The effect of high frequency trading on
stock market volatility
An econometric view
Jacob Versteeg
Universiteit van Amsterdam
17 December 2013
Bachelor Thesis Supervisor: Lin Zhao
Content
1.INTRODUCTION ... 3
2.BACKGROUND ON VOLATILITY AND HFT ... 4
2.1 Volatility ... 4
2.2 HFT ... 4
3.LITERATURE REVIEW ... 5
3.1.1 Short term trading ... 6
3.1.2 Algorithmic trading ... 6
3.1.3 HFT trading ... 7
3.2 Volatility determinants ... 9
3.2.1 Macro- economic determinants ... 9
3.2.2 Business cycle determinants ... 10
3.2.3 Market activity determinants ... 10
4.DATA DESCRIPTION ... 10 4.1.1 HFT trading firms ... 10 4.1.2 HFT market activity ... 11 4.1.3 Stock picking ... 11 4.2 Other determinants ... 12 5.METHODOLOGY ... 12 5.1 Daily analysis ... 12 5.2 Monthly analysis ... 13 6.STATISTICS ... 14 6.1 Summery statistics ... 14
6.2 Test for multicollinearity ... 14
6.3 Test for heteroskedasticity ... 15
6.4 Individual variables ... 16
6.5 Granger causality test ... 18
7.RESULTS ... 19
7.1 Results for daily analysis ... 19
7.2 Results for monthly analysis ... 20
7.3 General result ... 21
8.CONCLUSIONS AND DISCUSSION ... 22
9.REFERENCES ... 23
10.APPENDIX ... 26
Abstract
High frequency trading (HFT) has a large market share but research about the effect of HFT on market characteristics, as volatility is limited. This paper answers the question what the effect of high frequency trading is on stock price volatility. A unique database is created with the market share of HFT per trading day for a selection of Dutch traded stocks together with the daily volatility. A regression analysis is
performed with daily and monthly data with several variables in order to investigate the effect of HFT on volatility. Both models give a positive effect at the 1%
significance level, meaning that HFT increases stock price volatility. This is in contradiction with existing literature.
1. Introduction
The introduction of the electronic order book has allowed trading by computer. It is possible to give the software sets of rules whereby the computer can trade
automatically. This is called algorithmic trading. One particular form of algorithmic trading is high frequency trading (HFT). The main purpose of HFT firms is to receive data as fast as possible to arbitrage on small price changes.
Reports in economic journals show that economist and traders do not all share the same opinions about HFT. Opponents of HFT conclude that HFT destabilizes financial markets and increases volatility, while proponents argue that it increases market liquidity and decreases transaction costs. Dutch institutional investors have the complaint that HFT introduce phantom liquidity. HFT firms introduce typically a large amount of orders and therefore liquidity increases. However, if one wants to introduce a large order, which should be possible according to that liquid market, the HFT firm cancels the orders with the purpose to change prices. The HFT firm is able to follow this strategy because of the fast response time. These strategies introduce a lack of transparency.
Hendershott et al. (2011) showed that in 2011, 78% of US trade volume is created by HFT trading firms. Because of this high market share it is important to test the impact of this new form of trading on stock markets. Several papers introduce the problem and analyze whether there is a relationship between HFT and market
characteristics, like market liquidity, transaction costs and volatility. Menkveld (2012) investigates the entrance of HFT traders and the change in bid-ask spreads on Dutch stock markets. However, research about the relationship between HFT trading and stock price volatility on Dutch stock markets is not published yet. Volatility is the measure of variation of the stockprice over time. This variation is a measure of risk and therefore one of the most important market characteristics. Volatility is also a critical variable for option price calculation. Therefore, it is important to know what the effect is from HFT on stock price volatility. This paper answers the question what the effect of high frequency trading is on stock price volatility.
A unique dataset is obtained from NYSE Euronext consisting of the number of trades per member, member ID’s and if the member has HFT as main purpose. NYSE Euronext does research about the purpose of each member and categorized each member in HFT or non-HFT (nHFT). With this information the market share by HFT trading firms is determined on a daily basis. Second, the daily volatility and
several controlling variables are obtained. The relationship is tested with a regression model both on daily and monthly data, where the latter is implemented because most variables have monthly intervals.
The regression model on daily data, with the change in daily volume as only controlling variable, gives a positive and significant relationship between HFT and volatility. The model on monthly data, with more controlling variables, gives a positive and significant model as well. This means that HFT increases volatility. Several econometric tests are performed to test for heteroskedasticity, multicollinearity and causality.
The remainder of this paper is structured as follows. Chapter 2 gives a
background on volatility and HFT, chapter 3 summarizes previous research, chapter 4 contains the data description, chapter 5 the methodology, chapter 6 introduces some statistics, chapter 7 gives the results, chapter 8 gives the conclusions and chapter 9 contains the references.
2. Background on volatility and HFT 2.1 Volatility
Volatility is a measure of risk and therefore important for investors. For option
contracts, it is a vital factor for the Black and Scholes formula and therefore important for option price calculation. Future volatility is unknown, but there are several
methods to determine the volatility. First, the historical volatility can be determined. There are again different methods for this determination, with the 30 days average standard deviation of the underlying value as a common one. Second, with the Black and Scholes formula, one can determine what the future volatility is according to the market. This is called the implied volatility.
