Is Volatility Your Friend or Nemesis? The Links Between Transaction Costs, Market Conditions, and Trading Styles

Transcription

1 AUTHORS Milan Borkovec Managing Director Head of Financial Engineering Konstantin Tyurin Director Financial Engineering CONTACT Asia Pacific Canada EMEA United States Is Volatility Your Friend or Nemesis? The Links Between Transaction Costs, Market Conditions, and Trading Styles ABSTRACT This article summarizes results of our extensive empirical study motivated by the intuitively appealing statement that institutional clients average transaction costs are sensitive to market conditions. Using a comprehensive sample of client execution data covering two years of trading, we confirm that average cost of institutional trades varies considerably and systematically with volatility, volume, and trade imbalance surprises. For the overwhelming majority of buy-side institutions, implementation shortfall is higher than normal when volatility and volume exceed their historical average values. However, the deviations of trading volume in excess of the values typically observed in high volatility conditions dampen the effect of high volatility environment on execution costs of institutional orders. We document a strong dependence of transaction costs on contemporaneous trade imbalances, which is amplified by higher than normal contemporaneous volatility. We observe that cost curves are more sensitive to order size at the times of less favorable buy-sell trade imbalances, reflecting the role played by directional market pressure indicators. In summary, buy-side institutions should not neglect market conditions monitoring, as failure to adjust promptly to market conditions may result in deteriorated performance and missed cost savings opportunities. INTRODUCTION Monitoring and predicting the market environment is important for institutional traders, since transaction costs vary with market conditions. This maxim reflects conventional wisdom captured by many popular price impact models, resulting in practical recommendations to traders and their sponsors. For example, popular liquidity sourcing algorithms targeting VWAP and volume participation take advantage of abundant market volume intervals representing cost saving opportunities for large institutional investors. Volatility as a direct measure of price risk not only affects uncertainty of traders execution prices but also is a factor affecting their ability to keep own price impact under control. However, shortage of comprehensive execution data and substantial variation of traders behavior and their execution styles make the quantification of the links between market conditions and trade outcomes of quantitative models and their attribution more challenging.

2 2 In this study we provide answers to the following questions: What are important factors influencing trading costs of large institutions? How much would trading in a volatile environment hurt you? Is it actually hurting you? Would shifting your executions to episodes of abundant volume affect your cost? What is the order size beyond which we start materially affecting the market with our price impact? We investigate not only the sensitivities of realized costs to factors like volume, volatility, and trade imbalance individually, but also explore the joint influence of those factors, and find evidence of amplification or dampening of their effects, often in a non-linear fashion. The methodological approach in this paper focuses on exploration of conditional cost curves characterizing the dependence of implementation shortfall costs on market conditions and stock attributes at the parent order level. By doing that, we step away from granular modeling where the parent order is split into small pieces (child orders) and the impact of trading each of those pieces is modeled independently. To characterize market conditions and trading environment during the executions of parent orders, we create, for each order, strategy-weighted market condition metrics for volume, volatility, and trade imbalance (as weighted averages of the corresponding metrics at child order level, with weights obtained from the realized trading strategy of the parent order). We interpret the observed variation in scale and shape of the cost curves in the context of our knowledge of market impact and the nature of institutional trading. We find that average cost of institutional trades varies considerably and systematically with volatility, volume, and trade imbalance surprises. For the overwhelming majority of institutions, implementation shortfall is higher than normal when volatility and volume exceed their historical average values. However, the deviations of trading volume in excess of the values typically observed in high volatility conditions dampen the effect of high volatility on execution cost of institutional orders. We document a strong dependence of transaction costs on contemporaneous trade imbalances, which is amplified by higher than normal contemporaneous volatility. Finally, we observe that cost curves are more sensitive to order size at the times of less favorable buy-sell trade imbalances, reflecting the role played by directional market pressure indicators. We identify substantial heterogeneity of buy-side participants in the data sample, and suggest ways to correct the implied behavioral biases. A small but significant group of institutions exhibit trading styles that are different from the rest of the field. Those clients trade predominantly smaller orders through direct market access (DMA), often filling them in more favorable market conditions at negative average cost. Their larger orders are generally executed in dark pools shortly after the order has been submitted, or get cancelled otherwise. Failure to exclude such clients leads to downward-biased cost levels and negative slopes of aggregate cost curves for small order sizes. Another bias is detected for most of the institutions represented in our data for large order sizes. Large orders, especially those arriving late in the day, tend to be filled more frequently in favorable market conditions than smaller orders, resulting in a thinned sample of observed executions and downward-biased aggregate cost curves.

