Predictions of Intraday Volume, Volatility and Spread Profiles and Their Applications

Transcription

1 ITG Financial Engineering, March 2016 Predictions of Intraday Volume, Volatility and Spread Profiles and Their Applications INTRODUCTION The ability to anticipate market volumes and volatility has considerable value in a variety of trading applications. Accurate forecasts of market conditions allow buyand sell-side traders to adjust their strategies to improve trading performance. In addition, such information facilitates informed decisions regarding the difficulty of trading on a given day, the size of an order that can be realistically completed, and the true relative difficulty of trading the individual names in portfolio trades. ITG s Smart Market Indicators (SMI) widgets 1 have been developed to measure real time market conditions and compare them with their corresponding historical average values. Recently, ITG Financial Engineering developed a time series model to characterize and predict deviations of future market conditions from normal market conditions, given their current realizations and recent history. The model provides insights into how the current values of smart indicator statistics affect the future expected dynamics of those statistics and thus can be viewed as a natural application of the ITG SMI product. The resulting predictive analytics can be used not only as a stand-alone product for volume, volatility and spread prediction, but also are integrated into ITG s Smart Cost Estimator (SCE) model to provide pre-trade and real-time estimates of future expected trading cost for buy-side institutional orders and evaluate the dependence of trading cost on changes in the past and current market conditions. In the next section we briefly review the intuition and motivation behind our predictive model. Then we summarize the relevant literature and illustrate how the model can be used in conjunction with ITG s Smart Market Indicators (SMI) to generate and update predicted market conditions in real time. We also describe the methodology for model validation, and provide an example of applying this methodology to demonstrate improved quality of market condition forecasts. More technical aspects of the model are covered in section Opening the Black Box: Some Stylized Facts on Decay Profiles. The paper concludes with the summary of main results. MOTIVATION Suppose the realized volume in the recent 30-minute interval (10:00-10:30AM) is three times higher than normal for the same stock, and the realized volume in the 1 The SMI product cards and samples of historical data are available from the ITG Analytics Incubator website at 1

2 previous history of the day (from open to 10:00AM) being five times larger than normal. In addition, assume that the trading volume recorded yesterday was 50% higher than the normal daily volume. Naturally, one would expect the favorable market conditions for volume to persist. We would like to quantify the degree of persistence (how far into the future we expect the favorable liquidity) and the magnitude of future deviations from normal market conditions. In particular, How much higher is the expected volume going to be, relative to its historical average value, in the next 30-minute interval (10:30-11:00AM)? In the subsequent 30-minute intervals (11:00-11:30AM, 11:30AM- 12:00PM, and so on? How rapidly would one expect the unusually favorable (or unfavorable) market conditions to revert to their normal values? Should we expect partial or full reversion of market condition variables toward their average historical values during the remainder of the trading day? How accurate are our predictions of future market conditions? The predictive analytics supported by ITG s Financial Engineering team provide answers to the above and other related questions. The distinguishing features of our predictive model can be summarized as follows: Three non-directional market condition surprise 2 analytics spread, volatility, and volume are currently supported. Predictions of those analytics in the future 30-minute intervals 3 depend on the recent 30-minute surprise, the cumulative surprise (from the beginning of the day), and the previous day s surprise of the same analytic (see Exhibit 1 below). Our predictive model covers 40 countries. The geographic coverage may be expanded in the future, conditional on users interest and the quality of the available market data. The predictive models are calibrated every three months using one year of recent (historical) data. The estimates reflect some of the stockspecific characteristics, such as security type and liquidity, as well as their historical spread, volatility and volume profiles. Accuracy of the predictive models is monitored in- and out-of-sample on a quarterly basis. We discuss predictions of future deviations of the analytics of interest from their normal values on the baseline 30-minute grid. Naturally, the quality of short-term prediction is expected to be better when the prediction horizon (the time interval between the current and target 30-minute intervals) is shorter. Two countervailing effects affect the accuracy of model performance and motivate our choice of the model granularity. On the one hand, surprise values observed over longer time intervals tend to be less contaminated by random idiosyncratic factors such as microstructure noise, reducing the signal-to-noise ratio of predictive variables, and resulting in more reliable predictors. On the other hand, averaging predictive values over the time intervals that are too long tend to diminish their discriminatory power (everything is averaged out) and results in mixing the information that is relevant for future predictions with extraneous (or obsolete) factors. 2 Surprise ratio for an analytic of interest (spread, volatility, or volume) associated with stock a in interval j on trading day T is defined as the ratio of that analytic to its historical average (or median) value for the same stock, day, and intraday interval. The historical distributions (percentiles) of the above three analytics are provided by ITG s SMI widgets. 3 Predictions for more granular intervals are created over the 30-minute grid using heuristics. 2

