018. Trading days on the Dow Jones last from 9:30 till 16:20, which implies 411 observations per trading day.

The Tweets of Trump are obtained from http://www.trumptwitterarchive.com/archive. The data-set contains all tweets of president Donald Trump from the day of his inauguration untill the 1st of June. This results in 3078 tweets, retweets are not considered. Next to the tweet itself the time of posting is also included in the data-set. In order to calculate the volatility before and after a tweet, tweets that are placed between 2 hours after the market opens, and 2 hours before the market closes are considered. In total we are left with 597 tweets.

We first consider an example of a tweet. On the 30th of November Trump tweeted the following about North Korea:

“The Chinese Envoy, who just returned from North Korea, seems to have had no impact on Little Rocket Man. Hard to believe his people, and the military, put up with living in such horrible conditions. Russia and China condemned the launch.”

The tweet about the relationship with North Korea may be surprising for investors, which can cause uncertainty among them. The market reacted immediately as is shown in the plot underneath, the red dot indicates when the tweet is placed. After the tweet we see a short positive reaction whereafter the returns go down. The spread of the log returns seems to widen after the tweet.

Figure 5: Minute returns of the Dow Jones index on 30-11-2017 For another tweet we consider a tweet placed on the 23rd of October:

“The Democrats want to shut down the Government over Amnesty for all and Border Security. The biggest loser will be our rapidly rebuilding Military, at a time we need it more than ever. We need a merit based system of immigration, and we need it now! No more dangerous Lottery.”

This is a typical example of Trump practising politics on Twitter. He puts pressure on the democrats in order to get a merit based system of immigration. Because of a possible shutdown of the government the market reacted with a slightly higher variation, as is shown below. Again the red dot indicates the time when the tweet was posted.

Figure 6: Minute returns of the Dow Jones index on 23-10-2017

In order to use the Tweets in a regression the tweets are manually categorised into 11 categories. In the table below the categories are described.

Category Description # of observations

Media Tweets about fake news, and about several TV stations. 77 Foreign policy Tweets about foreign policy such as trade

and relationship with other countries. 56 Politics Tweets about American politics. 23 Elections Tweets about the elections (campaign) in 2016. 37 Safety Tweets about FBI, NSA, gun policy,

and other tweets focused on security/safety. 73 America First Tweets about the policy of Trump that puts America first. 7 Economy Tweets about taxes and business 25 Trade Tweets about trade agreements and import tariffs 31 Immigration Tweets about immigration laws/the wall 38 Healthcare Tweets about changing Health-care/anti Obamacare 34 War Tweets about the war against terrorism 8

A tweet can fit in multiple categories, or in none of the above stated categories. For instance tweets that are just meant for propaganda are not assigned to a category. The same goes for tweets that have nothing to do with the above mentioned categories e.g. a book he liked. A tweet about for instance trade can fit into more categories e.g. Trade, Foreign policy and America First.

4

Methodology

In this section the way in which the realised variance is used in order to estimate the effect of Trump’s tweet is described.

In order to estimate the volatility before and after a tweet, the realised variance as described in (3) is used. We calculate the realised variance a given time period before (ex ante) and a the same time period after (ex post) the tweet. Equation (6) describes the difference between volatility before and after tweet i. There is a trade-off between the time-horizon of a tweet having effect on volatility and having enough observations to estimate the volatility properly. This will be discussed in the results section.

∆ˆσ2_i = RVexpost,i− RVexante,i= n X j=1 r  Ti+ k n × (j − 1), k n 2 − n X j=1 r  Ti− k n× j, k n 2 ₍₆₎

In the equation above, Ti is the time of posting of tweet i rounded to whole minutes. To find

relevant results we try to explain the difference in volatility with some variables about the tweets.

∆ˆσ_i2 = c + θ0xi (7)

where c is a constant term and xi contains the variables about tweet i. The variables involved

are the categories described in the data section. This equation can be estimated simply with ordinary least squares. The focus will be on the value of θ which indicates which sort of tweets have an effect on the volatility of the American stock market. These coefficients will be used to zoom in on some particular tweets that cause volatility on the American stock market. The results of the estimated equations and the tweets that cause a higher volatility will be described extensively in the next section.

5

Results

In this section, the results will be presented and they will be analysed. First a sensitivity anal-ysis is conducted to determine the time period to measure the realised variance and the number of observations to use to have proper estimates of the difference in volatility, whereafter the output of several regressions will be shown, which will be analysed carefully. At last we zoom in on tweets that cause a higher volatility.

