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CONTRIBUTORS Milan Borkovec Head of Financial Engineering, ITG, Inc. +1.617.692.6733 milan.borkovec@itg.com Laura Tuttle Manager of Financial Engineering’s Algorithmic Trading Research, ITG, Inc. +1.617.692.6588 laura.tuttle@itg.com Konstantin Tyurin Manager of Financial Engineering’s Post-Trade Analytics, ITG, Inc. +1.617.692.6737 konstantin.tyurin@itg.com Zhaoyang Zhao Researcher, ITG, Inc. +1.617.692.6739 zhaoyang.zhao@itg.com

Alpha- Optimized Trading Schedules: Identifying Own Price Impact in Realized Returns ABSTRACT The trading and investment style of a fund manager often has a major impact on his trading costs. Practitioners recognize that trading schedules can be optimized over an alpha pattern, but without correct identification of the price impact of own trading activity, resulting schedules are suboptimal. We propose a framework to decompose the implementation shortfall cost of a realized trading schedule into a cost component due to the projected general market movement and trades of other market participants, and a cost component capturing the impact of own trades. We then present a methodology that simulates alternative hypothetical trading strategies and optimizes the client’s trading aggressiveness. The gains from accommodating the intraday alpha patterns of the fund managers’ executions lead to a significant reduction in the trading costs both in- and out-of-sample in most scenarios. The authors would like to thank Jeff Bacidore, Ian Domowitz, Benjamin Polidore, Naveen Rao and Olav Van Genabeek for their support, comments, and suggestions. Any opinions expressed herein reflect the judgment of the individual authors at this date and are subject to change, and do not necessarily represent the opinions or views of ITG, Inc. 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. The analyses discussed herein are derived from aggregated ITG client data and are not meant to guarantee future performance or results. This report is for informational purposes and is neither an offer to sell nor a solicitation of an offer to buy any security or other financial instrument. This report does not provide any form of advice (investment, tax, or legal). No part of this report may be reproduced or retransmitted in any manner without permission.


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INTRODUCTION Post-trade transaction cost analysis is a rapidly evolving field, driven by the practical needs of buy-side market participants, as well as compliance requirements of “best execution” spurred by implementation of MiFID2 (in Europe) and other regulatory initiatives.1 Historically, post-trade analysis has focused on the comparison of empirical execution costs with benchmarks such as VWAP (volume-weighted average price), PWP (participation weighted price) and pre-trade cost estimates for a given pre-determined, static trading schedule. VWAP and PWP benchmark prices are easy to calculate and implement in real time, and are essentially model-free. However, these measures fail to separate the price impact of own trading from that of other market participants, and therefore have limited usefulness, especially for large institutional orders. Moreover, as discussed at length in Kissell and Glantz (2003), all simple participation-based benchmarks are gameable, especially for large orders, as traders can manipulate trading intensity and delay execution when benchmarks are pre-announced. Alternative model-based approaches typically do not account for observed market conditions during the trading period and thus fall short in explaining implementation shortfall costs for individual orders. Various enhancements of the model-based approach have been made since the first benchmarks for post-trade analysis were introduced. For instance, ITG (Borkovec and Heidle, 2007) and Goldman Sachs (Sofianos et al., 2006) rely on the decomposition of the implementation shortfall metric of cost into components representing the price movement due to other market participants’ trading activity (such as the price drift associated with the general market movement) and own price impact. This is further decomposed into the pre-trade “expected” cost component and a number of adjustments reflecting deviations of market conditions from normal (for example, volume or spread). Modeling own price impact versus that due to other market participants relies on strong assumptions and, as a result, leaves some users uneasy about the “black box” nature of the resulting benchmarks. We present a new post-trade modeling framework which aims to bridge the gap between VWAP/PWP and model-based benchmarks. This novel approach allows separate analysis of each order, modeling one’s own price impact, and can be used for cost attribution and “what if” scenario analyses. The framework starts in the standard setting of liquidity trading models wherein a trader intends to execute a large, exogenously given number of shares within a fixed time interval, subject to the objective of minimizing the expected transaction cost. The transaction cost is measured by the implementation shortfall (Perold, 1988), defined as the difference between the share-weighted average execution price of the order and its arrival price (or another benchmark price of a hypothetical no-cost acquisition of the entire portfolio), which may also include fixed costs such as fees, commissions, and spreads, as well as the variable costs such as price impact caused by liquidity consumption. Kissell and Glantz (2003) and Borkovec and Heidle (2010) provide detailed reviews of transaction cost components. In order to measure Perold’s implementation shortfall cost for any given hypothetical trading schedule, we subdivide the trading day in seventy-eight five minute intervals; within each interval k we estimate the mid-quote return (which we call the F function) and the deviation of average execution price from the trend (which we refer to as the G function). These two quantities are assumed to be random variables that depend on a vector of market conditions MCk−1, which includes recent and lagged deviations of volume, volatility, and quoted spreads from their historical averages, as well as the contemporaneous trade imbalance TIk (difference between the number of buyer- and seller-initiated shares in time interval k).