3 3 DATA AND METHODOLOGY For our empirical analysis we use a sample of client orders executed via algorithmic trading. The sample covers trades in US-listed stocks 1 and is confined to two years of trading from January 13 to December 14. Our sample is special in the sense that most of the executions provide information about the algorithmic strategy (structured, liquidity seeking, etc.) and execution venue (dark or lit), trade time, as well as whether the trades were executed by buy-side institutions directly or by brokers on behalf of their institutional clients. The data is not limited to ITG executions only; all buy-side participants represented in the data sample trade through a variety of brokers. For our analysis, parent orders ( broker clusters ) are constructed by combining all individual trades made on behalf of the same client in the same name, direction (buy or sell), and day. With more than clients covered, the data sample represents a wide variety of institutions with heterogeneous trading styles. A small but significant group of those clients 2 exhibit trading styles that are different from the rest of the field, trading predominantly small orders through DMA by acting as liquidity providers most of the time, but filling some medium and large size orders opportunistically in dark pools. This kind of trading behavior, while being common in the marketplace, is not consistent with trading styles observed for most of the buy-side institutional clients. For instance, the average order life time of those clients with opportunistic trading styles (OTS clients) is 5 to 6 times shorter than for other clients and the order life time decreases significantly as signed trade imbalances become unfavorable, suggesting opportunistic trading behavior by cancelling orders that cannot be executed within a pre-specified price range and time period. As will be discussed in subsection 3.4, the cost curves of those OTS clients are typically much lower than for the entire sample and, in fact, qualitatively different for some scenarios, influencing the interpretation and some implications of our empirical findings. The liquidity of a stock should be taken in consideration while plotting the cost curves, since failure to account for stock heterogeneity (by bundling up very liquid and less liquid stocks in the same bucket) can contribute to noisy averages and may introduce biases in the cost curve estimates. To keep those distortions in check, we report and analyze the cost curves separately for tickers categorized into four liquidity groups. 3 We present summary statistics on implementation shortfall costs and other metrics separately for different order size categories, since market conditions and other variables may play a different role for large, medium, and small institutional orders. The liquidity group-dependent thresholds partition the sample in ten relative order size categories as described in Table 1. The relative order size is defined as percentage of the median 21-day daily historical volume of a given stock on the trading day. 1 Trades in ETFs are excluded. 2 Approximately % of clients in our data sample. 3 A stock is classified as Very liquid on day T if its 21-day median historical daily dollar volume (MDDV(T)) exceeds $56.2mln. Similarly, a stock is classified as Liquid / Less Liquid if its MDDV(T) is between $12.3mln. and $56.2mln / between $1.4mln. and $12.3mln, respectively. We categorize all other stocks as Illiquid.

4 4 TABLE 1 Order size group thresholds Small Orders Medium Orders Large Orders SG SG1 SG2 SG3 SG4 SG5 SG6 SG7 SG8 SG9 Very.5%.25%.% 1% 2% 4% 8% 16& 32% Liquid Liquid.%.% 1% 2% 4% 8% 16% 32% 64% Less.15%.75% 1.% 3% 6% 12% 24% 48% 96% Liquid Illiquid.% 1.% 3% 6% 12% 24% 48% 96% 192% Our sample consists of more than 5.2mln orders with an average dollar size of $453,. The average daily volume of trades captured by data analyzed in this report is nearly $4.7bln. Details of the sample composition are presented in Table 2. The sample is dominated by very small orders. For instance, the orders in the smallest size categories SG and SG1 represent, depending on liquidity group, between 44 and 81 per cent of the total number of orders. However, our sample is more balanced across size groups when comparisons are made in terms of dollar value of trades. The sample is only slightly dominated by orders from the medium size groups (SG4 through SG7) relative to small size (SG through SG3) or large size (SG8 and SG9) orders. 4 TABLE 2 Average daily number of orders and daily trading volumes 4 in the sample period (13 14) Relative order size category Small Orders Medium Orders Large Orders Average number of orders per day Very Liquid Liquid Less Liquid Illiquid Average daily value exchanged (in mlm.) Very Liquid Liquid Less Liquid Illiquid SGO $94 $11 $2 $.1 SG $298 $48 $13 $.8 SG $234 $44 $16 $1.3 SG $319 $67 $29 $2.4 SG $437 $4 $45 $3.7 SG $554 $!59 $67 $4.3 SG $62 $195 $66 $4.1 SG $538 $152 $48 $3.2 SG $272 $7 $25 $2. SG $1 $35 $17 $2.1 All Size Groups $34 $887 $329 $24. 4 All summary statistics presented in Table 2 are daily averages. Since there are 4 trading days in the sample period, all those averages should be multiplied by 4 to get the number and the dollar value of orders in each bucket.

