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ISSN : 1598-7248 (Print)
ISSN : 2234-6473 (Online)
Industrial Engineering & Management Systems Vol.19 No.1 pp.174-183
DOI : https://doi.org/10.7232/iems.2020.19.1.174

# Investigating the Performance of an Order Imbalance based Trading Strategy in a High- Frequency Trading

Faculty of Management, University of Tehran, Hasan Abad-e-Baqerof, Jalal ale ahmad highway, Chamran, Tehran, Iran
Faculty of Industrial Engineering, Amirkabir University of Technology, 424 Hafez Ave, Tehran, Iran
*Corresponding Author, E-mail: a.gholami@aftermail.ir
January 22, 2019 August 7, 2019 November 25, 2019

## ABSTRACT

One of the most interesting and challenging issues in the field of finance at the moment is high-frequency trading (HFT). This is because HFT is a relatively new issue for most of the financial markets and its activity is becoming more common all over the world. So, the study aim is to investigate the performance of an order imbalance based trading strategy in high-frequency trading. Besides, we used Multivariate GARCH models such as BEKK and DCC GARCH to estimate volatility, return and order imbalance relations. Our dataset includes stocks traded on the Tehran Stock Exchange from April 1, 2014, until March 30, 2016 (1095 trading days). Our dataset includes stocks traded on the Tehran Stock Exchange from April 1, 2014, until March 30, 2016 (1095 trading days). Also, the results of lagged return-order imbalance relations show that the percentage of positively significant lagged order imbalances is 1.00% and the percentage of negatively significant coefficients of lagged order imbalance is only 8.21% at confidence level 95% in 2016. Finally, it concluded that order imbalance is a proper measure for predicting future returns. Indeed, order imbalance could be proper measures for predicting returns in HFT.

## 1. INTRODUCTION

One of the most interesting and challenging is-sues in the field of finance at the moment is high-frequency trading (HFT). This is because HFT is a rela-tively new issue for most of the financial markets and its activity is becoming more common all over the world, reaching more than half of equity trading in the United States by 2010 (Menkveld and Yueshen, 2013).

HFT is not a strategy, but a technology which allows for the automation of a wide spectrum of trading strategies, propelled by the ongoing advances in computer technology. The HFT algorithms create probabilistic predictions in the price movements of securities and show the possibility to earn a profit from small price movements by holding a certain trading volume for a specific small amount of time (Ecaterina Bencheci and Rene Botvin, 2014).

HF traders create very tiny profits per stock, but according to the large value of the daily trading volume, the obtained profits are significantly more remarkable. HF traders benefit from their physical proximity to the exchange platforms, to minimize the latency and usually end their trading day with a “flat” position (Chordia et al., 2013).

High-frequency traders (HFTs) have become a potent force in many markets, representing between 40 and 70% of the trading volume in US futures and equity markets, and slightly less in European, Canadian and Australian markets. The potential profit from every stock resulting from an execution may be very tiny and be achieved a probability only slightly above 50%, but HFTs rely on this process being repeated thousands, if not more, times a day. As the law of large numbers and the central limit theorem relentlessly take their hold, profits ensue and presumably justify the HFTs’ large investment in trading technology (Ait-Sahalia and Saglam, 2017).

HFT condition their strategies on order book depth imbalances, which are a strong predictor of future price change. Investigating the order book imbalance immediately before each order submission, cancelation and trade, it shows HFT supply liquidity on the thick side of the order book and demand liquidity from the thin side. This strategic behavior is more pronounced during volatile periods and when trading speeds increase. However, by competing with non-HFT limit orders, HFT crowd out non-HFT limit orders.

This study aimed to investigate the performance of an order imbalance based trading strategy in a high-frequency trading. The study used the empirical literature on order imbalance effects in stock returns for different reasons.

First, there is no literature on imbalance–return relations for Iranian stocks. One of the differences of the Iranian data over most other country data is that all trades are determined as either buyer or seller, so it preventing errors from the use of trade classification algorithms.

