The influence of high-frequency trading on the Dutch market quality

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The Influence of High-frequency Trading

on

the Dutch Market Quality.

University of Amsterdam

a thesis presented by

Loek de Blauw to

The Faculty of Economics and Business in partial fulfilment of the requirements

for the degree of Master of Science in the subject of

Econometrics and Mathematical Economics University of Amsterdam

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The Influence of High-frequency Trading

on

the Dutch Market Quality.

Abstract

This thesis investigates the effect of high-frequency trading on the Dutch market qual-ity. As the market share of high-frequency trading has grown to a large proportion for several financial markets, it is an obvious question to ask what effect this has on the mar-ket quality. The intraday trade and quote data of eleven stocks of the AEX are used to perform several econometric tests being: the Augmented Dickey-Fuller test, the linear Granger causality test and the Diks-Panchenko nonparametric test for Granger causal-ity. The effect of high-frequency trading on the quality measures is measured by using a vector autoregressive model. Robust evidence is found for a positive effect of high-frequency trading on the market quality. Empirical findings suggest an improvement of the market liquidity and a lower volatility. On the other hand, the effect on the mar-ket efficiency has shown to be negative. There is no evidence that suggests nonlinear Granger causal relations exist. This does not indefinitely exclude the presence of nonlin-ear relationships between market quality measures and high-frequency trading.

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Statement of Originality

This document is written by Student Loek de Blauw who declares to take full respon-sibility 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.

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Acknowledgments

After a long period of intense months, I am finally finishing my thesis. These last few months have been hard for me. There were a few setbacks with the acquiring of my data set. Writing my thesis had a significant effect on me. Not only mentally, but also personally. I would like to express my honest appreciation to the people who supported, encouraged and guided me during this difficult period.

Firstly, I would like to express my appreciation and thankfulness to my advisor Professor Cees Diks for his insightful comments. His guidance helped me further and made me widen my perspective. I wish to show gratitude to his immense knowledge and I could not have imagined a better advisor.

Finally, I would like to express my gratitude to my girlfriend Barbara, whose sacrificial care for me made it possible to finish my thesis. I tested her patience, but she kept sup-porting me and showed me true love.

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1

Introduction

I

t was the Dutch East India Company that issued the first stocks in the year 1602. The VOC introduced easily transferable shares, and investors started to buy and sell these shares on the Amsterdam stock market. Soon the public was engaging in a variety of complex transactions, including forwards, futures, options and bear raids. And by 1680, the techniques deployed in the Amsterdam market were as sophisticated as any we practice today. A sheet of paper was used for almost 300 years to publish the stock prices twice a year. Until what is now known as the financial sector’s Big Bang. The trading floor was replaced by an automated quotation system. Instead of meeting face to face, brokers now rather use this screen-based quotations system. This resulted in a major impact on the financial markets. Masulis and Ng (1995) write that in 1987 the London Stock Exchange was transacting as much business in one month as it did in a

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whole year before 1986. Without technology that is able to process massive volumes in less time, these amounts could not possibly occur.

Before the technological revolution traders used to rely on intermediaries to provide access to the financial markets. Since the automation of the stock exchanges these in-termediaries’ use of technology increased rapidly. The whole structure of the market changed from operations to modes of trading and regulations. The role of the tradi-tional market makers decreased and a new kind of market maker emerged. Algorithmic traders (ATs) entered the financial markets. ATs base their predictions upon system-atic computer-based algorithms and pre-defined protocols, submit orders, and manage those orders after submission, with limited or no human intervention (Hendershott et al., 2011). First in relatively small numbers, but as the years passed by, the improving technology made it possible for algorithmic trading (AT) to occur at very high speed. This ultra-high speed version of AT is also known as high-frequency trading (HFT). According to an estimate of Tabb (2012), high-frequency traders (HFTs) accounted for 67% of the shares traded on the US market in 2009. Technology has changed the face of the markets.

The changing financial markets draw the attention from financial institutions, regula-tors, politicians and researchers. Resulting in a debate regarding the various arguments in favour of and against HFT. Those in favour argue that the appearance of HFTs im-proves the market liquidity, contributes to the market efficiency and may be partially responsible for the reduction of trading costs. Opponents, on the other hand, claim that HFT can give traders an unfair advantage if they engage in market manipulation. An-other argument against HFT is that it is unfair to small investors. The presence of HFTs increases the volatility and destabilises the financial markets (Brogaard et al., 2014). In

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addition, the critics, for the most part institutions and financial traders that are not able to take advantage of the opportunity to make a profit by HFT, argue that an unfair play-ing field is generated with the HFTs accessplay-ing the financial markets.

On May 6, 2010, the Dow Jones Industrial Average and other indices experienced ex-treme volatility over a very short period of time. The largest stock indices and other fi-nancial instruments had a substantial drop. The Dow Jones Industrial Average declined with approximately nine percent, followed rapidly by a recovery that covered for a sig-nificant part of these losses, within minutes (Kirilenko et al., 2010). This well-known phenomenon is called the Flash Crash. HFTs were accused of being responsible for this phenomenon. Kirilenko et al. (2010) did research using E-mini S&P 500 futures market audit-trail data to compare the trading of HFTs and other traders during the Flash Crash. Their data indicate that the accused HFTs are not the ones to blame. HFT might have resulted in an increased price volatility, but is not what started the crash. Price volatility can get amplified by HFTs, who try to stabilise their portfolios during volatile times and compete with other traders for liquidity.

Despite the great notice taken on this subject and the relevance to a large number of people and institutions, academic research on the influence of HFTs and its implications for financial markets is rare. The research question of this thesis is: What influence does HFT have on the Dutch stock market quality? Providing insights by looking at the market liquidity, volatility and efficiency using trade and quote (TAQ) data from Wharton Research Data Services (WRDS).

The rest of this thesis is organised as follows. The next chapter describes HFT, market volatility, liquidity and efficiency from a theoretical background. Chapter 3 describes the data, the model and statistics used in this thesis. Chapter 4 focuses on the

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empir-ical and statistempir-ical results. Chapter 5 concludes and discusses the implications of the findings.

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2

Literature Review

T

his chapter provides literature related to HFT and relevant research with re-gard to the market quality. In the first section HFT is the main topic. After this, studies related to the quality of the market and possible factors that influence it are dis-cussed.

2.1 High-frequency Trading

One of the problems with this subject is the amount of literature that is available. A rea-son for this is the fact that HFT has not been around for long. Because of this there is not much data at hand to conduct research. Another reason for this lack of research could

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be the line of demarcation between AT and HFT. Even now there is no clear definition of HFT. Brogaard (2010) e.g. stated

HFT is a type of investment strategy whereby stocks are rapidly bought and sold by a computer algorithm and held for a very short period [...] HFT is a subset of AT. AT is defined as “the use of computer algorithms to automatically make trading decisions, submit orders, and manage those orders after submission” Hendershott and Riordan (2009). AT and HFT are similar in that they both use automatic computer generated decision making technology. However, they differ in that ATs may have holding periods that are minutes, days, weeks, or longer, whereas HFTs hold their position for a very short time and try to close the trading day in a neutral position. Thus, HFT is a subset of AT, but not all AT is HFT.