2.2 HFT
Algorithmic trading is the use of electronic platforms to execute orders by an
algorithm, which consists of a predefined set of rules. The first generation algorithms give orders based on price, time and quantity variables. The second generation is able to make decisions itself. The last generation of algorithms is not only able to collect data and make decisions, but can also analyze its results and improve its strategy. A special kind of algorithmic trading is called High Frequency Trading
firm has an information advantage. One of the characteristics of HFT is that the algorithm can insert or cancel orders just milliseconds after the introduction of new information. Therefore, the purpose of the HFT firm is to arbitrage in small
timeframes in order to make profits.
In the 17th century the Rothschild’s had a large network and messengers all over Europe. Therefore, the Rothschild’s were able to receive information faster than others and they anticipated on that information. HFT rely on the same principle with modern techniques. HFT firms typically invest heavily in datacenters with the fastest connections and place their datacenters often next to the exchange to reduce
latency.
There are several strategies for HFT firms. Financial products can be traded at several markets and prices can differ between these markets. If an identical product has different prices, one can buy the cheap asset and immediately sell the expensive asset. The trader is able to receive a profit which is equal to the difference of both prices. If the trader executes both transactions on the same time, the trader has no risk and a positive payoff. This is called arbitrage. Due to arbitrage, price difference will vanish and therefore these price differences can only occur for small periods. Therefore, trading systems with the smallest latency have the best chances and therefore arbitrage is a well-known HFT strategy. Another strategy is to recognize large orders. Index funds often introduce large orders on fixed times to adjust their portfolio that mirrors an index. Due to that large order, prices will changes. HFT algorithms are programmed to recognize such trades and take advantage from the price change.
3. Literature review
Despite the ever increasing trading volume by HFT traders, only limited research has addressed to HFT. One of the reasons is that there is little data available for
research. Most HFT traders are private companies, which are not required to publish data. However, there is research done with databases from exchanges and proxies for the activity of HFT traders. The main purpose of these researches is to find the relationship between the mentioned market parameters and HFT. Because of the limited research on HFT, research on short term and algorithmic trading is included in this overview.
3.1.1 Short term trading
The most important aspect of HFT trading is that the firm can execute trades in a small time frame. Before the HFT era, short term trading was already of interest for economists. According to the classical market efficiency theory, the price of a stock must incorporates all available information and therefore, volatility is the result of new information. Froot, Scharfstein and Stein (1992) investigate how short-term horizons influence asset prices. One of their conclusions is that short term investors may have too much emphasis on short term information and therefore do not incorporate all available information. Therefore, in contrast with the classical market efficiency theory, prices do not incorporate all information and the market is not efficient.
Froot, Scharfstein and Stein (1992) conclude in their paper that because of short term traders, the informational quality of prices decreases, which causes misalignments with the classical market efficiency theory resulting in an increasing volatility.
De Long, Shleifer, Summers and Waldmann (1990) also conclude that short-term investment periods can increase volatility. They claim that short-short-term
investments act like noise traders and respond to noise traders. A noise trader is a trader whose decision to buy, hold, and sell are irrational and erratic. The presence of noise traders in financial markets can then cause prices and risk levels to diverge from expected levels even if all other traders are rational (Black, 1986). Therefore, they conclude that short term investment periods can increase volatility and diverge prices from their fundamental value because of systematical misperception. Both papers conclude, in accordance with other research, that short term trading can increase volatility.
3.1.2 Algorithmic trading
More recent research on algorithmic trading gives us valuable insights in the relationships of interest. Chabout, Hjamersson, Vega and Chiquoine (2009) investigate the relationship between HFT and total volume, price discovery and volatility on the foreign exchange market. They investigate euro-yen, euro-dollar and dollar-yen currencies. Chabout et al. (2009) find a negative, but not significant
relationship between HFT and volatility.
In accordance with the latter paper, Hendershott and Riordan (2009) cannot find a relationship between HFT and volatility. Hendershott and Riordan (2009)
investigate the DAX30 index, the index with the thirty largest German stocks, in a period from January 1st to January 18th 2007 and October 8th to October 12th 2007. Besides their conclusion about volatility, they find that algorithmic trading consumes liquidity when bid-ask spreads are low and provide liquidity when bid-ask spreads are high. This makes sense in a way that liquidity providers are more willing to provide liquidity when their payment, the spread, is larger. This is a simple market
mechanism which also works for non-algorithmic traders. However, in a market with many more trades, the market mechanism is more efficient and therefore, algorithmic traders contribute to a better price efficiency and market liquidity.
Groth (2011) finds evidence that HFT firms do not stop with liquidity providing in times of high volatility. In accordance with above researches, Groth (2011)
concludes that there is no relationship between algorithmic trading and volatility. Hendershott, Jones and Menkveld (2011) investigate if algorithmic trading narrows spreads and improves liquidity. They could not fully define whether an algorithm of human generates a trade. Therefore, Hendershott at al. (2011) use the rate of electronic messages as a proxy for algorithmic trading. They conclude that algorithmic trading improves liquidity and narrows spreads. The four articles above conclude that algorithmic trading does not have a relationship with market volatility, but does have an impact on other market characteristics. It does improve liquidity and narrows spreads.