5 5 While executing larger trades, buy-side institutions or their brokers are expected to minimize (or at least monitor, along with other performance metrics) implementation shortfall cost. The dollar-weighted average implementation shortfall in our sample is 16.4 bps, but it varies significantly by order size and arrival time. Also, as will be discussed later, implementation shortfall cost has high positive correlation with the signed trade imbalance 5 measure observed over the parent order execution horizon. Dependence of costs on relative order size (represented by the so-called cost curves ) is recognized in industry and academic studies and in commercial products. The cost curves exhibit qualitatively different features across three size-dependent regimes (details on summary statistics are provided in Table 3): Small order sizes: Average costs are small and often smaller than half of the bid-ask spreads (due to spread capture). Medium-small to medium order sizes: Average costs are steadily increasing with size, as long as percentage size does not exceed to percent of the median daily volume for the stock (this is the zone of the prototypical cost curve behavior that concerns most of institutional clients). Medium-large and large order sizes: Average cost curves flatten and, in many cases, start behaving erratically, because of small sample sizes and discretionary biases that are pervasive for large order size categories. This taxonomy provides a rather robust characterization of prototypical cost curves, although it is purely exploratory and qualitative in nature. While it is hard to expect that such an exploratory analysis alone would reveal deep insights in structural parameters affecting the price impact curves or the speed of their mean reversion, the observations of changes in shape of the cost curves and their relationships with the observed market conditions, order characteristics, and order execution strategies may suggest ways to improve execution timing or highlight approaches to building better performance benchmarks. Before presenting our findings in detail, we briefly discuss miscellaneous other factors at play. TABLE 3 Aggregate cost curves for the trimmed sample of institutional clients Relative order size category Average dollar-weighted cost, in bps (by liquidity group) Very Liquid Liquid Less Liquid Illiquid Small Orders SG SG SG SG Medium Orders SG SG SG Large Orders SG SG SG All size groups Trade imbalance of a parent order is defined as the execution strategy-weighted difference between buyer- and seller-initiated trading volumes, where the trade initiator (aggressor) is determined by the Lee Ready algorithm. Signed trade imbalance is obtained by multiplying the trade imbalance by ±1 depending on the direction of the order.

