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The Impact of High-Frequency Trading on Market Quality in the
European Futures Market
Thesis
Master of Science in Business Administration
Specialization: Finance
University of Groningen Faculty of Economics and Business
Author: F. Rijlaarsdam*
Student number: 1657364 Supervisor: dr. P. Smid Submission: May 6th, 2013
* I would like to thank my Thesis supervisor at the University of Groningen, dr. Smid, as well as my supervisors at Eurex, Bernard Hosman and dr. Wolfgang Eholzer, for their support, encouragement and feedback during the process of writing this
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ABSTRACT
Recently, ‘High Frequency Trading’ (HFT) has drawn negative attention from regulatory authorities, politicians and participants within the financial industry. At the same time the involved parties are not aligned on the definition of the term itself or on the (regulatory) changes, if any, to make to the trading
environment. In order to shed some light on the practices and effects of traders using fast infrastructures to deploy their strategies, this study investigates the effects of high-frequency trading
on the European futures market by looking at the three components of market quality that are most used in market microstructure literature: price formation, (order book) liquidity and market volatility.
A dataset provided by Eurex, the derivatives trading platform of Deutsche Börse AG, allows me to directly distinguish between high-frequency and non-high-frequency participants. Using this dataset, I find that participants in the HFT group generally contribute to market quality, as they allow (privately) informed traders to ‘infuse’ their knowledge into the market (-price) by taking the opposite side of trades. Furthermore, I find that HFT participants are relatively less involved in initiating trades in the
direction of large price moves, disproving the often heard argument that HFT activity causes excess volatility.
JEL CLASSIFICATION
D40, D53, G12, G13, G14
KEYWORDS
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Table of Content
I.
Introduction
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II.
Literature review
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2.1. Theoretical overview 2.1.1. Price Formation 2.1.2. Market Liquidity 2.1.3. Market Volatility 2.2. Previous empirical results
2.2.1. Results on high-frequency trading 2.2.2. Results on algorithmic trading
2.2.3. Results on the May 6, 2010 ‘Flash Crash’ 2.2.4. General Implications for Market Quality
III.
Data
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3.1. Data sample
3.2. Descriptive statistics
IV.
Methodology
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4.1. Measuring Contribution to Price Formation 4.1.1. Impulse Response Functions
4.1.2. Variance Decomposition 4.1.3. Data preparation for testing 4.2. Measuring Liquidity Provision 4.3. Measuring Impact on Volatility
V.
Results
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I. Introduction
The last decade has been one of tremendous alterations in the way securities markets operate as open outcry markets have evolved into highly automated and electronically supported markets. The ‘Markets in Financial Instruments Directive’ (MiFID) rules of 2007, applicable to investment firms and exchange platforms, fragmented the European equity markets (most shares now trade on multiple exchange platforms) and increased transparency. The MiFID rules require exchanges (and multilateral trading facilities) to display the best prices and the (aggregated) quantities available on their platform directly to the outside world, as well as to report executed trades. These MiFID rules thereby broke the monopoly of traditional exchanges and paved the way for alternative electronic trading platforms, which were often founded by consortiums of clients of the traditional exchanges. Technologically advanced trading platforms gained market share rapidly, leading to a network of linked electronic exchange platforms and an increase in automated trading. Automated traders use the variety of platforms to assess the best prices, and seek for arbitrage opportunities between the platforms. Automated trading systems are now used in up to 70% of all executed trades (Gomber, Arndt, Lutat, & Uhle, 2011).
The widespread term used for automated trading is algorithmic trading (AT; ATs will be used to refer to algorithmic traders). Algorithmic trading systems are used for the optimal timing of portfolio management decisions; they break up large buy or sell orders and decide when, where (on which venue) and how much to execute (Hasbrouck & Saar, 2011). The main advantages of AT are the reduced costs of trading (efficiency gains) and increased accuracy, i.e. the ability to trade in several fast moving markets at the same time. High-frequency trading (HFT; HFTs will refer to high-frequency traders), is as a subset of AT, and involves algorithms that make autonomous trading decisions at high speed. These algorithms are ‘event’ based: they are triggered by market events without upfront planning towards volume, time or direction (Hasbrouck & Saar, 2011). HFTs typically hold positions for a relatively short time –ideally (milli-) seconds to minutes– and do generally not hold positions overnight, to reduce inventory risk1. In that sense, HFTs can be seen as middlemen rather than ‘end-consumers’; after a day of trading, assets will be in the hands of those that will hold them for ‘investment’ rather than ‘trading’ purposes. Despite these (often) common characteristics, it is important that we do not see AT and HFT as strategies, but rather look at them as technological advancements in trading. HFT firms have technological infrastructures that help them participate in heavily contested trading opportunities, but these strategies are not fundamentally different from other participants’ strategies. Furthermore, the fact that firms try to use information-timing asymmetries to their advantage is not new; competition to be the first to receive and act upon
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information dates back to the first stock exchanges2. Recently, the Commodity Securities Trading Commission (CFTC) and its Technical Advisory Committee defined HFT as a subset of AT, based on infrastructural and messaging characteristics, such as co-location3, high speed (e.g. glass fibre) connections and a high number of orders intra-day4. I will follow this definition of HFT throughout this study.
AT, and HFT in particular, have long enjoyed very little public attention. Recently however, there has been a radical change in public involvement in the matter, mainly due to market structure disruptions like the so-called ‘flash crash’ on May 6th 2010. That day, the Dow Jones index dropped roughly 1000 points (9%), to recover to its previous level within 30 minutes. The initial public reaction was to blame HFTs for this crash, although general knowledge about these firms and their behavior was minimal, certainly at the time. The Securities and Exchange Commission (SEC), that took more than half a year to investigate and publish what happened in this one hour of trading, concluded that HFTs were not to blame for starting the crash. Despite the findings from the SEC, since then most market structure disruptions have been publicly attributed to HFT. This resulted in numerous social and regulatory debates regarding the effects of the (rapid) developments in market structure and how to regulate financial markets. The fundamental questions underlying the current debates concern the effect of algorithmic and high-frequency trading on the quality of financial markets, and in particular the benefits of the current market structure to society i.e. the end-investors (‘buy-side’). In line with these uncertainties, debates and concerns, the most important question to be addressed in this study is: ‘What is the effect of high frequency trading on market quality in the European futures market?’