3.1.3 HFT trading
A lot of researchers use algorithmic trading as a proxy of HFT. However, the behavior of algorithmic trading and HFT is different. Several kinds of firms use
algorithms to execute trades. If an individual investor make some trades at his broker system, it is plausible that his broker execute his order automatically with some algorithm. Further, pension funds, mutual funds and other buy-side institutional traders widely make use of algorithms to divide large orders into small orders to manage risk and market impact. However, these trades differ in a way that the main purpose is not to arbitrage in a small time frame. Because of these differences,
algorithmic trading is not the best proxy for HFT. A couple of researchers use another proxy for the market share by HFT trading firms. The first research about HFT is on a theoretical basis. Cvitanic and Kirilenko (2010) assume that HFT traders are uninformed traders without any extra information, which gives them speed as only
advantage. With this model, Cvitanic and Kirilenko (2010) show that transaction prices are distributed more closely to their center and have thinner tails. This means that HFT and volatility have a negative relationship.
There are further different empirical researches that agree in the conclusion that HFT reduces volatility. First, Brogaard (2010) make use of a dataset of 26 HFT firms at 120 stocks at the NYSE and BATS over the period of 2008 and 2009. BATS is an alternative and electronic exchange and in 2013 the third exchange in the world, measured by trade volume. Because BATS is an electronic exchange, with lower latencies, it is broadly used by HFT firms and therefore a good place to research HFT. With these data, Brogaard concludes that the market share of HFT trading firms does not change after a volatility change, implying that there is no relationship between volatility and HFT. Brogaard’s research differs with this paper because this paper measures the change in volatility after a change in HFT.
Therefore, it is important to test for causality, which is done in chapter 6.5. Brogaard (2010 conclude in an additional research that liquidity supplying activities decrease after a volatility increase and liquidity demanding activities increase after a volatility decrease. These counter-intuitive activities can dampen intraday volatility. The conclusion of Brogaard (2010) is that HFT may reduce volatility and improve the market quality.
Hendershott and Riordian (2011) make use of the same dataset and have the same conclusion with the explanation that HFT firms typically trade in the direction of reducing transitory pricing errors. This means that HFT firms are able to locate pricing errors and arbitrage very fast in the opposite direction. With this method, they can decrease the pricing error which dampens volatility. Hasbruck and Saar (2010) have the same conclusions.
Besides positive results, there are some researches with more concerning outcomes. Jovanovic and Menkveld (2010) develop a theoretical and empirical model which concludes that HFT can reduce welfare. If a HFT firm can obtain information faster than other participants, which is the case at HFT firms, they make gains on the back of others. It is the question if it is righteous that a couple of firms make huge profits, trampling others, because they have faster connections. On the other side, when a HFT firm is acting like a middle man, welfare can increase because of the better price quotes that reflect all available information. Jovanovic and Menkveld (2010) perform empirical research on Dutch stocks traded at CHI-X, an electronic
exchange which is acquired by BATS in 2011, to compare market quality of the stocks before and after the introduction of a HFT trader as middle man. They
conclude that the middle man have more information about the market and therefore trade for their own account and make profits regardless of the clients orders.
Kirilenko, Kyle, Samadi and Tuzan (2011), analyze the E-mini S&P500 future during the 6th may 2010 flash crash. That day, the Dow Jones Industrial Average plunged about 1000 points and recovered within minutes. Kirilenko, Kyle, Samadi and Tuzan (2011) conclude that HFT’s behavior can enhance volatility in time of high uncertainty like the 6th of May. However, it is important to note that this research concerns an exceptional trading day.
When taking above researches in to account, it can be concluded that most researchers agree that HFT have a negative effect on volatility and a positive effect on market quality. Besides normal trading days, it is possible that HFT firms increase volatility in times of high uncertainty.
3.2 Volatility determinants
When the variable HFT is regressed on the stock price volatility, the model will face omitted variable bias. In that case, all possible determinants are addressed to the single variable HFT and therefore it could be unreliable. In order to form a good model, we have to find other determinants of stock price volatility. Schwert (1989a, 1989b) does research on stock price volatility with data on US stocks from 1943 till 1987. He finds weak evidence between macro-economic variables and volatility. Second, he finds a negative relationship between the business cycle and volatility. The used dataset contains stocks in the period 2003-2013 which includes the financial crisis. The volatilities between 2007 and 2009 were high with a record of 70%. Therefore, it is important to control for variables that represent the business cycle. The following paragraphs will summarize the macro-economic, business cycle and market activity determinants.