3 Exhibit 1: Stylized flow of calculations inside the intraday predictive model For a given ticker XYZ, trading day T, and time of the day (the most recent 30-minute interval r), we determine the historical daily average value for the analytic of interest (e.g., trading volume) and the intraday historical profile for that analytic. The realized values of that analytic for the previous trading day T 1, cumulative intraday interval (1:(r 1)) on day T, and last 30-minute interval on T from real time data are used, along with their historical average counterparts (provided by ITG s Smart Market Indicators distributions), to obtain the surprise ratios Surprise(T 1), Surprise(T, 1:(r 1)), and Surprise(T, r) for the analytic of interest. The triplet of those surprise ratios is the input to our predictive model. The output of our model is the sequence of predicted future surprise ratios Surprise(T, r+h) for the remainder of trading day T. The values of inputs and outputs can be recalculated with progress of time if the model is repeatedly used throughout the trading day. Our predictive analytics can be immediately used in pre-trade transaction cost models. It is commonly accepted in transaction cost analysis (TCA) that both market conditions and execution strategy/schedule affect transaction costs. Adjustments of execution schedules to accommodate future projected market conditions can result in significant cost savings. For example, if a favorable market condition surprise hits the market and is expected to decay back to normal conditions by the end of the day, it usually makes sense to accelerate trading early to take advantage of the favorable market conditions. Both the 3

4 magnitude of the recent market condition surprise, the rate of its reversion (decay) to normal values, and the projected market condition surprise near the end of the execution horizon would affect the optimal strategy choice. Moreover, the predicted market condition surprises can be used in the attribution analysis for transaction costs and other market analytics. PREVIOUS WORK ON INTRADAY PREDICTION OF MARKET CONDITIONS Starting from the seminal work by Engle (1982), prediction of daily and intraday volatility has been a prolific area of research in finance for the last 35 years. Extensions of the original idea are encapsulated in models based on alternative methodologies, all of which have some advantages and drawbacks. Andersen et al. (2003) discuss how the past values of volatility recorded over daily and lower frequency time intervals can be combined to generate accurate future volatility forecasts. The approach was ultimately applied to obtain intraday realized volatility forecasts, see, e.g., Engle and Sokalska (2012). As for the volume predictions, similar ideas can be applied to build intraday volume forecasts. Brownlees et al. (2011) take a slightly modified approach to generate intraday volume forecasts. Other relevant models involve Białkowski et al. (2008) and Satish et al. (2014), with the methodology used in the latter paper sharing some common features with our framework. The models developed for intraday volatility and volume dynamics are usually not applied directly to capture spread persistence, primarily because of concerns about discreteness of spread distribution for most of stocks in the modern, post- Reg NMS, market environment. Still, since spread surprises, if properly specified, exhibit substantially similar time series dynamics, their prediction can also be approached similarly to that for intraday volume and volatility. Our model inherits several attractive features of other popular methodologies: We employ a multiplicative component decomposition similar to the one entertained for intraday volatility in Engle and Gallo (2005) and intraday volume in Brownlees et al. (2011) to decompose the intraday analytics of interest into the daily, intraday deterministic, intraday persistent stochastic, and idiosyncratic components. Our forecasts of realized volatility, volume and spread for intraday 30- minute intervals are built on the conceptual ideas of Corsi (2009) who proposed a HAR-RV model for daily realized volatility prediction. We also incorporate the intuition and some basic insights from the mixed data sampling (MIDAS) regression models (Ghysels et al., 2006). ESTIMATION METHODOLOGY AND MODEL VALIDATION Deviations of market conditions from normal manifest themselves in surprise ratios that are either very high (much higher than 1) or close to 0 (much lower than 1). Based on this information, we estimate surprise profiles that predict future deviations of market conditions from normal. In the absence of new information, one would expect the effect of those high or low surprises to gradually fade away ( decay ) in the future, resulting in future predicted surprise ratios converging to normal levels close to 1 in the long run. The longer the prediction horizon, the closer the projected future surprises would be to 1, reflecting the stylized fact that the market conditions (volume, volatility, and spread) tend to mean revert to normal, albeit gradually. 4