6 6 The dependence of results on order direction over the sample period (13 14) is weak, usually negligible, although it appears more significant if the analysis is performed separately by quarter. To limit the number of exhibits presented in this article, we confine our discussion to the combined sample of buy and sell orders. The order arrival time affects the horizon over which the order can be filled, the urgency of trading and, implicitly, the role played by market conditions in determination of the price impact. Moreover, there may be a clientele effect at play, since the balance between information-driven and liquidity-motivated orders may change depending on whether the order is received before the market opening time, shortly after the opening auction, or closer to the end of the trading day. Based on these considerations, we verify robustness of our results by repeating the analysis for the subsamples with order arrival times restricted to particular times of the day. While we detect some variation in the levels of cost curves and their interaction with market conditions, the qualitative effects are similar. Therefore, we report only the results based on the combined sample of orders. VARIATION OF COSTS WITH NON-DIRECTIONAL MARKET CONDITIONS As we discuss empirical evidence of cost dependence on the market conditions prevalent during institutional order executions, we will revisit some of the questions posed at the beginning of this article: Is high volatility a nemesis for institutional traders? Does the timing of one s own trading to high volume periods increase cost savings? Can liquidity and volatility risks be managed separately from each other? We focus on the role played by deviations of trading volume and volatility from their expected values over the execution horizon and ask whether buy-side institutional clients always benefit from lower than normal volatility and higher than normal volumes during their trading. Conditional cost curves by volatility surprise category We examine the effect of deviations of contemporaneous and recent volatilities from their historical average values on the implementation shortfall cost. We stratify (separately for each liquidity group) the set of orders according to the different contemporaneous volatility surprise categories (Low, Medium, or High) 6, and plot the corresponding cost curves for each volatility surprise and liquidity group combination. We establish the following empirical stylized facts: For the small and medium size categories, implementation shortfall cost reacts more strongly to increases in order size in a high volatility regime than in lower volatility regimes, indicating the higher incremental impact of trading in a high volatility regime. The aforementioned effect tends to be stronger for orders arriving closer to the end of the US trading day. For large order sizes, the empirical dependence of cost on order sizes flattens and gets more erratic as the bias due to discretionary trading starts kicking in, even though the cost levels in the high volatility regime are still higher. Overall, there is sufficient evidence that high volatility adversely affects execution costs for all orders. 6 We classify the realized volatility for the given order as High if the realized strategy-weighted volatility surprise value exceeds the 8th percentile of the volatility surprise distribution from our sample. Similarly, we classify the realized volatility for the given order as Low if the realized strategy-weighted volatility surprise value falls below the th percentile of the volatility surprise distribution. Realized volatility conditions for all remaining orders are classified as Medium (normal).

7 7 Similar (albeit less pronounced) empirical dependencies hold when the sample of orders is partitioned based on the value of volatility observed shortly before the order arrival. The dependence of cost curves on previous day s volatility is qualitatively similar, but the magnitude of cost variation by previous day s volatility is smaller than by contemporaneous volatility. In Figure 1, we present examples of cost curves conditional on realized volatility (strategy-weighted) for very liquid and less liquid stocks. The key conclusion that can be drawn from those plots and their counterparts for other liquidity groups is that trading an order of a given size when volatility is abnormally high adversely affects transaction cost for a typical institutional investor. There is only one caveat that should be applied to this statement: for discretionary traders participating in trades as liquidity providers most of the time, high volatility can reduce the cost, in which case the above conclusion will be reversed. FIGURE 1 Empirical cost curves conditional on volatility surprise category VERY LIQUID STOCKS 6 LESS LIQUID STOCKS Relative order size (%MDV) Relative order size (%MDV) Low Vola Med Vola High Vola Conditional cost curves by volume surprise category Examination of the effects of contemporaneous and recent trading volume deviations from their historical averages on implementation shortfall cost follows the blueprint that we previously applied to volatility. Similar to the analysis of volatility surprises, the entire sample of orders is split according to the volume surprise categories (Low, Medium, or High) 7, and the corresponding cost curves are reported for each volume surprise and liquidity group combination. 7 The realized market volume for the given order is classified as High if the realized strategy-weighted volume surprise value exceeds the 8th percentile of the unconditional market volume surprise distribution from our sample. Similar, we classify the realized volume for the given order as Low if the realized strategy-weighted volume surprise value falls below the th percentile of the unconditional market volume surprise distribution. Realized volume conditions for all remaining orders are classified as Medium (normal).

