Algorithm-Based Intraday Trading Strategies and their Market Impact

The activity of algorithmic trading is increasing steadily across capital markets due to technological developments. This thesis analyses the common algorithmic intraday trading strategies of momentum, mean reversion, and statistical arbitrage. Conclusions were drawn from a literature review of prior and current research. Algorithmic arbitrage was found to be the most profitable of the three evaluated strategies, because it typically takes place in high frequency trading. Furthermore, this thesis analyses the impact of algorithmic trading on market liquidity and volatility. While the literature mainly agrees that algorithmic trading has a positive effect on liquidity, its impact on volatility is subject to discussion. Algorithmic and high-frequency trading carry risks that will likely lead to new future regulations.


Background
Automation and artificial intelligence (AI) have developed significantly in recent years due to technological developments. 1 In businesses, automation can take place in nearly every departmentfrom the classical example of a factory that substitutes workers with machines, to the use of AI for targeted marketing, automated accounting, and even talent acquisition in human resources management. 2 Of course, this development also affects finance and investment management, as well as the whole capital market. A McKinsey study shows that automation has the potential to fundamentally transform the entire finance sector. This is especially true for investment decisions and trading, where considerable quantities of data arise from market situations and stock fluctuations. Both automation and AI use smart algorithms that are able to process large amounts of qualitative and quantitative data. Today, several types of algorithms are also able to improve themselves through machine learning. Thus, it follows that algorithmic trading will increase in line with technological improvements, since more and more data needs to be analysed in ever-shorter periods of time.

Problem description and goal of the research
The topic of algorithmic intraday trading is widely discussed in a large number of scientific articles and has been the subject of many discussions. Due to the rapid digitalization of data in the past decade, the field of AT has developed steadily. 6 Most professional literature on the subject investigates either one single trading strategy or focuses on further developing an algorithm that is applicable to multiple strategies.
Often, only one market is observed. Furthermore, many books and reports of personal AT success stories dominate the field. The effects on market liquidity 7 and volatility 8 have been tested in empirical studies and the development of AT through new technologies 9 has been observed. In the business world, big investment firms that control sizeable percentages of the world's capital spend large amounts of money on the research and development of AT strategies. This further underlines the relevance of the topic.
Despite extensive research on the topic, however, the literature lacks a holistic review which sums up the status quo of the most common AT strategies and the market impact of AT in one paper. The aim of this thesis therefore is to outline scientific research regarding common AT strategies. Furthermore, studies and scientific findings relating to the general impact of AT on the market are discussed. This part of the literature review focuses mainly on the impact on market liquidity and volatility.
Examples of both mature and current literature are subject to this review and the relationships between ideas and practices are identified. Given the fast-paced environment of trading in conjunction with technology, it is crucial to compile a current and comprehensive review of the literature. Specific research questions are given in the following section.

Structure of the thesis and research questions
This thesis examines the following overall research question, which arises from the research goal and the large number of existing studies: What is the market impact of algorithmic intraday trading?
In order to concretize this question the literature review focuses on two sub-questions that are reviewed in detail:

I.
What is the profit potential of the common algorithmic trading strategies momentum, mean reversion, and arbitrage?

II. What is the influence of algorithmic trading on the liquidity and volatility of markets?
Based on the research questions the thesis is structured as follows: After giving the background and explaining the relevance of the topic in the first chapter, the second chapter outlines theoretical fundamentals of intraday trading and AT.
Definitions and key characteristics of AT are presented.
The third chapter explains the methodologies used in this thesis, including the data collection and data analysis processes.
In the fourth chapter, the existing literature is reviewed and discussed. It focuses on algorithmic intraday trading strategies and the related trading returns generated. Three strategies are examined in detail, which are momentum, mean reversion and statistical arbitrage. These strategies have been chosen due to their popularity in AT and ongoing discussions and studies about them. Each strategy is explained as well as their underlying capital market theories. Then, studies regarding each strategy are compiled and analysed.
The data from each study, the mathematical model behind the algorithm, and the trading returns generated by the AT system, are summarized. The studies focus on different markets and trading assets to give a multifaceted overview. In addition, those studies that focus on the same strategy are compared. 4 The fifth chapter outlines the relevance of the topic to the entire marketplace. Impacts of AT on market liquidity and volatility are reviewed in detail. As with the review process in Chapter 4, several studies concerning liquidity and volatility are analysed and the findings are compared with each other.
In Chapter 6, the results of the thesis are finally summarized and deliberated. A brief explanation of the future developments of AT complete the thesis.

Theoretical fundamentals
This thesis requires a basic understanding of intraday and algorithmic intraday trading that the following sections will provide. It is favourable to delimit the terms intraday trading and algorithmic trading to ensure a sound understanding of both principles.
Furthermore, a general understanding of trading algorithms and their functionality is necessary, what the following sections will explain.

Financial instruments of intraday trading
These characteristics do not fit every market, so not all available securities are suitable assets for intraday trading. When researching markets that fulfil the criteria listed above, the FOREX market is identified as a highly liquid market. It is considered as a major financial market in the world, with a market capitalization of 6 trillion dollars per day. 19 Furthermore, it is a 24-hour market unrestricted by business times. The traded assets are currency pairs that represent the exchange rates of two currencies. Due to the high liquidity of the market, the bid-ask spread decreases, which will be further explained in Options contracts differ from futures in that they do not oblige the buyer to purchase the underlying asset, but give them the opportunity to buy or sell it. 25 Trading options are preferred over trading the underlying assets themselves, because they offer lower transaction costs, higher financial leverage, and higher volatility. 26 In intraday trading, the stock market itself is not preferred, because the risk that large market participants manipulate the market is high. 27

Goals and profit chances of individual intraday traders
The overall goal of day trading is to turn the small intraday price movements of an asset into profit without holding it overnight. Traders purchase an asset and try to sell it for a higher price. Hence, they try to leverage small price increases by purchasing a larger volume of assets. 28 The principle is simple, but the practice reveals differences in successfully applying these principles. There are several studies referring to the profitability of intraday trading. Barber

Algorithmic trading definitions
Algorithmic trading is the combination of conventional (day) trading and the increase of the use and creation of computer algorithms. Hendershott, Jones and Menkveld (2011) define algorithmic trading commonly as computer algorithms that make particular trading decisions, order submissions, and post-order management, automatically. 38

High-frequency trading
High-frequency trading (HFT) is an important subcategory of algorithmic trading and a clear differentiation between both terms is sometimes difficult. It is a later phenomenon than algorithmic trading since it requires higher technological standards. This form of algorithmic trading is characterized by its speed, because the trading system analyses market indicators that signal an order in milliseconds or seconds, much faster than humans are capable of. 42 Therefore, the profitability of HFT is reduced when the system reacts with a 300-millisecond delay. 43 The system can place large numbers of orders within a moment. Again, this process does not involve human intervention. HFT is also characterized by the short time-frame of buying and selling positions, the high daily portfolio order, and the high order-to-trade ratio.