Second, most of the literature uses time series regressions especially a tiny period like second, minutes and day, so in this study, we used a regression for the large period interval.

Third, it seems there is no literature on a recent sample of order imbalances because stock markets worldwide become more efficient, and it is more interesting whether effects reported for the last decades still is efficient at daily frequencies. So, in this study, we provide results for recent day-to-day effects. Fourth, we reported liquidity effects in the imbalance and return relation. Fifth, similar to literature, we provide strong evidence that order imbalances predict short-term future price movements. Finally, in contrast to the previous literature, we find imbalance effects to be weaker for very high levels of the order imbalance.

## 2. LITERATURE OF REVIEW

High-frequency trading has been vastly studied by many scholars, however, there is a long list of ques-tions that are still open and require further research.

Ait-Sahalia and Saglam (2017) in a study ana-lyze the consequences for liquidity provision of compet-ing for market makers operating at high frequency. Also, the results show that these policies are largely unable to induce high-frequency market makers to create liquidity that is robust across volatility issues (Ait-Sahalia and Saglam, 2017).

Goldstein (2017) examining the order book im-balance immediately before each order submission, cancelation and trade, we show high-frequency traders (HFT) supply liquidity on the thick side of the order book and demand liquidity from the thin side. This strategic behavior is more pronounced during volatile periods and when trading speeds increase. However, by competing with non-HFT limit orders, HFT impose a welfare externality by crowding out slower non-HFT limit orders. Overall, we document an important information channel driving HFT behavior (Goldstein et al., 2017).

Stav (2015) in a research entitled ‘High-Frequency Trade Direction Prediction’ declared that high-frequency trading involves large volumes and rapid price changes. The obtained results of the study compared with the previous literature in the high-frequency context. Some previous literature shows that idiosyncratic risk has an important on low-frequency trading, but has not yet investigated its effects on high-frequency trading (Stav, 2015).

Lehalle and Mounjid (2016) emphasize the ex-posure to adverse selection, of paramount importance for limit orders. For a participant buying using a limit order: if the price has chances to go down the probability to be filled is high but it is better to wait a little more before the trade to obtain a better price. To the authors’ knowledge, this paper is the first to make the connection between empirical evidence, a stochastic framework for limit orders including adverse selection, and the cost of latency. Our work is the first step to shed light on the roles of latency and adverse selection for limit order placement, within an accurate stochastic control framework.

Subrahmanyam and Zheng (2016) using a unique dataset consisting of limit order placement, execution, and cancellations on Nasdaq, we find that HFT firms do not cancel orders more frequently than non-HFT firms. HFT firms more effectively use order cancellation to strategically manage their limit orders in anticipation of short-term price movements than non-HFT firms. HFT firms increase their liquidity provision during periods of high volatility; their liquidity provision is less affected by order imbalance shocks than that of non-HFT firms. Overall, our results indicate that HFT limit orders exert a stabilizing influence on markets (Subrahmanyam and Zheng, 2016).

Bonart and Gould (2016) use a recent, high-quality data set from Nasdaq to perform an empirical analysis of order flow in a limit order book (LOB) before and after the arrival of a market order. For each of the stocks that we study, they identify a sequence of distinct phases across which the net flow of orders differs considerably. Based on our findings, we argue that strategic liquidity providers consider both adverse selections and expected to wait for costs when deciding how to act (Bonart and Gould, 2016).

Dinh (2016) in a research investigate the rela-tionship between returns, risk, and liquidity in high-frequency trading. Panel analysis for single stocks is employed to investigate this relationship. The empirical results imply that in high-frequency trading idiosyncratic risk plays a more pronounced role than the systematic risk in asset pricing. The empirical results of the paper contribute to the previous literature in the high-frequency context. Some previous literature suggests that idiosyncratic risk has a matter on low-frequency trading, but has not yet investigated its effects on high-frequency trading. High-frequency traders are considered to be market agents that base their trading activity on information about prices and order flow. They usually trade in opposition to price pressure (Dinh, 2016).

