Business School Discipline of Finance. Discussion Paper

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1 Business School Discipline of Finance Discussion Paper Investigating Price Discovery Using a VAR-GARCH(1,1) Model of Order Flow and Stock Returns Daniel Maroney University of Sydney Business School Stephen Satchell Trinity College Cambridge / University of Sydney Business School 1

2 Investigating Price Discovery Using a VAR-GARCH(1,1) Model of Order Flow and Stock Returns Abstract The VAR-GARCH(1,1) price discovery model developed and tested with ASX data represents an extension of both the Chordia, Roll and Subrahmanyam (2005) and Hasbrouck (1991) models. The VAR-GARCH(1,1) price discovery model functions in accordance with the explanation for price discovery described by Chordia, Roll and Subrahmanyam (2005). This model allows the causal relationships between order flow and stock returns to be assessed, and for important aspects of the price discovery process to be measured. Both these analyses and the model itself represent contributions to the literature. This study also introduces an active trader order flow variable for fiveminute intervals using broker identification data from the ASX, which enables the brokers who executed each trade to be identified, including whether they were retail or institutional brokers. The findings highlight that active trader order flow, including institutional order flow, has a positive causal relationship with stock returns. In addition, they show that active retail order flow has a negative causal relationship with stock returns. 2

3 1.1 Introduction A number of studies have measured the causal relationship between order flow and stock returns, many of which have used bivariate VAR models to capture the dynamics of price discovery. However, the existing literature has focused on one time interval alone. Most research has studied daily causal flows and few have assessed intraday intervals. The result of these studies is an understanding of the nature of the causal relationship between order flow and stock returns. However, apart from the CRS model (Chordia, Roll and Subrahmanyam 2005), the literature has not provided an approximation of the time required for price discovery. The time required for price discovery is important because it indicates the length of time that arbitrage activity or herding activity could take. A potential limitation of the CRS model is that it is not in the bivariate VAR structure that Hasbrouck (1991) initially modelled for price discovery. The advantage of the bivariate VAR structure is that it considers the dynamics between order flow and stock returns as a system of equations, not as separate regressions. It also allows the AR processes found in both stock returns and order flow to be modelled, rather than using only a single lag. Further, Jiang (2011) applied the CRS model to Chinese stocks and found as this study does that variance is not constant, but follows a GARCH(1,1) process. The VAR-GARCH(1,1) model introduced in this paper has the advantage of the CRS model in that it considers time intervals from five minutes up to 60 minutes, which allows a more precise estimate of the time for various components of the price discovery process to occur. However, it also has the advantages of a VAR approach, while more aptly modelling volatility with a GARCH(1,1) process. Price discovery is an important process and the VAR-GARCH(1,1) price discovery model introduced in this paper, as well as the analysis from this model, make a valid contribution to the price discovery literature that concerns the causal relationships between order flow and stock returns. This model is based on the explanations of the causal relationships between order flow and stock returns advanced by Chordia, Roll and Subrahmanyam (2005). It is expected that order flow is described by an AR process that reflects herding or spreading out of orders. This herding behaviour should lead to 3

4 order flow having a positive causal flow with stock returns. However, arbitrageurs act in the opposite direction to herders, leading to the positive causal relationship between order flow and stock returns becoming negative. Arbitrage activity captured by midpoint stock returns should follow an AR process with possible negative signs. The dynamics of these processes are all modelled by the VAR-GARCH(1,1) price discovery model, with the additional contribution being that the time required for these dynamics to occur can now be determined. In order to test the applicability of the VAR-GARCH(1,1) price discovery model, this study applied this model to ASX stock price data for the years 1996, 2003 and The CRS model was also replicated to provide an indication of the likely relationships and their duration. The variables in the VAR-GARCH(1,1) price discovery model were tested to ensure that the coefficients were consistent with Chordia, Roll and Subrahmanyam s (2005) explanation of the price discovery process. In addition, to be consistent with Hasbrouck (1991), the variables in the VAR-GARCH(1,1) price discovery model were required to be statistically significant to indicate that the variables are relevant in describing the price discovery process. The key causal relationship is between order flow and midpoint returns, with the latter being the dependent variable. This is because it describes how prices adjust to new public information. If the order flow variable is found to have a causal effect on stock returns, the analysis then considers whether there are other variables that capture the effect of trade flow, as Hasbrouck (1991) anticipated. The other trade flow variables that Hasbrouck (1991) considered were found in this study in the broker ID data. The advantage of using ASX data to evaluate the VAR- GARCH(1,1) price discovery model is that the data also contain broker IDs that make it possible to identify which trade was executed by which broker, and whether the broker was a retail or institutional broker. By extending Frino, Johnstone and Zheng (2010), this study considers whether active trade flow was informative, rather than focusing on consecutive trades alone. This study contributes to the literature concerning order flow because it considers whether active order flow including active retail and active institutional order flows have a causal relationship with stock returns. Active trader order flow is measured by aggregating trades that are executed by brokers in the current 4