3.2.1 Macro- economic determinants
According to Blanchard (1981) and Christie (1982) there is a strongly positive
relationship between interest rates and the volatility on stock price volatility. Second, in an article by Cutler, Poterba and Summers (1989) the authors prove that the natural logarithm of the money supply (M2) influence the stock price volatility. A part of the members of NYSE Euronext Amsterdam which trade in the used stocks are
foreign investment firms and therefore the exchange rate is important for their
returns. Therefore it makes sense that the exchange rate is correlated with the stock price volatility. Walid, Chaker and Masood (2011) and Tahir and Keung (2010) do research on this in emerging markets and concludes that there is a positive
relationship between exchange rates and stock price volatility.
3.2.2 Business cycle determinants
Corradi, Distaso and Mele (2009) find a strong correlation between business cycle determinants and the stock price volatility. They use the industrial production (IPI) and the consumer price index (CPI) as determinants for the business cycle. Brand and Kang (2004) also find evidence that the volatility is dependent on the business cycle. In recessions, stock price volatility is high while in periods of growth the stock markets experience low volatilities. Engle and Rangel (2005) use a Spline-GARCH model with data from the stock market in Turkey and Canada to prove that inflation is an important variable to predict the stock price volatility. Levine and Zarvos (1998) find that the real GDP growth has only a weak predictive power to the stock price volatility. For my research the industrial production, Consumer price index and
inflation are important to correct for the business cycle. Because the CPI and inflation are strongly correlated, only the CPI is included as explanatory variable to avoid any bias. At last, the Dutch trade balance is used to correct for seasonality. Appendix C plots the trade balance which clearly shows the seasonal effect.
3.2.3 Market activity determinants
Chuang, Hsiang and Susmel (2011) do research about the predictive power of daily stock volume and the stock price volatility within the ten largest stock markets in China. They conclude that the daily stock volume have predictive power in 8 stock markets. Xiao and Brooks (2010) do similar research at the Australian stock market. In their article they conclude that the daily market volume have a high predictive power for the stock price volatility.
4. Data description 4.1.1 HFT trading firms
I have created my own, unique database in order to obtain the daily market share of HFT trades. NYSE Euronext does research about HFT activity at the exchange in order to distinguish HFT from nHFT members. In most previous research, the part of
HFT in the market is approximated with an order-to-trade ratio higher than 10. NYSE Euronext does a more advanced study where they had meetings with all their
members in order to obtain information about their strategies. It is important to know that there are firms who have both HFT and other objectives. This research only includes firms which primary objective is HFT trading. From all 334 members, 21 are specified as HFT trading firms. The names of these firms are however confidential.
4.1.2 HFT market activity
The second step is to gather the HFT market activity. In the internal data system of NYSE Euronext, data from all AEX-index traded stocks between July 2003 and April 2013 are obtained, with different market shares per member as most important characteristic. The market shares are accounted in three different ways: market share introduced orders, market share trades and market share value traded. HFT firms have a high cancelation ratio and therefore, the number of introduced orders is much higher than the number of actual trades. Second, the market share value traded is the number of orders times the stock price and therefore more expensive stocks are accounted in a more important way than less expensive stocks. In order to prevent this bias the market share of trades is used.
Now, two groups are made. The first group consists of the traders who are specified as HFT trading firms, which is called HFT. The second group consists of all trading firms which are no primary HFT trading firms, which is called nHFT. The nHFT group is filtered so a database is created with the market share of trades executed by HFT trading firms between July 2003 and April 2013.
4.1.3 Stock picking
What is important for the research is the stock picking. It is important for HFT algorithms to have enough liquidity. Therefore, it is best to perform the research on AEX-index traded funds, which are most liquid by definition. Because the research is about the relationship between HFT and the volatility on the Dutch stock market, Air France-KLM is excluded because Air France-KLM is quoted at Euronext Paris. Second, the timeframe used for this research is from July 2003 and April 2013 and the AEX-index changed during this period. To abate this bias, only the companies are used which are in the index during this whole period. At last, TPG was split into TNT and PostNL and therefore TPG, TNT and PostNL are excluded. After all
4.2 Other determinants
Chapter 3.2 described why it is important to include other determinants in the model and which determinants are used in previous research. The natural logarithm of the money supply, the consumer price index (CPI), the Euro Dollar exchange rate, the trade balance, the industrial production index (IPI), the Euribor interest rate, the trading volume and the HFT market share are obtained to test whether they are useful in the model. This section describes how the data is obtained.
First, there are different measures for the money supply. In previous research the most common measure for money supply is the M2. The M2 money supply is gathered from the ECB database, since we are interested in the Euro area money supply. The Euribor interest rate and the Euro Dollar exchange rate are obtained from the same database. The Euribor is the most important European interest rate and therefore used in this model. The Euro Dollar exchange rate is used because most of the transactions by foreign members is paid in Dollars. Including other
exchange rates can cause a bias due to high correlations and therefore only the Euro Dollar rate is used. Second the CPI, IPI and the Dutch trade balance are gathered from the Dutch Central Bureau of Statistics. The trading volume is downloaded from Bloomberg for every individual stock, and added up. It is important to take the volume and not the turnover, otherwise high priced stocks have a higher weight in the model.
At last, for the volatility measure the 30 days historical volatility is obtained from Bloomberg for every individual stock and the average is taken. The money supply, Euro Dollar exchange rate Euribor interest rate and trading volumes are in absolute values. The CPI, IPI and Trade balance are indices and the volume and market share HFT are in percentages.