Brogaard et al. (2016) examine the stability of liquidity supply by high-frequency traders, who do not have the obligation to supply liquidity during stressful periods. They find that HFTs supply liquidity to non-HFTs during extreme price moves in a single security but demand liquidity when several stocks experience simul-taneous extreme price moves. Thus, HFT may be supplying liquidity on Nasdaq while demanding liquidity from other trading venues. By analyzing a mostly consolidated market, we provide further insights into HFT trading activity over the whole market (Brogaard et al., 2016).

Multivariate GARCH (MGARCH)-type models used in previous studies include the BEKK- MGARCH (Willcocks, 2010; Miao et al., 2011) and the Dynamic Conditional Correlation (DCC) model (Antonakakis et al., 2015).

Furthermore, Benghazi et al. (2016) used DCC and BEKK GARCH model to test volatility spillover among global Real Estate Investment Trusts (REITs) and found that the REIT market is becoming increasingly globalized.

Gardebroek and Hernandez (2012) followed a multivariate -GARCH model to evaluate the level of interdependence and the dynamics of volatility across oil, ethanol and corn markets. Their results indicate a higher interaction between ethanol and corn markets in recent years, particularly after 2006. The authors did not find major cross-volatility effects from oil to corn markets. The results did not provide evidence of volatility in energy markets stimulating price volatility in grain markets (Gardebroek and Hernandez, 2012).

Ntakaris et al. (2017) declared managing prediction of metrics in high-frequency financial markets as a challenging task. An efficient method to do it is by control the relationship of a limit order book and attempted to determine a data edge. Hence, they determine an experimental protocol that can be used to evaluate the performance of related research methods. Baseline results based on linear and nonlinear regression models are also provided and show the potential that these methods have for mid-price prediction (Ntakaris et al., 2017).

Shen (2015) in a research examining order im-balance, a measure of the difference in size of buy and sell orders in the market, a simple trading strategy by fitting a linear model using ordinary least squares against a 20 time-step (10 seconds) average price change developed. Lastly, we determined a confidence interval for the optimal regression and trading parameters: the forecast window for the average price change and the trading threshold and found that they were closer to 5 and 0.15 respectively (Shen, 2015).

In contrast to above work by Shen (2015) and Ntakaris et al. (2017) which describe the relation between exchange rate changes and order imbalance by regression model, we propose a GARCH model which can capture the time-variant property of the relation.

Cartea et al. (2018) use high-frequency data from the Nasdaq exchange to build a measure of volume imbalance in the limit order (LO) book. They show that our measure is a good predictor of the sign of the next market order (MO), i.e., buy or sell, and also helps to predict price changes immediately after the arrival of an MO. They show that introducing our volume imbalance measure into the optimization problem considerably boosts the profits of the strategy. Profits increase because employing our imbalance measure reduces adverse selection costs and positions LOs in the book to take advantage of favorable price movements.

Chen et al. (2019) examines short-run exchange rate dynamics in a small open economy, Taiwan, based on the microstructure framework of foreign exchange markets. This study develops a contrarian imbalance-based trading strategy given the negative interaction between lagged order imbalances and current returns. They find that imbalance-based strategy with large order imbalance consistently outperforms the benchmark, and an asymmetry trading performance in the currency appreciations versus depreciations period (Chen et al., 2019).

## 3. DATA

Our dataset includes stocks traded on the Tehran Stock Exchange from April 1, 2014, until March 30, 2016 (1095 trading days). For all stocks, the last available quotes before the closing auction together with order imbalances are available on a daily basis.