5 time period, provided that the same brokers were also active one period before. This extends to retail and institutional order flow as well. This study expected that active order flows would have a positive causal relationship with stock returns. Following Linnainmaa and Saar (2012), who used five-minute intervals, active retail order flow should have a negative causal relationship with stock returns, while active institutional order flow should have a positive causal relationship with stock returns. Retail traders have been found in the literature to be poor stock pickers, which should be reflected in intraday data (Grinblatt and Keloharju 2000, Odean 1999). Further, the effect should be more prominent for active retail order flow. In contrast, the literature consistently finds that institutional trade flow has a positive causal relationship with stock returns, which reflects that institutional traders are more informed about the future direction of stock prices. The results of this study show a positive causal relationship from order flow to stock returns, and the duration of this flow can be measured as occurring prior to arbitrage activity reversing the sign. Active order flows including active retail and active institutional order flows are of the expected sign and have a causal relationship with stock returns for some versions of these variables. Midpoint returns also follow an AR process reflecting arbitrage activity, and the duration can also be measured. Order imbalance follows an AR process reflecting herding and/or spreading out of orders. There is also an indication of contrarian activity directly influencing order flows. The remainder of this study is structured as follows. Section 1.2 discusses the literature, Section 1.3 details the data used. Section 1.4 describes the method, while Section 1.5 reports the results. Finally, Section 1.6 concludes. 5

6 1.2 Literature Review VAR-GARCH(1,1) Price Discovery Model Chordia, Roll and Subrahmanyam (2005) assessed the intraday efficiency of the NYSE using the equation: MPR t = α + β 1 MPR t 1 + β 2 OIB t 1 + ε t (3.1) where MPR t represents midpoint returns at time t; OIB t 1 is the lagged order imbalance, measured as the number of buy trades less the number of sell trades in the period t-1. Five-, 10-, 15-, 30- and 60-minute intervals were tested. The Hasbrouck (1991) VAR model of price discovery is: P t = i=1 α i P t i + i=1 β i x t i + v 1,t (3.2) x t = i=1 δ i P t i + i=1 γ i x t i + v 2,t (3.3) where i = 1,, n; P t is the stock price return; x t is a variable related to trade that is often applied in the literature as order imbalance; v 1,t captures new public information; and v 2,t contains trades with private information. The literature on order imbalance and stock returns often applies a modification of the VAR approach by including additional variables of interest; however, the price discovery process considered in this study has been modelled using the Hasbrouck (1991) VAR approach (Equations [3.2] and [3.3]). 6

7 The VAR-GARCH(1,1) price discovery model consists of 5 pairs of equations based on differing time intervals: p OIB t,i = α o,i + n=1 OIB t n,i + β M,i n=1 n MPR t n,i + ε o,t,i β n O,i p (3.4) 2 where ε o,t,i ~(0, h o,t,i ) h o,t,i = ω o,i + γ o,i ε o,t 1,i + ρ o,i h o,t 1,i i = 1,,5; p = 5. p MPR t,i = α m,i + n=1 OIB t n,i + β M,i n=1 n MPR t n,i + ε m,t,i (3.5) β n O,i p 2 where ε m,t,i ~(0, g m,t,i ) g m,t,i = τ m,i + θ m,i ε m,t 1,i + φ m,i g m,t 1,i i = 1,,5; p = 5. Where i = 1 corresponds to 5 minute intervals, i = 2 corresponds to 10 minute intervals, i = 3 corresponds to 15 minute intervals, i = 4 corresponds to 30 minute intervals and i = 5 corresponds to 60 minute intervals. Equations (3.4) and (3.5) are presented in matrix form in equation (3.6). Equation (3.6) describes a VAR (p) system of bivariate equations of dimension 2 with error variances following univariate GARCH(1,1) processes. n,i ( OIB t,i ) = ( α o,i p MPR t,i α ) + ( β 11 m,i n=1 n,i β 21 n,i β 12 n,i β ) ( OIB t n,i ) MPR t n,i 22 + ( ε o,t,i ε m,t,i ) (3.6) The VAR-GARCH(1,1) price discovery model contained in Equation (3.6) is an extension of the CRS model. It uses a VAR framework that has been consistently applied in the literature and is originally based on the Hasbrouck (1991) price discovery model. Equation (3.6) has the advantage of the CRS model in terms of identifying the time for price discovery with greater autoregressive parameters from a VAR approach. The papers on order imbalance and stock returns focus on the one time interval that best 7

8 shows a relationship between the variables of interest. In contrast, Equation (3.6) represents a systematic process of testing with each time interval (i) in order to determine the optimal time for price discovery. To be consistent with Chordia and Subrahmanyam (2004), who influenced the CRS model, Huang and Chou (2007) imposed a contemporaneous orthogonality condition that contemporaneously order flow impacted returns. As this study applied a variation of the CRS model, the ordering of variables in the VAR model is as it is reported, Equation (3.4) then (3.5). As detailed in the literature review section, the CRS model examines price discovery in the NYSE. Chordia, Roll and Subrahmanyam (2005) found that lagged order imbalance has a positive relationship with midpoint returns. In addition, they reasoned that order imbalance should have a positive effect on stock returns when the order imbalance is positive. The converse is also true that lagged negative order imbalance is associated with negative stock returns. In a study of the Chinese stock market using data from 2006, Jiang (2011) applied a GJR-GARCH(1,1) model and found that lagged order imbalance is positively correlated with stock returns for 10 minutes. In a key paper that assessed the intraday effect of lagged order imbalance on returns in the ASX using a Hasbrouck (1991) model, Lo and Coggins (2004) found a positive relationship. In a study of ASX stocks, Moshirian, Nguyen and Pham (2011) found that lagged order imbalance has a positive relationship with half-hourly stock returns. In the most recent study of the ASX, Smales (2014a) applied a VAR model, but used an absolute order imbalance variable, thereby making it inapplicable for the current study s analysis because our study aims to understand the role of the sign of order imbalance. For negative order imbalances, taking the absolute value should result in a negative relationship with stock returns; however, in the current study s model, this would be a positive relationship. Taking the absolute value has the effect of reducing the strength of the positive relationship observed in the literature between lagged order imbalance and stock returns. With 30-minute return data, Visaltanachoti and Luo (2009) applied a VAR(9) model and found that the coefficients for lagged order imbalances were 8