Kirilenko et al. (2010) on the other hand said

We define Intermediaries as those traders who follow a strategy of buying and selling a large number of contracts to stay around a relatively low target level of inventory. Specifically, we designate a trading account as an Intermediary if its trading activity satisfies the following two criteria. First, the account‘s net holdings fluctuate within 1.5% of its end of day level. Second, the account‘s end of day net position is no more than 5% of its daily trading volume. Together, these two criteria select accounts whose trading strategy is to participate in a large number of transactions, but to rarely accumulate a significant net position. We define high frequency traders (HFTs) as a subset of intermediaries, who individually participate in a very large number of transactions. Specifically, we order Intermediaries by the number of transactions they participated in during

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High-frequency Trading

a day (daily trading frequency), and then designate accounts that rank in the top 3% as HFTs. Once we designate a trading account as a HFT, we remove this account from the Intermediary category to prevent double counting.

Despite the lack of a proper definition of the characteristics, according to the US Secu-rity and Exchange Commission (Murphy, 2010) the HFT firms have a number of spe-cific features that differentiate them from other traders. HFT firms are private traders who program source codes for generating, routing and executing orders. By using high-technology and next-generation computers on co-location server farms close to the stock exchange with a private data feed they are able to execute trades in microseconds, minimising latencies. In order to create a liquidating position they use very short time-frames for their orders. They use fleeting orders (Hasbrouck and Saar, 2009), or orders that are cancelled almost immediately after they are sent. And at the end of a trading day they generally have a flat position if that is feasible.

HFT is characterised by Brogaard (2010) as a subset of AT largely associated with the sell side of the financial industry. Gsell and Gomber (2009) show that AT engines fun-damentally differ from human traders in their order submission, modification and dele-tion behavior as they exploit real-time market data and latest market movements.

2.1.1 Short-term Traders

A strategy that HFT firms frequently use for their investments is to buy and sell stocks in a very small time interval and hold them for a short time. In practice, depending on the circumstances of the trade, trading opportunities can last from milliseconds to a few hours. HFT firms make a profit from traders who use the short-term shifts in the

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market in their advantage. A few researches studied the influence of short-term trading decisions on the market before and after the emerging of HFT.

On a traditional trading floor humans were physically present. By trading faster than other traders, one could make a profit. It was a matter of survival of the fittest, the traders gained advantage from their physical capabilities. People running across the trading floor and shouting for attention, the one that runs faster or has a louder voice than his competitors got noticed by the market makers.

Today, on a completely automated trading floor the trades are made by the algorithms of HFTs. The ability to run fast is no longer an advantage. However, traders that are able to trade at high speed have a significant advantage. The key is to obtain data and execute orders at the lowest latency possible. If the market conditions at the time of decision making differentiate from the market conditions at the time of arrival of that trade, there is a risk that the order is no longer appropriate in terms of size and/or limit (Harris, 2003; Brown and Holden, 2005; Liu, 2009).

In order to minimise this risk, HFT firms try to reduce their latency. Therefore HFT firms make use of co-location, housing their servers on the same location as the stock exchange. This allows HFT firms to obtain the stock prices a millisecond earlier than the rest of the investors. Despite the fact that latency had a significant value from the beginning, its role became of more importance because of HFT.

Hasbrouck and Saar (2013) conducted empirical research on low-latency trading using a NASDAQ data set during turbulent times. They suggest that the presence of firms that respond to market events within milliseconds, the hallmark of HFT firms, improves traditional market quality measures. Decreasing spreads, increasing displayed depth in

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High-frequency Trading

the limit order book, and lowering short-term volatility.

It is difficult to take advantage of low latency. The competition on the HFT market is fierce, the lifetime of a code is not limitless. In order to stay in front of the competitors algorithms must be updated on a regular basis, sometimes after a few days (Duhigg, 2009).

2.1.2 Market Makers

Market makers serve an important role in the financial markets, as they help to reduce liquidity risk and facilitate the pace at which participants can enter or exit the market. HFTs play the role of formal or informal market makers by posting limit orders on both sides simultaneously. Market makers try to buy low at the bid price and sell high at the ask price in order to earn the bid-ask spread. But if the price of the stock drops below the bid price they lose money. The orders are not executed immediately and must rest on an order book, that is why market makers have to update their prices frequently to reflect changing market conditions. The market makers are compensated by fees for taking on risks like this. Because of the constant price changes, market makers submit and cancel a large number of orders per transaction. This way market makers contribute to narrowing the bid-ask spread and bring the overall transaction costs to a lower level. Moreover, market makers act as a liquidity providers.

Fees are a relatively big part of the “modern” market makers’ revenues. Menkveld (2013) shows that low-fee venues are entering the exchange market. And these lower fees result in a reduced bid-ask spread for the end users.

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can leave a quote at the limit order market. In the interval between the quote, infor-mation asymmetry creates adverse selection, and block a possible trade. By reducing the time needed to update the quote HFT can restore trade (Jovanovic and Menkveld, 2010).

2.2 Market Liquidity

If the market is liquid, stocks can be easily sold and when the stocks are sold this does not affect the price of this stock. HFT can provide easy access to stocks, this allows to sell the stocks rapidly. A different way to look at liquidity is the bid-ask spread. If a stock is traded often the bid-ask spread is small, for an illiquid stock on the other hand this spread can be relatively big.

Castura et al. (2010) look at the overall performance of the US market, the evolution of the market characteristics over time. They find an increased liquidity and a decrease in the bid-ask spreads during the rise of HFT. Despite the presence of noise on the market, these findings suggest that HFT contributed to an increased liquidity and decrease in bid-ask spread.

Riordan and Storkenmaier (2012) examine the Deutsche Boerse after they upgraded their trading system in 2007. They find a decrease in both quoted and effective spreads, which are mainly concentrated in small- and medium-sized stocks. Lower adverse se-lection costs to a limited extent causes the the liquidity to increase.

Hendershott et al. (2011) analyse AT and its effect on liquidity. They use a proxy to iden-tify AT. When the NYSE implemented the automated quote functionality in 2003, the

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Market Volatility

speed of algorithmic trading increased significantly. The automated quotes do not have a direct effect on the market liquidity and can be seen as an exogenous instrument to study the causal effect of AT on liquidity. Their findings suggest that the bid-ask spread of the larger stocks decrease after the introduction of the automated quote system. In-dicating a liquidity improvement caused by AT.

Boehmer et al. (2012) conducted a similar research, using the same proxy as Hender-shott et al. (2011). Their data consisted of a large sample of stocks from several coun-tries. Using co-location as an external instrument for their analysis, they find bid-ask spreads that become less wide in all countries. But it seems to improve the liquidity only for the larger stocks. Stocks with a high volatility experience no effect at all, while stocks with a small capitalisation experience a negative effect.

After the fees introduced by the Investment Regulatory Organisation of Canada there was a sharp decline in the HFTs activities, both in absolute terms and as a percentage of overall market activity. This can be seen as an exogenous instrument for a shock in the HFTs costs, resulting in an increase in the bid-ask spread (Malinova et al., 2012).

2.3 Market Volatility

The market volatility is a statistical measurement of the fluctuation of a market. Volatil-ity is expressed as the variance of the return from the market index. This makes the volatility a good risk indicator.