Any private data will reflect on the stock price efficiently, and thus eliminate the differential between share price and intrinsic value. Such characteristic can help improve the reliability of research results. The transaction data source in the Tehran Stock Exchange. The sample period covers from April 1, 2014, until March 30, 2016. Stock are included or excluded in term of following criteria:

• 1. All quotes and trading data must be occurring and be gathered from Tehran Stock Exchange.

• 2. A trade or quote is excluded if it is recorded before the open or after the closing time. (i.e. intraday data is collected from 9:00 AM to 14:00 PM.)

• 3. Quotes less than \$0.01 are discard-ed.

• 4. Any quote less than 5 seconds prior to the trades is ignored and the first one at least 5 seconds prior to the trade is retained.

### 3.1 Sample Selection

The statistical population includes all companies accepted in Tehran Stock Exchange from 2014 to 2016. The final sample size is determined by the screening method after applying the following constraints:

• 1) The data needed to calculate the operational variables of the research to be available to them.

• 2) At least from the year 2014 are ac-cepted to the exchange and will be active until the end of the research period.

• 3) The end of their fiscal year is 29th March.

• 4) It is not part of the financial institu-tion, investment, and banks.

• 5) There are no more than three months of trading interruption

• 6) From the beginning to the end of the sample period, members of the stock exchange will remain.

## 4. METHODOLOGY

A trade is classified as buyer-seller initiated, so if it is near to ask- bid of the prevailing quote. Any quote less than 5 seconds before the trades is excluded and the first one at least 5 seconds before the trade is included. So if the trade is exactly at the midpoint of the quote, a “tick test” classifies the trade as buyer-seller initiated if the last price change before the trade is positive or negative.

### 4.1 Variables

#### 4.1.1 Order Imbalance

There are three important methods on the literature for calculating order imbalance: 1) it is according to the number of buys and sell orders, 2) it uses the size of orders (i.e., the number of shares in each order), and 3) last methods is the current share price by multiplying it with the order size. Many researchers for calculating order imbalance uses the first one, sometimes integrated with the second method. According to Ravi and Sha (2014) observed a significant relationship between returns and order imbalance when the latter is calculated using the number measure approach.

So, we calculated the order imbalance for stock i on the given period t as

$M i , t = M i , t b u y e r − M i , t s e l l e r M i , t t o t a l$

$M i , t b u y e r$ refer to number of buyer-initiated trades in the given period, $M i , t s e l l e r$ is number of seller-initiated trades in the given period and $M i , t t o t a l$ is the total number of trades for stock i in the given time-period t at the frequency {5 sec, 10 sec, 30 sec, 60 sec, 5 min, 10min, 30 min, 1 h, 2 h, 1 day, 2 day, 1 week} (Rubisov, 2015).

#### 4.1.2 Returns

We calculate daily log returns based on the last mid-quotes before the closing auction:

Hence, aski,t is the last ask quote for stock i before the closing auction of given period t and bidi,t is the corresponding bid quote. Using mid-quotes instead of traded prices prevents any bid-ask effects, which would induce negative first-order autocorrelation in returns (Rubisov, 2015). In section 2 (review of literature), review on literature shows that there is a large number of papers investigating the relation between order imbalances and returns. In order to examine intraday time-varying relations between return and order imbalance, we employ a GARCH model. The GARCH model is an extended form to the ARCH model and includes in addition to lagged squared error terms also lags of the conditional variance in the model, which gives it the virtue that the number of parameters required to model persistence in volatility, is reduced.

The GARCH model developed in a directional effect of price change on conditional variance. An important benefit of the model is that it can distinguish between positive and negative returns and finally obtained potential asymmetry in volatility due to the direction of the returns. In fact, it has a better fit than the symmetric GARCH model for almost all financial assets (Alexander, 2009).

In order to calculate volatility, return and order imbalance relations, we employ a GARCH model:

$R t = α 0 + α 1 × O I t + ε t ε t ∥ Ω t − 1 ~ N ( O , h t ) h t = A + B 1 × h t − 1 + C 1 × ε t − 1$

where

• Rt is the return in given period t,

• OIt is the explanatory variable order imbalance.