Trading algorithm characteristics
Trading algorithms consist of at least one buying command and at least one selling command to determine the moment a trade should be placed. When the algorithm is simple, as mostly in conventional day trading, values and prices can be determined manually, but in algorithms that are more complex, computer systems are necessary to support the execution. The algorithms should detect the moment when the buying or selling command fits the market situation and promises a potential profit. For every instant of time, it gives a value that is often either true or false and indicates if a trading signal is generated. That is why the algorithms must be designed to run frequently and produce an outcome for every instant of time. 50 Trading algorithms stand out for some special attributes that include verifiability, consistency, quantifiability, objectivity, and expandability. The first attribute means that the algorithm must be checkable and traceable with the help of back-testing 51 and simulation. When the testing shows that the algorithm has the potential to generate profits,

Methodology
In order to answer the research questions, the approach of a systematic literature review framework by Parris and Peachey (2013) is used. Firstly, data adequate to the question was collected. Secondly, this information was analysed and evaluated. 53 The methods for these steps will be explained in the following sections to ensure confirmability and transparency.

Data collection
A literature review requires a collection of many types and sources of data. For this study, the process of data collection started with a search for appropriate data in the HTWK For the investigation of the market impact, the keywords 'market liquidity' and 'volatility' in relation with algorithmic trading were researched. These two market characteristics were identified as crucial subjects to discussion. Accordingly, the structure of the thesis was extended.
Regarding the time frame of the data, it was necessary to include both historical and contemporary studies. For capital market theories, older literature was used in terms of explaining the rationale behind certain trading strategies. In terms of individual studies, results were filtered for more current literature to present the status quo of AT and its market impact.
Finally, all suitable literature that met these criteria was downloaded and exported into an Excel spreadsheet. A duplicate check followed, since some documents are updated versions of prior ones or have been released by several publishers. Then the abstracts were read and searched for the keywords 'intraday' and 'algorithm(ic)' in each document in order to ensure their suitability for the topic of the thesis.

Data analysis
The the second research question refers to the market impact of AT in general. This approach was taken because it is impossible to determine the market impact of a single AT strategy.
On exchanges, one can determine which trades were executed by AT and which by non-AT through different proxies or systems. However, it cannot be determined what particular strategy lies behind a particular algorithm. Due to the limited scope of this thesis, the focus therefore lies on the three main strategies and AT's impact on market liquidity and volatility.

Algorithm-based intraday trading strategies and their profit potential
The trading algorithms subject to this research follow a particular strategy. In the following literature review, the most common strategies and selected studies are presented and discussed in detail.

Definition and basic principle of the strategy
The momentum strategyalso referred to as the trend-following strategyhas existed for a long time. Its principle is the opposite of the trading motto to buy low and sell high.
The leading statement of Driehaus, who is considered the father of this strategy, is to buy high and sell at an even higher price. 55 In momentum trading, a trader buys financial instruments whose value has increased in the past and sells those whose value has decreased. The underlying assumption is that the value of a trading object that has increased in the past will further increase, and vice versa. In AT, the algorithm is programmed so that it follows a momentum strategy. Therefore, it needs only historical price data. Wide varieties of financial instruments that can be subject to algorithmic trading with a momentum strategy are described in the literature and it is manifested in several markets. 56

Underlying theories of the momentum strategy
There is no consensus about the underlying scientific theory behind the momentum strategy. This is why the strategy is explained using risk-based as well as behavioural theories and hypotheses, which are the subject of many scientific articles and studies. 57 The risk-based explanations generally propose that greater risks can lead to higher returns.
The starting point for explaining the strategy is the efficient market hypothesis (EMH) of Fama (1970). 58 Its main statement is that " ( fully reflect all available information". 59 Fama uses three main points to support the hypothesis. Firstly, the rate of returns depend on the taken risk of an asset (the fair game model). Secondly, the value of an asset is expected to increase or not change (the martingale model), and thirdly, the price development follows a random walk and reflects only the current information (the random-walk theory). 60 Because of this, price changes that are dependent on current events and new information are not predictable and, therefore, future prices are not predictable either. 61 The hypothesis defines three types of market efficiency that depend on the amount of available information.
In the weak form, current market prices include all information that the historical prices provide and thus, the future prices follow a random walk. Abnormal returns are only achievable with a fundamental analysis, but not with a technical analysis. The technical analysis uses only past data to predict the future development of stock prices. In contrast, in the fundamental analysis the intrinsic value of a financial instrument is determined.
Therefore, macroeconomic factors, such as economy and industry conditions, as well as microeconomic factors, for instance management quality, are taken into account. 62 In the semi-strong form of market efficiency, all current public information is included additionally in the current prices. It is assumed that this information is immediately reflected in the prices and abnormal returns cannot be achieved, because all market participants act rationally and have access to public information. Thus, one can get abnormal returns only with insider knowledge and not with the fundamental analysis anymore.
In the strong form of market efficiency, all information, inclusive of insider knowledge, is inducted in the current prices. This means that no one can get abnormal returns from a trade. 59  Under the momentum strategy, which does not allow for a random walk of prices, the semi-strong and strong market efficiency aspects of the EMH are not feasible. In fact, the strategy stands in conflict to the hypothesis, caused by its unrealistic assumptions. In addition, the EMH is a much-debated issue. 63 Other risk-based explanations were studied in relation to the momentum strategy. Johnson (2002) explains momentum returns in the context of firms' growth rates, because he assumes that a positive shock or increase in returns is an indicator of the ensuing longterm growth of the firm, which will inevitably lead to an upward trend in returns.
Silk and Seasholes (2007) have developed another theory including the firms' growth rates as well. They explain higher momentum returns by linking a firm's growth rate and risk profile to each other. When the market value of a company rises faster than its revenues, it causes a higher risk for investors that leads to potential higher returns. Other risk-based momentum theories have been developed by Berk, Green and Naik (1999) In contrast to the risk-based theories, behavioural theories were also explored to explain the abnormal returns generated with this trading strategy. Market anomalies arise from investors' behaviour and its biases. Most studies agree that abnormal returns are a result of an underreaction or delayed overreaction of traders. When an underreaction takes place, new information influences the prices very slowly, due to several reasons such as the information diffusion between the traders, conservative trading attitudes, or liquidity issues. Evidence exists that investors react slowed to corporate earnings or the announcement of dividends. In an overreaction, prices increase further due to a feedback mechanism and lead to a momentum return. If momentum is caused by investor biases, this would be a rejection of the EMH. 66 Behavioural studies of the momentum strategy were conducted by Daniel et al. (1998), Barberis et al. (1998), Hong and Stein (1999), Grinblatt and Han (2005), Frazzini (2006), 67  These behavioural theories affect the markets and are important when analysing AT, because of the existence of human traders alongside automated trading systems.
Obviously, many theories try to explain the rationale behind the momentum strategy and its related returns, but there is no common explanation. 69