5 In a nutshell, we attempt to predict the future deviation of an analytic from its median by modeling it as a nonlinear function of its recent deviations from the median values. Specifically, we use as predictors of deviations in interval r+h on day T the previous 30-minute surprise of the analytic in interval r, the cumulative intraday surprise in interval 1:(r 1) on day T, and the cumulative surprise on day (T 1). In the spirit of the HAR-RV model (Corsi, 2009), we fit the nonlinear regression model Surprise(T, r, r+h) = f r,r+h (Surprise(T, r), Surprise(T, 1:(r 1)), Surprise(T 1)) + error(t, r, r+h) (1) for each combination of intraday interval r and prediction horizon h to accommodate a higher sensitivity of future surprise predictions to signals from recently observed surprises. Equation (1) results in the predicted future surprise function f r,r+h being more sensitive to recently observed surprises than to surprises observed in the more distant past, but it accounts for the incremental predictive power of those mixed frequency surprises due to their cross-sectional dependence and autocorrelation. Examples: Real time volume and volatility predictions Assume that we wish to obtain intraday volume forecasts for a liquid NYSE-listed stock AmerisourceBergen (ABC) at 12:30PM on August 3, The key inputs and outputs of the model are shown in Exhibit 2A below. To facilitate comparison, the light-colored blue bars in Exhibit 2A show the predicted intraday volume surprise profile for this stock if we utilized only the volume information for the stock on the previous trading day, July 31, 2015 (i.e., the forecast was made at 9:30AM on August 3, 2015). This predicted surprise profile is uniformly above 1 (corresponding to the long-term historical median values of volume), since the trading volume on July 31, 2015 was much higher than historical median daily volume. The orange bars in the same exhibit show the realized volume surprises observed in six 30-minute intervals between 9:30AM and 12:30PM on August 3, Almost all of them are noticeably higher than 1 but lower than the predicted volume surprises based on the previous day s information only (shown by light blue bars on the plot). Given this information, we generate predictions for median volume surprises in time intervals 12:30-1:00PM, 1:00-1:30PM, and so on, as shown on the plot by circles collected by the solid black line. The predicted surprise values exhibit a tendency to grow, reflecting the high volume surprise realization on the previous day (T 1) (July 31, 2015). However, the black prediction line does not converge to the level of light blue bars, since it is affected materially by lower than expected observed surprise values observed so far (between 9:30AM and 12:30PM on the same trading day T). The predicted volume patterns can be updated sequentially every half-hour (as shown by the red, green, yellow, and violet curves) to reflect the realized surprises in the time interval r = 7 (12:30-1:00PM) and every 30 minutes thenceforth. In particular, since the realized volume surprise in 12:30-1:00PM is very close to the level predicted by the black curve, the red curve showing the new predicted surprises at the end of interval r = 7 is nearly identical to the black curve. Since the surprise levels observed in intervals r = 8 and r = 9 (1:00-1:30PM and 1:30-2:00PM, respectively) are significantly lower than what was predicted for those intervals, the corresponding green and yellow predictive curves are noticeably lower than the black and red predicted surprise curves. Also notice that at 2:00PM, as the end of the trading day is getting closer, even the long-term predicted surprise levels shown by the yellow curve drop below 1, only to recover after the new volume surprise is observed in interval r = 10 (between 2:00PM and 2:30PM). 5

6 Exhibit 2A: Realized and predicted real time volume surprise profiles Exhibit 2B: Realized and predicted real time volume profiles The information encapsulated in the volume surprises (actual and predicted) in Exhibit 2A can be easily translated into the actual and predicted share volume levels as displayed in Exhibit 2B. The important reference curve in Exhibit 2B, shown in dotted black pattern, represents the historical median share volume levels in each 30-minute interval of the trading day. It corresponds to normal surprises, i.e., values equal to 1 at the unit level in Exhibit 2A. All other patterns shown in Exhibit 2B are obtained from their counterparts in Exhibit 2A by scaling them (multiplicatively) to the level of the historical median share volume curve (black dotted line). 4 4 To avoid crowding the plots on Exhibit 2B, we remove the red and violet predicted curves. We also cut off the shown prediction horizon at 3:30PM. 6