• α1 is the coefficient describing the effect of “Order Imbalance” on stock returns

• εt is the residual of the stock return in given period t

• ht is the conditional variance in given period t

• $Ω t − 1$ is the dataset in given period t-1

• are coefficients

The multiple regression models are presented below to calculate lagged return-order imbalance rela-tions:

Hence: Rt is the current stock return at given period t of the sample stock

$O I t − i , j = 1 , 2 , 3 , 4 , 5$ are the lagged order imbal-ance variable (at given period t-1, t-2, t-3, t-4, t-5) of the sample stock

$a + b t − i , j = 1 , 2 , 3 , 4 , 5$ are the intercept and co-efficients of the lagged order imbalance variable

εt is the residual of the stock return in given pe-riod t

According to Chordia et al. (2002), multiple re-gression models are employed to examine the relationship between stock return and lagged order imbalance.

The model could create the potential predictability in stock return. So that, if the relationship between stocks return and lagged order imbalance can be determined, the lagged imbalance can be used to provide an imbalance-based trading strategy.

In order to determine the relation between mar-ket capitalization and order imbalance impact, we use size effect regression model:

Hence Coefficientk is the coefficient describing the effect of “Order Imbalance” on the return of stock k

Cap k is the market capitalization of stock k

εk is the residual of stock k

α, β are coefficients

The financial reality shows that a price and re-turn movement in one market can spread very quickly to another market, i.e. financial markets are interrelated. Consequently, a set of multivariate GARCH type models have been specified to test for the covariances between the asset returns over time: the VECH model (Soenen and Hennigar, 1988); the BEKK model (Lawal and Ijirshar, 2015) and DCC (Griffin and Stulz, 2001); constant and dynamic conditional correlations, respectively.

In our case, we use the diagonal BEKK model to test for the volatility transmission between oil and food markets. The BEKK model has the form Bartov and Bodnar, (1994):

$H t = ​ c c ′ + ∑ j = 1 q ∑ k = 1 k A k j ' r t − j r t − j A k j + ∑ j = 1 p ∑ k = 1 k B k j H t − j B k j$

where Akj, Bkj and C are N × N parameter matrices and C is triangular. Ht = [hijt] is the conditional covariance matrix of rt and rt is a N × 1 stochastic vector process. q and p are ARCH and GARCH orders.

The several parameterizations that contain the above form make the estimation of the model more difficult. Thus, Lawal and Ijirshar (2015) give conditions for eliminating redundant, observationally equivalent representations.

$H t = c c + A k j ' r t − j A t − j ' A k j + B k j H t − j B k j '$

Since we have only two variables and in order to restrict the number of parameters and simplify their interpretation, we use the diagonal form of the BEKK model as shown in the above matrix form. The estimated parameters of the own lagged innovations quantify the effects of “news “on the variances (ARCH effects), while the parameters of the lagged variances measure the extent of volatility clustering (GARCH effects) and thus reveal the persistence of volatility. This paper estimates the following three variance and covariance equations:

$h 11 , t = c 11 2 + a 11 2 r 1 , t − 1 2 + b 11 2 h 11 , t − 1 h 22 , t = c 22 2 + a 22 2 r 2 , t − 1 2 + b 22 2 h 22 , t − 1 h 21 , t = c 21 2 + a 11 2 a 22 2 r 1 , t − 1 2 r 2 , t − 1 2 + b 11 2 a 22 2 h 11 , t − 1 h 22 , t − 1$

The conditional covariance matrix Ht in MGARCH model is estimated using quasi-maximum likelihood (QML) by maximizing the Gaussian log-likelihood function. The time series treated in MGARCH-BEKK should be stationary and the distribution of its residual is pre-defined as a conditional Gaussian distribution (normal).