One of the most significant proposed ‘solutions’ to the issues raised before, has been the financial transaction tax (FTT), a tax on financial asset trading, ranging from 0.1% on the value of equity- to as low as 0.01% on the value of derivatives-transactions. Another popular imposed measure is the so called ‘minimum order resting time’, where orders submitted to the order book cannot be modified or cancelled for a minimum amount of time5. Measures such as FTT and minimum order resting times are currently under vote in the European Parliament to be included in MiFID II6 rules though there is no clear consensus on both the desirable and presumable outcomes of such measures, not in the least because of a lack of available data. A rather small group of academics and governmental organizations have studied the impact of AT, HFT, or specifically the May 6th flash crash, but as most HFTs are proprietary traders, they are (understandably) reluctant to hand out trading details and/or other
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For example: trained pigeons used to spread news to investors, a flag-signing system set up by investors between New York and Philadelphia and the development of ever faster stock market ‘tickers’.
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Co-located firms servers’ are located in the same building as the exchanges’ matching engines; they use the fastest means of information-transporting and are therefore able to achieve the lowest possible latency. Exchange members can subscribe for example to co-location, the fast infrastructure and low latency data-feeds.
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http://www.securitiestechnologymonitor.com/news/hft-defined-by-cftc-as-subset-of-automated-trading-31398-1.html
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The current proposal is a minimum order resting time of 500 milliseconds. One millisecond is one thousandth of a second.
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strategic information. These ongoing debates and issues around our financial markets have so far been mainly political and emotional rather than rational and factual; providing regulators, academics and society with more knowledge on HFT and current (derivatives) market structure might aid future regulatory decision-making.
Where AT is aimed at the efficient execution of (client-) orders, HFTs have in common that latency plays a crucial role in the profitability of their proprietary7 strategies (Brogaard, 2010). Latency is here referred to as the time t it takes for new market information, generated at the exchange at time T, to result in an transaction8 that reaches the matching engine of the exchange at time T + t. For the fastest participants, the sum of these latencies is typically well below one millisecond. HFT firms therefore tend to invest heavily in their technological infrastructure. In order to handle these low latencies, most of today’s exchanges facilitate an electronic limit-order book, in which market participants can submit either limit-, or market-orders. Once submitted, limit-orders rest in the limit order book until they are changed, cancelled or executed, while market orders are orders to buy (sell) at or above (below) the prevailing best ask (bid) price. The submission of a limit-order that rests in the order book is referred to as liquidity9 supply10, trading against these ‘resting’ orders as liquidity demand11. Execution priority within the order book is often based on a price/time priority principle: the first participant to submit its order at a certain price is the first in line in case of a match at that price; hence the importance of latency. All market participants will form an opinion on the price of an asset, and price equilibrium will stem from these opinions. Typically, the orders that are resting in the limit order book are not submitted at the equilibrium price, but will be posted around it. The liquidity providing (market-making)12 participants posting these orders are consequently committing firm resources to trade, thereby inter-mediating the unsynchronized arrival of buyers and sellers. As a compensation for their passive behavior in the order book, market-makers are willing to buy at prices lower than the equilibrium price and sell at a higher price. These resting orders make it possible for other market participants to immediately trade at any point in time, and thus provide profit opportunities to those that demand liquidity13. If the market’s opinion on the price equilibrium moves enough, some of the resting orders can become mispriced. Depending on the magnitude of the mispricing and the sensitivity of the market participants to the price move, some market participants, mainly
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HFT firms tend to trade with their own resources and have no clients or outside shareholders and are thus ‘proprietary’ firms. They do not have to disclose key strategic information to the outside world.
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In this study ‘transaction’ can refer to multiple messages: e.g. add, update or cancel a limit-order.
9 In trading, liquidity is defined as the number of buy and sell orders (number of contracts) in the limit order book, combined
with the magnitude of price differences between these orders.
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Liquidity supply will also be referred to as ‘passive’, ‘market-making’ or ‘providing’ behavior. These definitions will be used inter-changeable throughout this study.
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Liquidity demand is seen as ‘aggressive’ or ‘initiating’ behavior. These definitions will be used inter-changeable throughout this study.
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I will use market-making and liquidity providing interchangeably in this study.
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arbitrageurs14, may try to take advantage of this situation while most of the liquidity providers will try to prevent them from doing so at their cost. As indicated above, market participants, and therefore HFTs, use different strategies and one firm is not restricted to a single strategy. MacKenzie et al. (2012) state five main HFT strategies based on interviews with market insiders: electronic market-making, cross-market arbitrage, statistical arbitrage, order-anticipation and momentum ignition. Market makers quote on both sides of the order book, thereby earning the spread. Arbitrageurs try to profit from discrepancies between markets and/or products, order anticipation is focused on the prediction of arrival of orders that move the price, while momentum ignition is focused on trading in the direction of the price move. HFTs operate mainly as market makers under a very small margin; due to the high level of competition they earn fractions of basis points on each trade (Menkveld, 2012). Executing a large number of trades and quick order updating is essential in recovering their fixed investments and reducing their spread; not being able to trade according to the existing boundaries will disproportionally affect them. Therefore, apart from the discussion on the justification or issues regarding the implementation, any regulatory restriction will very likely have a tremendous effect on the (electronic) trading landscape.
Market quality is mainly based on an assessment of the fairness of prices, the equality of information, the risk of possessing assets and balance between supply and demand. HFTs are said to disturb the market by manipulating prices, supply & demand conditions and consequently the risk of possessing an asset. Debates around HFT relate closely to topics such as ‘quote stuffing’, ‘spoofing’ and ‘front running’, which have a negative impact on market quality15
. This study’s focus is not mainly on identifying potential abusive behavior of one single firm, but on general market quality. Basis of the analyses is the fact that, due to HFT, short lived trading opportunities are spotted and acted upon and that this development might have impact on market quality. If prices are able to reach equilibrium faster and liquidity in the order book is enhanced, this might be a beneficial development. On the other hand, computerized trading is not without risk: the speed and number of transactions with which participants react on news (a change in the state of the limit order book could be seen as new information) makes diligent risk management key to the success of both the individual participants and the market as a whole.
There are many examples of sectors/markets that experienced similar (technological) development as financial markets have in the past years; steps forward suddenly become leaps forward. This process is often paired with incumbents’ resistance against - and unfamiliarity of regulating authorities with - the
14 Arbitrageurs spot differences between quoted prices and the ‘real’ price, and try to take advantage of these (short-lived)
opportunities.
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new situation. It is this unfamiliarity that can cause fear towards -and a tendency to resist- innovation that is not commonly adopted. On this note, it is revealing that major regulatory organizations like the European Securities and Markets Authority (ESMA), Commodity Futures Trading Commission (CFTC) and SEC only started to define HFT and implement market-monitoring a few months rather than years ago.