7 Similar plots can be obtained for the predicted intraday volatility and spread surprise levels. Exhibit 3 on the bottom of this page shows the plots of realized and predicted values of intraday volatility surprises for Loews Corporation (NYSE: L) on August 25, The updating mechanics are exactly the same as those for volume: at 9:30AM on the prediction day T (August 25, 2015), we generate the predicted future volatility surprise profile for each 30-minute interval based on the volatility surprise level observed on the previous day (T 1) (August 24, 2015). The predicted profiles are then sequentially updated as the new information on realized volatility surprises arrives and gets encapsulated in up-todate predictions of future volatility surprise profiles every 30 minutes. To avoid congesting the plot, we show those predicted volatility surprise profiles only at 10:00AM, 10:30AM, 12:30PM, and 2:00PM. Since the volatility level for the Loews Corp. stock on August 24, 2015 was 3½ times higher than its historical average daily volatility, the surprise volatility profile generated by our model at 9:30AM (and displayed by light blue bars on Exhibit 3) is also between 50% and 100% higher than normal. As the early morning trading on the prediction day T (August 25, 2015) resulted in the levels of volatility higher than was predicted at 9:30AM based on the previous day s information only, the projected future volatility surprises generated at 10:00AM (and shown in solid black line on the plot) are even higher, indicating the future projected volatility levels to be twice as high as their historical average values. However, similar to our first example, the realized volatility surprises observed in most of the subsequent 30-minute intervals are fairly lower than expected (although still comparable or slightly higher than their historical averages). Because of that, the predicted volatility surprise patterns obtained at 10:30AM (red line), 12:30PM (green line), and 2:00PM (yellow line) indicate the predicted volatility levels below what was expected at the beginning of the day. Exhibit 3: Realized and predicted real time volatility surprise profiles Another observation is about the speed of mean reversion of the projected volatility surprises. The information embedded in the last 30-minute surprises is typically short-lived, as most of mean reversion occurs within the next 30 minutes. However, the residual effect of surprises accumulated over longer 7

8 intervals of day T and over the entire previous day (T 1) linger much longer. This observation applies more generally: the longer the measurement period of the predictive surprise variable, typically the longer the horizon over which it is expected to be relevant. Evaluating prediction accuracy The predictive model is hard to evaluate for individual stocks, since the prediction accuracy metrics are prone to outlier activity as they are inevitably affected by the short in-sample and out-of-sample intervals. Therefore, we present the performance metrics for groups of individual tickers, which are segmented by their security type, liquidity, and country of exchange. As we increase the sample size, the influence of random outliers is reduced, resulting in fairly stable confidence intervals. We measure predictive accuracy of our model both in- and out-of-sample. The insample accuracy metrics keep track of how well the fitted values provided by the model explain the surprise analytics realized over the model estimation period. The out-of-sample accuracy metrics attempt to do the same when the model is applied outside of the estimation period. For brevity, we focus on prediction accuracy plots out-of-sample, which is usually more challenging to establish than in-sample accuracy, especially if the predictive model is prone to overfitting. This is clearly not the case for our model, as we observe the quality of fit metrics that are surprisingly similar in-sample and out-of-sample. Exhibit 4 on the next page provides an example of display that we use to monitor the predictive performance of our model. We showcase the outcome of intraday trading volume prediction tests for a group of actively traded US-listed common stocks (with average daily volume between $2.0 bln. and $2.9 bln.). We calibrate our predictive model every three months using a 12-month long rolling window for its estimation. The model performance is subsequently evaluated both in-sample (using the last three months of the rolling window) and out-of-sample (using the three-month period immediately after the rolling window). For each intraday interval r and prediction horizon h, we collect three stockspecific surprise variables Surprise(T 1), Surprise(T, 1:(r 1)), and Surprise(T, r), used for prediction of future values of Surprise(T, r+h) for the analytic of interest (see equation (1) at the beginning of this section). We subdivide the sample used for performance evaluation into 27 alternative scenarios as follows: Split the sample into the three groups L (low), N (normal), and H (high) by 30 th and 70 th percentiles of Surprise(T 1); Split each of those three groups into the three groups L (low), N (normal), and H (high) by 30 th and 70 th conditional percentiles of Surprise(T, 1:(r 1)); Finally, split each of those nine groups into the three groups L (low), N (normal), and H (high) by 30 th and 70 th conditional percentiles of Surprise(T, r). In each of the 27 scenario subsamples, we compare the median surprise ratios f r,r+h (Surprise(T, r), Surprise(T, 1:(r 1)), Surprise(T 1)) predicted by our model for the specified horizon h with the 10 th, 50 th, and 90 th empirical percentiles of the 8