Hendershott and Riordan (2009) examine the role of AT in the process of price discov-ery, using data containing the thirty DAX stocks on the Deutsche Boerse in 2008. They

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find no evidence of AT behaviour that would contribute to volatility. Chaboud et al. (2014) study the impact of AT in the foreign exchange market over the period 2006-2007. Like Hendershott and Riordan (2009), they conclude that there is no causal relationship between AT and volatility.

Zhang (2010) studies the implication of HFT for stock price volatility and price dis-covery. He found that HFT is positively correlated with stock price volatility after con-trolling for firm fundamental volatility and other exogenous determinants of volatil-ity.

Brogaard (2010) studies the effects of HFT on market quality using the TAQ data of a group of 120 stocks over the period 2008-2010. He finds that during volatile times HFTs trade relatively more on the short run, but have a tendency to reduce their fre-quency of trading in the long run. He shows that HFT trades and quotes contribute more to price discovery than non-HFT activity does and that HFT tends to have no effect on the volatility, or even reduces it.

Kirilenko et al. (2010) analyse HFTs’ behaviour using E-mini S&P 500 futures market audit-trail data to compare the trading behaviour of HFTs and other traders on the day of the Flash Crash, although HFTs were not responsible for igniting the flash crash. The behaviour of HFT did increase the volatility according to them. Moments before the big drop on the market, HFTs were reducing their inventories, after at first supplying liquidity and building long positions. The authors say that by reducing their inventories, HFTs can compete for liquidity and intensify the volatility.

There are several variables that influence both the market quality and the behaviour of HFTs, such as public news. It is hard to control for these factors, some of which are

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Market Efficiency

not empirically observable. Furthermore, HFTs behaviour on the market and factors that have influence on the market quality are jointly endogenous. This allows for HFTs affecting the volatility of the asset they trade, while their behaviour is also affected by this volatility.

Hasbrouck and Saar (2013) did research related to this problem of endogeneity by using the number of “linked messages” over intervals as a proxy for AT, in a market where AT can have effect on volatility and the other way around. They conclude that AT has a negative effect on volatility.

Biais et al. (2015) made a theoretical model for this phenomenon. They conclude that a decrease of the price stability of a certain asset increases the incentive to invest in HFT technology. This helps to deal with market fragmentation. Brogaard (2011), on the other hand did an empirical investigation. He shows that the press releases of news are causing changes in the activity of HFTs. His findings show the effect of volatility on the activity of HFTs.

2.4 Market Efficiency

One important aspect of market quality is the pricing efficiency. The efficient market hypothesis was formulated by Fama (1965). He stated that a market is efficient if “secu-rity prices at any time ’fully reflect’ all available information.”

AT has a positive effect on the price efficiency, as well as a larger role in the process of price discovery than humans traders (Hendershott and Riordan, 2009). Brogaard et al. (2014) find that overall HFTs facilitate price efficiency by trading in the direction of

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price changes. The direction correlates with the information known by the public, such as macro news announcements, market-wide price movements, and limit order book imbalances. Suggesting that HFT does not prevent market overreaction.

Theoretically, the models described by Jarrow and Protter (2012) and Jovanovic and Menkveld (2010) characterise a number of processes that could make the market more or less efficient. The total volatility can be split in two components: excess and fun-damental volatility. By reducing the excess volatility the prices on the market become more efficient. Hagströmer and Nordén (2013) and Hasbrouck and Saar (2013) indi-cate that HFT results in a decrease in volatility. But both studies only look at the total volatility. Moreover, Hasbrouck and Saar (2013) also show an increase in liquidity be-cause of HFT. Chordia et al. (2008) suggest that liquidity is linked with a improved market efficiency.

Carrion (2013) finds a positive correlation between HFT activity and increases in mar-ket efficiency. On the days that HFT is high the prices seem to be more efficient. More of the available information in past order flows and past market returns is used during days with active HFTs. Carrion (2013) shows that HFT is related to market efficiency, but could not conclude whether HFT caused the increase in market efficiency.

Brogaard et al. (2014) find a correction for the transitory pricing error as a result of HFT using the same data set as Brogaard (2010) during volatile times. Their conclusion holds for normal as well as more volatile times.

Hudson and Manahova (2014) use state-space models to study the effect of HFT on the efficiency and price discovery of exchange rates. They find that HFT improves the market efficiency and contributes to price discovery, through trading in the opposite

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Market Efficiency

direction of the transitory component of the state-space model. These findings are in line with the findings of Brogaard et al. (2014)

In pursuance of Brogaard et al. (2014), Martinez and Rosu (2013) show theoretically that if HFTs respond fast to changes in the market conditions, they make the market way more efficient and do not disrupt the stability of the market. On the condition that market makers take care of the liquidity during turbulent times.

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3

Data and Methodology

T

his chapter describes the data that are used for this research and also gives a description of proxies used in order to identify high-frequency trades. Further-more, it provides a detailed report of all the relevant characteristics used to measure the markets liquidity, volatility and efficiency.

3.1 Data

The data in this thesis consist of intradaily TAQ data, coming from the WRDS, contain-ing eleven stocks traded on the Amsterdam Exchange index over a five year time period, from January 2010 until December 2014.

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The data come as one monthly file, one for trades and one for quotes because of the large amount of data. The total data set consists of a large amount, 3.308.259.638, rows. After data cleaning the remaining set consists of 3.272.919.463 lines of data.

MySQL is used to create a large database, in order to store all the data and be able to ma-nipulate the data as well as the possibility of creating tables. All these tables are used to create several proxies and variables in order to measure the effect of HFT on the market quality. The combination (1-day, 5-minutes) of time period t and sub-interval j is used for the proxies.

3.1.1 Identifying Trades

It is not possible to directly see whether a trade is placed by HFTs or by a human trader. Flagged data were not available for this research. The only data at hand concerns the trades and quotes themselves. As mentioned by Hasbrouck and Saar (2013) the pres-ence of HFTs is ordinarily combined with fast order submissions and cancellations. Hendershott et al. (2011) made a proxy that uses the number of messages, defined as a trade or quote update, and the euro volume. In such a way that a higher proxy repre-sents an increase in HFT, defined as

HFT_volumei,t =−

pi,t· Vi,t

Messagesi,t

, (3.1)

where pi,tis the price in local currency, and Vi,tis the trading volume of stock i, on the

tthtime period. Messagesi,tis the number of messages for stock i at time period t. The

submission, changes, cancellation and the trade itself are counted as a message. And without normalising the messages could potentially only capture the increase in

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trad-Data

ing volume. By correcting it, the proxy concentrates on the number of submissions, modifications and cancellations, which are mainly sent by HFTs.

The second HFT measure is the number of messages over the number of trades each time period, resulting in

HFT_tradesi,t=

Messagesi,t

Tradesi,t

, (3.2)

where Tradesi,tis the number of trades for stock i on time period t. Because HFTs use

high-tech computers to send their orders digitally to a trading market, the number of messages per trade is a good indicator for the increase in HFT.

The intuition behind these two measures is, according to Hendershott et al. (2011), the fact that HFTs place an order electronically instead of relying on a human intermedi-ary. The number of messages is therefor used as a proxy, but without normalisation there is the possibility that only the increase in trading is captured instead of the kind of trading.