Selected studies of an algorithmic intraday momentum strategy
Since the research question focuses on the execution of trading strategies through automated trading systems based on algorithms, the contents and results of algorithmic momentum studies are analysed further. Trading algorithms nowadays involve highspeed systems and cutting-edge mathematics to earn abnormal returns. This complex mathematics is not discussed in this thesis due to its limited scope.
Generally speaking, algorithms often use technical analysis for their trading decisions.
This analysis examines past data: under a momentum strategy, only past data are analysed to predict future development of stock prices. It considers factors such as volatility, moving averages (MA), bid-ask spreads, price trends, mathematical ratios, and momentum indicators such as the rate of change or the Sharpe ratio. The latter is widely used for measuring risk-adjusted returns. 70 To increase profit chances, several algorithms are also able to process qualitative as well as quantitative data, and are therefore able to interpret verbal statementsconducting a Twitter sentiment analysis, for example. 71 The following algorithms are several of those tested on past data to find evidence for generated returns. The results can be used to improve strategies and the algorithms themselves. Gsell stated in 2006 that algorithms could not execute a momentum strategy, because they worked one-sidedly and so were unable to follow a buy-low/sell-high strategy. 72 However, with today's AT systems, the execution of a two-sided momentum strategy is possible, as the following sections testify.

Study A -Schulmeister (2009)
In 2009, Schulmeister tried to answer the research question of whether trading algorithms could turn a profit using intraday data. He stated that the returns of 2,580 technical intraday trading models had decreased constantly during the prior decades and were not considered profitable anymore. Schulmeister also determined whether the same models could produce good returns from a 30-minute database. Data from the S&P 500 Spot and the S&P 500 Futures Market from 1983 to 2007 were subject to the study.
The author created algorithms that produce buy and sell signals from current movements in prices. In addition, they point out if the trend will continue or revert. Two types of model are presented. The first uses moving averages for its calculationa short-term MA that includes data from the past 1-10 days, and a long-term MA whose length varies between 10 and 30 days. These are applied to a 30-minute database, or data divided into 30-minute intervals instead of days. These moving average models follow the rule to buy when the short-term MA moves faster than the long-term MA and intersects it from below and vice versa. The second type, momentum models, use percentage rates of change to determine the trading signals. They follow the rule to buy when the trend changes its direction from negative into positive, and to sell when the opposite takes place. Based on these models, Schulmeister presents six different algorithmic rules that generate buy and sell signals at different points in time. 73 Three rules follow a momentum strategy (see Figure 1 Schulmeister found that these technical trading models are more profitable in intraday trading. With the momentum trading rules, a gross rate of return of 6.8% (approximately 2% net return) in the stock futures market based on 30-minute data could be generated.
In contrast, the algorithms using a MA performed worse than the ones using the Momentum oscillator.
As reasons for the higher profitability of intraday trading strategies, the author mention the adaptive market hypothesis (AMH) and the rise of speed in trading. The AMH states that a market becomes more efficient due to the evolutionary learning processes of the traders. 75 This means, basically, that some traders start to use trading rules that prove to be profitable. The more traders use these rules, however, the more unprofitable they become. Therefore, other traders might discover even more profitable trading rules and the cycle of learning and efficiency starts again.
Applied to Schulmeister's study, the profitability of the original trading models decreased, while the 30-minute models were shown to be profitable. 76

Study B -Christensen, Turner and Godsill (2020)
The authors Christensen, Turner and Godsill (2020)  Further remarks on the calculations are presented in detail in the study.
The basic assumption in applying the HMM to momentum trading is that the price changes of trading objects can be observed and are measurable, while the state of the underlying trend cannot be observed and thus is hidden (see Figure 2).  The authors tested the approach on data from the e-mini S&P 500 Futures from 2011 at one-minute sampling frequency. This gave 258 days of data, with 856 observations per day. The authors do not give exact return rates in their conclusion, but instead provide Sharpe ratios and the number of hidden states.
All techniques deliver similar results, which are that there are two or three hidden states.
This is plausible in a momentum strategy; the number of two hidden states relates to an upward/downward-trending momentum, while three hidden states suppose an additional side-moving market state without a significant trend into one direction.
The piecewise linear regression algorithm performs worst. On the other hand, the Baum-Welch algorithm performed better than the MCMC due to no scientific reason, but the authors believe that the result comes from the difficulty in correctly using the MCMC algorithm. Both strategies have a high correlation, but MCMC execute the trades less optimally. The Sharpe ratio decreases by approximately 15% post-cost. Furthermore, the Baum-Welch algorithms with the input of side-information outperform the one without side-information. Their Sharpe value is approximately 10% higher. This proves that the algorithm is able to consider input information and, thus, has a predictive value. Due to the conclusion from Sharpe ratio to returns, this study supports the thesis that a momentum or trend-following strategy is profitable (pre-and post-cost). 80