9 realized surprise ratios Surprise(T, r+h). Exhibit 4 summarizes the outcomes of our performance tests for trading volume of liquid US-listed stocks when the prediction time is 10:30AM (r = 2) and the prediction horizons are h = 1 (30 minutes) and h = 3 (90 minutes). factors. Comparison of predicted and realized volume surprise ratios out-of-sample For summarizes our performance tests for trading volume of liquid US listed stocks when the model predictions are made at 10:30AM (r = 2, i.e., two 30-minute intervals after the US market opening) for the horizons h = 1 (the next 30-minute interval 10:30AM-11:00AM after the prediction time) on the left-hand side plot and h = 3 (the third 30-minute interval 11:30AM-12:00PM past the prediction time) on the right-hand side plot. The colored dots indicate median predicted volume surprise ratios when the volume observed in the last 30- minute interval is low (shown in blue), medium (shown in green), or high (shown in red), whereas nine previous day volume and cumulative same day surprise scenarios is characterized by the pair of symbols below the horizontal axis. The colored lines mark the median realized volume surprises in the above scenarios, while the top and bottom end points of each vertical segment indicate the 10 th and 90 th percentiles of realized volume surprises in those scenarios. For example, the level of green line at the market condition category L:H on the left-hand side plot shows the median future volume surprise ratio predicted for the next 30-minute interval if a low previous day volume surprise was observed on the previous day, a high cumulative volume surprise was observed between 9:30AM and 10:00AM on the prediction day, and a medium (normal) volume surprise was observed in the previous 30-minute interval 10:00-10:30AM. We make the following observations after inspection of plots on Exhibit 4: The realized median surprise values (marked on each plot by the dots ) match closely the predicted surprise values (indicated by solid lines) in each of the 27 considered scenarios. The historical unconditional estimates (corresponding to the normalized volume surprise values equal to 1 and shown on each plot by the horizontal dotted black lines) clearly fail to capture the variation of the realized surprise values. All three predictive surprise variables measured over different time intervals previous day, same day between 9:30AM and 10:00AM, and same day between 10:00AM and 10:30AM contribute to capturing some variation in the realized surprise values. 9

10 The gaps between the 10 th and 90 th empirical percentiles in each scenario indicate a considerable residual uncertainty. Qualitatively similar conclusions about predictive performance of our model at alternative prediction intervals (r) and horizons (h = j r) can be made for other analytics and for other groups of stocks. OPENING THE BLACK BOX: SOME STYLIZED FACTS ON DECAY PROFILES The qualitative properties of our model for various market segments, analytics, and prediction horizons can be evaluated by analyzing the patterns of sensitivities of median predictive values in the target intervals r+h to the three predictors (surprises) measured in the reference interval r. Empirical evidence suggests that a log-linear surprise prediction function f r, r+ h = exp( δ ( Surprise( T, r), Surprise( T,1: ( r 1)), Surprise( T 1)) 0, r, r+ h )( Surprise( T, r)) δ 1.r,r + h δ2.r,r + h.r,r + h Surprise T r Surprise T 1))) δ3 ( (,1: ( 1))) ( ( (2) provides a good approximation of the general functional form in equation (1). The sensitivities (elasticities) of predicted values to recent surprises represented by the exponents δ 1,r,r+h, δ 2,r,r+h, δ 3,r,r+h summarize parsimoniously the properties of forecasts and the relative contributions of each surprise variable used for prediction. The patterns of delta coefficients for each of the three predicted analytics (volatility, volume, and spread) can be compared across multiple reference intervals r, prediction horizons h, groups of stocks, and countries (or regions). Before discussing some of the most prominent features of the patterns captured by those exponents, we emphasize the special role played by the first exponent δ 1,r,r+h = (logsurprise(t,r,r+h)) / (logsurprise(t, r)), which can be interpreted as the sensitivity (responsiveness) of the model predictions at the horizon h to variation in the surprise values recorded in the 30-minute reference interval r. Sequences of those exponents viewed as functions of h exhibit robust patterns that drop from 1 (for zero prediction horizon h) to values between 0 and 1 for short prediction horizons, and further to much smaller (often near-zero) positive values for longer prediction horizons, and can be interpreted as impulse responses to a unit shock experienced by the analytic of interest in the last 30- minute interval. The coefficients δ 1,r,r+h (viewed as functions of h) are also called the decay profiles. In addition, the levels of predicted surprises are also affected by realized values of two other predictors, whose influence is magnified or reduced depending on the realization of the other two exponents δ 2,r,r+h and δ 3,r,r+h and the values of Surprise(T, 1:(r 1)) and Surprise(T 1). Our discussion will be primarily focused on the patterns of decay coefficients δ 1,r,r+h from equation (2). We also comment briefly on the properties and interpretation of exponents δ 3,r,r+h. The set of exponents δ 2,r,r+h associated with cumulative same day surprises can be interpreted similarly. We report several robust patterns for the decay profiles across securities with different levels of trading activity (liquidity) and across securities traded in different markets. 10