9 negative after including lagged midpoint returns. The negative causal flows can be explained by arbitrage activity, which acts in the opposite direction to the herd. The effect of arbitrage activity is that the positive causal flow between order imbalance and stock returns becomes negative. The consensus from the literature is that lagged order imbalance for one lag should have a positive effect on midpoint returns. Subsequent lags should also be positive in sign; however, lags of greater magnitude such as 30 minutes and 60 minutes could be negative. The CRS model, upon which the VAR-GARCH (1,1) model is based, states that order imbalance from both a theoretical and practical perspective, should be positively correlated with midpoint returns. Deference should be shown to the CRS model where there is divided opinion. However, Chordia, Roll and Subrahmanyam (2005) did not consider the large time horizon that is assessed by our study; thus extending their herding/order spreading and arbitrageur participant model to larger lags should eventually result in negative causal flows between order imbalance and stock returns, as observed in Visaltanachoti and Luo (2009) Causal flows between order imbalance and stock returns In the direction from OIB to MPR we need to consider β n,i 21 ; n = 1,...,5; i = 1, 5. Finding that β n,i 21 = 0 implies that OIB is not influencing MPR. Finding that β n,i 21 > 0 implies that there could be herding or the spreading out of orders. Finding that β n,i 21 < 0 implies that there could be arbitrage activity. There are causal flows between order imbalance and stock returns. Those flows remain positive until the influence of arbitrage activity is such that the flows become negative. The significance of order flow means that it is capturing the volume component of the price discovery process. By observing the results, it is possible to estimate the time at which this switch occurs. The relevant literature supporting all of the above outcomes is summarised below. According to Chordia, Roll and Subrahmanyam (2005), the positive causal flow reflects herding/spreading out of orders. When the coefficient becomes negative, the causal flow 9

10 reflects arbitrage activity. The ability of the VAR-GARCH(1,1) model to capture the trade-related component of the price discovery process does not conclude the analysis. In fact, Hasbrouck (1991) stated that the trade-related component can be adapted depending on the market. This leads the analysis to identify other measures of order flow that could have a causal relationship with midpoint returns. In particular, subsets of the order imbalance variable could have a causal relationship with midpoint returns. Specifically, does the level of trader activity contain information so that order flows from more active traders are causally connected with stock returns? Causal flows between active order imbalance and stock returns Frino, Johnstone and Zheng (2010) found that consecutive buy (sell) trades initiated by the same broker in the same direction have a greater price impact (measured as the natural logarithmic change in price six trades before and five trades after the consecutive trade) than those executed by different brokers. Applying the principle from Frino, Johnstone and Zheng (2010) led this study to develop a new measure of broker activity. This measure is calculated by first aggregating consecutive buyer-initiated trade volume with the same broker and in the same direction for a five-minute interval. Subtracted from that sum is the aggregate of consecutive seller-initiated trade volume by the same broker and in the same direction. The net amount is divided by the total share volume either bought or sold for the same five-minute interval. The findings from Frino, Johnstone and Zheng (2010) indicate that the new active order imbalance variable should have a positive causal flow with midpoint returns. The fact that it is an order imbalance variable also means that it should have a positive causal relationship with midpoint returns (Chordia, Roll and Subrahmanyam 2005). With ASX intraday data and focusing on large trade events, Avila, Fabre and Jarnecic (2015) developed a new variable that captured the level of broker competition at the depth associated with the market price. Using a Herfindahl index, the level of broker competition experienced by liquidity suppliers was classed into high or low levels of broker concentration. The results highlighted that, for purchases, lower broker concentration on the opposite side of the order book is associated with greater price impact than when there is a high level of concentration. For sales, lower concentration 10

11 on the opposite side of the order book is associated with greater price impact than when there is a high level of concentration on the opposite side. The current study differs from Avila, Fabre and Jarnecic (2015) because it measures the level of broker concentration on the same side as the trade, and constructs a new active order imbalance variable that is implemented for retail and institutional trades. In addition, for a broker to be defined as active, that broker must have traded in the current period as well as the previous period. Avila, Fabre and Jarnecic (2015) also found that their broker concentration variable was associated with information-based price impact. Following from this, as well as Frino, Johnstone and Zheng (2010), the causal flows between future returns and the active order imbalance variable could also be information based, thereby highlighting that active brokers are informed. Under the same conditions, for a given first-level opposite side depth, the greater the level of active broker activity on the other side of that depth, the greater the price impact. In Equation (3.6), the OIB t n,i variable is exchanged with six variants of active trader order flow at n = 1, as additional regressions to identify the coefficient β n,i 21. Finding that β n,i 21 0 implies that the activity level of traders trading through a particular broker, when aggregated, is informative of the future direction of prices. The positive relationship could indicate that active traders contribute to price discovery because prices move in the same direction in which they are trading. Another version of the VAR-GARCH(1,1) model could incorporate the active trader flow variable that can capture another aspect of volume dynamics in the context of the CRS and Hasbrouck price discovery models. It also leads to the questions: Does the causal relationship between active trader activity and stock returns also hold when the broker used is retail or institutional? What sign should the impact of an active trader using a retail or institutional broker have? Causal flows between active retail order imbalance and stock returns The literature concerning the impact of retail order flow has different views. Kaniel, Saar and Titman (2008); Barber, Odean and Zhu (2009); Barrot, Kaniel and Sraer 11