To answer the main research question proposed above, I will use a unique dataset provided by Eurex. This dataset will separate aggregate HFT and non-HFT participants’ activity in the ten best prices available in the limit order book on a per second basis, as well as HFT and non-HFT involvement in trades. To that end, Eurex developed a methodology to classify participants on their platform as HFT participants, and based the separation between HFT and non-HFT on that classification. The features of the futures market -standardized, liquid and without physical delivery- are likely to attract a high share of HFT firms, since most of their strategies are driven by high liquidity, high volumes and standardization. This makes the futures market particularly suited for an analysis on the relationship between HFTs and market quality. I will assume price discovery, liquidity and volatility to be the main variables in assessing market quality. The future on the Eurostoxx50 index is very suited for analysis, as it is one of the most liquid on-exchange traded products in Europe and the underlying index components are also traded at Deutsche Börse AG. To quantify the market quality variables specified above I will make use of existing theoretical frameworks developed in academic literature. To assess the contribution of HFTs to price formation, I will use Hasbrouck’s (1995) price impact framework, based on participants’ involvement in trades. To examine liquidity I will have a look at the width of the bid-ask spread, depth and resilience of the order book, with and without HFT participants. Lastly, to examine whether there is a relationship between HFT and intra-day volatility, I will use a realized volatility measurement with and without (aggressive) HFT participation (Aït-Sahalia, Mykland, & Zhang, 2011).
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II. Literature review
This study is one among a small but growing number of studies on automated trading -HFT in particular- and its effects on market structure. Most studies focus on automated trading, without distinguishing AT from HFT (e.g. Chaboud, Chiquoine, Hjalmarsson, & Vega, 2009; Hendershott & Riordan, 2012), some studies use proxies for HFT (e.g.; Zhang, 2010; Hasbrouck & Saar, 2011) and others study the 2010 flash crash (e.g. Kirilenko, Kyle, Samadi, & Tuzun, 2011). One exception is a study by Brogaard (2010): using explicit HFT data from NASDAQ he studies the effect of HFT on the US equity market quality. To formally introduce the subjects assessed and tested empirically in this study –price formation, liquidity and volatility– I will first provide a theoretical overview of the existing literature on these market-microstructure variables. Thereafter I will provide the reader with previous empirical results regarding these subjects.
2.1. Theoretical overview
2.1.1. Price formation
One of the main functions of a market is its contribution to price discovery; “the impounding of new information into the security price” (Hasbrouck, 1995, p.1). However, “the process of trading itself may generate price movements because of various market imperfections and frictions” (Madhavan, Richardson, & Roomans, 1997, p.1). Price formation and price impact, the quantification of price movements over time, are strongly linked with information flow. Information in the stock market can be categorized as either public or private information (Vega, 2006). If asymmetries between public and pivate information are suspected but not (yet) revealed to the market, traders will act upon their premises of these asymmetries. Froot et al. (1992) model such behaviour: in their model, speculators in search for information do not put enough weight on fundamental value. The speculators will ‘bet’ on movement direction, and the liquidity providers will adjust their bid-ask spreads to avoid adverse selection16, thereby reducing price efficiency (Hasbrouck, 1991).
Public information is often presumed to lead to normal (anticipated) price movements, and it is thus the private information that leads to excess (unanticipated) buying or selling pressure, or ‘abnormal order flow’ (Hasbrouck, 1995; Vega, 2006). In a market where market-makers intermediate between buyers and sellers with different arrival times, one sided (excess) pressure leads to price movements as market-makers demand a premium for the higher inventory risk. The relationship between such order imbalances and price formation is well documented in academic literature (e.g. Blume, MacKinley, & Terker, 1989; Chan & Fong, 1999; Chordia, Roll, & Subrahmanyam, 2002).
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Glosten & Milgrom (1985) introduce a model in which the arrival rate of (privately) informed investors is closely related to the size and movements of the bid-ask spread, and hence to price formation. In their model, ask (bid) prices are set to reflect “both current information and information that will be inferred if the next customer is a buyer (seller)” (Glosten & Milgrom, 1985, p.73). We can assume that, if prices move, these boundaries have to be re-set again. In the meantime, liquidity providers run great risk of being adversely selected. A market development that is highly linked to a more efficient price formation process but also induces more adverse selection risk is the cutback of tick sizes17 over time. This fosters opportunities to decrease spreads and make prices more informative, however less new information will force prices to move (one tick), resulting in a higher risk of adverse selection for liquidity providers. Roll (1984) identifies the microstructural noise associated with this behavior: efficient prices are not visible and bid-ask spreads are subject to a so called ‘bid-ask bounce’18. He therefore suggests using ‘mid-quotes’, the mid-price between best bid
and ask prices, as the best proxy for the efficient price. The bid-ask spread can then be seen as the uncertainty parameter surrounding that efficient price that liquidity providers face.
Based on the assumption that private information is fully disseminated into market prices over time, one of the main theories on information in asset prices is developed by Hasbrouck (1991). In his study he assesses the amount of information in trades by means of a ‘permanent price impact’ framework, where information is incorporated in the price of an asset over time. Trades are compared to assess which trades add to actual price formation, and which trades are ‘noise’. Brogaard (2010) uses this model to assess HFT versus non-HFT permanent price impact, and therefore their respective contributions to price discovery. Trades with significant permanent price impact will contribute more to price discovery than trades with transient price impact; transient impact is likely to reflect the beliefs of uninformed investors. Hendershott & Riordan (2012) assess the relationship between HFT, transitory and permanent prices using a state space model, in which stock prices are based on a permanent and a transitory component. In their model, traders associated with transitory price components could have a higher need for portfolio rebalancing, or they could manipulate the market on short time intervals. Trades associated with permanent price impact however contribute to price formation and market quality.
Contrary to liquidity demanders (which either have private information or not), we would generally expect liquidity suppliers to be involved with both informed and non-informed traders. Liquidity providers have orders that are visible in the order book and therefore make their (private) information visible to the outside world. Potential counterparties can assess these orders and potentially adjust their
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The lowest increment by which asset prices can fluctuate (in euros).
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opinion. By definition, a liquidity provider is passive, i.e. he does not have the ability to exclusively pick uninformed traders as their counterparty, because the counterparty can pick him. According to multiple authors however, HFTs pull back their liquidity from the order book upon (before) informed investor arrival (e.g Zhang, 2010). If HFTs indeed pull back upon informed investor arrival, we can expect HFT traders to supply less liquidity in trades which have a permanent price impact.