11 Do yesterday s volatility, volume, and spread surprises still matter today? The answer is affirmative, in general. The effects of previous day s surprise on today s level of volatility, volume, and spread are positive and often quite large. The left-hand side plot of Exhibit 5 displays how predictions for future 30-minute volume surprises built at the beginning of a trading day depend on the previous day s volume surprises, based on the recent (2015) data for US-listed stocks with various liquidity levels (ranging from most liquid, shown in red, to most illiquid, shown in purple). The right-hand side plot of Exhibit 5 shows the sensitivities of future 30-minute volume surprises to the previous day s volume surprises when predictions are made 30 minutes after the start of a trading day. Exhibit 5: Sensitivities of 30-min volume surprises to yesterday volume surprise Conditional on information prior to 9:30AM Conditional on information prior to 10:00AM The plots of Exhibit 5 show the sensitivities of intraday 30-minute volume surprises at horizon h (i.e., in 30-minute intervals j = r+h, shown on the horizontal axis) to yesterday s volume surprises for stocks from the very liquid (red), liquid (orange), medium liquid (green), less liquid (blue), and illiquid (violet) segments of the market. The numerical values of sensitivities represent the degree of shrinkage ( decay ) for yesterday s volume shocks as their impulse responses get propagated through the course of the day. For example, the value of 0.5 shown at horizon h = 1 in violet color on the left-hand side plot indicates that, assuming yesterday s volume is twice as large as the historical MDV for very illiquid stocks, our model predicts (on average) today s first 30-minute interval volume (between 9:30AM and 10:00AM) to be 1.41 (= ) times larger than normal. The values shown on the right-hand side plot should be interpreted as incremental contributions of the previous day s surprises, on top of the information contained in volume surprises for the first 30-minute interval of the day. 5 Three observations are in order: The effect of yesterday s surprises reflected by δ 3,0,h diminishes with the prediction horizon h (see the left-hand side plot of Exhibit 5 for the volume analytic), as the previous day s information becomes less relevant for more distant future predictions. The sensitivities of future market surprises to yesterday s surprises tend to be lower for illiquid stocks, reflecting the more significant incremental 5 For instance, the sensitivities of volume surprise in the first 30-minute interval of the day j = r = 1 to yesterday s volume surprise are set to zero, since volume in interval 9:30-10:00AM is known with certainty by 10:00AM and yesterday s volume does not contain any incremental information that could improve predictions for that interval. 11

12 information provided by yesterday s market conditions for predictions of today s market conditions for liquid stocks. The incremental information contained in previous day surprises and captured by coefficients δ 3,r,r+h diminishes once r > 0, as the morning intraday (30-minute and cumulative) surprises of the analytic of interest are accounted for (see the right-hand side plot of Exhibit 5 for the volume analytic and r = 1). However, the decline is relatively modest for bid-ask spread prediction across the entire liquidity spectrum, and for volatility of illiquid stocks. How strong is the influence of morning shocks on market conditions dynamics? Once the contribution of yesterday s surprise to today s volume, volatility, and spread predictions has been established, it is natural to fix its magnitude and focus on incremental contributions of volatility, volume, and spread surprises observed at the beginning of a trading day (within the first 30 minutes after local market opening) or over the 30-minute interval later in the day. Those contributions are captured by coefficients δ 1,r,r+h of regression (2). Exhibit 6: Sensitivities of 30-min volume surprises to same day surprises Conditional on information prior to 9:30AM Conditional on information prior to 10:30AM The plots of Exhibit 6 show the sensitivities of intraday volume surprises observed in the future (in 30-minute intervals j = r+h, shown on the horizontal axis) in response to the volume surprise observed in 30-minute interval r for US stocks from the very liquid (red), liquid (orange), medium liquid (green), less liquid (blue), and illiquid (violet) segments of the market. The numerical values of sensitivities represent the degree of shrinkage ( decay ) for 30-minute volume shocks observed in interval r as their impulse responses get propagated through the course of the day. The left-hand side plot displays the sensitivities of future surprises to 30-minute volume surprise observed in the first ½ hour of a trading day (9:30-10:00AM, r=1). The right-hand side plot displays the sensitivities of future surprises to 30-minute volume surprise observed in the third ½ hour interval of a trading day (10:30-11:00AM, r=3). Both values are incremental sensitivities that are conditional of the previous day s volume surprises and surprises observed today before the end of interval r 1 (during the first hour of trading 9:30-10:30AM, if r=3). We observe the following (see Exhibit 6 above): Volume and volatility shocks observed during the morning trading tend to dissipate faster for less liquid stocks and have longer lifetimes for more liquid stocks, reflecting the stylized fact that volatility and volume 12