3.1.2 Liquidity Measures

The first method used to measure the liquidity is a variation of the Amihud (2002) mea-sure of illiquidity. This is one of the most widely used liquidity meamea-sure methods in the financial literature. Amihud (2002) uses the ratio of absolute one day stock return to dollar volume as a measure for illiquidity of a stock. The intuition behind this measure-ment is that the most liquid markets experience the least fluctuation in the price after a trade.

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Hasbrouck (2009) writes that: “among the daily proxies, the Amihud illiquidity mea-sure is most strongly correlated with the TAQ-based price impact coefficient”

Some changes have been made to the Amihud (2002) measure, as stated by van Dijk et al. (2012). In order to minimise the effect of outliers a logarithm is added. And finally everything is multiplied by -1 in order to get a variable that is increasing in liquidity, resulting in

liqi,t=−log

( |ri,t|

pi,t· Vi,t

)

, (3.3)

where ri,t, the basis point consolidated return, is defined as

ri,t= ln ( pi,t pi,t−1 ) , (3.4)

the return of stock i for time period t. And pi,tis the price of stock i on time period t in

local currency, and Vi,tis the trading volume of stock i during the tthtime period.

In addition, another liquidity measure is computed as suggested by Hendershott et al. (2011) and Goyenko et al. (2009). The quoted bid-ask spread is the difference between the ask price and the bid price for a stock.

q_spreadi,t=

Aski,t− Bidi,t

MQi,t

, (3.5)

where Aski,tand Bidi,tare the quoted ask and bid prices for stock i at time period t, and

MQi,tis the midpoint of the consolidated quotes prevailing at the time of the trade. The

quoted spread is a fine cost indicator for trades. The quoted spread is calculated for every stock every time period on all trades, subsequently taking an average of all trades that particular time period.

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Data

3.1.3 Volatility Measure

Volatility measures the risk of a stock, calculated by the standard deviation of the re-turns. Because daily volatility is not directly visible from one observation, more in-formation is needed than just the daily return in order to calculate the daily volatility. Volatility needs time to manifest itself. By using the intraday high-frequency return from TAQ data, the interdaily volatility can be estimated.

For this measure the notation needs to be extended. An intradaily interval, j, is intro-duced to calculate the the volatility on time period t. For every time period, the statis-tical volatility is calculated as the standard deviation of the stock’s return over a smaller interval, as follows si,t= v u u t∑D j=1 r2 i,t,j, (3.6)

where the jthinterval return for stock i at time period t, ri,t,j, is calculated as the natural

logarithm of the ratio between the average price in an interval j and the average price in one interval earlier j− 1

ri,t,j= ln ( pi,t,j pi,t,j−1 ) , _(3.7)

where pi,t,jstand for the average price at interval j at time period t.

An unbiased estimator of the return volatility is the sum of intraday squared returns, the realised volatility is

r_voli,t=

√∑J

j=1(ri,t,j− ri,t)2

J− 1 , (3.8)

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per time period t ri,t= 1 J J ∑ j=1 ri,t,j. (3.9) 3.1.4 Efficiency Measures

The market efficiency measures how the relevant data that is available is used to value the markets stock prices. The first method used to measure the efficiency is suggested by Hendershott and Jones (2005), the autocorrelations. A positive as well as a nega-tive autocorrelation suggest information efficiency that is less efficient. When the au-tocorrelations are small the market is more efficient because a change in price is less correlated.

For every time period, the absolute value of the first order autocorrelations of the stock’s return over a interval are calculated, as follows

ACi,t=|Corr (ri,t, ri,t−1)| =

∑_J

j=2(r_∑i,t,j− ri,t)(ri,t,j−1− ri,t) J

t=1(ri,t,j− ri,t)2

, (3.10)

where ri,t,jis the jthreturn as mentioned earlier in (3.7). By taking the absolute value,

the proxy catches both sides of informational efficiency. Resulting in a measure that is increasing in inefficiency.

The changes in stock prices are independent of each other and have the same distribu-tion. That is why changes in the past can not be used to forecast future returns. Random walk theory shows that stock prices follow a random walk. If this is the case the variance of the stock return is a linear function of its measurement frequency. Lo and MacKinlay

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Stationarity

(1988) use this property for the variance ratio measure

VRj,kji,t = σ2_kji,t k· σ2 j i,t − 1, _(3.11)

where σ2j and σ2kjare the variances of j-minute and kj-minute returns on time period t,

where the (j, kj) combination equals (5-minutes, 30-minutes).

The prices on an efficient market behave more like a random walk, so a smaller VR in-dicates higher market efficiency.

3.2 Stationarity

The statistical properties of stationary time series do not change over time. The con-structed measurement time series can be tested for stationarity.

Definition 3.2.1. The time series Xt, t∈ Z, is said to be stationary if

(i) E (X2

t) < ∞ ∀ t ∈ Z

(ii) E (Xt) = μ

(iii) γ_X(s, t) = γ_X(s + h, t + h)∀ s, t, h ∈ Z

By testing for the presence of a unit root, with the use of the Augmented Dickey-Fuller (ADF) statistic. Time series are tested for stationarity, with a unit root null hypoth-esis H0, against the stationary alternative H1, corresponding to a stationary time

se-ries.

Most financial time series follow a trend or show non-stationarity in the mean. The ADF test can determine whether non-stationary data should be corrected, for example by

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tak-ing the first differences or regresstak-ing on a deterministic time variable. After calculattak-ing all the relevant variables, they are all tested for stationarity.

Δyi,t= αi+ β_it + πyi,t−1+ k

∑

j=1

γ_i,jΔyi,t−j+ εi,t, (3.12)

where in this case yi,trepresents one of the time series e.g. liquidity or volatility time

series for stock i. In order to determine the number of lags, k, the Schwarz information criterion (SIC) is minimised.

The t-test for the ADF test tests for

H0 : π = 0 against H1: π < 0.

The test statistic can be computed as follows

ADF = ˆπ

SE (ˆπ). (3.13)

3.3 Linear Granger Causality

Granger causality is a technique for determining whether one time series is useful in forecasting another. In the case that prior and current values of Xthave information on

values of Ytin time that have not yet come to pass, then time series Xtis a Granger cause

of time series Yt.

Granger (1969) defined causality as follows

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Linear Granger Causality

Y is useful for predicting the future state of X over and above knowledge of the past history of X itself.

Whether HFT is causing the changes in the quality measures is tested by checking for Granger causality. Testing for linear Granger causality under the null hypothesis

H0: Xtis not Granger causing Yt,

according to the following definition of pairwise Granger causality,

Definition 3.3.1. For a strictly stationary bivariate time series process {(Xt, Yt)}, t∈

Z, {Xt} is a Granger cause of {Yt} if, for some k≥ 1,

(Yt+1, . . . , Yt+k)| (FX,t,FY,t)≁ (Yt+1, . . . , Yt+k)|FY,t, (3.14)

whereFX,tandFY,tare the information within the past observations of Xsand Ys, for s

≤ t.

The vector autoregressive (VAR) model is used to test for Granger causality. For {Xt}

and {Yt} two stationary time series, a bivariate VAR(p), where p is the optimal number

of lags, is given by Xt = α + p ∑ j=1 β_jXt−j+ p ∑ j=1 γ_jYt−j+ εxt, (3.15) Yt = α + p ∑ j=1 β_jYt−j+ p ∑ j=1 γ_jXt−j+ εyt. (3.16)

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{Xt} values are zero the series {Xt} does not Granger cause {Yt}.