Having a reliable measure for the volatility is very important in order to obtain reliable es-timation results. The interval length is of great importance to have a reliable estimate of the volatility. Comparing obtained (daily) realised variances with intervals (k_n) of 1 minute (red line) and 5 minutes (black line) results in a very similar trend.

Figure 7: Comparison realised variances using 1 and 5 minute interval

Both obtained realised variances seem very similar. When taking the mean over all trading days the realised variance using 1-minute intervals is even smaller than the ones calculated with 5-minute intervals. When micro-structured noise will play a role, the estimated variance should be higher when intervals getting smaller. When only considering a constant and the categories mentioned in the data section as variables in xi, the following results are obtained with intervals

Coefficient value Standard error P-Value Constant -0.00000041 0.00000057 0.47 Media -0.00000030 0.00000122 0.81 Foreign.policy -0.00000120 0.00000150 0.43 Politics -0.00000169 0.00000207 0.41 Elections -0.00000171 0.00000166 0.30 Safety 0.00000133 0.00000128 0.30 America.first 0.00000106 0.00000374 0.78 Economy 0.00000002 0.00000201 0.99 Trade -0.00000131 0.00000196 0.50 Immigration 0.00000274 0.00000168 0.10 Healthcare 0.00000006 0.00000174 0.97 War -0.00000351 0.00000351 0.32

Table 1: Obtained coefficient values with k of 2 hours and k/n of 5 minutes

The reported p-values are obtained with a simple t-test. The interpretation of the coeffi-cients is that a positive sign indicates a rising effect on the volatility, a negative sign indicates a decreasing effect on the volatility. We see that none of the above parameter values significantly differ from 0 at a 5% level. The coefficient of Immigration is significant at a 10% level, and it has the sign that was expected (+).

To see if 1 minute intervals is a good way to go we compare the 1 minute estimation results with the 5 minute estimation results. The results with 1 minute intervals are reported below:

Coefficient value Standard error P-Value Constant -0.0000003 0.0000010 0.78 Media -0.0000005 0.0000022 0.81 Foreign.policy -0.0000010 0.0000027 0.72 Politics -0.0000011 0.0000038 0.78 Elections -0.0000022 0.0000030 0.48 Safety 0.0000047 0.0000023 0.05 America.first -0.0000016 0.0000068 0.81 Economy 0.0000008 0.0000036 0.84 Trade -0.0000036 0.0000036 0.32 Immigration 0.0000038 0.0000030 0.21 Healthcare -0.0000008 0.0000032 0.81 War -0.0000069 0.0000064 0.28

coefficients America.First and Healthcare differ. Both coefficients have in both regressions a p-value larger than 75% which implies not a big difference. Other p-values are more or less the same when looking at the significance of the coefficients. The only one that differs is the coefficient of Safety, but the difference is not shocking. We see that the coefficient of Immigra-tion has lost its significance at a 10% level, so apparently the effect of those tweets is not that big.

The results are also sensitive to what kind of time-interval is taken to measure the realised variances. An effect of a tweet can fade out, so maybe tweets have an effect of only 1 hour instead of the 2 hours as we assumed before. We take a time horizon of 1 hour instead of 2 hours to measure the difference of the realised variances before and after a tweet. This results in the following results:

Coefficient value Standard error P-Value Constant 0.0000000 0.0000004 0.92 Media 0.0000002 0.0000008 0.76 Foreign.policy 0.0000001 0.0000010 0.89 Politics -0.0000012 0.0000014 0.40 Elections -0.0000007 0.0000011 0.51 Safety 0.0000024 0.0000009 0.00 America.first 0.0000055 0.0000025 0.03 Economy 0.0000004 0.0000013 0.79 Trade -0.0000004 0.0000013 0.75 Immigration 0.0000007 0.0000011 0.54 Healthcare -0.0000002 0.0000012 0.87 War -0.0000030 0.0000023 0.21 Table 3: Obtained coefficient values with k of 1 hour and k/n of 1 minute

We see that the results differ from the previous ones. We now have 2 coefficients that signif-icantly differ from 0 according to the t-test. Tweets about America First and Safety both seem to have a rising impact on the volatility of the Dow Jones. Both coefficients have the expected sign (+). This implies that tweets about America First, which are tweets about protective measures to make America great again, could have a surprising effect on stock brokers. The same goes for tweets about safety which are mostly tweets about the FBI and the Mexican Wall. Other coefficients almost do not differ from the earlier regressions.

The time of tweeting can play an important role. The opening hour of the stock market is regularly more volatile than any other hour during the trading day. The bar-plot beneath shows the average realised variance of every hour of the trading day since Trump became pres-ident. The realised variances are computed with k equal to 1 hour and n of 60. Because the trading day lasts 6 hours and 50 minutes the last hour is corrected with a factor of 6₅ in order

to have a good comparison.