Study C -Herberger, Horn and Oehler (2020)
Another result can be found in the analysis of Herberger, Horn and Oehler (2020)

Definition and basic principle of the strategy
The concept of mean reversionin literature also referred to as the Contrarian strategyis that the prices of financial assets revert to their particular long-term mean. 86 When there is a decline in prices, the probability is high that it will be followed by a positive price movement, and vice versa. Stock prices will always return in the direction of the mean. 87 In order to express it correctly in terms of statistics: the more a random variate deviates from its mean, the higher is the probability that the next variate will diverge to a lower degree from the mean. 88 Time to reversion equates, therefore, to the time of the price return to the mean. Generally, this strategy can be used in every market that fulfils the criteria for intraday trading mentioned in section 2.1.2. At this point, it should be noted that Baz et al. (2015) found that mean reversion in foreign exchanges tends to be slower than for equity and commodities. Its time to reversion is therefore longer. 89

Underlying theories of the mean reversion strategy
The underlying assumption is that the prices of trading objects oscillate around a stable trend. Therefore, a MA of different periods, such as 30 or 90 days, can be calculated and treated as an underlying trend or mean to which prices will revert. 90 This strategy speaks against the random walk theory, because prices do not move randomly after a price shock, but return to a particular price level. 91  Other studies explore both strategies and their relation to each other, such as Jegadeesh and Titman (1993), Ferri and Min (1996), Daniel, Hirshleifer and Subrahmanyam (1998), Lobe and Rieks (2011), Maher and Parikh (2011) 97 , and Heldens (2017. 98 In addition, Herberger, Horn and Oehler (2020) confirm the causality of momentum and mean reversion. They investigate both trading strategies at the XETRA market and find higher and statistically significant gross returns in reversal strategies, but not in momentum trading strategies. Thus, they find the more efficiency in terms of returns than Plastun et al. Nevertheless, the reversal returns they identify are lower than the transaction fees.
The execution of mean reversion strategies through algorithms are analysed in the following studies. It should be noted here that the duration of momentum and reversal periods have become shorter over the years due to the increasing speed of algorithmic trading. 99

4.2.4
Selected studies of an algorithmic intraday mean reversion strategy

Study A -Schulmeister (2009)
In 2009, Schulmeister analysed reversal trading as well as momentum strategy. In section 4.1.3.1 the trading rules SG1 to SG3 were explained with regard to the latter. The following section examines the rules that follow a contrarian strategy (see Figure 3).
The SG4, SG5 and SG6 trading rules aim to find overbought or oversold market states.
When the oscillator is positive, but falls under a particular level, the situation is overbought, and if it rises, but is still negative, the situation is oversold. The fourth trading rule generates a selling signal when the situation is overbought and the oscillator crosses decreases to zero or below, and vice versa. For both rules, the Relative Strength Index is calculated and used as a gauge of the current market conditions.
In the last trading rule mentioned, SG6, an additional upper and lower bound is included, where a neutral position is always hold, and when the oscillator takes a value that lies between either the two upper or the two lower bounds. 100 Figure 3: Signal generation rules 4-6 following a mean reversion strategy (Source: following Schulmeister, S. (2009), p. 192) The contrarian signal generation rules show a higher performance and thus a higher profitability than the momentum trading rules, with an average gross rate of return of 9.1% (approximately 4.5% net return). The study determines that an average gross return of 7.2% is produced by all trading rules acting together, which equates to a net return of 2.6% per year in the stock futures market, based in the intraday 30-minute data. This is the overall result, but in the last years of the sample (2004)(2005)(2006)(2007), the models performed worse and gross returns turned negative. This is explained by the author in terms of the AMH and the rise of speed in trading. 101

Study B -Wiśniewska (2014)
At this point, it is relevant to highlight another study based on one-minute intraday data

The author tests the mean reversion of the currency pair EUR/USD with an augmented
Dickey-Fuller test (ADF) 102 and concludes that a mean reversion exists in this case. It confirms the theory that the EUR/USD reverts to a mean that changes over time.
Therefore, a regression analysis of the moving average of the last bid rates (as an explanatory variable) is executed. With the computations, the authors determine two trading strategies that should be undertaken by automated algorithmic trading systems.
The going-long strategy advocates purchasing EUR/USD initially and selling it afterwards. On the other hand, the short-sell strategy proposes selling EUR/USD and repurchasing it back afterwards. Calculated with a 99% confidence interval, the average maximum return for the first strategy is 0.005525% per day while for the second strategy it is 0.006046%. With the calculations and both strategies that provide positive returns on average, the author is able to confirm mean reversion. Thus, the author rejects the market efficiency hypothesis. On the other hand, trading fees are not included in the study, and further research is needed to determine if the strategies are able to provide a net return. 103

Study C -Herberger, Horn and Oehler (2020)
Herberger, Horn and Oehler have also analysed intraday reversal and momentum returns.
They used five-minute return data from 2013-2014 from all 30 stocks on the DAX 30 (German blue chips) traded on the platform XETRA. These stocks have extremely low bid-ask spreads and so there is a low risk for biases.
The authors linearly transform the trading frameworks of De Bondt and Thaler (1985) and Jegadeesh and Titman (1993)  In order to gain meaningful results, the 5-minute mean and median returns are calculated as well as the standard deviation, skewness and kurtosis. The analysis reveals that all 16 reversal strategies show significant positive mean returns, higher than the market proxy does. This means that the stocks of the losing portfolios experienced a price increase during the holding period. The results also show that a higher return is linked to higher risk. Furthermore, the results are classified as robust due to the high number of stocks and many combinations of ranking and holding periods of different length.
Despite the positive abnormal returns, another point must be mentioned. The study found that the intraday overreactions of stock prices cannot normally be exploited by retail investors. Only institutional investors might make a profit, because they face lower costs than retail investors, especially in short trades. Even so, the investigation showed that due to the high transaction costs at XETRA, institutional investors would be unable to take the profit in this scenario.
Herberger et al. conclude that only HTF traders or market makers (further explained in section 5.1.1) would be able to reach low enough transaction costs to take a profit. Thus, the strategies do not contradict the EMH. For retail traders, it would be more successful to buy a market index. 106

Comparison of the selected studies
The three studies contain data from different markets (S&P 500 Spot and Futures market,