However, the pairwise test for Granger causality does not take into account the possible effects of a third variable, which may find spurious Granger causality. An extension of Definition 3.3.1, suggested by Diks and Wolski (2015), controls for the possibility of more then two interacting variables by adding variable {Qt}.

Definition 3.3.2. For a strictly stationary multivariate time series process {(Xt, Yt, Qt)},

t∈ Z, where {Xt} and {Yt} are univariate and {Qt} univariate or multivariate, {Xt} is a

Granger cause of {Yt} if, for some k≥ 1,

(Yt+1, . . . , Yt+k)| (FX,t,FY,t,FQ,t)≁ (Yt+1, . . . , Yt+k)|FY,t,FQ,t. (3.17)

The higher-variate VAR model takes the additional variable {Qt} into account, let ytbe

a n× 1 vector

yt = [Yt, Xt, Qt]′. (3.18)

The higher-variate VAR model of or order p is

yt = φ₁yt−1+ . . . + φ_pyt−p+ εt, (3.19)

where φ_iis a n× n coefficient matrix.

For the Granger causality test the Wald test statistic is calculated under

H0 : φ112 = . . . = φ

p

12 = 0,

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Model Estimation

Under the null hypothesis the Wald statistic has a limiting χ2_{(p) distribution.}

Let h(θ) be a function of the parameters θ under the restriction that all the coefficients of the lagged values of Xtequal zero

H0 : h(θ) = 0.

Let bV be the estimate of the covariance matrix of the unrestricted OLS estimate ˆθ and

A(θ) = ∂h(θ) ∂θ _ˆ θ .

The Wald test statistic can be computed as

W = h′(ˆθ) (

A(θ)bVA′(θ) )₋₁

h(ˆθ)), (3.20)

where bV is an estimator of the covariance matrix.

3.4 Model Estimation

The VAR model is used to look at the joint dynamic behaviour, in order to estimate whether the effect of HFT on the market quality measures is positive or negative. The VAR model does not require strong assumptions to identify underlying structural pa-rameters.

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3.4.1 Liquidity and High-frequency Trading

After finding evidence of stationarity and Granger causality, the effect can be measured by using the coefficients of the higher-variate VAR model. Model specification is as follows

log liquidityi,t = α + p ∑ j=1 β_jlog HFTi,t−j+ p ∑ j=1 γ_jQi,t−j+ εi,t, (3.21)

where multivariate Qi,t−jincludes all other measures of liquidity, volatility and efficiency.

HFTi,t−jstands for one of the two HFT proxies.

3.4.2 Volatility and High-frequency Trading

To determine whether HFT causes volatility, the Granger causality test is performed. If HFT is Granger causing volatility and the series are stationary, the impact of HFT on volatility is measured by VAR.

The model specification is as follows

log volatilityi,t = α + p ∑ j=1 β_jlog HFTi,t−j+ p ∑ j=1 γ_jQi,t−j+ εi,t. (3.22)

3.4.3 Efficiency and High-frequency Trading

After acquiring the efficiency measures, they are tested for Granger causality as well. If there is evidence of Granger causality a regression is conducted in a VAR model, in order to analyse the effect of HFT on the market efficiency.

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Nonparameric Granger Causality

The model specification is as follows

log efficiencyi,t= α + p ∑ j=1 β_jlog HFTi,t−j+ p ∑ j=1 γ_jQi,t−j+ εi,t. (3.23)

3.5 Nonparameric Granger Causality

As the linear Granger test is unable to identify any nonlinear causal relationship, the nonparametric test for Granger causality, introduced by Diks and Panchenko (2006), is used in order to examine the nonlinear Granger causality relationship.

Equation 3.3.1 is equivalent to a statement about the invariant distribution of the vector Wt = (Xt, Yt, Zt), where Zt = Yt+1. It can be restated in terms of ratios of joint

distribu-tions. Specifically, the joint probability density function fx,y,z(x, y, z) and its marginals

must satisfy the relationship

fx,y,z(x, y, z) fy(y) = fx,y(x, y) fy(y) · fy,z(y, z) fy(y) . (3.24)

Diks and Panchenko (2006) show that the reformulated null hypothesis implies

q≡ E[fx,y,z(x, y, z) fy(y)− fx,y(x, y) fy,z(y, z)

]

. (3.25)

The test statistic developed by Diks and Panchenko (2006) takes the form

Tn(ε) =

(n− 1)

n(n− 2)

∑

i

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where the local density estimators of a dW-variate random vector W at Wiequals bfW(Wi) = (2ε)−dW n− 1 ∑ j,j̸=i IWij, (3.27)

where ε is the bandwidth and the indicator function equals IW

ij = I(∥Wi − Wj∥ <

ε).

As stated by Diks and Panchenko (2006), the above-mentioned test statistics satisfies √

nTn(ε)− q sn

d

−−→ N (0, 1) , (3.28)

where snis the HAC estimator of the long term variance of

√

n (Tn(ε)− q) .

Additional to the standard linear Granger causality test, the Diks-Panchenko test is con-ducted. For this test the residuals of the higher-variate VAR model are used to investi-gate whether the Granger causal links detected in the VAR-ﬁltered residuals, are strictly nonlinear.

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4

Results

T

his chapter presents the empirical results of econometric estimations. Tests and regressions were conducted on the models. First the variables have been tested for stationarity, the existence of unit root has been tested by the ADF test. Fol-lowed by a Granger Causality test to test the existence of any Granger causal relationship between HFT and the market quality variables. If the data set is stationary and there is evidence of causality the VAR model coefficients are used to measure whether the effect is positive or negative.

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4.1 ADF test results

Before investigating and quantifying the effect of HFT on the market quality indicators, the ADF test is applied to the model to check the stationary characteristics of all the time series. The ADF test tests a null hypothesis of a unit root against an stationary alternative hypothesis. The best fitted lag lengths are determined by minimising the Schwarz information criterion.

Table 4.1.1 shows the t-statistics and lags of the ADF unit root tests. The results from the ADF tests in Table 4.1.1 show that, only HFT_trades of ATC is nonstationairy, for that reason the first-differences are used. At the levels, the null hypothesis of a unit root cannot be rejected for the HFT_volume and liq measure of AGN; the liq measure of AH; the liq and r_vol measure of ASML; HFT_trades, liq, VR and q_spread for ATC; liq, r_vol and AC for DSM; liq, AC and VR for HEIA; HFT_trades, liq and VR for MT; liq, AC and q_spread for RAND; liq for REN and HFT_volume, liq and q_spread for UL. In terms of ADF tests including constant terms, for all series except one, HFT_trades of ATC, there is enough evidence to reject the null hypothesis of a unit root. For the ADF test including constant and trend terms the null hypothesis can not be rejected for q_spread of AH, HFT_trades of ATC and HFT_trades of RDSA. For all other series the null hypothesis can be rejected.

The tests indicate that the analysed time series do not posses a unit root i.e. the measures seem to be stationary. This suggests that there is no need to use co-integration and er-ror correction models. Stationarity is a necessary condition for time series in order to conduct VAR estimation.