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The H function for time interval k provides a stochastic link TIk =Hk(nk|MCk-1) between the number of shares nk traded in this interval and the realized aggregate market trade imbalance in the same interval; consequently, the F and G functions in interval k become order size dependent upon substitution of the H function expression into the F and G functions. Conceptually, the new framework separates the modeling of price dynamics into two parts: in the first, own trading is mapped into aggregate order flow and in the second, market-aggregated order flow impact price dynamics. In other words, we remove the direct impact of trade size on prices, and assume an indirect impact on prices through the effect of our trading on the trade imbalance in the market. The default H distribution profile, which is calibrated to ITG’s Peer Group data2, can be further customized to capture clients’ execution styles and alpha patterns. For each order, realized implementation shortfall costs can be easily measured in this framework by substituting realized market conditions, realized values of the F, G and H functions as well as the client’s realized trading schedule. After observing the empirical distribution of the F, G and H functions, we incorporate the expected probability percentiles to other hypothetical trading schedules and market conditions. This allows us to have more precise (ex post) estimates for F, G and H and, ultimately, the implementation shortfall cost of an order for a hypothetical trading scenario. This optimization is ultimately dependent on the client’s observed alpha pattern, which is the residual return pattern identified when we remove market effects and the price impact of own trading. One can define the intraday alpha of an investment fund manager as a pattern of intraday average cumulative returns, trade imbalances, or other directional variables for the securities traded by the manager on the days when the fund manager is actively trading. Most fund managers have a distinct and identifiable pattern of intraday returns, which manifests as unique alpha pattern that is stable over time and usually falls into five broadly defined categories: neutral, momentum, momentum with reversal, contrarian, and contrarian with reversal, or some combination thereof (Figure 1 shows an example of an alpha patterns of signed average cumulative returns3 for a sample investment fund). Returns of some funds accumulate in the direction of buy and sell orders, thereby making delayed executions of such funds more costly in comparison to early executions. Returns of other funds (including our sample fund illustrated in Figure 1) have a tendency to accumulate in the direction opposite to the direction of its trades, as prices of purchased or sold securities tend to move up when sell orders are executed and down when buy orders are executed. For these funds, adoption of delayed execution schedules proves to be a viable alpha-preserving strategy. Although the cumulative signed return patterns are qualitatively similar for buy and sell orders, the magnitude of those patterns can differ substantially, implying strategies of varying degree of aggressiveness could be customized for individual funds depending on order attributes and time of day. In this paper, we identify and measure the intraday alpha patterns based on trading histories of individual portfolio managers. While we remain agnostic about the origin of such identifiable alpha patterns, we show subsequently how the post-trade modeling framework can be used to customize each manager’s or fund’s optimal trading strategies with the goal of reducing implementation shortfall costs in comparison to the currently implemented execution schedules. The projected gains from adopting the optimized trading schedules are substantial, varying between 0.6 and 7.4 bps. For a fund with 4.6 billion in annual trading (as our median dollar volume fund has), our median savings of 4.48 basis points translates into annual dollar savings of $2.06 million.