12 (2014) and Bailey et al. (2009) all found a positive relationship between retail order imbalance and returns. However, Han and Kumar (2013); Qian (2014); Colwell, Henker and Walter (2008) and Henker and Henker (2010) all reported a negative relationship between retail order imbalance and returns. However, these studies did not consider intraday relationships and subsequently are not directly applicable to the current study. Kelley and Tetlock (2013) considered intraday price impact and found that retail order imbalances were positively correlated with future returns. However, the positive measure was observed on a trade-to-close basis, rather than the five-minute horizon that is used in the current study. From an intraday perspective, Linnainmaa and Saar (2012) measured the price impact of trades from the instant before the trade to five minutes later, and consistently found that households have a negative price impact. As with the current study, Linnainmaa and Saar considered a five-minute horizon. The literature on active retail order imbalance is not as comprehensive. Kaniel, Saar and Titman (2008) and Vieru, Perttunen and Schadewitz (2006) found a positive relationship between active retail trading and future stock returns. However, Han and Kumar (2013) found a negative relationship between active retail trading and future stock returns. As the current study has an intraday perspective with broker ID data, the study that is most directly applicable is the Linnainmaa and Saar (2012) paper. The aggregation of retail trades into the new active retail order imbalance variable should result in a negative causal flow with future returns. However, Linnainmaa and Saar did not offer an explanation for the negative relationship. Given that theirs is the only previous study to use a five-minute measurement, the other literature is not directly applicable to the intraday context. The current study offers the explanation that traders using retail brokers do not contribute to price discovery on the intraday level, and prices move in the opposite direction to prior active retail order flow. Following from Odean (1999) and Grinblatt and Keloharju (2000), individual as opposed to institutional traders are poor stock pickers. This poor stock picking is likely to be exacerbated on the intraday level, where individual traders trade with institutional traders who possess far greater information and execution skill. The impact of active traders using retail brokers should also be consistent with Frino, Johnstone and Zheng (2010), and should be larger in 12

13 magnitude than all traders using retail brokers. This leads to the following subhypothesis: In Equation (3.6), the OIB t n,i variable is exchanged with six variants of active retail order flow at n = 1, as additional regressions to identify the coefficient β n,i 21. Finding that β n,i 21 < 0 implies that retail traders could be poor stock pickers. The negative causal relationship means that stock prices move in the opposite direction to prior active retail order flow Causal flows between active institutional order imbalance and stock returns After considering the effect of traders using retail brokers, the next related analysis concerns the effect of traders using institutional brokers. Unlike the retail order flow literature, the literature on institutional order flow and the impact on future stock returns is more homogenous. Hendershott, Livdan and Schüroff (2014); Boulatov, Hendershott and Livdan (2013); Henker and Henker (2010) and Bailey et al. (2009) all found a positive relationship between lagged institutional order imbalance and stock returns. However, Boulatov, Hendershott and Livdan (2013) considered active institutional trading. In contrast, Colwell, Henker and Walter (2008) found a negative relationship between lagged institutional order imbalance and future stock returns. While all these results generally point to a positive relationship, the data were not at the intraday level, as in the current study. From an intraday perspective, Linnainmaa and Saar (2012) measured the price impact of trades from the instant before the trade to five minutes later. They consistently found that domestic institutions have a positive price impact. The literature presents the view that institutional traders have a positive effect on price. This is the case for both intraday and beyond. Institutional traders are informed about the direction of stock returns and contribute to the price discovery process. The impact of active traders using institutional brokers should also be consistent with Frino, Johnstone and Zheng (2010) and should be larger in magnitude than all traders using institutional brokers. 13

14 In Equation (3.6), the OIB t n,i variable is replaced by six variants of active institutional order flow at n = 1, as additional regressions to identify the coefficient β n,i 21. Finding that β n,i 21 > 0 implies that institutional traders are more informed about the future direction of stock prices. The question remains: are stock returns explained by an autoregressive process? Another key component of the VAR-GARCH (1,1) model is the lagged midpoint return variables in the model Arbitrage Activity Chordia, Roll and Subrahmanyam (2005) stated that the lagged midpoint return variable captures the autoregressive characteristic of midpoint returns, as well as the action of arbitrageurs that act in the opposite direction of positive order imbalance autoregression in the market. They stated that they expected lagged midpoint returns to be negatively correlated with midpoint returns, and the results of their analysis confirmed their expectations. Extending the CRS model to a five-lag process should continue to find a negative relationship at higher orders, as implied by the Hasbrouck (1991) model. The significance of the highest significantly negative lag represents the time taken for price discovery to occur from arbitrage activity. Jiang (2011) found that lagged midpoint returns had a negative coefficient for 10-, 15-, 30- and 60-minute intervals when applying a CRS approach with GJR-GARCH(1,1). With ASX intraday data and implementing a Hasbrouck (1991) VAR approach, using one lagged midpoint return variable, Lo and Coggins (2004) found that lagged midpoint returns have a positive impact on current midpoint returns. This is different to Chordia, Roll and Subrahmanyam (2005) and Jiang (2011), and could be a result of the varying time periods and lags used for each stock in the sample, resulting in inconsistency and a mean figure that is not representative. In a recent ASX study with 30-second returns, Smales (2014a) found a positive relationship at lags of up to 90 seconds. The intention of Smales s study was to identify the impact of non-scheduled news arrivals by controlling for a number of factors. The 14