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A DF te st re sults

Table 4.1.1: Results of the Augmented Dickey–Fuller unit root test

AGN AH ASML ATC DSM HEIA MT RAND RDSA REN UL

HFT_volume

None −1,478(4) −2,504(2)b −1,733(4)c −12,420(0)a −3,773(7)a −8,401(3)a −4,162(3)a −18,454(0)a −3,889(1)a −3,566(6)a −0,047(6) Intercept −5,181(3)a −6,594(2)a −7,451(2)a −14,776(0)a −7,882(4)a −15,820(1)a −7,772(3)a −21,505(0)a −9,931(1)a −4,741(6)a −4,954(4)a Trend & intercept −5,941(3)a −7,220(2)a −7,964(2)a −15,257(0)a −7,922(4)a −17,010(1)a −7,749(2)a −21,564(0)a −11,073(1)a −5,681(6)a −5,632(4)a HFT_trades

None −2,689(4)a −2,509(4)b −2,902(2)a −6,888∗_(3)a _{−28,978(0)a} _−8,998(2)a _−0,564(4) _−4,819(2)a _−1,681(2)c _−1,730(4)c _−1,747(4)c

Intercept −4,879(4)a −5,286(4)a −6,321(2)a −6,916∗_(3)a _{−31,457(0)a} _{−11,835(2)a} _−4,566(4)a _−5,719(2)a _−2,897(2)b _{−22,510(1)a} _−5,724(3)a

Trend & intercept −4,936(4)a −6,039(4)a −6,995(2)a −6,982∗_(3)a _{−31,542(0)a} _{−17,268(1)a} _−6,242(3)a _−5,846(2)a _−3,058(2) _{−22,544(1)a} _−5,910(3)a

liq

None 0,598(6) 0,231(6) 0,675(6) 0,018(2) −0,542(5) 0,452(5) −0,556(5) −0,009(2) 0,095(7)a 1,388(6) 0,149(6)

Intercept −17,937(1)a −3,724(5)a −14,012(2)a −16,175(0)a −30,267(0)a −27,088(0)a −10,593(3)a −16,257(0)a −18,880(1)a −25,021(0)a −11,173(3)a Trend & intercept −33,018(0)a −3,565(5)b −14,705(2)a −16,470(0)a −31,051(0)a −27,565(0)a −31,557(0)a −17,464(0)a −31,471(1)a −25,166(0)a −30,672(0)a q_spread

None −2,136(3)b −1,915(3)c −3,368(2)a −0,961(4) −1,894(5)c −2,124(6)b −4,981(9)a −1,469(5) −3,090(3)a −3,127(5)a −1,577(5) Intercept −5,207(3)a −3,851(3)a −6,647(2)a −3,089(4)b −4,506(5)a −4,689(6)a −8,237(9)a −3,050(5)b −8,761(2)a −5,007(5)a −4,943(5)a Trend & intercept −5,351(3)a −1,075(1) −6,666(2)a −3,506(4)b −4,977(5)a −7,135(3)a −8,157(9)a −5,094(5)a −9,128(2)a −5,175(5)a −5,270(5)a r_vol

None −4,844(5)a −2,892(6)a −3,803(6)a −15,082(1)a −2,124(7)b −4,018(5)a −1,232(6) −33,955(0)a −2,969(6)a −3,675(7)a −3,331(6)a Intercept −10,324(3)a −11,744(2)a −14,390(2)a −31,717(0)a −29,276(0)a −14,408(2)a −5,131(5)a −34,603(0)a −5,897(6)a −4,509(7)a −10,792(3)a Trend & intercept −33,471(0)a −11,879(2)a −15,493(2)a −32,481(0)a −30,917(0)a −28,527(0)a −6,385(5)a −34,578(0)a −29,424(0)a −4,602(7)a −11,639(3)a AC

None −3,214(10)a −4,921(5)a −5,349(8)a −2,030(5)b −1,500(7) −0,805(9) −6,852(5)a 0,156(6) −4,865(7)a −3,414(9)a −6,936(0)a

Intercept −35,607(0)a −28,951(0)a −35,777(0)a −22,896(0)a −35,098(0)a −6,604(7)a −33,505(0)a −25,461(0)a −33,376(0)a −34,304(0)a −32,931(0)a Trend & intercept −35,699(0)a −28,988(0)a −35,918(0)a −23,086(0)a −35,083(0)a −34,274(0)a −33,494(0)a −25,845(0)a −33,526(0)a −34,400(0)a −32,918(0)a VR

None −15,049(3)a −5,627(5)a −26,309(0)a 1,021(3) −26,594(0)a −0,479(6) −1,311(7) −2,142(a)b −1,685(9)c −34,037(0)a −3,946(5)a

Intercept −22,200(0)a −31,275(0)a −26,368(0)a −21,947(0)a −30,579(0)a −20,292(1)a −47,810(0)a −25,777(0)a −34,031(0)a −34,742(0)a −30,759(0)a Trend & intercept −22,211(0)a −31,552(0)a −26,414(0)a −21,932(0)a −30,584(0)a −21,649(1)a −47,788(0)a −25,758(0)a −34,020(0)a −34,744(0)a −30,768(0)a

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4.2 Liquidity

Subsequently Granger causality tests are applied on all proxy measurements in order to test for any Granger causal relationship between the HFT proxy and liquidity. If there is evidence for a Granger causal relationship between HFT and liquidity the effect is estimated by a VAR model.

If the evidence of a relationship can not be found in the Granger causality test, no fur-ther actions have been taken to quantify the relationship. Table 4.2.1 indicates the re-sults of the Granger causality tests and subsequently the VAR model coefficients. The first column shows the name of the company and the second column gives HFT proxy. The next two columns give the χ2-statistic and lags of the Granger causality test, respec-tively. The right part of the table, the last eight columns, gives the results of the VAR coefficients, with the standard error in the parenthesis and the t-statistic in the square brackets.

Table 4.2.1 shows a Granger causal relationship between HFT_trades and liq for seven companies, where the null hypothesis of AGN, AH, MT, RDSA and UL can be rejected at 1%. For HFT_volume seven companies differ significantly from the null hypothesis as well. The four companies that show no evidence for Granger causality are AH, DSM and HEIA and RAND. Neither HFT_trades nor HFT_volume show evidence of Granger causality for DSM and HEIA.

All the significant coefficients are positive, except one. Only HFT_trades on ATC shows a negative sign. The positive coefficients of the VAR model suggest an increase in liq-uidity caused by HFT. Liqliq-uidity means being able to rapidly trade a large volume at low

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Liquidity

cost, which sorts a positive effect on the market quality.