Definition and basic principle of the strategy
Arbitrage is an intraday trading strategy where a profit is generated by buying an asset on one exchange and selling it for a higher price on another exchange nearly simultaneously. 109 The definition is common, but does not cover all of the many kinds of arbitrage, which is a multifaceted term. In a wider sense, it can be defined as "(…) a set of trade operations based on a certain model that yield profit at negligible risk". 110 The latter point is important, because the literature often classifies arbitrage profits as completely risk-free, which is not achievable under real market conditions. 111 This strategy aims to exploit the pricing differences of financial instruments. These price discrepancies are based on market inefficiencies, caused by not including the latest news immediately in the prices on all exchanges. Arbitrage can be find on markets with high transparency and liquidity. For retail investors, emerging markets might be profitable due to the lower competition and lower arbitrage activity. Currency pairs are a common subject of arbitrage. 112

Types of Arbitrage
Arbitrage trading is a complex issue split into deterministic and statistical arbitrage. The first kind guarantees a certain profit, which cannot be calculated ex ante, because of potential market rate changes in the future. Sure value assets, such as gold and other raw materials, as well as some public bonds, belong to the deterministic type of arbitrage assets.
In Further classification methods for arbitrage are also possible. These include distinguishing arbitrage by the asset classes involved, or the marketssuch as bilateral arbitrage and multilateral arbitrageas well as by the trade location, for instance intraand inter-exchange arbitrage. 115 Numerous statistical arbitrage algorithms rely on the concept of mean reversion in order to reduce the risk. 116

Underlying theories of the arbitrage strategy
Using an arbitrage strategy to make profits relies on market inefficiencies that contradict the EMH. Additionally, the strategy stems from the Arbitrage Pricing Theory (APT) devised by Ross (1976)  is necessary to identify how certain risk factors might influence the financial instruments and how sensitive they are to each one. The stronger the asset reacts to the risk factor, the higher the beta value is. Then, the expected return is calculated. 119

Selected studies of an algorithmic intraday statistical arbitrage strategy
Since arbitrage trading is highly multi-faceted, with many strategy types, the following

Study A -Werl (2014)
In 2014, Werl developed a multilateral arbitrage algorithm and tested it using data from East Asian currency exchange rates from January to May 2014. 121 The written code, which consists of more than 2,000 lines, involves an algorithm that searches for an arbitrage opportunity and an algorithm which produces all possible arbitrage loops for triangular, quadrangular and quintangular arbitrages. For pairs trading, the authors follow the framework of Gatev (1999Gatev ( , 2006. Assets of synchronous stocks, which prices converged prior, are formed into pairs. Then the price spreads are analysed. The undervalued stock is bought, and the overvalued stock is sold short with the assumption of generating a profit, because the prices will revert back to their historical mean. 124  analyses. The trading assets include stocks, exchange traded funds (ETF), currencies, index futures, and commodity futures from different markets. 128 Firstly, they set up a formula for the portfolios and model the mean reverting portfolio price behaviour that fits an OU process and includes a factor for the Brownian motion.
Then, they optimize the mean reversion with the maximum likelihood estimation. In order to test if the determined parameters fit the model, the authors simulate 100 or more OU price paths.
Following this, they compare the average log-likelihood from the simulated paths with the maximum average log-likelihood from the empirical prices. The result shows that a three-month lookback-period best fits the OU model. They accordingly adapt their pairs formula with a time-dependent factor. With this, they construct a trade exit rule that determines a critical price level for the trade liquidation in terms that maximize profits.
Finally, the researchers test their algorithm on the data. They include fees for trade execution while measuring profits. Furthermore, they use a 30-hour standard deviation and a 30-hour simple moving average to measure the performance of the trading exit rule.
At every market opening (NYSE market opening time), the model parameters are updated and at every hour the algorithm checks for trade entry and for liquidation when the parameters reach a particular value. This is performed for the baseline model, without the optimal exit rule, and for the authors' model, including the rule.
As result, the framework proves as profitable for arbitrage pairs trading. The Sharpe ratio increases by 0.7 and the daily turnover decreases by 34% on average for seven of eight tested pairs. The performance is measured for the portfolio as a whole, consisting of the eight pairs as well. The annualized return is 7.4%, which is 2% higher than for the portfolio without an optimal exit rule, while the Sharpe ratio increases to 1.43. Daily turnover decreases by 35%.
Another finding of the study was that the optimal exit level is broader in periods with high volatility. The authors define their algorithm as profitable and applicable to several asset classes. 129

Comparisons of the selected studies
In conclusion, all analysed studies obtain positive returns, despite their use of different data periods from different markets. Werl (2014) uses data from the FOREX market, Stübinger and Schneider (2017/2019) from the S&P 500 stock market and Leung and Lee (2020) from several markets including currencies, futures, ETFs and stocks. Werl (2014) and Stübinger and Schneider (2017) determine positive returns generated by their algorithmic trading models that have a high variance. This means that there is an inequality in the returns of different arbitrage loops or pairs. Stübinger and Schneider (2019) also reached an outperformance of conventional strategies. Furthermore, Leung and Lee (2020) developed a trading rule, which generated higher returns than a portfolio without such an optimal exit rule.
The recent literature under review displays more of a consensus regarding the returns of the algorithmic arbitrage strategy compared with the momentum and mean reversion strategies. The difference is that arbitrage is mostly found in high-frequency trading, which has increased due to technological developments. 130 Furthermore, fewer studies exist on the topic of algorithmic momentum and mean reversion strategies for algorithmic intraday trading. Due to the fact that arbitrage is mostly used in HFT and consequently in intraday trading, more literature can be found.

Further trading algorithms and strategy components
Besides momentum, mean reversion and arbitrage, there are of course a number of other AT strategies. However, many trading algorithms unite and combine more than one strategy in a single trading system. For these combined algorithms, which cannot be assigned to a single strategy, it is not possible to compare returns as in the previous sections.
The following algorithms can be classified as speed advantage and accuracy advantage algorithms. The speed advantage is mainly exemplified by HFT whereas the accuracy advantage results from the evaluation of more various data. 131 Both advantages will be further explained in section 5.2.2.2.