5. Methodology 5.1 Daily analysis
A first regression is made with the variables which contain daily data. In that first model HFT and the change in trading volume are used as determinants to predict volatility. The relationship is tested with the following model:
where HFT stands for the daily percentage market share traded by HFT-firms, and ln(Volume) stand for the percentage change in the volume of the traded shares. To test whether both variables are individual significant, a test is performed with HFT as only variable and a test with ln(volume) as only variable. Model 1 is used when both variables are individual and together significant for the 10% significance level. At last, in section 6.3 a heteroskedasticity test is performed which gives the result that a robust regression model must be used.
5.2 Monthly analysis
For the monthly analysis, the following model is made:
Volatility= β0 + β1 * HFT + β2 * Ln(Volume) + β3 * ln(M2) + β4 * CPI + β5 * EuroDollar +
β6* ln(tradebalance) + β7 * IPI + β8 * Euribor + ui (model 2)
Using above regression model gives biased coefficients because not all variables are significant. Therefore, a stepwise regression is performed where variables are
included using a significance level of 10%. With these criteria, the following final model is made:
Volatility= β0 + β1 * HFT + β2 * ln(tradebalance) + β3 * Euribor + β4 * EuroDollar + ui
(model 3) Section 6.3 shows that the model suffers heteroskedasticity and therefore a robust regression model must be used. With the robust model and the 10% significance level threshold, the final model is obtained:
Volatility= β0 + β1 * HFT + β2 * ln(tradebalance) + β3 * Euribor + ui (model 4)
The number of observations of this model is 118 which is enough to perform a multiple regression model with three explanatory variables.
6. Statistics
6.1 Summery statistics
First of all, some summery statistics are reported in appendix B, following by the correlation matrix below.
HFT Ln(volume) Volatility
HFT 1
Ln(volume) 0,013 1,00
Volatility 0,27 0,038 1,00 Table 6.1.1 – correlation matrix for daily data
CPI E u ro Do lla r IP I Euri b o r HFT Ln( tr ad eb al an ce) V o lat ility L n V o lume L n M2 CPI 1,0 Euro Dollar 0,2 1,0 IPI 0,2 0,3 1,0 Euribor 0,0 0,3 0,0 1,0 HFT 0,5 0,3 0,2 -0,6 1,0 Ln (tradebalance) 0,2 0,3 0,5 -0,1 0,4 1,0 Volatility 0,2 0,1 0,0 0,1 0,3 -0,1 1,0 Ln Volume -0,1 -0,1 0,1 0,0 0,0 0,1 0,1 1,0 Ln M2 0,0 -0,1 -0,1 0,8 -0,7 -0,3 0,0 0,0 1,0 Table 6.1.2 – correlation matrix for monthly data
6.2 Test for multicollinearity
As seen in figure 6.1.1 and 6.1.2, some variables have a high covariance and therefore a test for multicollinearity is necessary. A variance inflation factor test is executed giving the results in table 6.2. The rule of thumb says that VIF value’s above 10 needs further investigation. With these values of VIF for both the daily and monthly data, it can be concluded that none of the variables suffer from
Variable VIF 1/VIF
HFT 1.00 1.00
Ln(volume) 1.00 1.00
Mean VIF 1.00
Table 6.2.1 - VIF test for daily data
Variable VIF 1/VIF
HFT 2.62 0.382024
Euribor 2.47 0.405494
Euro Dollar 1.76 0.567136 Ln Trade balance 1.23 0.814900
Mean VIF 2.02
Table 6.2.2- VIF test for monthly data 6.3 Test for heteroskedasticity
One of the OLS assumption is that the variances must be equal, in other words, the model may not suffer heteroskedasticity. It is therefore important to test for this heteroskedasticity. The Breusch-Pagan / Cook-Weisberg test compare the variances with a chi2 test reported in table 6.3.1 and 6.3.2. As seen in both tables, the model with daily data and the model with monthly data both suffer heteroskedasticity. Therefore, it is important to use a regression model with robust standard errors. Ho: Constant variance
Variables: hft and lnvolume
Chi2 (2) 286,17
Prob > chi2 0,0000
Table 6.3.1 Breusch-Pagan / Cook-Weisberg test for heteroskedasticity for daily data
Ho: Constant variance
Variables: EuroDollar, Euribor, lnTradeBalance and HFT
Chi2 (2) 45,31
Prob > chi2 0,0000
6.4 Individual variables
The progress of some individual variables is interesting and therefore this section describes some of the determinants. First, the progress of HFT over time is
interesting and shown in figure 6.4. As seen in the graph there is a strong increase around March 2008. In 2008 the economic crisis in the US started and therefore stock trading volumes decreased. The sharp increase in HFT market share could therefore be caused by a decrease in traditional trades, and not by an increase in HFT. This could give biased results. Figure 6.5 shows however that the actual number of trades by HFT trading firms follows a similar path and therefore the sharp increase is caused by a sharp increase on the total number of shares by HFT trading firms.