Figure 8: Average realised variance

We see that the first hour of the trading day is indeed more volatile than the other hours. To take this effect into account we introduce a variable which equals the fraction of the first hour that is used in calculating the ex ante realised variance. In formula form the variable looks like this: F irstHour = I(Ti<11:30)  1 −Ti− 11 : 30 60  , (8)

where Ti− 11 : 30 equals the difference in minutes and I is an indicator function. When adding

the time variable to the model, where we use a 2 hour time horizon and intervals of 1 minute, we get the results as is shown in the table below. The first hour of the trading is not taken into account when calculating the realised variances with a 1 hour time horizon. This way we can compare the results below with the results stated in Table 3.

Coefficient value Standard error P-Value Constant 0.0000010 0.0000006 0.12 Media -0.0000006 0.0000012 0.60 Foreign.policy -0.0000007 0.0000015 0.63 Politics -0.0000024 0.0000020 0.23 Elections -0.0000012 0.0000016 0.45 Safety 0.0000014 0.0000013 0.28 America.first 0.0000015 0.0000036 0.68 Economy 0.0000007 0.0000020 0.72 Trade -0.0000015 0.0000019 0.43 Immigration 0.0000023 0.0000016 0.16 Healthcare -0.0000003 0.0000017 0.87 War -0.0000038 0.0000034 0.27 FirstHour -0.0000066 0.0000013 0.00

We see that the coefficient of FirstHour has the sign that was expected. Because the opening hour is more volatile than regular hours during the trading day the ex ante realised variance is higher when the opening hour is included in the calculating. A higher ex ante realised variance results in a lower ∆ˆσ2_i, which is represented by the minus sign of the coefficient of FirstHour. The added time variable is the only significant coefficient at a 5% level. We can compare these results to the results in table 3. In the regression above the results are corrected for including the first hour in the calculations. We do not see the significance of the coefficients of safety and America first back in these results. The reason could be that shocks fade out in time.

The next thing to add is the sentiment of the tweets. The expectation is that positive tweet have a negative impact on the volatility (volatility decreases) and negative tweets have a positive im-pact on the volatility (volatility increases). We see that the constant has changed its sign and is now positive with a p-value of 0.12. The coefficient of Health-care also changed sign but with a p-value of 0.87 there is not much to say. Other coefficients still do not significantly differ from 0.

Next the sentiment has to be added. Sentiment is added to only two categories which seems the two most intuitive to add sentiment to. These categories are foreign policy and trade. A negative tweet about trade, for instance threatening to bring up trade barriers, is likely to have a stimulating effect on the volatility. A positive tweet, for instance mitigating the earlier threat about the trade barriers, is likely to reduce the volatility on the stock market. The results of this estimated equation are reported below.

Coefficient value Standard error P-Value Constant 0.0000010 0.0000006 0.12 Media -0.0000006 0.0000012 0.60 Politics -0.0000024 0.0000020 0.23 Elections -0.0000012 0.0000016 0.45 Safety 0.0000014 0.0000013 0.28 America.first 0.0000015 0.0000036 0.68 Economy 0.0000007 0.0000020 0.72 Immigration 0.0000023 0.0000016 0.16 Healthcare -0.0000003 0.0000017 0.87 War -0.0000038 0.0000034 0.27 ForeignPolicyPositive -0.0000007 0.0000020 0.71 ForeignPolicyNegative -0.0000007 0.0000021 0.75 TradePositive -0.0000015 0.0000028 0.60 TradeNegative -0.0000015 0.0000026 0.56 FirstHour -0.0000066 0.0000013 0.00 Table 5: Obtained coefficient values with k of 2 hours and k/n of 1 minute

the expected sign which are TradeNegative and ForeignPolicyNegative do not significantly differ from 0. Again it could be that shocks of the tweets fade away within an hour. Because of this we add the sentiment to the results with computed realised variances with an interval of 1 hour. The results of this are given below.