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The remainder of this paper is organized as follows. In section 2 we give an overview of our post-trade model and detail the intuition behind the alpha execution algorithm. After presenting the theoretical foundations behind the building blocks of the model (F, G and H functions), we briefly discuss the model estimation methodology, and finish the section with the built-in functionality that allows the user to adopt model parameters to better represent client’s trading style and execution patterns. Section 3 applies the modeling framework to client execution data discussed in subsection 3.1. Subsection 3.2 defines clients’ intraday alpha patterns. Subsection 3.3 describes the methodology that is applied to find custom optimal trading schedules, which is followed by a brief review of our optimal strategy selection methodology in subsection 3.4 and empirical results in subsections 3.5. Subsection 3.6 presents a case study of one client’s trade schedule optimization. Section 4 recaps the main features and applications of the new post-trade modeling framework.

BUILDING BLOCKS OF THE PROPRIETARY POST-TRADE MODEL The post-trade modeling framework applies to the implementation shortfall (IS) metric (Perold, 1988) calculated as follows:

where Pat,k and Pat,k are, respectively, the mid-quote price at the end of time interval k = s −1, …, J of day t, and the volume-weighted average own execution price within interval k of day t, nk is the number of shares scheduled for execution in time interval k, S is the total number of shares scheduled to be filled, Sell is a (+1/−1) indicator function, and at,k is a multiplicative factor (typically close to ½) calibrated to match the timing of trading activity within interval k of day t and the patterns of contemporaneous high-frequency price movements.

MARKET, SECTOR, AND INDUSTRY MOMENTUM COMPONENTS The post-trade framework is applied to implementation shortfall cost (1), which is constructed for each stock a using its intraday returns rtja=(Ptja–Pt,ja-1)/Pt,ja-1 after the market, sector, and industry factors Fatj have been removed, as the component of intraday returns rtja attributed to common factors Fatj is assumed to be determined exogenously and is thus unaffected by trading in the individual stock. Specifically, the expected returns are obtained from the linear regressions of stock-specific returns on the market index return rtjMkt, sector returns rtjSec(a), and industry returns rtjInd(a) as follows:


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and the net returns are the residuals rtja,net[Ftja]=rtja–E[rtja | Ftja] from regression (2). The regressions are run stock-by-stock on a weekly basis, using a rolling window of 60 days of recent intraday returns data. Note that in order to retain the property that common factors underlying regression (2) are unaffected by own trading for actively traded stocks that represent a large portion of their own industries’ trading volumes, we refrain from using the industry factor, conditioning on market and sector movements only. After extracting common factors from the realized returns, we obtain the implementation shortfall cost net of the market and sector (and industry, for less liquid securities) momentum components from (1) as follows:

STOCK-SPECIFIC MID-QUOTE MOMENTUM AND EFFECTIVE SPREAD COMPONENTS The F and G functions in time intervals k = s, …, J of day t in the implementation shortfall formula (3) are defined, respectively, as the market/sector/industryadjusted mid-quote return Ftja=rtja,net[Ftja] and the effective spread (liquidity premium). Gtja=((Ptja–Pt,ja-1)– tjaFtja Empirical evidence suggests that both functions depend crucially on the contemporaneous trade imbalance TItja (the appropriately normalized difference between buyer- and seller-initiated trade volumes4 in time interval j) and on the vector of market conditions MCt,ja-1 which includes recent and lagged deviations of volume, volatility, and quoted spreads from their historical averages.5 The multiplicative factor tja captures the relative arrival time within a time bin. We normally expect it to be close to ½, but expect a smaller value near the market open and a larger value near the market close as traders shift their executions to the beginning or the end of the corresponding time intervals to participate in opening and closing auctions. The F and G components described above represent the essential building blocks of our post-trade framework. The shape and magnitude of their conditional expectations (and, more generally, their entire probability distributions) depend,