2.1.2. Market liquidity
Arguably the most important function of the market is the actual meet of supply and demand. The availability of buy and sell orders visible in the limit order book is referred to as liquidity. Liquidity suppliers submit limit-orders to the order book, where liquidity demanders can access (hit) them. The demand for liquidity can be described as demand for immediacy; an order is executed directly against the current best price available in the order book (Grossman & Miller, 1987). In current market structure the liquidity provider/supplier is rewarded for its (counter-) part of the immediacy by the liquidity demander. The size of this reward is based upon two dimensions; width and depth of the order book. The bid-ask spread determines the ‘width’ of the price premium paid for immediacy (e.g. Brogaard, 2010; Hendershott & Riordan, 2009), while the number of contracts available typically determines the depth of liquidity, i.e. an indication that the average cost of liquidity rises with an increasing number of contracts (Hasbrouck & Saar, 2011). Harris adds (1990) another dimension to liquidity, resiliency, the time it takes for markets to correct to efficient prices after a liquidity shock. With a large amount of ‘impatient’ traders in the market, Foucault et al. (2005) assume market resilience to be lower and spreads to widen. In this case, investors might give immediate execution higher priority than price efficiency. Doing so will lead to temporary over- or underestimation of the efficient price of a security, possibly resulting in more uncertainty and liquidity providers widening their spreads. In general it can be stated that a lower spread, a higher number of contracts close to the midpoint and a high level of resilience to liquidity shocks are beneficial to market quality.
The provision of liquidity is risky. Adverse selection risk and inventory risk are borne by liquidity providers, while the reward usually consists of a few basis points per trade. In that sense, the amount of liquidity provided in the order book is based on an assessment of uncertainty in the market. Therefore, total liquidity will tend to be relatively high (abundant) in ‘normal’ markets, while it will be relatively low (scarce) in volatile, uncertain, markets (Hendershott & Riordan, 2011). However, highest need for immediacy occurs during volatile periods, when prices move and liquidity is relatively expensive. This correlates with the previous section on price impact: a higher ratio of new information generally leads to more risk and less liquidity provision. With few liquidity providers in the market the best price levels19 will be taken out more quickly, resulting in larger price up- or
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swings, implying higher uncertainty and trading costs for liquidity demanders (Domowitz & Wang, 2002). Liquidity provision at these moments will dampen these price swings and is highly beneficial to market quality. It is also important to examine who provides the liquidity; as risk is higher for liquidity providers compared to liquidity demanders, the former may seek protection from that risk through means of HFT (Jovanovic & Menkveld, 2011).
By measuring the spread –distance between best ask-price and best bid-price– the width component of liquidity can be assessed; this gives the immediacy20 premium of trading one contract. In order to assess liquidity depth there are two widely accepted measures: the number of contracts up to x ticks from the best bid or offer and a framework to measure the average price impact of trades (done for different trade sizes) (Hasbrouck & Saar, 2011; Brogaard, 2010). The latter measurement has the advantage that it can take into account both the widening of the spread and the availability of contracts when trade sizes larger than the depth on the best-bid or best-ask price alone hit the market. This measure was developed by Gomber et al. (2011) as the ‘Xetra Liquidity Measure’ (XLM). Multiple amounts of euros can be used to measure the impact of small, medium, and large trades on the order book. To measure resilience, constructing a window of best bid (ask) updates before and updates after a trade can be used to study the development of prices, spreads and depths around trades (Degryse, de Jong, van Ravenswaaij, & Wuyts, 2005).
2.1.3 Market Volatility
Asset pricing theory states that asset prices should follow a stochastic (Markov) process in which previous asset prices do not have influence on future prices. Asset price returns consist of two components: a ‘drift rate’, which is the expected (long term) return, and a ‘shock’ rate, which is the (short term) deviation of the asset price from the drift rate. The shock component is not constant, but depends on the arrival timing of new information in the short run. Evidence suggests that, in the long run, the shocks revert to the (mean) drift rate, and therefore asset prices depend on the drift rate rather than the shocks (Lee & Engle, 1993). These shocks are better known as the standard deviations of return, or volatility, which is the uncertainty component of an investment; the higher the volatility, the more future returns can deviate from expected future returns (Merton, 1976).
From this we can infer that, when looking at low-frequency21 data, returns will revert to their long-term mean. If we look at high-frequency data however, the drift rate is virtually equal to zero and all changes in asset prices will therefore stem from shocks. These shocks mainly exist due to unstable conditions of supply and demand, which are often clustered around the disclosure of new information to the market. As HFTs do generally not hold positions overnight, for every contract bought by an
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Instead of submitting the contract to the book on the other side, the choice is made to execute immediately, effectively paying the spread.
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HFT there will be a contract sold by that HFT and vice versa. Therefore, HFTs will only have an opinion on an asset’s value on a timescale shorter than the business day. To that extent, we will focus on the relationship between HFT and volatility in very short timeframes and expect the drift rate to be zero.
HFT might increase (short-term) volatility if the arrival of investors with the same beliefs -and therefore temporary supply and demand inequalities- are more concentrated than without HFT activity (Maheu & McCurdy, 2004). The above stated can hold, as many HFTs have the ability to react within a millisecond timeframe. The best measurement for volatility on such a short-term level would be tick-by-tick realized variance (RV). To estimate RV, one would sum up all squared differences between lognormal returns; ∑ where r could be the trade-price or the mid-quote price returns (Hansen & Lunde, 2006). Unfortunately, measuring volatility in time-frames of seconds –or even minutes– proves to be biased: efficient prices are never ‘real’ but based on spreads, tick sizes are not infinitely small and trading is auto-correlated in the short run (Aït-Sahalia, Mykland, & Zhang, 2011). To estimate volatility on such short timeframes it is necessary to account for the kind of microstructural biases mentioned above. To overcome this problem, Aït-Sahalia et al (2011) provide a general model that combines (averaged) realized variance measured on a short timeframe and (averaged) realized variance measured over a longer timeframe to overcome microstructural noise when measuring volatility. Barndorff-Nielsen & Shephard (2002) use realized kernel estimators with a Kalman filter to overcome biased estimations of volatility. Both studies conclude that accounting the RV for microstructural bias yields a better and more stable estimate of short-term volatility.
When focusing on volatility based on short-term supply and demand inequalities, which is asset pricing noise that is detrimental to market quality, the importance of liquidity provision becomes clear. As stated before, liquidity providers accommodate the asynchronous arrival of (opposite) investors in search of an immediate execution. Therefore, liquidity providers dampen some of the supply and demand inequalities that cause short-term volatility. Supplied contracts that were traded will enhance market quality, as there clearly was a demander in need for that contract.
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2.2. Previous empirical results
2.2.1 Previous studies on high-frequency trading
Using quarterly data from CRSP and Thomson Reuters Institutional Holdings, ranging from 1985 to 2009 and defining HFT as “all short-term trading activities by hedge funds and institutional traders not captured in the 13f database22 ”, Zhang finds that HFT contributes to excess volatility and is detrimental to price discovery (Zhang, 2010, p.14). After running regressions using stock price fundamental volatility drivers as controls he finds that HFT is positively correlated with stock price volatility. Furthermore he finds that the market overreacts to firm fundamental news when there is more HFT trading. Initial price changes then reverse in subsequent periods. Egginton et al. (2012) find that episodic spikes of order updating, associated with degraded liquidity and elevated short term volatility, are caused by HFT trading. They use NYSE trade and quote data to identify periods of low-latency trading where frequent updates are a proxy for HFT ‘quote stuffing’. While unnecessary quote stuffing is detrimental to market quality, frequent updating is used in volatile times to reduce adverse selection and inventory costs. Brogaard (2010) finds that HFT traders (in the US) add substantially to market quality, particularly price discovery, by frequently trading inside the bid-ask spread. The depth of liquidity they provide in the order book is mixed; HFTs try to avoid trading with informed investors. Using the 2008 short-sale ban as an experiment, and hypothetical price paths as proxies for HFTs’ influence on volatility, he finds that intraday volatility can be dampened by HFT. HFTs supply more liquidity if short term volatility is higher, and less if long term volatility is high. Overall he concludes that HFT benefits market quality.