The first step in calculating a DCC model is to obtain conditional correlations from the covariance matrix Qt, which is typically estimated with a GARCH equation governed by two scalar parameters a and b

$Q t = ( 1 − a − b ) Q 0 + a ∈ t − 1 ∈ ′ t − 1 + b Q t − 1$
(9)

where Q0 is the unconditional covariance matrix. The matrix Qt does not replace Ht; its sole purpose is to provide conditional correlations

$Q i j , t , i ≠ j$

The Ht matrix is created by fitting univariate GARCH models to calculate the variances, and combining these variances with

$Q i j , t$
(11)

to calculate the covariances. The process is obtained as

$H i j t = Q i j , t H i i , t H j j , t Q i i , t Q j j , t$

When we calculate the DCC, we apply a VAR-MA specification for the variances in Ht

$H i i , t = c i i + ∑ j = 1 3 a i j ∈ j , t − 1 2 + ∑ j = 1 3 b i j H j j , t − 1 + d i i u t − 1 2$
(13)

where the last term shows the asymmetry coefficient. This specification permits for spillovers among the variances of the three series and also makes the form that identical to applying for the BEKK model, permitting for direct comparisons of model performance.

fGarch is an alternate GARCH package used for comparison and control. dynlm was used to estimate linear models with lag terms easily. FinTS has an ARCH LM test function which does not necessitate constructing a VAR model.

## 5. RESULTS

### 5.1 Descriptive Analysis of Research Data

Of the companies selected for review, eventu-ally, 66 companies from the automotive, pharmaceuti-cal, food, cement, petrochemical and ceramic industries accepted in the Tehran Stock Exchange have had the necessary collaboration with the researcher, all of whom have at least one activity. Given that the research has been done over three years, there are a total of 132 data for each company divided into the following diagram:

According to Figure 1 the frequency of 66 com-panies surveyed was 21% ceramic and tile, 24% automotive & tires, 27% cement and petrochemical and 28% pharmaceutical and food industry.

The statistical results of the present study are as follows:

According to Table 1 the average of CFC is 0.747288 with the minimum 0.2440 and maximum value 1.2030. The average of CP is 0.2171with the minimum -0.126 and maximum value 2.202. The average of TCQ is 17.2812 with the minimum .98 and maximum value 274.96. The average of CBO is 0.1498 with the minimum 0 and maximum value 0.845.

In this regard, we analyze the resulting measures for the selected stocks from Tehran Stock Exchange from the beginning of 2014 to the end of 2016. By including all trading signals, the return pattern and results can be observed under an order-imbalance trading strategy. In this study, the GARCH model distinguishes between positive and negative returns and finally obtained potential asymmetry in volatility due to the direction of the returns. It has a better fit than the symmetric GARCH model for almost all financial assets (Alexander, 2009). To calculate volatility, return and order imbalance relations, we use a GARCH model. The results of return-order imbalance relation at the confidence level of 95% are shown in Table 2.

More than 90% of the samples were significant at the confidence level of 95%, it shows that order imbalance has a significant effect on return- volatility for most selected samples. Hence, the direction of effect on return- volatility fails to show consistency. 48.6% of the samples show the positive significance and 42.5% show negative significance at the confidence level of 95% in 2014. 45.9% of the selected samples show the positive significance and 43.6% show negative significance at the confidence level of 95% in 2015. 42.2% of the samples show the positive significance and 43.6% show negative signif-icance at the confidence level of 95% in 2016.

According to Table 3, the results show the sig-nificance of order imbalance relationship between order imbalance and return. It concluded that stocks with positive order imbalance coefficients account for more than 97% of the samples that show order imbalance has a positive effect on stock return. 88.1% of the samples show a positive significant relationship between order imbalance and return, and 9.7% of them show a negative significant relationship between order imbalance and return at the confidence level of 95% in 2014. 83.2% of the samples show a positive significant relationship between order imbalance and return, and 8.2% of them show a negative significant relationship between order imbalance and return at the confidence level of 95% in 2015. 79.9% of the samples show a positive significant relationship between order imbalance and return, and 9.1 % of them show a negative significant relationship between order imbalance and return at the confidence level of 95% in 2016.