The sharp increase in March 2008 is however a result in itself and interesting for further research.
Figure 6.4. The x-axis gives the date and the y-axis the HFT market share as a fraction. 0.05 0.10 0.15 0.20 0.25 0.30 Jul -03 De c-03 M ay -04 Oct-04 M ar -05 Aug-05 Ja n-06 Jun-06 N ov-06 A pr -0 7 Se p-07 Fe b-08 Jul -08 De c-08 M ay -09 Oct-09 Ma r-10 A ug-10 Ja n-11 Jun-11 N ov-11 A pr -1 2 Se p-12 Fe b-13
Market share HFT
HFTFigure 6.5. The x-axis gives the date and the y-axis the total number of trades by HFT trading firms.
Second, figure 6.6 shows the pattern of the Euribor during the period. As seen in the figure the Euribor increased starting in 2005 in accordance with the economic growth. Early 2008 there is a small drop at the start of the US subprime mortgage problems and after the fall of Lehman brothers there was a huge drop. At early 2010 the interest rate increased and when the European economic crisis worsens interest rates drops again. Therefore, the Euribor variable is a good determinant to control for the economic crisis.
Figure 6.6. The x-axis gives the date, the y-axis gives the Euribor interest rate in percentages. 0 20,000 40,000 60,000 80,000 100,000 120,000 140,000 160,000 180,000 200,000
Total trades HFT
Total Trades 0 1 2 3 4 5 6 Jul -03 De c-03 M ay-04 Oct-04 Ma r-05 A ug-05 Ja n-06 Jun-06 N ov-06 A pr -0 7 Se p-07 Fe b-08 Jul -08 De c-08 M ay-09 Oct-09 M ar -10 A ug-10 Ja n-11 Jun-11 N ov-11 A pr -1 2 Se p-12 Fe b-13Euribor
Euribor6.5 Granger causality test
In section 3.1.3 the problem of causality is introduced. Brogaard (2010) tests whether the fraction of HFT changed after a volatility change while this research test the opposite relationship. It is important to test for the direction of the relationship and therefore a granger causality test is included.
Before the Granger causality test is performed, the number of lags must be determined. When introducing an extra lag in the model, the marginal benefit decreases while the marginal cost of the additional estimation uncertainty rises. Therefore, it is important to test whether the marginal benefit is higher than the marginal cost in the last used lag. The test is performed using the F-statistic
approach (Stock and Watson, 2012) on 4 lags. The test concludes that the chosen 4 lags is a good length selection.
It is important to know that the granger causality test doesn’t test real causality but determines whether HFT is a useful predictor of volatility, given the other
variables in the regression. Therefore, granger causality is more jargon for
econometrics and granger predictability is a more accurate term (Stock and Watson, 2012).
Before performing the granger causality test, it is important to test whether the variables HFT and volatility are stationary. A Dickey-Fuller test is performed to test for a unit root. The null-hypothesis, stating that the time-series follows a random walk, can be rejected for both variables for the 99% significance level. Table 6.8 shows the test statistics. Because both variables suffer a unit root, the granger causality test must be performed with the first difference of both HFT and Volatility.
Table 6.8 The table shows the Augmented Dickey Fuller statistic
To test the direction, two models are made where both directions are tested. First, a model is made which tests whether HFT granger causes volatility. Second, a
ADF test statistic 1% critical value
HFT -1.73 -3.504
model is made where volatility granger causes HFT with the same number of lagged values. Both models are shown in the below equations, followed by the outcomes in table 6.7.
∑ ∑ (model 5)
∑ ∑ (model 6)
Table 6.7. The table shows the F-statistic and between brackets the p-value. *, ** and *** denotes the 10%, 5% and 1% significance level respectively.
The Granger causality test results answers the question regarding the relationship direction. The null-hypothesis that HFT does not causes volatility is rejected which is shown in table 6.7. Second, the null-hypothesis that volatility does not cause HFT is not rejected. Therefore, HFT causes volatility and not the other way around.
7. Results
7.1 Results for daily analysis
Table 7.1 shows the results for the daily analysis. Two individual regressions are shown in the second and third column and the last column shows the regression with both variables. In the first regression with HFT as the only descriptive variable, HFT has a coefficient of 0,366, which means that for every percent increase in market share by HFT trading firms, the volatility will increase with 0,366 percent. This result is significant for the 1% significance level. The coefficient of determination for each model is shown in the last row of table 7.1. The second regression is made with only the change of trading volume as explanatory variable. The regression coefficient is 0,361 with a significance level of 10%.
Both variables are significant for the 10% significance level and are therefore included in the complete model. The complete model gives a HFT coefficient of 3,654
F statistic HFT does not granger cause Volatility 0.86 (0.5525)
and a Ln(volume) coefficient of 0,032 for the 1% and 10% respectively. This means that for every 1% increase in HFT market share, the volatility increases with 3,654%. The conclusion for the regression model with daily data is that HFT increases stock price volatility.
The complete model gives a coefficient of determination of 0,0743. The F-statistic of the model, which is shown in the last row of table 7.1, concludes that the model as a whole is significant for the 1% level.