Speed Advantage algorithms
Spread capturing algorithms: Using this class of algorithm, liquidity providers buy and sell securities constantly. With this, they generate revenues from the bid-ask spreads (further explained in section 5.1.2) in prices through working as intermediaries and filling the gaps between market participants. 132

Rebate trading algorithms:
Rebate trading algorithms search for unequal fee arrangements on trading venues. Traders who trade large volumes and remove liquidity from the market often have to pay higher fees. The principle of liquidity will be further explained in section 5.1.1. By comparison, traders who provide market liquidity are subject to lower fees or rebates. The algorithms post offers in order to catch these rebates. 133 Volume weighted average price (VWAP) and time weighted average price (TWAP) algorithms: VWAP and TWAP strategies are often employed in trading systems, but are rarely the only strategy an algorithm follows. VWAP and TWAP mainly belong to the technical analysis indicators and serve as intraday price benchmarks. 134 The VWAP presents the average price of all transactions of an asset in a particular period that is weighted by each trade's volume. Thus, the influence of large volume trades is higher on the benchmark. 135 The period in which a trade should take place is divided into benchmark. 136 When the transacted price of a buy trade is lower than the VWAP, it is favourable, and vice versa for sell trades. The use of this metric should help to reduce execution costs and balance the liquidity demand. Thus, it should not cause extreme volatility. 137 The TWAP has a similar aim. Time slots of a desired trading period are formed again. In contrast to the VWAP, the trade volume is distributed in similar parts over this time slots.
An example therefore would be to buy 30,000 shares in one hour. This result in six buy transactions with 5,000 shares each. 138 Thus, the market impact is reduced in comparison to execute a single trade with a large volume at once. 139

Implementation shortfall algorithms:
Another algorithm class includes what are known as implementation shortfall algorithms.
Their aim is to unite the least possible influence on the market with a the risk of appropriate timing. Large orders that are executed as a whole have a big market impact, while split and time-shifted orders are exposed to the risk of price changes. Thus, the algorithms evaluate past data and set an order process. With this, large orders are divided in the least amount of sub-orders that is possible. 140

Adaptive execution algorithms:
These algorithms are similar to the previously mentioned VWAP and TWAP. The difference is that the algorithms are able to align themselves and thus the order execution to new market situations. 141

Liquidity detection algorithms or 'sniffing' algorithms:
Algorithms following the liquidity detecting principle try to spot large orders of other market participants. Some of these algorithms have also the ability to detect splitted or hidden orders. When the algorithm detects large orders, it can anticipate price movements and use this information for its own order placement. 142

Accuracy Advantage Algorithms
Data/text-mining algorithms: These algorithms search for hints of future price movements on huge databases regarding different markets and asset classes. These databases can now contain trillions of observations. 143 The algorithms are able to set big data from several databases in relation to each other and draw conclusions. In text mining, the algorithms can process textual information into formats that are useable by an algorithm. 144 Therefore, algorithms are able to undertake a Twitter sentiment analysis. Different keywords can be set prior to analysis and messages classified into categories such as positive, negative, or neutral.
With this information, the algorithm adapts its trading orders. 145

Neural network algorithms:
Neural networks belong to the state-of-the-art class of algorithms designed for machine learning. Neural networks seek to imitate the connections and learning processes of brains. The algorithms learn from training sets and perform various cycles of instructions.
By repeating the cycles and changing the chain of actions based on prior performance, the cycle is improved. 146 They aim to predict market movements have been applied successfully by asset management funds. Trading algorithms that use neural networks are considered to be 'black boxes'. This term is used to describe predictive models that are highly complex or even impossible to understand and reproduce. A reason for this is the huge amount of data processed by the algorithm and the way in which they are set up in interaction with each other. In addition, the algorithm carries out the data processing with the use of hidden layers. 147 However, due to their ability to find relationships in convoluted datasets, the algorithms can detect trends that are too complex to be discovered by humans alone. Thus, neural networks can serve as a forecasting tool. 148

Reinforcement learning algorithms:
Reinforcement learning (RL) algorithms are another class of machine learning algorithms. In contrast to neural networks, the RL algorithms learn dynamically and not from training sets. The algorithms adjust their actions due to permanent feedback and 41 learn from trial and error. RL algorithms try various actions and learn from the feedback.
Then, the algorithms reinforce the actions with positive results. These are improved further until they reach the best outcomes. Related to AT, these are of course

Impact of algorithmic trading on market liquidity and volatility
The following chapter focuses on the research question of how AT influences market liquidity and volatility. As previous parts of this thesis have made clear, numerous different AT strategies and algorithms exist. Therefore, it is not possible to measure the market impact of one particular trading strategy that is executed by many different algorithms and traders. As a result, the impact of AT on market liquidity and volatility is examined in general terms. The studies are analysed on this basis.

Definition
As already defined in section 2.1.2, liquidity represents the possibility of executing large volume orders within a desired time without causing significant price changes. In order to assess the function of a trading system, Harris defines liquidity as the most important criterion. The reason is that liquidity shows how effectively buyers and sellers are brought together on the exchange, reflected by bid-ask spreads. 150 One can also adopt a broader definition of market liquidity, which determines a market as liquid when a trade can be executed without or with little cost, risk or inconvenience. 151 Markets become liquid through liquidity providers, which include financial institutions such as banks and principal trading firms (non-banks). These parties, also referred to as market makers, are intermediaries and fill gaps (bid-ask spreads) between market participants. Due to these liquidity providers, traders can buy or sell at the desired time without waiting to find a particular seller or buyer. 152

Bid-Ask Spread
The bid-ask spread measures the liquidity of an individual financial asset. It reflects the gap between the highest price a buyer would pay (bid) and the lowest price a seller would request (ask). 153 Normally, the ask price is higher than the bid price. The spread is lower for actively traded assets and higher in the opposite case. That means that the spreads of assets in liquid markets are generally lower than the spreads in an illiquid market. Liquid securities include, for instance, large-cap stocks and currencies. 154 Furthermore, one can estimate transaction costs with the bid-ask spread. In an illiquid market with large bidask spreads, transaction costs are high; whereas in a liquid market with small bid-ask spreads, transaction costs are low. Thus, a liquidity premium (transaction cost) arises, which measures the half bid-ask spread when an order is placed. The more illiquid a market is, the higher is the liquidity premium. It belongs to the implicit trading costs. 155