According to Table 4, the results of lagged re-turn-order imbalance relations show that the percentage of positively significant lagged order imbalances is 88.25% and the percentage of negatively significant coefficients of lagged order imbalance is only 74.68% at confidence level 95% in 2014. Besides, the results of lagged return-order imbalance relations show that the percentage of positively significant lagged order imbalances is 4.00% and the percentage of negatively significant coefficients of lagged order imbalance is only 22.08% at confidence level 95% in 2015. Also, the results of lagged return-order imbalance relations show that the percentage of positively significant lagged order imbalances is 1.00% and the percentage of negatively significant coefficients of lagged order imbalance is only 8.21% at confidence level 95% in 2016. The result of study does not match with the results of Chordia et al. (2002), they show a positive and predictive relation between returns and lagged imbalances in the regression model (Chordia et al., 2002). So, the use of lagged return-order imbalance as a predictive indicator of return needed more study to determine the direction of effect before developing an order imbalance–based trading strategy.

Table 5 summarized the results of size effect test. The result shows that there is a negative relationship exists between the market capitalization and order imbalance. Order imbalance coefficients with market capitalization and logged market capitalization, show that the positive T statistics are not consistent with the results of Chordia et al. (2002), so there is a negative relationship between market capitalization and logged market. The estimations results are provided in Table 3. It shows that most of the parameters are positive and significant indicating the existence of ARCH and GARCH effects and volatility persistence. The significant and positive parameter of h11 means that the current conditional variance of the return is affected by its previous variance in the previous time. i.e. the existence of volatility in the market. The covariance equation h21 indicates a strong positive and significant interrelation between volatilities market; the significant parameters means that the variances in the market are affected by the shock market (significant a21) and the previous volatility (conditional variance) of the market (significant b21) and vice versa. To confirm the estimation results, the figures below plot the conditional variances of the series individually and the conditional covariance of the model.

So, it shows a strong impact of market capitali-zation on order imbalance and other strong impacts of the global financial crisis 2014-2016 on the two markets which confirms the interrelationship between the financial markets including the global market.

## 6. CONCLUSION

In this paper, we investigate the performance of an order imbalance based trading strategy in high-frequency trading. Choosing models that are direct multivariate extensions of the GARCH models allows us to examine the forecasting performance of multivariate models. It used a multivariate GARCH type model diagonal BEKK model. The results showed strong evidence of volatility clustering in the markets. Since it concluded that HFT is a cover for different order imbalance based trading strategies with different impact on market return. The practical study is based on a dataset that currently provided. The dataset identifies HFT’s fraction of the total trading return on Tehran stock for the period from 2014 to 2016, both for a daily and a monthly frequency. It founded that the impacts of lagged order imbalance on returns can be negative for the given period. The result can be attributed to market maker behaviors because they have enough inventories to mitigate the effects of discretionary investors in tender offers. This is also confirmed by a low average return from tender offers. Order imbalance coefficients with market capitalization and logged market capitalization, show that there is a negative relationship between market capitalization and logged market. However, it would be better to analyze the nonlinear effects of volatility by GARCH models to have a clearer idea of the impact of persistence. So the BEKK GARCH model shows more significant results than other models. Finally, according to the result of a study there observed a relationship between return and order imbalance, it concluded that order imbalance is a proper measure for predicting future returns. Indeed, order imbalance could be proper measures for predicting returns in HFT.

## Figure

Frequency of companies surveyed by industry.

## Table

Descriptive analysis of the overall statistical results of the research

The results of return-order imbalance GARCH relation

The results of return-order imbalance relation

Results of lagged return-order imbalance relations

Result of size effect test

BEKK and DCC estimation results

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