15 intervals studied were very small up to 90 seconds which is not enough time for price discovery to be measured. The smallest interval in the current study s results (as discussed in Section 3.6) is five minutes, which is longer than that considered by Smales. Visaltanachoti and Luo (2009) found that, with 30 minute lags and a VAR approach, the coefficients of lagged midpoint return variables are significantly negative, consistent with Chordia, Roll and Subrahmanyam (2005) and Jiang (2011). Finding that β n,i 22 < 0 implies that the impact of a small change in MPR t n,i on MPR t,i is negative and also provides support for the explanation that the negative impact reflects the action of arbitrageurs, in accordance with Chordia, Roll and Subrahmanyam n,i (2005). The largest significantly negative lag number n from β 22, multiplied by i (time interval length), represents an approximation of the time required for arbitrage activity to facilitate price discovery Herding/Spreading of Orders If there is a relationship between order imbalance and lagged order imbalance, the relationship is not of sufficient magnitude for a positive causal relationship between order flow and stock returns captured by β n,i 21 to persist. Arbitrage activity can offset the impact of order imbalance autoregression. The CRS model predicts that there should be positive order imbalance autoregression in the market, but that this is insufficient to induce a positive relationship between lagged midpoint returns and current midpoint returns. Combining Hasbrouck (1991) and CRS should report a positive impact of lagged order imbalance on current order imbalance in the market for the five lags in the VAR-GARCH(1,1) model. The residual term that occurs when the Hasbrouck (1991) model (Equation [3.4]) is applied captures trades containing private information. For the VAR-GARCH(1,1) model to remain important as a price discovery model, the coefficients for lagged order imbalance and lagged midpoint returns should be significant. 15

16 Chordia, Roll and Subrahmanyam (2005) reported positive order imbalance correlation for NYSE stocks. Lo and Coggins (2004) observed that, for intraday ASX data, the coefficient of lagged order imbalance in a Hasbrouck (1991) model is also positive. With 30-minute intervals applying a VAR model, Visaltanachoti and Luo (2009) reported positive order imbalance autoregression for up to eight lags. Avila, Fabre and Jarnecic (2015) observed herding behaviour in the ASX. The theory underpinning the CRS model and the literature supports the view that order flow autoregression should be positive. The finding that β n,i 11 > 0 implies that the impact of lagged order flow on current order flow is positive and provides support for the explanation that traders are herding and/or spreading out their orders over time (Chordia, Roll and Subrahmanyam 2005). The largest significantly positive lag number n from β n,i 11, multiplied by i (time interval length), represents an approximation of the duration of the herding and/or spreading out of orders Contrarian Trading Under the CRS model, arbitrageurs act in the opposite direction to the price pressure placed by order imbalance. Arbitrage activity captured by the negative coefficient of lagged midpoint returns offsets the positive impact on order flow of herding/spreading out of orders. When order imbalance is the dependent variable, order imbalance and arbitrage activity captured by lagged midpoint returns should work in the opposite direction. Therefore, if lagged order flow has a positive impact on order flow, lagged midpoint returns should have a negative impact on order flow. In this manner, the market excluding arbitrageurs behaves in a contrarian manner by trading in the opposite direction to previous stock returns. The literature also supports this idea. Lo and Coggins (2004) reported a significantly negative lagged midpoint return coefficient, while Visaltanachoti and Luo (2009) observed a significantly negative variable up to one hour. Finding that β n,i 12 < 0 implies that stock returns have a negative causal relationship with order imbalance as the dependent variable. The negative causal flow reflects contrarian 16

17 trading activity. The largest significantly negative lag number n from β n,i 12, multiplied by i (time interval length), represents the duration of contrarian activity. 1.3 Data In this study, data were obtained from Thomson Reuters Tick History for 2003 and For 1996, data from AusEquity were used because data were not available for that year from Thomson Reuters. Those years were chosen because they are approximately equidistant in a manner similar to Chordia, Roll and Subrahmanyam (2005). The analysis conducted for 2013 measured the effect of active order flows by using AusEquity data that also contained broker IDs. Data for 2013 were obtained because it was the most recent year with available data 1. The data collected encompassed the full transaction dataset for the top 50 stocks by market capitalisation. Following the approach in Chordia, Roll and Subrahmanyam (2005), the top 50 stocks are the top 50 by market capitalisation at the start of each year. The dataset used provided transaction prices, the prevailing bid and ask quote at the time of the trade, and the volume traded at each transaction. The actual prevailing quote was matched to the transaction price. Using the quote rule, a trade was defined as either buyer- or seller-initiated with complete accuracy for the Thomson Reuters data. The AusEquity data included a buyeror seller-initiation qualifier. For the CRS model, replication order imbalance was calculated using two different measures. The measure OIB(#) referred to trade order imbalance, indicated by the number of buyers less the number of seller-initiated trades in the time interval. The measure OIB($) referred to the dollar value of shares bought less the dollar value of shares sold in the time interval. For the VAR-GARCH(1,1) model, trade order imbalance was used because of its continued significance in the CRS model replication compared to dollar value order imbalance. The analysis of active trader order flows including retail and institutional flows focused on order imbalance based on volume 1 ASIC placed a ban on naked short selling in 2008 subject to a few exceptions. Covered shorts were banned but late in 2008 were allowed for non-financial assets. In 2009 ASIC lifted the ban on covered short selling of financial assets. At the time of the study in 2011 and 2013, covered short selling was allowed and this facilitated arbitrage activity consistent with the CRS (2005) model. 17