2.2.2. Previous studies on algorithmic trading
Boehmer et al. (2012) use an international dataset based on intraday equity quotes and trades from the Thomson Reuters Tick History (TRTH) and find that AT adds to liquidity and improves price formation. The volatility increase they find is merely due to more (detrimental) noise, and not the result of higher price efficiency. When tested for days on which market making is hard they find higher price efficiency, but also higher excess volatility and a lower level of liquidity in the market. Overall they conclude that liquidity and price efficiency generally benefit from AT, while intra-day volatility is systematically higher. Hendershott et al. (2011) prove, using New York Stock Exchange equity data, market quality is improved by algorithmic trading if the traders using these systems both demand and supply liquidity. Chaboud et al. (2009) study the impact of AT on market quality in the
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foreign exchange market. They use Electronic Broking Services (EBS) data to assess price discovery, liquidity and volatility. According to their study, AT strategies are more correlated than non-AT strategies, but this is not negative; AT reduces volatility. They find that liquidity is provided by ATs, even in times of highly stressed markets. However, non-ATs are more informed and contribute more to price discovery than ATs.
Hasbrouck & Saar (2011) use NASDAQ data, containing all orders, to define ‘strategic runs’ -linked submissions, changes and cancellations with short intervals- to measure the impact of low-latency trading on market quality. They find that, in general, low-latency trading adds to market quality. Low latency traders add to liquidity and price discovery, but the study also finds that the speed advantage corresponding to low-latency trading might impose costs for other market participants. The increase in intermediation they found may or may not be beneficial to market participants, depending on their need for execution immediacy. In the end, the authors are not certain that, in the current framework, long-term investors benefit from low-latency trading activity. Jovanovic & Menkveld (2011) study middlemen in limit-order markets. Their study assesses one electronic market-maker active on two platforms: Chi-X and Euronext. They find that this market-maker uses HFT in order to minimize adverse selection risk, i.e. to (re)submit their quotes in the order book first in case of a price change.In general, they find that HFT technology might be used to reduce adverse selection risk, i.e. fast adjustments of (market-maker) bid-ask spreads, or to exploit such adverse selection opportunities.The first is associated with positive externalities, as it is in general good for a market if he weak party (liquidity provider) has a mechanism to protect itself. The second point raised above however, might force market-makers to widen their bid-ask spread as the risk of adverse selection increases.
Hendershott & Riordan (2011) find, using data from Deutsche Börse AG, that AT consumes liquidity when it is cheap and provides liquidity when it is expensive23. They find no evidence of AT contributing to volatility, but remark that studies seperating HFT from AT (or rather separate each strategy) should be conducted. Furthermore they conclude that ATs contribute more to price discovery than human traders do, because of their constant information monitoring.
2.2.3. Previous studies on the May 6, 2010 ‘Flash Crash’
Kirilenko et al. (2011) state that HFTs have a trading pattern that differs from the traditional definition of market making: HFT liquidity providers will exacerbate price movements by aggressively trading in the direction of the movement. They argue that markets become fragile if liquidity providers can withdraw from the market when large liquidity demanders step in. They hold HFTs accountable for the fast and large decline on May 6; their algorithmic models would have reacted by removing liquidity from the market. The Securities and Exchange Commission (SEC), which fired up
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investigation following this event, found that HFT traders had been supplying liquidity to the market at first, thereby dampening the price swing. However, market conditions during the crash were said to be so unique that some algorithms’ risk evaluation systems decided that market data was out of normal bounds and therefore shut down trading, mainly due to the (obliged) risk systems these traders have installed. Unlike the stock market crash of 1987, where brokers and market makers deliberately stopped trading and recovery took over one year, the SEC also found that HFTs were the main contributors to the fast recovery of the market. After a short complete stop of trading24, giving all participants (including non-HFTs) time to restructure their models and assess market conditions, prices reflected ‘normal/expected’ levels within half an hour.
2.2.4. Previous studies on implications for market quality
Given the theoretical models and empirical findings in this chapter we can expect HFT to have impact on market quality. Overall, these studies find mixed results on the influence of HFT on market quality, mainly depending on the (granularity) of the datasets and which factor(s) of market quality is weighted most. Findings suggest that HFT contributes to price formation by actively monitoring, updating and searching for information. However, they will mainly do so by looking at publicly available information. Therefore, when looking at liquidity demand in the market, I expect HFTs to have less private information inferred in their (initiated) trades.
‘Trades initiated by HFTs provide less private information to the pricing process than trades initiated by non-HFTs.’
Among some authors, there is belief that HFT firms tend to revoke their liquidity when dealing with informed traders, thereby hampering price formation. I will test this statement in Chapter V.
‘HFT firms supply less liquidity to relatively informed traders.’
After assessing private information in trades, I will study whether this private information is directly responsible for (permanent) price movement. Based on the fact that most non-HFT business models depend on long term information, I expect that non-HFTs are responsible for more of the permanent price moves and therefore contribute more to price formation.
‘Non-HFT firms contribute more to overall price formation than HFT firms do.’
Liquidity provision is generally seen as the most important determinant of market quality and is an attribute often propagated by HFTs. According to previous literature and results, HFTs do contribute to liquidity but there is no clear consensus on the overall benefit of this liquidity provision. I will first
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check whether the withdrawal of HFT liquidity from the order book will have a significant effect on the cost of trading, which I expect will be true.
‘There is significant price impact for incoming orders when HFT liquidity is removed from the order book.’
Next, I will directly compare the impact of HFT versus non-HFT liquidity providers on the cost of trading.
‘HFT firms contribute more liquidity to the order book than non-HFT firms do.’
The relationship between volatility and HFT remains ambiguous: depending on the timeframe-selection and available data the results suggest that HFT may dampen, exacerbate or have no significant influence on volatility. I will assume that liquidity providing HFTs can have either no effect, or a positive effect on intra-day volatility: if they would all fully withdraw liquidity, there would be no effect of liquidity providing HFTs, while any supplied contract can reduce the supply and demand inequalities that cause intra-day (excess) volatility. Therefore, I will focus on any negative effects that liquidity demanding HFTs might have.