8 8 The procedure yields results that are qualitatively similar (but slightly weaker) as those for volatility: the larger the trading volume is during order execution, the more expensive it is to trade for an institutional investor. 8 This finding appears to contradict the conventional wisdom of investors and is seemingly in conflict with the common investors belief. However, the result is less controversial than it appears to be. Recall that volatility and volume surprises are highly correlated, as the times of higher than normal volumes are also the times when volatility is typically higher than normal. While larger than normal volumes are associated with a lower cost primarily attained by horizontal stretching of baseline cost curves, especially for less liquid stocks, those gains from high liquidity surprises are typically denied because of high volatility. Therefore, trading at the times of high volumes does not lead automatically to cost savings unless the volatility is kept under control. One way to control (and even take advantage of) high volatility is by showing flexibility in executing a large portion of the order using discretionary or opportunistic trading strategies (place more limit orders, tap other sources of liquidity) and being alert to new opportunities Conditional cost curves by volume and volatility surprise category Next we explore the joint effect of volume and volatility deviations from their historical average ( normal ) values on the implementation shortfall cost. First, we stratify all orders (separately for each liquidity group) into three volatility surprise categories (Low, Medium, or High) as described above, and then each of those groups are split further into three conditional volume surprise groups (Low, Medium, and High) as we subdivide each volatility surprise bucket along the cutoffs implied by the volatility category-dependent conditional volume percentiles. We refine the stylized facts established above for the impact of volatility and volume surprises as we analyze the cost curve plots for each conditional volatility surprise and liquidity group combination. Examples of such cost curves for very liquid and less liquid stocks are presented in Figure 2A and 2B, respectively. We reach the following conclusions: The cost curves exhibit consistent but weak dependence on the conditional volume surprise category for all volatility surprise groups in high liquidity stocks. The cost dependence gets noticeably stronger for less liquid stocks. For small and medium order sizes, we see that the costs exhibit strong positive dependence on size across all volatility and volume regimes and liquidity groups. The cost curves flatten out once the order sizes enter the large order range. As expected, the flattening is especially visible in the low volatility regime in combination with the high volume surprise group. The cost curve dependence on volume surprises (conditional on volatility) is tangible for all order arrival times; however, the dependence tends to be slightly stronger for orders arriving closer to the end of US trading hours. 8 In contrast to volatility, however, previous day s trading volumes do not affect the implementation shortfall costs of today s executions.

9 9 FIGURE 2A Empirical cost curves for very liquid stocks conditional on volatility and volume surprise VERY LIQUID STOCKS IN LOW VOLATILITY REGIME 7 6 VERY LIQUID STOCKS IN LOW VOLATILITY REGIME Relative order size (%MDV) Relative order size (%MDV) Low Vlme Med Vlme High Vlme FIGURE 2B Empirical cost curves for less liquid stocks conditional on volatility and volume surprise category LESS LIQUID STOCKS IN LOW VOLATILITY REGIME 6 LESS LIQUID STOCKS IN MEDIUM VOLATILITY REGIME Relative order size (%MDV) Relative order size (%MDV) Low Vlme Med Vlme High Vlme In summary, the evidence presented in this section indicates that volume surprises (conditional on volatility) result in horizontal stretching of baseline cost curves, suggesting that measuring the order size as a fraction of the realized (rather than historical) daily volume is a more natural normalization for post-trade analysis of price impact.

10 Cost curves of OTS clients and their dependence on volatility While our discussion so far has been focused on the full sample of institutional client execution data, it is important to understand whether there are clients in the sample that display a somewhat different trading style that might skew the results and, if so, what features of those clients trading styles make their cost patterns different. In this subsection we address the following questions: What features of parent order executions represent a signature opportunistic trading style (OTS)? How are the cost curves of OTS clients affected by volatility surprises? Figure 3 presents the cost curves based solely on the subsample of all OTS clients executions, which should be reviewed in conjunction with the cost curves based on the full sample presented in Figure 1. We see a significant cost reduction effect across all order sizes and liquidity groups for the OTS clients sample. Most importantly, for small orders (less than 1.5% of historical daily volume for very liquid stocks and less than 5% of historical daily volume for less liquid stocks) we observe that the high volatility cost curves from the OTS clients sample represented by solid lines in Figure 3 are systematically lower than the cost curves for low and medium volatility. In fact, the costs are negative and decreasing in the range of very small order sizes when volatility surprises are high. Therefore, from the perspective of a representative small order trader, high volatility market conditions cannot be viewed as uniformly unfavorable since that interpretation would not universally represent the real experience of institutional traders executing small parent orders. In contrast, for medium and large order sizes, the cost curves based on the full and OTS clients samples of parent orders have qualitatively similar behavior although the magnitude of costs is different (OTS clients costs being on average 5- times smaller). FIGURE 3 Empirical cost curves conditional on volatility surprise category for OTS clients VERY LIQUID STOCKS (OTS CLIENTS) 6 LESS LIQUID STOCKS (OTS CLIENTS) Relative order size (%MDV) Relative order size (%MDV) Low Vola Med Vola High Vola