Table 4.2.1: Results of the empirical analysis to measure the impact of HFT on liq

Symbol X and X* χ2_-stat. _lags _X_t−1 _X_t−2 _X_t−3 _X_t−4 _X∗

t−1 X∗t−2 X∗t−3 X∗t−4 AGN HFT_trades 30,980*** 3 0,021 0,030* −0,002 0,033*** 0,021 0,004 HFT_volume 59,951*** 3 (0,015) (0,016) (0,015) (0,013) (0,013) (0,013) [1,413] [1,894] [−0,154] [2,602] [1,543] [0,291] AH HFT_trades 14,161*** 3 −0,029*** −0,007 0,025** HFT_volume 3,729 3 (0,010) (0,011) (0,010) [−2,963] [−0,635] [2,562] ASML HFT_trades 7,768 4 0,014* 0,001 0,005 −0,003 HFT_volume 27,618*** 4 (0,008) (0,008) (0,008) −0,008 [1,831] [1,197] [0,649] [−0,358] ATC HFT_trades 6,440** 2 0,031** 0,018** 0,028** −0,012 HFT_volume 7,537** 2 (0,015) (0,009) (0,012) (0,013) [2,069] [1,968] [2,249] [0,935] DSM HFT_trades 4,564 2 HFT_volume 9,360 2 HEIA HFT_trades 3,160 4 HFT_volume 2,898 4 MT HFT_trades 49,985*** 3 0,030** 0,026* 0,008 0,028*** 0,020* 0,008 HFT_volume 66,601*** 3 (0,013) (0,014) (0,013) (0,011) (0,011) (0,011) [2,253] [1,839] [0,630] [2,648] [1,736] [0,788] RAND HFT_trades 0,664 1 HFT_volume 1,389 1 RDSA HFT_trades 12,939*** 3 0,009 0,020* 0,009 0,017** 0,009 0,014* HFT_volume 18,051*** 3 (0,010) (0,010) (0,010) (0,008) (0,008) (0,008) [0,878] [1,943] [0,925] [2,235] [1,069] [1,802] REN HFT_trades 8,0176** 2 0,007 0,015 0,009 0,018** HFT_volume 26,612*** 2 (0,009) (0,009) (0,007) (0,007) [0,746] [1,541] [1,344] [2,558] UL HFT_trades 10,372*** 2 0,016 0,017 0,017** 0,022*** HFT_volume 23,076*** 2 (0,011) (0,011) (0,008) (0,008) [1,516] [1,624] [2,156] [2,652]

Note: ***,**,* means rejection of H0at 1%, 5% and 10% respectively. Figures in parenthesis indicate the standard errors and the figures in the square

brackets the t-statistics. Both the dependent variable liq and the independent variables are log-transformed.

Table 4.2.2 indicates the results of the Granger causality test and VAR estimation of

q_spread. There is sufficient evidence to reject H0for both of the HFT proxies for two

companies. The null hypothesis can only be rejected at a 10% level for HFT_trades The most significant Granger causal relation is found with HFT_volume for REN at a 1% level.

For the companies where the Granger causality test reveals a causal relationship be-tween HFT and q_spread a VAR model is estimated. The impact of HFT on q_spread is doubtful, the coefficient of HFT_trades is negative for two of the three companies that

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show a significant coefficient. HFT_volume suggest an increase in QPREAD as three of the four significant estimates are positive. although the two most significant estimates are in the opposite direction. As q_spread is a good cost indicator and can be used as an instrument to measure liquidity, and a negative coefficient suggests an increase in liquidity. It is hard to draw a conclusion for q_spread, because of the coefficients being both positive and negative.

Table 4.2.2: Results of the empirical analysis to measure the impact of HFT on

q_spread.

t−1 X∗t−2 X∗t−3 X∗t−4 AGN HFT_trades 3,230 3 −0,042 0,014 0,142* HFT_volume 8,043** 3 (0,075) (0,080) (0,079) [_−0,561] [0,173] [1,785] AH HFT_trades 7,305* 3 0,039 0,011 0,046 0,046 0,042 0,008 HFT_volume 9,411** 3 (0,048) (0,052) (0,047) (0,039) (0,042) (0,039) [0,818] [0,212] [0,979] [1,174] [1,017] [0,219] ASML HFT_trades 4,523 4 HFT_volume 4,369 4 ATC HFT_trades 5,445* 2 −0,033 −0,055** HFT_volume 2,916 2 (0,040) (0,024) [_−0,822] [_−2,324] DSM HFT_trades 3,81 2 HFT_volume 2,382 2 HEIA HFT_trades 2,619 4 HFT_volume 5,316 4 MT HFT_trades 0,581 3 HFT_volume 1,748 3 RAND HFT_trades 0,225 1 0,061** HFT_volume 3,856** 1 (0,031) [1,964] RDSA HFT_trades 4,827 3 HFT_volume 2,667 3 REN HFT_trades 4,64* 2 −0,059 0,103** −0,090** 0,119*** HFT_volume 11,248*** 2 (0,049) (0,048) (0,035) (0,036) [−1,208] [2,135] [−2,541] [3,345] UL HFT_trades 5,166* 2 −0,025 −0,129* HFT_volume 4,480 2 (0,075) (0,074) [−0,334] [−1,739]

Note: ***,**,* means rejection of H0at 1%, 5% and 10% respectively. Figures in parenthesis indicate the standard errors and the figures in the

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Volatility

4.3 Volatility

The Granger causality test is carried out to statistically examine the relationship between HFT and volatility. The test determines whether an increase in volatility is induced by an increase of HFT. The results of the test are reported in Table 4.3.1.

The results show that the Granger causality test of HFT_trades is significant for six com-panies and of HFT_volume is significant for seven comcom-panies. For six comcom-panies there is evidence that both measures are significant, ASML, REN and UL are the most signif-icant at a 1% level, meaning that there is strong evidence for Granger causality.

Table 4.3.1: Results of the empirical analysis to measure the impact of HFT on

r_vol.

Symbol X and X* χ2_-stat. _lags _X

t−1 Xt−2 Xt−3 Xt−4 Xt−1∗ X∗t−2 X∗t−3 X∗t−4 AGN HFT_trades 3,072 3 HFT_volume 3,780 3 AH HFT_trades 1,379 3 HFT_volume 0,950 3 ASML HFT_trades 19,905*** 4 −0,098 0,033 −0,151 0,016 −0,091 0,000 −0,092 −0,011 HFT_volume 22,908*** 4 (0,081) (0,087) (0,084) (0,080) (0,061) (0,066) (0,063) (0,061) [−1,209] [0,377] [−1,800] [0,197] [−1,480] [−0,007] [−1,455] [−0,174] ATC HFT_trades 5,099* 2 0,182** 0,001 0,129* −0,168** HFT_volume 5,613* 2 (0,084) (0,050) (0,070) (0,071) [2,180] [0,013] [1,849] [−2,365] DSM HFT_trades 5,333* 2 −0,071* −0,046 −0,091** −0,073* HFT_volume 11,337*** 2 (0,041) (0,041) (0,039) (0,039) [−1,728] [−1,119] [−2,313] [−1,862] HEIA HFT_trades 3,443 4 HFT_volume 3,300 4 MT HFT_trades 3,964 3 −0,069 −0,038 −0,054 HFT_volume 8,327** 3 (0,087) (0,091) (0,085) [−0,801] [−0,418] [−0,638] RAND HFT_trades 0,074 1 HFT_volume 0,023 1 RDSA HFT_trades 8,498** 3 −0,089 −0,108 −0,041 −0,062 −0,128** −0,068 HFT_volume 13,095*** 3 (0,077) (0,080) (0,075) (0,061) (0,062) (0,060) [−1,150] [−1,351] [−0,543] [−1,025] [−2,070] [−1,148] REN HFT_trades 18,030*** 2 −0,180*** −0,009 −0,166*** −0,034 HFT_volume 40,277*** 2 (0,059) (0,058) (0,043) (0,043) [−3,068] (−0,147) [−3,879] (−0,791) UL HFT_trades 13,349*** 2 −0,050 −0,269*** −0,121* −0,260*** HFT_volume 28,501*** 2 (0,097) (0,096) (0,072) (0,073) [−0,519] [−2,806] [−1,675] [−3,565]

Note: ***,**,* means rejection of H0at 1%, 5% and 10% respectively. Figures in parenthesis indicate the standard errors and the figures in the square brackets

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The VAR model estimations of Equation 3.22 gives a clear view of the effect of HFT on volatility. Five of the seven companies show significant evidence to reject the null hypothesis. All five companies show evidence of Granger causality. The significant esti-mated VAR coefficients are negative for all companies except one, only the coefficient of HFT_trades for ATC suggests a positive effect. Notice that for DSM, REN and UL the same lags of both the proxies are significant. Four of the negative estimations are signif-icant at a 1% level. Overall these results indicate a negative effect of HFT on volatility, which means that these results suggest that an increase in HFT reduces volatility. As volatility implies potential high risks, a reduction of volatility leads to a positive effect on the market quality.