Coefficient value Standard error P-Value Constant 0.0000001 0.0000004 0.89 Media 0.0000002 0.0000008 0.77 Politics -0.0000012 0.0000014 0.39 Elections -0.0000008 0.0000011 0.50 Safety 0.0000024 0.0000009 0.00 America.first 0.0000056 0.0000025 0.03 Economy 0.0000003 0.0000013 0.80 Immigration 0.0000006 0.0000011 0.58 Healthcare -0.0000002 0.0000012 0.86 War -0.0000031 0.0000024 0.19 ForeignPolicyPositive -0.0000003 0.0000014 0.85 ForeignPolicyNegative 0.0000006 0.0000014 0.68 TradePositive -0.0000006 0.0000019 0.75 TradeNegative -0.0000004 0.0000018 0.81 Table 6: Obtained coefficient values with k of 2 hours and k/n of 1 minute

The Firsthour variable is not included in this regression because the calculations of the re-alised variances do not have the first hour in it. We see that just like the previous regression the sentiment does not have an effect on the significance of the coefficients. Still the tweets about Safety and America First seem to have a rising impact on the volatility. To have an idea of the value of the coefficients we look at the average of the realised variance over an hour. This average equals 3.8 × 10−6 with a coefficient value of America First of 5.6 × 10−6 this is more than the average realised variance. Also the coefficient of Safety is relatively big with a value of 2.4 × 10−6, which is more than 60% of the average realised variance. It might be interesting to zoom in on those categories in other to see what kind of specific tweets have the greatest effect on the volatility.

To have an idea how the distribution of those tweets is a histogram of the category Safety is shown in Figure 9.

Figure 9: Histogram of change in realised variance of category safety

We see that 2 tweets are on the far right compared to the others. The one that caused the highest difference in realised variances is posted on the 9th of February. The tweet is show below.

“Just signed Bill. Our Military will now be stronger than ever before. We love and need our Military and gave them everything and more. First time this has happened in a long time. Also means JOBS, JOBS, JOBS!”

The other tweet is also posted on the 9th of February just 20 minutes after the first tweet.

“ Costs on non-military lines will never come down if we do not elect more Republicans in the 2018 Election, and beyond. This Bill is a BIG VICTORY for our Military, but much waste in order to get Dem votes. Fortunately, DACA not included in this Bill, negotiations to start now!”

Both tweets are about the same Bill. By signing this Bill Trump ended a shutdown of the government. Because this day was extremely volatile the difference of the realised variance before and after the tweets is relatively not that big. We can verify this by looking at the plot below which shows the minute returns of the 9th of February.

Figure 10: Minute returns of Dow Jones 9th of February

So these tweets do not necessarily cause volatility but are posted on a very volatile day. Because of this tweets the category are not actually causing volatility.

The other category that has a significant impact on the volatility is the category America First. The histogram of the difference in realised variance before and after a tweet is shown in Figure 11.

Figure 11: Histogram of change in realised variance of category America First

Again 2 tweets cause much more fluctuation on the stock markets than the other tweets. The tweet which caused the highest difference in realised variances is stated below.

“Our Steel and Aluminum industries (and many others) have been decimated by decades of unfair trade and bad policy with countries from around the world. We must not let our coun-try, companies and workers be taken advantage of any longer. We want free, fair and SMART TRADE!”

of uncertainty among stock brokers. Traders feared a trade war. Next to this it could have an indirect effect on the car industry in the United States. By charging import tariffs the American car industry is forced to buy more expensive American steel and aliminum.

“From Bush 1 to present, our Country has lost more than 55,000 factories, 6,000,000 man-ufacturing jobs and accumulated Trade Deficits of more than 12 Trillion Dollars. Last year we had a Trade Deficit of almost 800 Billion Dollars. Bad Policies & Leadership. Must WIN again! #MAGA”

The tweet above is again about trade deficits. This time a bit more general and again this caused uncertainty among investors. Trump sort of heads towards a trade war with these kind of tweets. Trump seems to have an impact on the stock market with these kind of tweets about trade. With executive orders Trump has a lot of power on these kind of subjects.

To look if single tweets have a great impact on the volatility of the stock market the histogram of all tweets is shown below.

Figure 12: Histogram of change in realised variance

The three tweets that are placed on the right of the histogram are again tweets of 9 February 2018. Those tweets all have to do with the signed Bill, these are not really interesting. So maybe it is more interesting to look at relative differences instead of absolute difference. The histogram of relative differences is shown Figure 13.

Figure 13: Histogram of relative change in realised variance

The histogram above seems interesting. We see quite an amount of observations above 2, this means that the ex post realised variance is 2 times as big as the ex ante realised variance . So let’s zoom in on the tweets that caused a doubling of the realised variances. In total there are 17 tweets with a more than doubled realised variance. We see 2 tweets about North-Korea, which is of course a very important subject. The first one is mentioned in the Data section of this thesis. This tweet caused a ex post realised variance which is 2.5 as high as the ex ante realised variance. The other tweet is about the responsibility of China in the whole North-Korea Case. He tweeted the following on the 21st of April 2017:

“China is very much the economic lifeline to North Korea so, while nothing is easy, if they want to solve the North Korean problem, they will”