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among other things, on time of day and market conditions. The asymmetric F and G distributions in our model capture the observation that trades in the direction of the existing trade imbalances tend to have smaller price impacts than similar trades in the opposite direction6. We estimate the F and G distributions from Level 1 market data and find that the upper and lower tail probabilities of the F and G conditional distributions are indeed concave functions of signed trade imbalance, with the shape and scale of tail probabilities dependant on market conditions and time of day. The model for the F and G distributions captures the monotonic (and concave, for positive values of trade imbalance ) dependence of the expected values of F and G functions on trade imbalance, as well as the asymmetric character of the upper and lower tail probabilities for extreme realizations of mid-quote returns and effective spreads. Accurate modeling of the entire distributions of F and G, especially their tails, is one of the crucial input variables for our post-trade framework.7 The conditional distributions of Ftja and Gtja are assumed to be independent, both in the cross-section and over time, once the realizations of market, sector, and industry returns, stock-specific trade imbalance, and realized market conditions are factored in.8 As discussed previously, the Ftja function is modeled as a drift in the mid-quote price within the given time interval, though not necessarily a “permanent” component.

TRADING STYLE AND THE DISTRIBUTION OF TRADE IMBALANCES The H function (for stock a in interval j of day t) for any given order provides the distribution of signed standardized trade imbalances zTItja=(–1)Sell•(BuyInittja – SellInittja)/MDVtja as a function of the number of shares noj traded and the market conditions MCtja observed in interval j of day t when the order was placed. The H distribution function Htja( |nj,MCtja)=Pr{zTItja< |noj,MCtja} attempts to capture, for any vector of market conditions and order size, the typical magnitude and dispersion of trade imbalances experienced by market participants (ITG Peer group clients) at the times of their actual executions. Whereas the distribution of unsigned trade imbalances (BuyInittja – SellInittja)/MDVtja is approximately symmetric and centered around zero, the distribution of signed trade imbalances associated with any trade size noj is non-symmetric and has positive expected values. By construction, the H distribution gives the realization of a random variable that affects the price dynamics, and depends on the deviation of volume and volatility from their recent historical average values, the number of shares actually executed in bin j, and the trader’s own style. The trading style may include systematic characteristics of the group of trades performed by the client that reflect how much information the trader reveals to the market, including the tendency for limit versus market order placements, prevalence of opportunistic versus non-discretionary trades, tendency to trade more frequently (or more aggressively) when the broadly defined market index is up or down, and so on. The H distribution is estimated using ITG’s Peer Group database. By estimating the H function with client execution data we ensure that we capture, on average, the empirically observed behavior of institutional clients. Any opportunistic behavior or other feedback effects between one’s own trading and other market participants is also taken into consideration by construction. For example, the observed average trade imbalance increases with order size; for very large orders, however, it increases considerably less, suggesting a prevalence of opportunistic trading (see the blue curves on Figure 2, representing the expected values of H distributions for two securities under normal market conditions). For non-discretionary traders, the mean of trade imbalance matches the empirical mean from clients’ execution data only up to a certain trade size, and starts curving upwards thereafter, reflecting the observation that there exists a certain market capacity threshold beyond which the total trade size can only be increased by performing more trades through market


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orders. As a result, we obtain the so-called “hockey stick” pattern for the expected values of H distributions, illustrated with the red curves on Figure 2 for two securities under normal market conditions. The black diagonal line on both plots of Figure 2 shows the expected values of the H distribution for a hypothetical trader who completes 100% of trades using market orders only. After having observed the deviation tja*=zTItja*–EH[zTItja|n*j,MCtja*] of the signed observed normalized trade imbalance zTItja* from the mean EH[zTItja|n*j,MCtja*] implied by the H distribution function for a typical order of the observed size n*j under the realized market conditions MCtja*, we determine the mean projected value of trade imbalance for any other hypothetical trade size nj by adding a small increment = (nj, a*tj) to EH[zTItja|n*j,MCtja*], where the function (nj, a*tj) has the following properties: ¬¬

= tja* for all hypothetical trade sizes nj smaller or equal than the observed trade size n*j,9

¬¬

0 as the trade size nj approaches the floating number of shares of the company. 10