11 11 A distinct characteristic of the OTS clients executions is their almost exclusive reliance on executions through DMA and dark pools, DMA executions being particularly dominant for small order sizes. Inspection of individual order executions of such clients suggests that most of them originate from execution of limit or hidden orders as well as through discretionary (opportunistic) trading in dark pools. These observations suggest labeling the trading style of this group of clients as opportunisitic. The negative average cost of OTS clients for small order sizes appears to be especially strong when market volume is abnormally high, suggesting more room for cost saving in high volume and high volatility conditions. Price impact eventually becomes a factor for sufficiently large order sizes albeit still much weaker than for the remaining clients. But, as long as those clients are prepared to wait for good opportunities while trading moderately (and what is moderate depends, among other things, on the prevailing volume conditions), such favorable opportunities would eventually come up. Negative dependence of cost on order size for small orders in high volatility market conditions is amplified by larger than normal conditional volume surprises, but appears much smaller for normal and below-normal conditional volume surprises. Traders can take advantage of high volatility market conditions by spread and momentum capture, but most of those advantages are materialized only when volume is above normal. In other words, high volatility and volume conditions create the environment with more opportunities to fill small orders at negative cost. As long as the discretionary trader can bear the risks associated with trading in such environment, volatility and volume may indeed be her best friends. The discretionary style of the OTS clients can be indirectly observed from Figure 4, showing the average duration of orders in less liquid stocks for our full and OTS clients sample. The duration of an order is normalized such that the duration metric is restricted between and 1, representing immediate execution of the entire order at the order arrival time and 1 corresponding to the order with the last fill at the close. We argue that the larger the average duration, the more likely a client is committed to filling his orders, fitting closer to a non-discretionary trading style. OTS clients exhibit much shorter order durations than the full sample (order durations are 3 to 5 times shorter on average). In addition, there is a clear difference in the average order duration for OTS clients orders when controlling for market directionality via signed trade imbalances: the more unfavorable the signed trade imbalances are the shorter the order executions become. This observation can be explained by the bias in reported execution data as order cancellations are not being tracked and the likelihood of order cancellation without any order fill increases, particularly for clients with discretionary trading styles.

12 12 FIGURE 4 Empirical cost curves for less liquid stocks conditional on volatility and volume surprise category LESS LIQUID STOCKS (ALL CLIENTS) 1. LESS LIQUID STOCKS (OTS CLIENTS) Average Duration.6.4 Average Duration Signed trade Imbalance Signed Trade Imbalance SG SG1 SG2-3 SG4-6 SG7-9 TRADE IMBALANCE, VOLATILITY, AND INSTITUTIONAL TRADING STYLE In this section we complement our discussion of market conditions as a key contributing factor behind trading cost as we focus on the interplay between trade imbalances 9, non-directional market conditions, and execution costs. We revisit the questions posed at the beginning of this article: How does the sign and magnitude of buyer/seller pressure prevailing during an institutional order execution affect its cost and market impact? Do volatility surprises affect execution costs for favorable and unfavorable trade imbalances? Do the above effects vary by institutional client or client s trading style? Do the signed trade imbalances affect the transaction costs of institutional orders? Since trade imbalance represents a proxy for real time buyer/seller pressure, it captures some of the directional activity observed through the lifetime of the order. Trade imbalance observed during executions of small and medium size institutional orders is not only affected directly by the client s choice of market or limit orders, but also by environmental factors at the time of execution such as prevalent short-term price dynamics (buyer or seller pressure) during the time of execution. As a result, trades associated with positive (unfavorable) signed trade imbalance will end up having higher costs than trades associated with negative (favorable) signed trade imbalance. While the cost curve dependencies uncovered in the previous section are qualitatively preserved (although possibly dampened or amplified) across all kinds of prevailing trade imbalance conditions, there are important nuances that will be explored in this section. 9 Trade imbalances of parent orders are standardized by their standard deviations.