Volatility Volatility Volatility
HFT 0,366 (0,000) *** 3.654 (0,000) ***
Ln(volume) 0,361 (0,052) * 0,032 (0,066)*
Constant 0,239 0,032 0,183 (0,879)
R-squared 0,0731 0,0015 0,0743
F statistic 273,29 (0,000) *** 3,79 (0,052) * 137,72 (0,0000) ***
Table 7.1. The table shows the coefficient and between brackets the p-value. *, ** and *** denotes the 10%, 5% and 1% significance level respectively.
7.2 Results for monthly analysis
The first result is that not all determinants are significant for the 10% level. Therefore a stepwise regression model is performed to determine the significant variables. There are several combinations of significant determinants, and the model with the highest F-value is chosen. Table 7.2 shows the results for the model with the significant variables (model 4).
Both variables to control for the business cycle are negative as expected. When the economy worsens, the uncertainty in stock market increases and therefore volatility increases. However, both variables are not significant for the 10% level.
An increase of the Euro Dollar exchange rate with one point, will decrease the volatility with 25,71%. This seems quite much, however, the 2013 difference in high-low in this exchange rate is only 0,104. With the robust model, which corrects for heteroskedasticity, the Euro Dollar variable is not significant for the 10% significance level.
The Euribor interest rate is significant for the 1% level and has a coefficient of 0,037. This implies that the volatility increases with 0,037% at an Euribor interest rate increase of 1%. The significance is strong, however the effect is quite small, taking into account that the periods high-low is only 4,92%.
The change in the trade balance gives a negative relationship with the volatility. This is in accordance with economic theory because the volatility will decrease when the economy become stronger.
At last, the variable HFT have a positive relationship with the volatility. A 1% increase in HFT market share will increase volatility with 0,853%. This result is significant for the 1% significance level. The 95% confidence interval is in both extremes positive implying a strong statement that the relationship is positive. Therefore, the conclusion for the regression model with monthly data is that HFT increases stock price volatility.
Volatility HFT 0,853 (0,000) *** Euribor 0,037 (0,005) *** Ln(tradebalance) -0,121 (0,005) *** Constant 0,240 R-squared 0,2166 F statistic 5,69 (0,0011) ***
Table 7.2. The table shows the coefficient and between brackets the p-value. *, ** and *** denotes the 10%, 5% and 1% significance level respectively.
7.3 General result
Both the results for the daily and monthly analysis gives a positive relationship between HFT and volatility. The individual variables and the complete models model significant for the 10% level and the rates of determination are relatively high.
8. Conclusions and discussion
HFT is a form of algorithmic trading where the main purpose is to arbitrage within small timeframes. The last decade the part of HFT is increasing and therefore research on the relationship between HFT and market characteristics is necessary. This research focuses on one market characteristic, namely volatility.
There are various researches about the relationship between volatility and different proxies of HFT. First, research concludes that short term trading can increase stock price volatility. Second, there is no relationship found between algorithmic trading and volatility. Research regarding the relationship between HFT and volatility predominantly agrees that HFT has a negative relationship on the stock price volatility.
This paper answers the question as to the relationship between stock price volatility and HFT. A unique database is created consisting of the daily market share of trades executed by HFT trading firms. The volatility and explanatory determinants are obtained in the timeframe from May 2003 till April 2013. With this data, a
regression analysis is performed on the daily and monthly data and tests for heteroskedasticity, multicollinearity and granger causality are conducted.
Both the model for daily and monthly data gives a positive relationship between HFT and volatility at the significance level of 1%. This means that, in contradiction with previous research, HFT increase stock price volatility. The main conclusion in this paper is that HFT increases stock price volatility.
There are however, some improvements possible for further research. First of all, in this research the daily market share of total trades is used to determine the market share. There is a possibility to split the buy side from the sell side orders. Research by Brogaard (2010) found that liquidity supplying activities decrease after a volatility increase while liquidity demanding activities increase after a volatility
increase. This suggests that splitting up the buy and sell side could be a better method. Second, due to the two-way causality, it could be useful to perform a two stage least square model instead of the ordinary least square method.
9. References
Books
Stock, H.S., Watson, M.W., 2011, Introduction to Econometrics, Pearson Education Limited.