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III. Data
This chapter describes the data source, data-sample selection process, overall content and the descriptive statistics of the data used in this study.
3.1. Sample Data
To analyze the proposed hypotheses, I will use a unique dataset provided by Eurex®, containing book-updates and trades on the ‘future on the EuroStoxx 50 Index’ (symbol: FESX) contract. The data available for this study ranges from September 3rd, 2012 to September 14th, 2012. This sample was arbitrarily chosen due to the fact that it did not contain any special events but it contained business days with diverse, non-extreme characteristics. Furthermore, we will focus mainly on intra-day market microstructure, which is less dependent on long term macro-economic factors. I will look at the first-expiring (front-month) contract, as this is the most liquid one; virtually all trading (activity) occurs in this contract. The order book data sample is made up of intra-day, one second snapshots of the limit order book, containing the ten best prices and sizes on both sides of the book. Order adds, modifications, deletes and the traded quantities are aggregated within the second, and shown as mutations in that seconds snapshot. Next to that, the per-second order book modifications are split for HFT and non-HFT activity25. Every change to the order book can therefore be explained by the liquidity provision (mutations) of HFT and non-HFT participants on a per-second basis. The firms that are classified26 as HFT are selected by Eurex® based on their knowledge of the market, market participants, the participants’ infrastructures and their trading behavior. Based on these characteristics, Eurex has developed an HFT selection method which compares true inter-arrival rates of technical transactions with expected inter-arrival rates. The list includes proprietary trading firms only and therefore might exclude high-speed trading desks of banks and orders routed through brokers27. As can be seen in the next section, these selected HFT firms represent 40% to 50% of all trading, which is comparable to the figures given by e.g. Swinburne (2010) for the European market.
However, snapshots of the order book do not provide a full understanding of market behavior. It is important to know which part of orders that are ‘removed’ from the order book is caused by trades, and which part by modifications/deletes. The trade data sample, provided for the same window, is time stamped to the microsecond, and contains: the trade price, the ‘side’ of the order book the incoming order matches against28, and both HFT and non-HFT contributions to either side of the trade29. It
25
See Appendix A for an example of the order book data used in this study.
26
Classification as an HFT is subject to change, as the selection is revised on a continuous basis to account for market structure changes. The firms in this sample were classified as HFT on September 1, 2012.
27
The customer order flow and proprietary order flow of banks are separable, but doing so would complicate the data gathering to a significant extent. Clients routing their orders through a broker’s infrastructure are not directly visible in the data, and therefore brokers are excluded.
28
In case a market participant sends a market order to buy (sell) futures, the indication will be “buy” (“sell”), and will match against the ask (bid) side of the order book.
29
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shows me which trades are initiated by HFTs and non-HFTs respectively, as well as the passive counterparties of these trades. This allows me to assess the impact HFTs and non-HFTs have on the limit order book as (passive) liquidity providers and as (initiating) liquidity demanders.
To process the large amount of data in the full sample of 10 trading days, I have written some scripts in the programming languages Python and Perl, in order to rearrange the data to a workable format for analysis30. The outputs of these scripts will be used to analyze the hypotheses formulated in Chapter II, with help fromEviews® econometric software.
3.2 Sample Data Descriptive Statistics
Panel A in table 1 contains the descriptive statistics of the data sample used to test the hypotheses in this study on variables such as the mid quote, daily volume, and daily number of traded contracts. Each statistic is based on a daily figure: in case of the mid quote, I took a daily average of the mid quote first, and compared the 10 daily averages (N) in the descriptive statistics below. The bid and ask sizes (in contracts) in panel A describe the average number of contracts available on the best bid and best ask prices respectively for each day in the sample. The days in the sample are various in nature, which makes this sample suited to investigate market quality in general.
Panel B in table 1 distinguishes between HFT and non-HFT participants and their contributions to trades. Again, these figures are a representation of daily averages. Average trades and contracts demanded, as well as the number of contracts supplied will add up to 1 (100%) for HFT and non-HFT. The (average) number of trades supplied is somewhat more complicated: as can be seen in Appendix A2, an initiating participant can execute against liquidity (in the book) partially supplied by HFTs and partially supplied by non HFTs. Therefore, these numbers have a maximum sum of 2 (200%). It follows from panel B that non-HFTs in this dataset demand more liquidity, both in terms of contracts as well in terms of number of trades. On the liquidity supply side things are rather equal between HFTs and non-HFTs.
30
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Table 1: Descriptive Statistics. Panel A describes the overall book and trade data for the whole sample of 10 days (September 3rd, 2012 – September 14th, 2012) including both HFT and non-HFT participation in the limit order book and trades. The table shows statistics over daily averages for the mid quote price, the bid-ask spread (in ticks, one tick is €10,-), the number of contracts on the best-bid price, the number of contracts on the best-ask size, the daily trade volume in contracts, the traded contract size (per trade), and the daily number of trades. Panel B shows daily statistics on HFT vs. non-HFT liquidity supply (S) and liquidity demand (initiated) (D). The participation of HFTs and non-HFTs in the number of trades and the number of contracts is given as a percentage of 1 (i.e. 1 = 100%).
Panel A: Book and Trade Descriptive Statistics
Mean Std. Dev. Maximum Minimum Skewness Kurtosis N
Mid quote (ticks) 2477.585 25.487 2514.660 2447.742 0.071 1.484 10
Spread (ticks) 1.013 0.005 1.025 1.010 1.662 4.707 10
Bid size (contracts) 553.314 33.934 588.295 472.408 -1.359 4.246 10
Ask size (contracts) 555.547 29.320 582.174 489.039 -1.236 3.581 10
Daily volume (contracts) 780187.200 308076.300 1164461 306397 -0.065 1.599 10
Trade size (contracts) 21.321 3.217 24.920 14.513 -1.074 1.058 10
Nr. of trades 36076.800 11705.820 47596 17197 -0.421 1.527 10
Panel B: HFT and Non-HFT Participation in Trades
HFT Mean Std. Dev. Maximum Minimum Skewness Kurtosis N
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IV. Methodology
This chapter lists the rationales and used formulas behind the empirical tests I will perform to come to a statement on the effects of HFT on market quality in the European futures market. Most of the concepts and equations are derived from previous studies as described in Chapter II. This chapter will also test the assumptions I make in order to get the data sample in shape to perform the outlined tests.