18 traded because the aim was to identify other measures of order flow that could explain the price discovery process. The definitions of the other measures of order flow relevant to the active order flow analysis are addressed in more detail in the following section. 1.4 Method VAR-GARCH(1,1) Price Discovery Model Combining the CRS and Hasbrouck (1991) price discovery models produced the VAR- GARCH(1,1) price discovery model described in equations (3.4) to (3.5) and in matrix form in equation (3.6). To identify the number of lags to be included in the model as detailed in Equation (3.6) the ACF and PACF for both order flow and midpoint returns were examined. F- tests found serial correlation. Reviewing these tests indicated that using five lags was the optimal setting 2. Consistent with Jiang (2011), the model in Equation (3.6) was extended to account for GARCH effects. Numerous tests were performed to assess whether the models had ARCH effects, including Q, Lagrange Multiplier, Lee and King, Wong and Li and F-tests, for up to 12 lags. The consensus was that ARCH effects did exist for the models; thus, the key assumption of homoscedasticity was violated. As homoscedasticity was violated, the classical linear regression model could be improved upon. Chordia, Roll and Subrahmanyam (2005) did not address the issue of ARCH effects in the data instead, they used a classical linear regression approach that controlled for cross-sectional correlation in the residuals. To achieve more accurate results, the current study implemented the GARCH(1,1) model. Inherent in a GARCH(1,1) model is infinite ARCH effects; thus, the ARCH effects observed in the diagnostic tests were controlled for 3. 2 The firm effect is present in the data and refers to serial correlation in the residuals of a given firm. However, including a VAR (5) process in the model removes the effect of serial correlation. 3 The time effect refers to cross-sectional correlation in the residuals for a given year across stocks. The model does not control for the time-effect but it does address the presence of ARCH/GARCH effects that a panel data approach alone will not do. The issue of ARCH/GARCH effects was more important than the issue of cross-sectional correlation that Chordia, Roll and Subrahmanyam (2005) corrected. Also as the model is an extension of the CRS(2005) model by incorporating the Hasbrouck(1991) VAR framework, a panel data approach would not be consistent with those studies. 18

19 By assessing numerous time intervals (i), the VAR-GARCH(1,1) price discovery model enables the time for various aspects of the price discovery process to be determined Active Trader Flows As Hasbrouck (1991) indicated, the volume dynamics captured by β n,i 21 in Equation (3.6) can be exchanged with another trade-related variable. It is for that reason that this study sought to find other volume-related variables that are a subset of the order imbalance variable in Equation (3.6). The new volume variables were evaluated based on their performance measured by β n,i 21, as stock returns were also the dependent variable in Chordia, Roll and Subrahmanyam (2005), and β n,i 21 is more directly relevant to the price discovery process. The definition of trader activity is an extension of Frino, Johnstone and Zheng (2010), who studied the price impact of consecutive trades by the same broker in the same direction. In the measures of trader activity detailed below, trades by the same broker in the same direction in period t (where t is a five-minute time period) given that the brokers also traded during time interval t 1), are aggregated for both buys and sells to form an active trader order flow variable that has not previously been tested in the literature Active Trader Flow Equations A number of different models of active trader order flow were considered after including an AR(5) process for midpoint returns that was also factored into the VAR- GARCH(1,1) model. As there is no previous literature on active trader order flow and because five-minute intervals have only previously been examined by Linnainmaa and Saar (2012) for trade impacts rather than flows, a number of new measures of order flows were developed in this study. The model with statistically significant returns is detailed here. The other models are described in the Supplementary section. 19

20 Standardised Active Volume Order Flow t n,i is the active buy volume less the active sell volume as a proportion of total buy/sell volume. MPR t,i = ς m,i + p n=1 β n M,i MPR t n,i O,i + β n=1 SAVOF t n,i + n m,t,i (3.7) where p = 5; i = 1. SAVOF t n,i = Standardised Active Volume Order Flow t n,i = Active Buy Volume t n,i Total buy volume t n,i Active Sell Volume t n,i Total Sell Volume t n,i = Active Buy Volume t n,i Active Sell Volume t n,i Total Buy t n,i or Total Sell Volume t n,i Active Buy Volume represents the volume associated with brokers who executed buy trades during time period t and also bought at t 1, where t is a five-minute interval. Active Sell Volume represents the volume associated with brokers who executed sell trades during time period t and also sold at t 1, where t is a five-minute interval. Total Buy or Total Sell Volume is the quantity of total volume on either the buy side or sell side, without factoring whether the volume was buyer initiated or seller initiated. For that reason, either buy or sell volume can be used. 2 where n m,t,i ~(0, f m,t,i ) f m,t,i = κ m,i + ν m,i n m,t 1,i + ψ m,i f m,t 1,i Retail and Institutional Order Flows The literature highlighted that active retail order flows have a negative causal relationship with stock returns. This negative causal flow could mean that traders using retail brokers are poor stock pickers because prices move in the opposite direction to retail order flow. The literature provides support for active institutional order flow having a positive causal relationship with stock returns. This positive causal flow could 20