4.4 Efficiency

The Granger causality test is organised and carried out for efficiency measures, AC and VR, as well. The test results, reported in Table 4.4.1 and Table 4.4.2, do not suggest strong evidence for HFT having a large effect on efficiency.

Table 4.4.1 demonstrates the test results for the autocorrelation variable. The results of the Granger causality test indicate that the proxy HFT_trades Granger causes AC for AGN and ASML. And for AGN, AH as well as MT there is significant evidence for HFT_volume Granger causing AC at a 10% level.

The VAR estimation of the effect of HFT on the efficiency proxy AC gives a poor result. Only one HFT_volume coefficient of AH is significant. Although it is significant at a 5% level, only one coefficient differs from zero and the evidence for Granger causality is less

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Efficiency

Table 4.4.1: Results of the empirical analysis to measure the impact of HFT on AC.

t−1 X∗t−2 X∗t−3 X∗t−4 AGN HFT_trades 7,694* 3 −0,007 −0,065 −0,035 −0,012 −0,071 0,002 HFT_volume 6,403* 3 (0,065) (0,070) (0,068) (0,056) (0,060) (0,059) [−0,109] [−0,941] [−0,520] [−0,214] [−1,193] [0,027] AH HFT_trades 5,778 3 0,060** −0,041 0,010 HFT_volume 6,519* 3 (0,026) (0,028) (0,026) [2,271] [−1,437] [0,374] ASML HFT_trades 9,647** 4 0,052 −0,052 −0,044 −0,010 HFT_volume 3,841 4 (0,037) (0,040) (0,039) (0,037) [1,394] [−1,309] [−1,129] [−0,273] ATC HFT_trades 0,410 2 HFT_volume 2,424 2 DSM HFT_trades 2,824 2 HFT_volume 2,517 2 HEIA HFT_trades 2,451 4 HFT_volume 0,212 4 MT HFT_trades 5,102 3 −0,049 −0,060 0,061 HFT_volume 6,683* 3 (0,042) (0,044) (0,041) [−1,163] [−1,359] [1,476] RAND HFT_trades 0,029 1 HFT_volume 0,594 1 RDSA HFT_trades 2,28 3 HFT_volume 0,925 3 REN HFT_trades 4,078 2 HFT_volume 3,992 2 UL HFT_trades 0,782 2 HFT_volume 1,419 2

brackets the t-statistics. Both the dependent variable AC and the independent variables are log-transformed.

significant. This makes the conclusion of an increase in autocorrelation doubtful. There is more statistical evidence for the effect of HFT on the variance ratio, as shown in Table 4.4.2. The Granger causality test shows evidence of Granger causality for five companies. The most significant one is the HFT_volume proxy of ASML, at a 1% level. The coefficient estimations show an increase in the variance ratio as all five significant coefficients are positive. For RDSA the results indicate that both HFT proxies Granger cause VR. Furthermore, HFT_volume is overall the most significant, with the Granger causality test statistic and a VAR coefficient of 5% and 1% respectively. Hence, these findings show sufficient evidence to form a conclusive verdict about the effect of HFT on efficiency. Despite the fact that the number significant coefficient estimates is five,

(50)

they all point in the same direction and are remarkably significant. The results suggest an increase in the measured variance ratio with an increase in HFT. As an efficient market behaves more like a random walk, an increase in the measured variance ratio leads to a negative effect on the market quality.

Table 4.4.2: Results of the empirical analysis to measure the impact of HFT on VR.

Symbol X and X* χ2_-stat. _lags _X

t−1 Xt−2 Xt−3 Xt−4 Xt−1∗ X∗t−2 X∗t−3 X∗t−4 AGN HFT_trades 1,903 3 HFT_volume 1,072 3 AH HFT_trades 0,475 3 HFT_volume 0,972 3 ASML HFT_trades 7,429 4 −0,216 0,293* 0,041 0,182 HFT_volume 14,002*** 4 (0,148) (0,158) (0,152) (0,147) [−1,461] [1,856] [0,273] [1,237] ATC HFT_trades 0,485 2 HFT_volume 0,622 2 DSM HFT_trades 2,605 2 HFT_volume 2,252 2 HEIA HFT_trades 5,760 4 0,022 −0,010 0,100** 0,039 HFT_volume 8,240* 4 (0,046) (0,046) (0,046) (0,045) [0,467] [−0,218] [2,150] [0,860] MT HFT_trades 5,254 3 HFT_volume 3,920 3 RAND HFT_trades 0,001 1 HFT_volume 1,776 1 RDSA HFT_trades 7,506* 3 0,112 0,023 0,344** −0,037 0,081 0,382*** HFT_volume 10,563** 3 (0,177) (0,183) (0,172) (0,139) (0,142) (0,136) [0,630] [0,128] [1,996] [−0,263] [0,572] [2,808] REN HFT_trades 5,088* 2 −0,040 −0,255 HFT_volume 3,941 2 (0,169) (0,168) [−0,235] [−1,517] UL HFT_trades 4,127 2 0,403** 0,021 HFT_volume 7,264** 2 (0,177) (0,179) [2,278] [0,117]

brackets the t-statistics. Both the dependent variable VR and the independent variables are log-transformed.

4.5 Nonparametric Diks-Panchenko Granger Causality

The final test carried out is the Diks-Panchenko test, applied to raw data and VAR resid-uals. The results are presented in Table 4.6.1. The test results of the raw data are com-pared to the results of the previous sections, summarised in Figure 4.6.1. Figure 4.6.2

The influence of high-frequency trading on the Dutch market quality

The Influence of High-frequency Trading

on

the Dutch Market Quality.

University of Amsterdam

The Influence of High-frequency Trading

on

the Dutch Market Quality.

Statement of Originality

Acknowledgments

Contents

1

Introduction

I

2

Literature Review

T

2.1

High-frequency Trading

2.2

Market Liquidity

2.3

Market Volatility

2.4

Market Efficiency

3

Data and Methodology

T

3.1

Data

3.2

Stationarity

3.3 Linear Granger Causality

3.4

Model Estimation

3.5

Nonparameric Granger Causality

4

Results

T

4.1 ADF test results

4.2 Liquidity

4.3

Volatility

4.4 Efficiency

4.5 Nonparametric Diks-Panchenko Granger Causality