4.1 Measuring Contribution to Price Formation
4.1.1 Impulse Response Functions
I will use Hasbrouck’s permanent price impact model, discussed on Chapter II, to assess the contributions of HFT and non-HFT traders to price discovery. We can differ between price impact that is incorporated in prices over a longer period of time and has value, ‘permanent impact’ and a portion of price impact that is ‘transient’; only based on overreaction to new information. A larger permanent price impact will imply more private information in a trade. In order to assess this information we need a lagged framework for trades; that way we can test whether trades cause gradual implementation of new information, or overreact to that information. Price impact will be represented in basis points31 to allow (future studies) to compare between products. I have three variables in this model: ‘midpoint return’, ‘HFT-initiated’ trades and ‘non-HFT initiated’ trades. I will run three regressions based on these variables as indicated in Hasbrouck (1991), Brogaard (2010) and Hendershott & Riordan (2011), which together form a lagged vector auto regression (VAR):
∑ ∑ ∑ (eq. 1)
∑ ∑ ∑ (eq. 2)
∑ ∑ ∑
(eq. 3)
Where t is a time indicator32, i a specific lagged event, mid quote returns between events (measured as the difference between the mid quote in one trade and the next trade, independent of time), is ‘+1’ if an HFT is a buyer, ‘-1’ if an HFT is selling, and ‘0’ if an HFT is not involved and represents the same for non-HFTs. X is the total number (length) of events used in the impulse response function (variance decomposition) and are the errors, or noise components (Brogaard, 2010).
It is the noise component in the long run, or the (unexpected) permanent private information in the trades, that is the point of interest in this model, as that represents a permanent contribution to (previously unknown) price formation. In order to find this unexpected permanent price information, I
31
One basis point is 1/100 of one percent.
32
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need to estimate a Vector Moving Average (VMA) model by inverting (VAR) equations 1, 2 and 3. Using the VAR based on these equations, we can apply a Choleski decomposition to find the VMA model (equation 4). With help of equation 4, it is possible to find the impulse response functions for both HFT- and non-HFT initiated trades.
[ ] [ ] [ ] (eq. 4)
The vectors a(L) – i(L) in equation 4 are lagged operators (as: a(L) = ∑ , where is structural shock i (based on the values and correlations of α – φ in theVAR) and the operator moves the time index back by i). More specifically, b(L) and c(L) give the accumulated impulse response functions of HFT and non-HFT trading. The impulse response function describes the reaction of the variables to an exogeneous ‘shock’, i.e. a trade in this model, at the time of the shock and over subsequent periods. I assume that the expected (public) portion of information is fully reflected in the market at the time of the event, while the unexpected (private) information will be incorporated gradually to prices in later periods. To exclude the fact that the unexpected (private) information is only transient of nature, we have to look at relatively many events.
So far, I focussed on the impact of liquidity demanding traders to price formation. Since I want to analyze the contribution to price formation of liquidity supplying HFTs and non-HFTs as well, we can use the same method as the one used above and replace ‘HFT initiated’ and ‘non-HFT initiated’ trades by ‘HFT supplied’ and ‘non-HFT supplied’ trades respectively. More specifically, doing so would analyze whether HFTs (non-HFTs) deliberately avoid informed traders when supplying liquidity33, which would reduce the value of the provided liquidity. In order to perform this test, I assign passive HFTs and non-HFTs a value of ‘-1’ when buying contracts passively and a value of ‘+1’ when selling contracts passively34. The difference with the previous analysis on liquidity demanding traders is that there can be multiple liquidity supplying parties in one trade. Hence, there can be trades where both HFT and non-HFT liquidity suppliers will have a value of ‘-1’ or ‘+1’ 35. To compare the daily HFT impulse response function samples with the daily non-HFT impulse response function samples, I will use two-sample t-tests.
4.1.2. Variance Decomposition
While impulse response functions provide a good overview on which group inserts private information to the pricing process, they can not determine the importance of this information in the overall price-formation process. To find out more, I will use the VAR and the VMA frameworks defined in
33 By removing liquidity from the order book before the informed trade arrives.
34 If an aggressive participant buys a contract, there is another participant that is ‘passively’ selling a contract. 35
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equations 1, 2, 3 and 4 to ‘decompose the variance of the pricing process’, i.e. to determine for which amount each variable contributes to price formation.
I follow Hasbrouck (1991) and Hendershott & Riordan (2011), and assume the mid quote return to be: , where is a transitory component and is a random walk component.
is also referred to as the efficient price where = and
When defining , , as in the VMA model, the model for decomposition of variance is:
(∑ ) (∑ ) (∑ ) (eq. 5)
The first component, , corresponds to the the variance caused by lagged r (public information), is variance caused by HFT liquidity demand (or supply), and is given as the variance caused by non-HFT demand (or supply). The total of the three components determining the variance will sum up to 100 percent. I will use the same amount of lags as in the previous analyses on impulse responses in the variance decomposition models. Once I find the daily shares of variance for liquidity demanding (supplying) HFTs and non HFTs, I can use two-sample t-tests to check whether one group contributes significantly more to the price formation process than the other when demanding (supplying) liquidity. 4.1.3. Preparation for testing
To formally test hypotheses using the models described in the previous sections, I will first have to select the optimal number of lags to be used in the regressions of equations 1, 2 and 3, in order to correct autocorrelation in the data samples. Akaike’s Information Criterion (AIC) for lag length selection will be used; Ozcicek & McMillin state that the AIC yields the best outcomes when the selected lag is used in VAR models (Ozcicek & McMillin, 1999). The optimal lag lengths for the model when assessing liquidity demand for each trading day used in this study can be found in Table 2.
Table 2: Lag Length Selection for Liquidity Demand. Using Akaike’s Information Criterion, the average optimal number of lags over the ten sample dates is found to be 23 ‘events’. Therefore, I will use 23 lags as the lag parameter in equations 1, 2 and 3 when assessing price formation based on liquidity demand.
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Optimal Lag Length Selection
Date Optimal lag length AIC value Observations
03-09-2012 13 -13.76800* 17197 04-09-2012 24 -13.80991* 26226 05-09-2012 30 -13.73939* 38495 06-09-2012 21 -13.80377* 46724 07-09-2012 29 -13.96438* 45171 10-09-2012 20 -13.83261* 22717 11-09-2012 21 -15.07345* 47188 12-09-2012 22 -13.68851* 43072 13-09-2012 26 -13.99118* 26261 14-09-2012 24 -14.02351* 47596 Average 23 *optimal value
In order to do the test the hypothesis on the supply of liquidity to informed traders, we again have to select an optimal number of lags to be used in the regressions of equations 1, 2 and 3, which is done in Table 3.
Table 3: Lag Length Selection for Liquidity Supply. Using Akaike’s Information Criterion, the average optimal number of lags over the ten sample dates is found to be 19 ‘events’. Therefore, I will use 19 lags as the lag parameter in equations 1, 2 and 3 when assessing price formation based on liquidity supply.