Dimensions of liquidity
Liquidity can be measured according to four dimensions, which are immediacy, market width and market depth, and renewability. Immediacy means the required time to execute a trade to a given price and fixed transaction costs. Market width is described by the placement of large volume orders without a significant market impact. A market is furthermore liquid if a particular market depth is given. This means that transactions can be executed close to a theoretical equilibrium price. 156 The fourth dimension is renewability, which is the time needed by the market to return to the previous situation after uninformed investors cause a price change. The authors carry out several approaches that measure the correlation of AT and liquidity and make a distinction between large-and small cap stocks. The research concludes that AT improves liquidity for large-cap stocks. The authors find that, especially after the implementation of autoquote, AT narrows spreads. This is a result of a decrease of information asymmetry between trading parties, also called adverse selection. For smaller-cap stocks, they find no significant effects, but the authors cannot determine if this is a result of an error in statistical validity or a real fact. Nevertheless, from these findings Hendershott et al. conclude that AT improves market liquidity and thus, market quality as well. 162 Hendershott and Riordan conducted another study using data from the 30 DAX stocks regarding AT in 2011 and 2013. They found that AT demands liquidity when market conditions are good and transaction costs low, while it provides it in the opposite case. 163

Boehmer, Fong and Wu (2015)
In 2015, Boehmer, Fong and Wu studied the effect of AT on 42 equity markets with intraday data from 2001-2011.
In order to determine AT from all orders and trades, the authors follow the approach of Hendershott, Jones and Menkveld and use a similar AT proxy. The authors use several liquidity measures for the computation. These are the best-quoted intraday spreads per stock, relative effective spreads and the total price impact of the trades. Furthermore, they calculate an illiquidity ratio and test the approach of robustness. 164 Boehmer et al. come to several findings. On average, a higher degree of AT on the market leads to increased liquidity, faster price volatility, and so to higher market efficiency.
Furthermore, the authors find that the market liquidity is lower on days where AT leads to an increase in volatility. Thus, the AT effect in this situation is not desirable. Boehmer

Golub, Glattfelder and Olsen (2017) -The Alpha Engine
Golub, Glattfelder and Olsen did not study the effect of AT on liquidity as in previous studies, but instead developed a trading algorithm. The so-called Alpha Engines supplies liquidity to the market. Their trading model focuses on the FOREX market, which is highly liquid. Investment strategies that enhance market liquidity are able to create positive market effects. They lead to more stable prices and reduce uncertainty on the market. Thus, the returns of these strategies are the payoff for their value-adding market effect. The authors state, in addition, that there is a large profit potential on liquid markets.
The Alpha Engine works in a counter-trending manner and primarily follows a reverting strategy. The strategy is tested on 23 exchange rates with data from 2006 to 2014. The algorithm opens a position when the market overshoots. In addition, positions that go against the trend are maintained or increased. Thus, the algorithm provides liquidity. The algorithm leads to an unleveraged return of 21.34%. 168

Statements by public institutions
The Markets in Financial Instruments Directive of the European Parliament (2014) states that HFT generates benefits for markets, such as increased market liquidity and narrower bid-ask spreads. It also determines obligations for the liquidity provision of parties that conduct a market making strategy through AT. 169 The US Securities and Exchange Commission is another public entity that states AT improves market liquidity provisions, particularly when the market is in a normal state and not in a period of extraordinary stress. In the latter situation or during crises, AT might worsen the market conditions, it says. 170 The Bank of Japan notes similar effects of AT on the market. This institution determines that AT takes place more in Europe and the US than in Japan, but an upward trend is visible there, too. A study was conducted regarding the USD/JPY (Japanese Yen) in the FOREX market. It was found that AT improves market liquidity in common, non-extreme situations, especially liquidity provision through market making. However, the study could not confirm that AT has a significant negative influence on market liquidity in times 168 See online: Golub, A. et al. (2017) In a follow-up study in 2019, Boehmer, Fong and Wu specify that AT increases shortterm volatility in particular. Thus, the daily price range, return variances, and daily return volatility rise as AT increases on the market. Furthermore, the volatility of smaller stocks is increased to a higher degree by AT. As in the previous study, the authors cannot attribute the increasing volatility to more market efficiency, volatility-seeking traders, or volatility increases due to news announcements. 185

Gamzo (2017)
As Gamzo studies the market impact of AT, he divides the algorithmic traders into two different groups, which are represented by System 1 and System 2. System 1 is characterized by superior speed in processing information, while System 2 owns a superior accuracy in computing future variables and is slower than System 1.
With this, both systems have their own informational advantage. The speed advantage of System 1 comes from high-speed market connections and co-location facilities, for example. This enables actors to trade faster, more frequently, and with shorter holding periods. In the short term (intraday, often in only seconds or minutes), the asset price is rather determined by the order flow instead of fundamental values. Thus, the traders of System 1 generate a profit that consists of the difference of the entry and exit price (and not of the difference between entry price and fundamental value). This is why the order flow is a key focus of the system.
In order to have an accuracy advantage, System 2 traders use information beyond data provided by the order book. The algorithms analyse information, such as news, firm fundamentals and other macro-economic factors. The intrinsic worth of the traded financial assets has more relevance in the computations and a firm-specific forecast is days with an upward-movement, 20 with a downward-movement. 188 Zhou et al. find that stocks traded algorithmically to a higher degree face a lower volatility. When the market declined by more than 2%, these stocks experienced fewer price decreases and less downward price pressure than stocks with a lower AT intensity.
The same is valid for a market increase by more than 2%. Their findings support the AT lowers price pressure and extenuates pricing errors. Furthermore, Zhou et al. analysed the returns on the days after the turbulent period. They find return reversals in stocks with low AT intensity. This implies non-AT or low AT-intense stocks experience a higher market pressure and the prices deviate significantly from the fundamental value. This is not the case for stocks with a high AT intensity. This is why AT tends not to contribute to price volatility. 189

Statements of public institutions
The Markets in Financial Instruments Directive of the European Parliament (2014) states that AT and HFT lead to a reduction in short-time volatility. However, they mention that AT systems can also lead to an increase in volatility. This increase is explained by the overreaction of AT systems to market events. In addition, the condition of a pre-existing market problem must be fulfilled for an  The US Securities and Exchange Commission states some types of AT are able to exacerbate market volatility. It is mentioned that a momentum effect in stock prices might appear through AT strategies that depend on volatility. These strategies increase the sale of financial instruments, when the prices fall what is an indicator for a rise in volatility.
This leads to a downward trend in prices while volatility increases.