13 surprises for less liquid stocks are more affected by market microstructure noise and other idiosyncratic short-memory factors. 6 The only exception is the effect of bid-ask spread surprise shocks for tickers from the most illiquid segment of the market, as the rate of their dissipation is much slower, primarily because of the quote staleness. The rate of decay for any 30-minute surprise exhibits a tendency to slow down after the initial 30-minute period (reference interval r) where the shock (impulse) is measured. 7 Comparison of decay profiles for North American, European, and Asian markets In this subsection we discuss some of the decay profiles observed for representative common stocks from major equity markets around the globe. For illustration, we select two North American (USA, CAN), two European (GBR, DEU), and two Asian-Pacific (AUS, HKG) markets. We present the representative country-specific profiles for each of those countries by picking at random multiple tickers from different liquidity groups and constructing the median decay rate profiles, where the median is determined separately for each country. Our goal here is to provide an illustration rather than embark on a full scale comparative analysis. Exhibit 7 on the next page compares some of the decay profiles for representative common stocks traded in six international markets. For illustration, we chose the decay profiles in response to spread surprises. The left-hand side plot of Exhibit 7 illustrates how rapidly the incremental information contained in spread surprises observed in the first 30 minutes after the local market opening becomes obsolete with progress of time, showing the sensitivities of future predicted spread by 30-minute increment intervals (indexed from 1 through 17 according to the number of half-hour intervals since the local market opening time). 8 Although the predictive power of the bid-ask spread exhibits qualitatively similar decaying behavior in all six of those international markets, the information of the post-opening spread becomes obsolete within the next 30-minute interval (between half-hour and an hour after opening) at the fastest rate for HKG and AUS, and at the slowest rate for DEU and CAN. The right-hand side plot of Exhibit 7 shows the decay of incremental information provided by spread surprise observed between 1½ hours and 2 hours after the market opening. For consistency of the interpretation of regression coefficients in equation (2), it is important to remember that the effect of spread surprise reported here is incremental on top of the spread surprise information accumulated over the previous 1½-hour interval of the same day trading day as well as the deviation of spread from its historical average observed on the previous trading day. This information in 30-minute spread surprises decays more slowly since surprisingly large or small values of bid-ask spread in the middle of a trading day are indicative of more persistent asymmetric information in the market, in contrast to temporary character of spread surprises shortly after market opening. 6 This observation also generally tends to apply for 30-minute shocks observed in the middle of a trading day. 7 This property is reminiscent of the typical impulse response profiles observed for persistent GARCH(1,1) processes (Zivot and Wang, 2006), where initial fast (near instantaneous) decay of initial volatility shocks is followed by very slow decay afterwards. 8 USA and CAN markets are open for 6½ hours resulting in 13 half-hour increments. GBR and DEU are open for continuous trading for 8½ hours, resulting in 17 half-hour increments. AUS stock exchange is open for 6 hours (12 half-hour increments), whereas HKG is open for 2½ hours before lunch and 3 hours after lunch resulting in 13 half-hour increments (including two increments over the lunch hour). 13

14 Exhibit 7: Decay profile comparison for spread surprises across international markets The plots of Exhibit 7 show the sensitivities of intraday spread surprises observed in the future 30-minute intervals j = r+h (shown on the horizontal axis) in response to the spread surprises observed in 30-minute interval r for equities traded in six international stock markets. The numerical values of sensitivities represent the degree of shrinkage ( decay ) for 30-minute spread shocks observed in interval r, as their impulse responses get propagated through the remainder of the trading day. The left-hand side plot displays the sensitivities of future surprises to the 30-minute spread surprise observed in the first ½ hour of a trading day (r=1). The right-hand side plot displays the sensitivities of future surprises to 30-minute spread surprise observed between 90 and 120 minutes since the local market opening (r=4). Both values are incremental sensitivities that are conditional of the previous day s spread surprises and same day spread surprises observed prior to the end of interval r 1 (during the first 1½ hours of trading if r=4). The following two observations apply to predictions of international volume and volatility surprise analytics alike. For brevity, we provide the illustration (Exhibit 8 on the next page) only for volume. Aftershocks of 30-minute volume surprises detected early in the day (during the first half-hour interval after local market opening) tend to linger much longer than aftershocks for spread surprises, especially for the HKG market; for instance (see the left-hand side plot of Exhibit 8), between 20% and 30% of a 30-minute volume surprise in interval r = 1 remains relevant for the late date trading volume, whereas the information value of a 30-minute spread surprise in interval r = 1 for the end-of-day spread does not exceed 10% (the left-hand side plot of Exhibit 7). The 30-minute volume response patterns to surprises observed later in the day (see the right-hand side plot of Exhibit 8 for r = 4) exhibit a larger initial decay but slower subsequent convergence to end-of-day values than for spread. 14