Optimal Lag Length Selection
Date Optimal lag length AIC value Observations
03-09-2012 12 -13.345* 17197 04-09-2012 21 -13.401* 26226 05-09-2012 30 -13.427* 38495 06-09-2012 11 -13.429* 46724 07-09-2012 26 -13.595* 45171 10-09-2012 20 -13.395* 22717 11-09-2012 17 -14.419* 47188 12-09-2012 17 -13.390* 43072 13-09-2012 18 -13.626* 26261 14-09-2012 19 -13.710* 47596 Average 19 *optimal value
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for the impulse response functions to be 50 events36. X will remain the same (50) for all scenario’s tested (i.e. liquidity supply and demand in both impulse response functions and variance decompositions). The descriptive statistics for the daily outcomes of all scenarios can be found in Appendix B (Table 11).
After computing the values for the daily impulse response functions and variance decompositions using the variables given above, I have to check whether the assumptions of normality and equality of variance for the outcome samples (HFT and non-HFT) hold.
From Table 4 it is clear that all samples can be assumed to follow a normal distribution when measured using the Bera-Jarque test for sample normality. When looking at the results for Levene’s test for homogeneity of variance, the impulse response functions for liquidity demand and liquidity supply can be assumed to have equal variance. However, both samples involving variance decomposition show significant deviation of variances, which means that the sample variances cannot be assumed equal. In order to overcome the unequal variance, I will use the Satterthwaite-Welch t-test, which compensates for unequal variance when using the two-sample t-tests.
Table 4: Testing for Homogeneity of Sample Variance. Panel A in Table 4 tests whether the assumption of normality holds for all sample outcomes of both the impulse response functions and the variance decompositions using the Bera-Jarque test for normality. Panel B tests whether the assumption of homogeneity of variance holds. Levene’s test for homogeneity of variance is performed for all sample outcomes, comparing the HFT to the non-HFT outcomes.
36 This is approximately 10 seconds on average, and should be enough in order to exclude transient information.
Sample Bera-Jarque p-value
Impulse Response Functions HFT liquidity demand 1.605 0.448
Impulse Response Functions non-HFT liquidity demand 0.420 0.811
Impulse Response Functions HFT liquidity supply 0.402 0.818
Impulse Response Functions non-HFT liquidity supply 0.592 0.744
Variance Decomposition HFT liquidity demand 1.183 0.553
Variance Decomposition non-HFT liquidity demand 1.875 0.392
Variance Decomposition HFT liquidity supply 1.241 0.538
Variance Decomposition non-HFT liquidity supply 4.258 0.119
Sample Levene statistic p-value
Impulse Response Functions (liquidity demand) 3.591 0.074
Impulse Response Functions (liquidity supply) 1.010 0.328
Variance Decomposition (liquidity demand) 1.531 0.001**
Variance Decomposition (liquidity supply) 4.660 0.045*
* significant on a 5% level ** significant on a 1% level
Panel A: Testing for Sample Normality
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4.2 Measuring Liquidity Provision
To assess liquidity in the order book, I will use the XLM method developed by Gomber et al. (2011), and described in Chapter II, to assess the spread and volume available on both sides of the order book, which provides the advantage that it is able to account for both the depth and width of the order book together. I will test the liquidity available in the order book by simulating a purchase and sale for some amount of euros at the exact same point in time for each second37 during the main trading hours (9.00 – 17.30). I will start with the (approximate) average trade size of €500,00038
, and will run the same test again for amounts of: €1,000,000; €2,000,000; €3,000,000; €4,000,000 and €5,000,000. Different trade sizes are important in assessing order book liquidity as they are likely to yield different uncertainty assessments for liquidity providers.
The following formulas describe the measurement to come to the cost of purchasing for the amounts of euros mentioned above:
10000 ⋅
(eq. 6)
10000 ⋅ (eq. 7)
(eq. 8)
Where V is the given amount in euros, is the cost in basis points of buying amount at time t, is the cost in basis points of selling amount V (against the prevailing bid prices) at time t and is the cost in basis points of a simultaneously buying and selling amount V at time t. and are the weighted average prices at which amount V can be bought and sold respectively. is the prevailing mid quote price at time t. Overall, a lower cost of liquidity, shows a more liquid market39. As I will remove liquidity from the order book, a lower impact of liquidity removal indicates relatively more importance for that particular liquidity, i.e. HFT- or non-HFT-liquidity, in the overall liquidity of the market.
I will start assessing the daily impact of the (simulated) trades with all liquidity available in the order book as the benchmark sample. Thereafter I will subsequently perform the impact measurement as if only the HFT liquidity was available and as if only the non-HFT liquidity was available. The
37 Granularity of the order book data used in this study is in on a second basis (See Appendix A1).
38 Average traded contract size times average contract price during the sample period yields €525,919.92 as the average trade
size in euros.
39
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descriptive statistics on the samples where I removed the HFT- and non-HFT-liquidity respectively can be found in Appendix B (Table 12).
Next, I will have to test these samples for normality and homogeneity of variance in order to continue to the actual testing of hypotheses, which will consist of a paired sample t-test to determine whether the impact of removing HFT and non-HFT liquidity is significantly different from zero, and a two sample t-test to compare the impacts of HFT and non-HFT removal samples. I find that only the ‘non-HFT removed’ sample that involves a simulated amount of €500,000 is not normally distributed at a 5% level. As all the other samples (amounts) are generously within the boundaries of normality, I will assume that there is no need for this non-normality to be resolved at first glance40. When checking for homogeneity of variance using Levene’s test for homogeneity of variance, I find that none of the amounts in the two samples have a significantly different variance when measured on a significance level of 5%. The lower trade sizes are close to the boundary however, so we can expect the relatively large trade sizes to be less biased than the relatively small trade sizes. The exact results of these tests can be found in Table 5.
Table 5: Testing for Sample Normality and Homogeneity of Variance. Panel A gives the Bera-Jarque normality-test results for the sample with removed HFT liquidity as well as for the sample with the removed non-HFT liquidity. Panel B gives the results for the test of homogeneity of variances for the HFT removal’ and ‘non-HFT removal’ samples.
Panel A: Testing for Normality
HFT removed Non-HFT removed
XLM Value Bera-Jarque p-value Bera-Jarque p-value
€500.000 0.461 0.794 8,297 0.016* €1.000.000 0.558 0.756 4,297 0.117 €2.000.000 0.331 0.847 2,308 0.315 €3.000.000 0.373 0.830 1,567 0.457 €4.000.000 0.552 0.759 1,346 0.510 €5.000.000 0.574 0.751 1,294 0.524
Panel B: Testing for Homogeneity of Variance
XLM Value Levene statistic p-value
€500.000 3.259 0.088 €1.000.000 3.447 0.080 €2.000.000 3.477 0.079 €3.000.000 1.211 0.286 €4.000.000 0.210 0.652 €5.000.000 0.017 0.897 * significant on a 5% level ** significant on a 1% level 40