Comparison of the selected studies and further literature
The literature regarding AT's impact on market volatility comes to different conclusions. Gsell (2008), Chaboud, Hjalmarsson, Vega and Chiquoine (2009), Brogaard (2010), Groth (2011), Hendershott, Jones andMenkveld (2011) 192 andZhou (2020) 193 analyse different data from different exchanges and find no increase in volatility through AT. Hasbrouck and Saar (2013) conclude the similar effect and add that AT even lowers shortterm volatility. 194 An example therefore is the Alpha Engine of Golub et al. 195 Their trading algorithm buys and sells counter-trending and thus, works against a trend reducing volatility.
On the other hand, Zhang (2010), Martinez and Roşu (2011), Boehmer et al. (2015) Foucault, Hombert and Roşu (2016) 196 and Kelejian and Mukerji (2016) 198 In terms of HFT, Boehmer, Li and Saar (2018) come to another result. They find that volatility decreases through HFT. The reason therefore is the high competition between HFT market makers. 199 Brogaard et al. (2018) find that HFT stabilize prices in high volatility periods instead of increasing it. This is explained with the fact of trading against price movements. 200 The opposite is found by Roşu in 2019. The author concludes that when more high-frequency traders enter the market, volatility increases. 201 The US Securities and Exchange Commission states that some types of AT exacerbate market volatility while others decrease it and stabilize the markets. 202

Conclusion and future developments of algorithmic trading
Due to ongoing research into automated trading and its steady development, AT is a significant issue for capital markets. This thesis gives an overview of the AT strategies momentum, mean reversion and statistical arbitrage. In the process, studies by different authors over many years and various research approaches have been analysed. The evaluation of several studies for each strategy revealed different profits that could be generated by the trading algorithms.
The literature varies on the question of whether the algorithmic momentum strategy is profitable. Herberger et al. (2020), using a 35-minute momentum period, find that the trading strategy does not generate positive abnormal returns. 203 In contrast, Christensen et al. (2020) created an algorithm that turns out to be profitable for a one-minute momentum period. This finding indicates greater profitability over a shorter momentum period. 204 This is logical given the increasing market share of HFT. The German Federal Bank (2016) also supports this hypothesis. It states that HTF has a share of approximately 50% of all trading activities in liquid European and US-American markets. 205 Regarding the mean reversion strategy, there is a greater agreement. Although the studies analysed in section 4.2.4 use data from different periods and different algorithms, all approaches show minimal or no profits. In contrast to this, algorithms following a statistical arbitrage strategy provide positive net returns. 206 Once again, the reason can be largely attributed to HFT, in which arbitrage mainly takes place. Due to the increasing market speed, the price differences that arbitrage tries to exploit change faster and so faster trading is required to gain a profit. 207 In general, it can be concluded that AT is profitable for momentum and especially arbitrage strategies in the HFT sector.
Besides the evaluation of the three AT strategies, further trading algorithms were mentioned. Due to the large number of strategies and its relevance for capital markets, the impact of AT on market liquidity and volatility was analysed further.
In terms of the influence of AT on market liquidity, researchers mainly agree in their conclusions. The majority of research finds that AT and HFT improve liquidity and have a positive effect on the market. 208 In addition, Hendershott et al. (2011) and Boehmer et al. (2015) determine that the liquidity-providing effect is valid specifically for large-cap financial assets. There is no consensus on whether AT still provides liquidity when there is a situation of market stress.
Furthermore, the literature provides a range of opinions on the effects of AT and HFT on volatility. Section 5.2.2 evaluates those studies that argue whether AT increases or decreases market volatility. , for instance, determines there is an increase in short-term and a decrease in long-term volatility through AT. 209 In addition, it is worth mentioning that HFT was found responsible for the so-called 'Flash Crash' of 2010. The high-speed automated trading program of a US company placed a selling order of S&P futures contracts worth 4.1 billion USD. The execution of the entire order took only 20 minutes and caused orders of other automated trading systems. As a result, there was considerable volatility and high liquidity fluctuations occurred. After this event, it was concluded that AT and HFT programs play a critical role in capital markets. 210 In conclusion, AT and HFT are able to influence market liquidity and volatility positively, but can also exacerbate the market state.
Therefore, risks and potential future regulations need to be explained briefly. place in form of pinging and spoofing. These HFT tactics aim to gain information about the trading intentions of other market participants. In both strategies, many orders are placed, but with the intention of cancelling them before they can be executed. The placement of these orders creates a false picture of the current market state. Thus, the reactions of other market participants are provoked that reveal their buying or selling intentions. The pinging or spoofing party then uses this information to their advantage. 212 Overall, these state-of-art algorithms as well as market manipulation algorithms carry particular risks for the field of AT. The more complex and opaque the algorithms become, the higher the risk they represent. Besides this, the dependency on high-speed actions presents another risk. 213 The increasing complexity and speed of AT as well as growing volatility over time will lead to new regulations and laws. 214 This will occur gradually and in a piecemeal fashion: spoofing has been illegal in the US since 2010, while it was still being executed by European banks in 2018. 215 The points outlined in this thesis are intended to encourage further research. Since many trading algorithms and a large number of strategies exist that are the subjects of current research and development, they represent an issue of major importance for capital markets. In order to get a clearer view of AT's influence on liquidity and especially volatility, studies about the market movements during the COVID-19 pandemic would be pertinent. This would enable algorithmic traders and investment firms to develop their algorithms further to ensure positive impacts on market quality. In order to decrease the risk of market manipulation and increase the transparency of trading, research and development of the connection of AT and blockchain technology is purposeful with the aim of reproducing the chain of trades and increasing transparency. 216

Declaration of Honor
I hereby declare that no part of this work has been submitted in support of another module, degree, or any other qualification at the HTWK Leipzig or any other university or institute of higher education. I confirm that the work presented has been performed and interpreted solely by me except where explicitly identified to the contrary. Any use made of the works of other authors, in any form (e.g. ideas, figures, text, tables, etc.) have been properly cited and /or acknowledged.