Articles and working papers
Black, F. (1986), Noise. The Journal of Finance, 41: 529–543
Blanchard, O., J., 1981, Output, the Stock Market and Interest Rates, The American Economic review, 1: 132-143
Brandt, M.W., Kang, Q., 2004, On the Relationship between the Conditional Mean and Volatility of Stock Returns: a Latent VAR Approach, Journal of Financial Economics, 72: 217-257
Brogaard, J., 2010, High Frequency Trading and its Impact on Market Quality, Northwestern Univeristy, Working Paper
Christie, A., A., 1982, The Stochastic Behavior of Common Stock Variances: Value, Leverage and Interest Rate Effects, Journal of Finance, 3: 436-445
Chaboud, A., Chiquoine, B., Hjalmarsson, E., Vega, C., 2009, Rise of the Machines: AlgorithmicTrading in the Foreign Exchange Market, International Finance
Discussion Papers – Board of Governors of the Federal Reserve System, #980
Corradi, V., Distaso, W., Mele, A., 2009, Macroeconomic Determinants of Stock Market Volatility and Volatility Risk Premia, Working Paper
Cvitanic, J., Kirilenko, A. A., 2010, High Frequency Traders and Asset Prices, Working Paper, California Institute of Technology
Cutler, D., Poterba, J., and Summers, L. “What Moves Stock Prices.” The Journal of Portfolio Management, 15 (1989), pp. 4-11
Chuang, W. I., Hsiang, H. L., Susmel, R., 2011, The Bivariate Approach to Investigating the Relation Between Stock Returns, Trading Volume, and Return Volatility, Working Paper
De Long, B. J., Shleifer, A., Summers, L. H., Waldman, R. J., 1990, Noise Trader Risk in Financial Markets, Journal of Political Economy, 980(4): 703-738
Engle, R. F., Rangel,J.G., 2005, The Spline GARCH Model for Unconditional Volatility and its Global Macroeconomic Causes, Working Paper
Froot, K.A., Scharfstein, D.S., Stein, J.C., 1992, Herd On The Street: Informational Inefficiencies In a Market with Short-Term Speculation, Journal of Finance,
47(4):1461–1484
Groth, S. S., 2011, Does Algorithmic Trading Increase Volatility? Empirical Evidence from the Fully-Electronic Trading Platform Xetra, Goethe University Frankfurt,
Working Paper
Hendershott, T., Riordan, R., 2009, Algorithmic trading and Information, NET Institute Working Paper #09-08
Hendershott, T., Riordan, R., 2011, High Frequency Trading and Price Discovery, Working Paper
Hendershott, T., Jones, C., Menkveld, A., 2011, Does Algorithmic Trading Improve Liquidity? Journal of Finance 66:1
Hendershott, T., Riordan, R., 2011, High Frequency Trading and Price Discovery, Working Paper
Hasbrouck, J., Saar, G., 2010, Low-Latency Trading, New York University, Working Paper
Jovanovic, B., Menkveld, A. J., 2010, Middlemen in Limit Order Markets, VU University Amsterdam, Working Paper
Karpoff, J.M. 1987. The relation between price changes and trading volume: A survey. Journal of financial and Quantitative Analysis 22, 109-126
Kirilenko, A., Kyle, S. A., Samadi, M., Tuzun, T., 2011, The Flash Crash: The Impact of High Frequency Trading on an Electronic Market, Working Paper
Levine, R., Zervos,S., 1998, Stock Markets, Banks, and Economic Growth, The American Economic Review, 88: 537-558
Menkveld, A. 2012. High Frequency Trading and the New-Market Makers. AFA 2012 paper.
Schwert, G.W., 1989a, Why Does Stock Market Volatility Change over Time? Journal of Finance, 44: 1115-1153
Schwert, G.W., 1989b, Business Cycles, Financial Crises and Stock Volatility, Carnegie- Rochester Conference Series on Public Policy, 31: 83-125
Tahir, M. F., Keung, W. W., Linkage between Stock Market Prices and Exchange Rate: A Causality Analysis for Pakistan, National University of Singapore, Working Paper.
Walid, C., Chaker, A., Masood, A., 2011, Stock Market Volatility and Exchange Rates in Emerging Countries: A Markov-State Switching Approach, Emerging Markets Review, 12: 272-293
Xiao, J., Brooks, R.D., 2009, GARCH and Volume Effects in the Australian Stock Markets, Annals of Financial Economics, 5: 79-1053
10. Appendix Appendix A Included funds HEINEKEN UNILEVER DR
ROYAL DUTCH SHELLA PHILIPS KON DSM KON AKZO NOBEL KPN KON AEGON ING GROEP KONINKLIJKE AHOLD ASML HOLDING REED ELSEVIER WOLTERS KLUWER
A. The appendix shows the used stocks.
Appendix B
Obs Mean Std, Dev, Min Max
HFT 2534 0,10 0,09 0,00 0,37
Ln(volume) 2534 6,76 0,13 6,39 7,24
Volatility 2534 0,28 0,12 0,14 0,91
Variable Observations Mean Standard Deviation Min Max CPI 118 1,77 .648 .2 3.2 Euro Dollar 118 1,32 .099 1.11 1.577 IPI 118 103.43 9.67 80.36 124.8 6 Euribor 118 2.18 1.41 .19 5.11 HFT 118 .098 .088 .0014 .28 Ln(Trade Balance) 118 1.065 .269 .34 1.62 Volatility 118 .276 .122 .15 .87 Ln(Volume) 118 .155 .00295 .15 .16 Ln(M2) 118 .007 .0028 .00079 .01
B. The appendix shows the summery statistics for the monthly data.
Appendix C
C. The figure shows on the x-axis the date and on the y-axis the natural logarithm of the trade balance.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Jul -03 M ar -04 N ov-04 Jul -05 M ar -06 N ov-06 Jul -07 M ar -08 N ov-08 Jul -09 M ar -10 N ov-10 Jul -11 M ar -12 N ov-12