21 mean that traders using institutional brokers are more informed about the direction of future prices. The previous literature has not measured active retail or active institutional order flow. In addition, this study s use of five-minute retail and institutional order flows is unique in the literature. These models provide an intraday perspective on the influence of active retail and institutional order flows on price discovery, which has not previously been addressed in the literature. The model with statistically significant returns is detailed here. The other models are described in the Supplementary section. Active Institutional Trader Flow t n,i measures the information contained in the net active institutional broker numbers alone, without considering the volume traded by those brokers. MPR t,i = π m,i + p n=1 β n M,i MPR t n,i O,i + β n=1 AITF t n,i + ρ m,t,i (3.8) where p = 5; i = 1. where AITF (Active Institutional Trader Flow) = (Active Institutional Buy Sum Active Institutional Sell Sum)/(Active Institutional Buy Sum + Active Institutional Sell Sum); Active Institutional Buy Sum represents the number of distinct institutional brokers who executed buy trades during time period t and had also executed buy trades at time period t 1 (where t is a five-minute interval); and Active Institutional Sell Sum represents the number of distinct institutional brokers who executed sell trades during time period t and had also executed sell trades at time period t 1 (where t is a five-minute interval). 2 where ρ m,t,i ~(0, c m,t,i ) c m,t,i = χ m,i + ζ m,i ρ m,t 1,i + φ m,i c m,t 1,i Active Retail Volume Order Flow (BISI) t n,i measures active buyer- and sellerinitiated volume. MPR t,i = Α m,i + p n=1 β n M,i MPR t n,i O,i + β n=1 ARVOF (BISI) t n,i + Ν m,t,i (3.9) 21

22 where p = 5; i = 1. Where, ARVOF(BISI) t n,i = Active Retail Volume Order Flow (BISI) t n,i = (Active_BIBuyVolSum_Ret Active_SISellVolSum_Ret) Total Buy or Total Sell Volume t n,i where Active_BIBuyVolSum_Retail represents the buyer-initiated trade volume executed by traders through retail brokers at time t who had also executed buyer-initiated trades at time t 1; Active_SISellVolSum_Retail represents the seller-initiated trade volume executed by traders through retail brokers at time t who had also executed sellerinitiated trades at time t 1; and Total Buy or Total Sell Volume is the quantity of total volume on either the buy side or sell side, without factoring whether the volume was buyer initiated or seller initiated. For that reason, either buy or sell volume can be used. 2 where N m,t,i ~(0, s m,t,i ) s m,t,i = Η m,i + Π m,i Ν m,t 1,i + Λ m,i s m,t 1,i Active Institutional Volume Order Flow(BISI) t n,i measures active buyer- and active seller-initiated volume. MPR t,i = Ψ m,i + p n=1 β n M,i MPR t n,i O,i + β n=1 AIVOF(BISI) t n,i + Ω m,t,i where p = 5; i = 1. Where, AIVOF(BISI) t n,i (3.10) = Active Institutional Volume Order Flow (BISI) t n,i = (Active_BIBuyVolSum_Insto Active_SISellVolSum_Insto) Total Buy or Total Sell Volume t n,i where Active_BIBuyVolSum_Insto represents the buyer-initiated trade volume executed by traders through institutional brokers at time t who had also executed buyer-initiated 22

23 trades at time t 1; Active_SISellVolSum_Insto represents the seller-initiated trade volume executed by traders through institutional brokers at time t who had also executed seller-initiated trades at time t 1; and Total Buy or Total Sell Volume is the quantity of total volume on either the buy side or sell side, without factoring whether the volume was buyer initiated or seller initiated. For that reason, either buy or sell volume can be used. 2 where Ω m,t,i ~(0, b m,t,i ) b m,t,i = Μ m,i + Τ m,i Ω m,t 1,i + Ε m,i b m,t 1,i 1.5 Results Summary Statistics The key variables of order imbalance and midpoints returns are presented in Table 3.1. From 1996 to 2011, for all time intervals, there appeared to be a slight reduction in the mean of the order imbalance variable. However, the standard deviation of order imbalance also increased. Although order imbalance had a lower mean, reflecting less order imbalance in the ASX, there was greater variation in the magnitude of order imbalance. The ASX tended to be in balance for the years studied, which reflects buyerinitiated orders being offset by seller-initiated orders of similar magnitude. The mean of midpoint returns increased in magnitude and was more negative in 2011 than in 1996 or This table contains a description of the data used in the application of the VAR- GARCH(1,1) model. In this study, data were obtained for the ASX. Order imbalance was equal to the difference between the number of buyer-initiated trades and sellerinitiated trades. Midpoint returns were calculated by taking the natural log of the current stock price and the stock price one period prior. The number, mean and standard deviation of both order imbalance and midpoint returns are reported. 23