13 13 To enhance our understanding of interactions between relative order size and trade imbalance as they jointly affect execution costs for institutional orders, we consider dependence of average execution costs on both size and trade imbalance variables, keeping the liquidity group fixed and arrival times confined to a limited range to control the sample heterogeneity due to varying execution horizons. To address the curse of dimensionality problem that would emerge as a side effect of excessive partitioning of the sample into a large number of buckets, we combine some of the size buckets to ensure that every element of the partition satisfies the minimum sample size requirements. Even though results for equally- and dollar-weighted average costs are qualitatively similar, we document only the equally-weighted average values, which are more stable and less sensitive to outliers. The representative plots are shown in Figure 5 for institutional orders in less liquid stocks. To facilitate comparison, the plots are reported separately in low volatility and high volatility regimes. Our observations are summarized as follows: While adverse (positive) signed trade imbalance pushes the average execution cost upwards even for tiny orders (the solid black curve corresponds to SG, comprising of orders smaller than.15% of average daily volume), those tiny orders in sufficiently favorable (negative) trade imbalance environment clearly get filled without price impact. As the order size increases, the cost grows more rapidly when trade imbalance is unfavorable. For example, in the low volatility regime (the left-hand side chart in Figure 5) the average cost changes from 8.5 bps (solid curve) to 17.6 bps (dashed curve) as the order size increases from approximately.1% MDV (SG) to 8% MDV (SG4 6) when signed trade imbalance is unfavorable (TI = +2), whereas the average cost increases from 2.7 bps to 3.1 bps only when signed trade imbalance is favorable (TI = 2). The magnitude of average execution costs and their variation with trade imbalance and relative order size are much larger in the high volatility regime (the right-hand side chart in Figure 5). For example, the average cost changes from 19.6 bps (solid curve) to 58.4 bps (dashed curve) as the order size increases from.1% MDV (SG) to 8% MDV (SG4 6) when signed trade imbalance is unfavorable (TI = +2), whereas the average cost increases from 3.2 bps to 8.4 bps when signed trade imbalance is favorable (TI = 2). Finally, the range of low relative order size values where the average cost is flat as a function of order size is wider for high negative (favorable) values of signed trade imbalance, and virtually non-existent for positive (unfavorable) or neutral values of signed trade imbalance. As order size grows even more (24% MDV and beyond), the difference between the cost for the highest relative order size group (represented by the dashed dotted curve) and the cost for tiny relative order size group (solid line) becomes substantial for both favorable and unfavorable trade imbalance conditions, providing empirical evidence for price impact of large orders. Still, this difference is much larger for unfavorable trade imbalance conditions in the high volatility regime.

14 14 FIGURE 5 Empirical cost for full sample of institutional clients as function of order size group (SG) and signed standardized trade imbalances LESS LIQUID STOCKS IN LOW VOLATILITY REGIME Signed Trade Imbalance LESS LIQUID STOCKS IN HIGH VOLATILITY REGIME Signed Trade Imbalance SG SG1 SG2-3 SG4-6 SG7-9 Similar comments can be applied to the counterparts of the above plots in more liquid segments of the market. While unfavorable (positive) signed trade imbalances adversely affect the average execution cost even for smallest orders, favorable (negative) signed trade imbalances produce a significant countervailing effect when relative order size is relatively small. In summary, trading at times of favorable (negative) signed trade imbalance improves the probability of reducing the final execution cost, and the ability to trade when trade imbalance is favorable can be viewed as an important cost savings resource. Whether one takes advantage or foregoes such cost savings opportunities depends on trader s discretion, willingness to deal with the risks of adverse price movement and non-execution, and ability to identify these scenarios at the point of trade. Price impact and trading style One way to assess institutional clients price impact is to measure the increase of the implementation shortfall cost on order size while controlling for market conditions. This assumes that very small orders have minimal or no impact, and the excess average cost of larger orders can be attributed to their liquidity demand and/ or information leakage, hence market impact. As can be seen in Figure 5, the impact of buy-side institutions as a whole in the low volatility regime is generally much lower than that under high volatility. Furthermore, in the highvolatility regime, favorable trade imbalances (TI<) result in much lower average impact (for moderate order sizes) than unfavorable trade imbalances (TI>) because the combination of highvolatility and favorable trade imbalance conditions offer more scope for opportunistic trading.