Trump tries to shift the responsibility for the North-Korea case to China, which may have an impact on the relationship of the US with China and North-Korea. This tweet led to an almost 4 times higher realised variance after the tweet. This tweet caused a lot of volatility on the market. Trump tweeted a few other tweets about North-Korea which did not have a big impact on the markets. So it is hard to see why one tweet has a big impact, and another tweet about North-Korea has not an impact. North-Korea is a very important topic for the United States of America, it may cause a nuclear war, which effects the behaviour of traders. Another interesting tweet is about the Iran deal. In that tweet Trump states that is was very bad negotiated, and that the United States don’t need John Kerry’s ’shadow diplomacy’. The Iran deal was around May a big topic. This tweet was another big hint that he would ditch the Iran deal. One day later Trump finally quitted the Iran deal. The last interesting tweet is about immigration.

“We must have Security at our VERY DANGEROUS SOUTHERN BORDER, and we must have a great WALL to help protect us, and to help stop the massive inflow of drugs pouring

into our country!”

This tweet was a tweet when the republicans negotiated with the democrats about the DACA program. These negotiations could have led to a shutdown a few days later. With this tweet Trump did not make the negotiations any easier. This probably led to uncertainty under in-vestors which caused the higher volatility on the market. This tweet only caused volatility because of the possible shutdown. Other tweets are mostly posted on very quiet trading days, on these days it is easier to double the volatility. Because of this a doubling of the volatility could just be a coincidence.

6

Conclusion

The aim of this thesis is to investigate if tweets of president Trump have an impact on the volatility of the American stock market. Twitter is the main communication platform of presi-dent Trump. Where former presipresi-dents communicated via traditional media, Trump avoids the traditional media and communicates with social media. Because the president also practices politics on Twitter it is interesting to see if the tweets of Trump have an impact on the American stock market. The difference in volatility before and after a tweet is measured by the difference in realised variance. The tweets are divided in 11 categories. A regression of the difference of the realised variances is done on the dummy variables of the categories. With this regression it is made clear which categories cause the most volatility. The parameters of the realised variance are changed in order to perform a sensitivity analysis.

Following the results of the estimated models, tweets about Safety and America First cause uncertainty among investors. However the tweets about Safety don’t seem to cause volatility. Because a few tweets are posted on a very volatile day, the tweets of the category actually do not have an effect on the volatility of the American stock market. In the category America First there are some very interesting tweets. These tweets are about trade. Trump’s tweets about trade barriers seem to have an impact on the volatility of the American stock market. Trump has a lot of power with possible executive orders on this subject. This is why the mar-ket becomes more volatile after a tweet in which he gives signs of a trade war. Next to tweets about trade wars some tweets about North-Korea seem to have an impact on the volatility. The North-Korea topic is really important for the US, so it is logical that this influences the stock markets.

The results of this thesis has to be placed in the right perspective. Factors other than the tweets of trump are not taken into account in this thesis. A rise in realised variances could be the result of another event that happened in the same period, which may effect the results. By zooming in on tweets and finding reasons behind the change in volatility, it is tried to exclude the effect of other events.

References

Andersen, T. G., Bollersev, T., Diebold, F. X., & Labys, P. (2001). The Distribution of Realized Exchange Rate Volatility. Journal of the American Statistical Association, 96(453), 42-55.

Andreou, E., & Ghysels, E. (2002). Rolling-Sample Volatility Estimators. Journal of Business & Economic Statistics, 20(3), 363-376.

A¨ıt-Sahalia, Y., Mykland, P. A., & Zhang, L. (2011). Ultra high frequency volatility estimation with dependent microstructure noise. Journal of Econometrics, 160, 160-175. Campbell, J. Y., Lo, A. W., & MacKinlay, A. C. (1997). The econometrics of financial markets. Princeton, NJ: Princeton University Press.

Engle, R. F. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica, 50(4), 987-1007.

Foster, D. P., & Nelson, D. B. (1996). Continuous Record Asymptotics for Rolling Sample Variance Estimators. Econometrica, 64(1), 139-174. Martens, M. (2002). Measuring and forecasting S&P 500 index-futures volatility using high-frequency data. The Journal of Futures Markets, 22(6), 497-518.

Merton, R. C. (1980). On Estimating the Expected Return on the Market. Journal of Financial Economics, 8, 323-361.

Zhang, L., Mykland, P. A., & A¨ıt-Sahalia, Y. (2005). A Tale of Two Time Scales: Deter-mining Integrated Volatility with Noisy High-Frequency Data. Journal of the American Statistical Association, 100(472), 1394-1411.