15 Exhibit 8: Decay profile comparison for volume surprises across international markets The plots below show the sensitivities of intraday volume surprises observed in the future 30-minute intervals j = r+h (shown on the horizontal axis) in response to the volume surprises observed in 30-minute interval r for equities traded in six international stock markets. The numerical values of sensitivities represent the degree of shrinkage ( decay ) for 30-minute volume shocks observed in interval r, as their impulse responses get propagated through the remainder of the trading day. The left-hand side plot displays the sensitivities of future surprises to the 30-minute volume surprise observed in the first ½ hour of a trading day (r=1). The right-hand side plot displays the sensitivities of future surprises to 30-minute volume surprise observed between 90 and 120 minutes after the local market opening (r=4). Both values are incremental sensitivities that are conditional of the previous day s volume surprises and same day surprises observed prior to the end of interval r 1 (during the first 1½ hours of trading if r=4). SUMMARY This article introduces a new product that can be used in conjunction with ITG SMI to predict future intraday values of volatility, volume, and spread from the recent surprises of those analytics. It reviews the intuition behind observed decay profiles, illustrates how the product can be applied to generate and update predicted market conditions in real time, and demonstrates the improved quality of market condition predictions relative to their static historical averages. Discussion of technical details is kept short or omitted altogether for the sake of simplicity. The review of other real time and TCA applications (e.g., dynamic cost optimization, cost attribution) is relegated to future white papers and technical reports. 15

16 References Andersen, T.G., T. Bollerslev, F.X. Diebold, and P. Labys (2003) Modeling and Forecasting Realized Volatility Econometrica 71, Białkowski, J., S. Darolles, and G. Le Fol (2008) Improving VWAP Strategies: A Dynamic Volume Approach. Journal of Banking and Finance 32(9), Brownlees, C.T., F. Cipollini, and G.M. Gallo (2011) Intra-Daily Volume Modeling and Prediction for Algorithmic Trading. Journal of Financial Econometrics 9(3), Corsi, F. (2009) A Simple Approximate Long-Memory Model of Realized Volatility. Journal of Financial Econometrics 7(2), Engle, R.F. (1982) Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica 50(4), Engle. R.F. and G. Gallo (2006) A Multiple Indicators Model for Volatility Using Intra-Daily Data. Journal of Econometrics 131(1), Engle, R.F. and M.E. Sokalska (2012) Forecasting Intraday Volatility in the US Equity Market. Multiplicative Component GARCH. Journal of Financial Econometrics 10(1), Ghysels, E., P. Santa-Clara, R. Valkanov (2006) Predicting Volatility: How to Get Most Out of Returns Data Sampled at Different Frequencies. Journal of Econometrics 131(1), Satish, V., A. Saxena, and M. Palmer (2014) Predicting Intraday Trading Volume and Volume Percentages. Journal of Trading 9(3), Zivot, E. and J. Wang (2006) Modeling Financial Time Series with S-Plus. Springer-Verlag, Berlin Investment Technology Group, Inc. All rights reserved. Not to be reproduced or retransmitted without permission These materials are for informational purposes only and are not intended to be used for investment purposes. The information contained herein has been taken from sources we deem reliable but we do not represent that such information is accurate or complete and it should not be relied upon as such. No guarantee or warranty is made as to the reasonableness of the assumptions or the accuracy of the models or data used by ITG or the actual results that may be achieved. Broker-dealer products and services are offered by: in the U.S., ITG Inc., member FINRA, SIPC; in Canada, ITG Canada Corp., member Canadian Investor Protection Fund ( CIPF ) and Investment Industry Regulatory Organization of Canada ( IIROC ); in Europe, Investment Technology Group Limited, registered in Ireland No ( ITGL ) and/or Investment Technology Group Europe Limited, registered in Ireland No ( ITGEL ) (the registered office of ITGL and ITGEL is Georges Court, Townsend Street, Dublin 2, Ireland and ITGL is a member of the London Stock Exchange, Euronext and Deutsche Börse). ITGL and ITGEL are authorised and regulated by the Central Bank of Ireland; in Asia, ITG Hong Kong Limited, licensed with the SFC (License No. AHD810), ITG Singapore Pte Limited, licensed with the MAS (CMS Licence No ), and ITG Australia Limited (ACN ), a market participant of MATCH Now SM is a product offering of TriAct Canada Marketplace LP ( TriAct ), member CIPF and IIROC. TriAct is a wholly owned subsidiary of ITG Canada Corp. 16