15 15 To demonstrate that the cost and impact reductions are associated with opportunistic trading, we compare the plots based on the full sample of clients orders (Figure 5) with their counterparts based on the sample of OTS clients orders in Figure 6 (note the different scale). As noted before, average costs are significantly smaller for the OTS clients sample across all size and trade imbalance categories (a possible reason is the fact that the average life time of those orders is much smaller as discussed in section 3.4). Similarly to Figure 5, we see that costs for the OTS clients grow faster with order size in the high volatility regime. There are subtle differences in the behavior of costs though. First, the OTS clients costs for small orders (solid and dotted lines) are either negative or zero practically for all trade imbalance categories, confirming our opportunistic trading style nomenclature for such clients. For each trade imbalance category, the price impact / cost increase with order size is consistently lower for OTS clients than for the full sample. In fact, for small and medium order sizes we see that the costs do not increase (and in some cases even decrease) with the order size. In the low volatility regime and under favorable trade imbalances (TI<), we see that all cost curves with the exception of the one for SG7 9 are below the solid line. Restating the results of Figure 6, under favorable trade imbalances and low volatility conditions, OTS clients can avoid market impact costs for orders up to 24% of historical MDV. For the high volatility regime and favorable trade imbalances, the average market impact starts at 3 6% of MDV, albeit very gentle and controlled, never exceeding bps. In contrast, for traditional, non-ots institutional clients, price impact kicks in much earlier and stronger. FIGURE 6 Empirical cost for sample of OTS clients as function of order size group (SG) and signed standardized trade imbalances LESS LIQUID STOCKS IN LOW VOLATILITY REGIME (OTS CLIENTS) LESS LIQUID STOCKS IN HIGH VOLATILITY REGIME (OTS CLIENTS) Signed Trade Imbalance Signed Trade Imbalance SG SG1 SG2-3 SG4-6 SG7-9 In summary, the identified OTS institutional clients consistently achieve negative average costs for small order sizes by trading opportunistically, often in a volatile market environment, taking advantage of favorable trade imbalances. The key to their success is to trade passively (provide liquidity using hidden limit orders and visible orders placed away from the current market price), be flexible with respect to the trading size (almost all filled parent orders of OTS traders are either small and executed through DMA or executed in dark pools), and be willing to cancel orders as the market price moves away. Monitoring volatility jointly with directional signals, and sourcing liquidity in real time are clearly important for OTS traders. Needless to say, traditional buy-side institutions cannot afford to neglect monitoring market conditions either, since failure to adjust promptly to market conditions would result in deteriorated performance and missed cost savings opportunities.

16 16 CONCLUSION This article summarizes results of our extensive empirical study motivated by the intuitively appealing statement that institutional clients average transaction costs are sensitive to market conditions. Using a comprehensive sample of buy-side client execution data covering two years of trading, we confirm the following stylized facts: Execution costs of peer institutions change systematically with deviations of price volatility, trading volume, and Lee Ready trade imbalance from their normal values during order executions. Volatility is a dominant factor that adversely affects transaction costs of a representative institutional client. For a given stock and fixed order size, the average cost can vary by a factor of 3 to 4 when conditioned on the low or high volatility regime. Trading volume plays an incremental but secondary role in cost determination; for any given volatility value, large volume surprises affect clients ability to keep cost under control while increasing the order size (roughly in proportion to trading volume). The signed trade imbalance is an important factor that determines the order size at which market impact becomes noticeable. For favorable trade imbalance, market impact can start at relatively large order sizes, especially for clients with opportunistic trading styles. However, trading under unfavorable trade imbalances has a material impact on transaction costs even for very small orders, especially when volatility is high. We also find evidence of heterogeneity in clients trading styles, and demonstrate that failure to account for this heterogeneity can distort the dependence of cost curves on market conditions estimated for a representative buy-side institution. In particular, higher than normal volatility favorably affects the realized transaction costs of some clients who trade passively and execute predominantly small orders. The cost curve distortions can be alleviated if the sample of executions is parsed after identifying clients with unconventional trading styles. The cost curves based on the parsed sample provide unbiased cost benchmarks for the majority of buy-side institutional clients. Finally, we document and emphasize the importance of modeling the interactions between trade imbalance and non-directional market condition variables for accurate reconstruction of the asymmetric effects of trade imbalance on the shape and scale of the estimated cost curves. 15 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 trading or investment purposes or as an offer to sell or the solicitation of an offer to buy any security or financial product. The information contained herein has been taken from trade and statistical services and other 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 market data used by ITG or the actual results that may be achieved. These materials do not provide any form of advice (investment, tax or legal). ITG Inc. is not a registered investment adviser and does not provide investment advice or recommendations to buy or sell securities, to hire any investment adviser or to pursue any investment or trading strategy. The positions taken in this document reflect the judgment of the individual author(s) and are not necessarily those of ITG.