24 Table 3.1: Descriptive Statistics Order imbalance Midpoint returns 1996 N Mean Std dev N Mean Std dev 5 mins 881, , E mins 440, , E mins 289, , E mins 151, , mins 75, , N Mean Std dev N Mean Std dev 5 mins 881, , E mins 431, , E mins 283, , E mins 148, , E mins 74, , E N Mean Std dev N Mean Std dev 5 mins 826, , E mins 423, , mins 277, , mins 145, , mins 60, , CRS Model Table 3.2 replicates the CRS model. This replication provides an indication of price discovery using a one lag model (Equation [3.1]). From the perspective of Hypothesis 3.1, lagged order imbalance with a trade-based measure (although the coefficient was smaller in magnitude) remained significant for 30 minutes in 1996 and There was a further decline in both magnitude and significance in 2011, and trade order imbalance was significant for 15 minutes. For dollar-based order imbalance, a decline in magnitude and significance also occurred so that, in 2011, no lagged dollar order imbalance variables were significant. This reflected price discovery of the dollar order imbalance variable; thus, it was no longer relevant in describing market dynamics. Table 3.2 appears to indicate that trade-based order imbalance has a greater role in price discovery than does dollar-based order imbalance. Thus, trade-based order imbalance was used in the VAR-GARCH(1,1) price discovery model. 24

25 Hypothesis 3.1d states that the action of arbitrageurs is displayed by negative coefficients for lagged midpoint returns. The coefficients of lagged midpoint returns were both negative and significant for 30 minutes in This actually increased in 2003 to 60 minutes, then declined to 30 minutes in It took arbitrageurs up to 60 minutes to facilitate price discovery in Table 3.2 displays the Fama-Macbeth cross-sectional regressions performed for the ASX 50 for the years 1996, 2003 and In this table: midpoint return (t 1) is the lagged midpoint return OIB#(t-1) is the lagged trade order imbalance, and refers to the number of buyer- less the number of seller-initiated trades at time t 1 OIB$(t-1) is the lagged dollar value imbalance, and refers to the dollar value of shares bought less the dollar value of shares sold at time t 1 the t-statistic is the standard student t-test the adjusted t-statistic is the t-statistic adjusted for cross-correlation in the residuals coefficients in bold are significant at a one-sided 5 percent level or greater. the adjusted R 2 controls for the number of independent variables. 25

26 Table 3.2: Multiple Regressions of Returns on Lagged Returns and Two Different Measures of Lagged Order Imbalance Explanatory variable Return interval (minutes) Five Midpoint return Coefficient (t 1) t-stat Adj t-stat OIB#(t-1) Coefficient (x 10 ^ 5) t-stat Adj t-stat OIB$(t-1) Coefficient (x 10 ^ 5) t-stat Adj t-stat Adj R Midpoint return Coefficient (t 1) t-stat Adj t-stat OIB#(t-1) Coefficient (x 10 ^ 5) t-stat Adj t-stat OIB$(t-1) Coefficient (x 10 ^ 5) t-stat Adj t-stat Adj R Midpoint return Coefficient (t 1) t-stat Adj t-stat OIB#(t-1) Coefficient (x 10 ^ 5) t-stat Adj t-stat OIB$(t-1) Coefficient (x 10 ^ 5) t-stat Adj t-stat Adj R

27 1.5.3 VAR-GARCH(1,1) Price Discovery Model Results Results: Hypothesis 3.1 Table 3.3 contains the results for the VAR-GARCH(1,1) model. Panel A focuses on When midpoint returns were the dependent variable, the lagged order imbalance coefficients were positive and significant for all lags in the five-minute time interval, thereby providing support for Hypothesis 3.1. Consistent with this hypothesis, the causal flows for 10-minute intervals became negative at a lag of 50 minutes, with a coefficient of and t-value of For 15-minute intervals, the positive causal flows remained significantly positive for all lags. However, for 30-minute intervals, the positive causal flows became negative from a lag of 120 minutes, with a coefficient of and t-value of For 60-minute intervals, the lagged order imbalance coefficient was negative at a lag of 180 minutes. Table 3.3 provides some support for Hypothesis 3.1 and the CRS model that underpins this hypothesis because the causal flows were positive; however, from a lag of around 50 minutes, 120 minutes and 180 minutes, the relationship became negative. This could reflect arbitrage activity, which reduces the positive impact of lagged order flow on current order flow, that would tend to maintain a positive causal flow between lagged order flow and midpoint returns. The negative causal flows observed were consistent with those observed by Visaltanachoti and Luo (2009), who also noted negative coefficients from 30 minutes. All the lagged order imbalance coefficients were significant, which supports the ability of the VAR-GARCH(1,1) model to capture the price discovery process. Panel B of Table 3.3, where the dependent variable is midpoint returns, presents the results for The most important aspect is that the positive causal flow between order flow and midpoint returns was less, which provides support for the explanation that arbitrage activity could reduce the influence of the positive impact of lagged order flow on current order flow in the market. For five-minute intervals at a lag of 20 minutes, the causal flow became negative. At 10-minute intervals, causal flows were negative from 30 minutes, compared to 50 minutes in For 15-minute intervals, the flows were negative from 45 minutes, with a coefficient of and t-value of For 30-minute lags, the causal flow was negative from 60 minutes with a coefficient of 27