As a result, we obtain the percentiles of H distributions for hypothetical orders of varying size nj under the observed market conditions (see Figure 3 in the Appendix). The value of the trade imbalance from the H distribution is subsequently substituted into the F and G functions.11 As previously mentioned, the H distribution can be customized based on the observed trade imbalance distributions during trades of individual clients. Individual clients’ or fund managers’ behavior may systematically deviate from the representative ITG Peer Group client, as they may exhibit a tendency to trade more or less aggressively at different times of the day and for different order sizes. This tendency may warrant estimation of client-specific distributions of trade imbalances that are systematically different from those described by the generic H function of our model. By the same token, the trading style of a client can manifest itself in larger or smaller price impact of clients’ trades at the times when market returns significantly deviate from their average values.

APPLYING THE NEW POST-TRADE FRAMEWORK TO THE ALPHA ALGORITHM The new post-trade framework outlined in the previous section provides a more flexible and accurate tool for post-trade analysis and cost attribution perfectly suited to the problem at hand, as the trading schedule can be adjusted to accommodate the observed stable intraday alpha pattern as discussed in the introduction and illustrated in Figure 1. We take as inputs the number of shares n*j actually traded in each interval j of day t, the vector of market conditions MCtja* reflecting the recent history of volume, volatility, and bid-ask spreads, and the observed standardized trade imbalance zTItja*, as well as the observed realizations of price drift ftja* and effective spread gtja* in each interval j of trading day t. Within this framework, we pose the question: what would be the expected shift in the distribution of trade imbalances zTItja and the ensued change in the distributions of the price drift and the effective spread if the number of shares traded in each interval is changed to nj, while all other inputs observed ex post, including exogenous market conditions and trade imbalances originating from transactions performed by other traders, remain the same?


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Once all building blocks are in place, one can run simulations to obtain hypothetical price trajectories for the same security a on the same trading day t for a set of pre-defined trading strategies. Figure 4, Panels A and B present examples of such hypothetical price trajectories under alternative trading strategies that can be implemented for the same order. For illustration, we exclusively focus on fixed horizon VWAP-style strategies, as described in subsection 3.3, although the same approach can be applied to a set of execution strategies expanded beyond this list.

DATA Our client execution data captures trades for managers of seven funds over the time period between January 2010 and September 2011; each fund provides three to seven consecutive quarters of complete execution data. All individual trades are combined into clusters (orders), where the trades are assigned to the same cluster if they are executed in the same direction (buy or sell) on the same date on behalf of the same fund manager and in the same security (ticker). Thus each observation of our final execution data set contains the following information: ¬¬ Portfolio name (investment fund or portfolio on behalf of which the buy or sell transaction is made) ¬¬ Ticker symbol and side (buy or sell) of the cluster ¬¬ Trade date and cluster arrival time, which is the earliest arrival time among all orders in the same cluster ¬¬ Fill size (number of shares traded) and dollar-weighted average execution prices across all trades in the cluster within each five-minute interval during the regular trading hours (between 9:30 am and 4:00 pm EST). Panel A of Table 1 provides key summary statistics of sample client execution data by fund, side, and liquidity segment.12 The fund managers in our sample, while maintaining relatively balanced ratios between the transaction count and dollar volume of buy and sell orders, represent a variety of trading styles in terms of their investment universe and turnover. The dollar turnover of funds vary from 2.1 to 43.2 billion USD. Some funds are invested almost entirely in the liquid large cap segment of the market, whereas other funds’ trade more actively in less liquid stocks. The mean dollar size of an individual cluster also varies significantly across funds and liquidity segments; the mean cluster for one fund in low liquidity stocks is $176,556 while another fund’s average trade in high liquidity stocks exceeds $2 million We augment the sample of client execution data with daily statistics of the security involved in the trade (the cluster benchmark price, 21-day median daily dollar volume, historical 60-day volatility, historical time-weighted average spread, and previous day’s closing price), and numerous intraday analytics describing the security (volume-weighted average price, mid-quote price, trading volume, time-weighted average spread, and trade imbalance) at a five-minute frequency on the day of order execution. Based on the GICS industry classification of the security, we also create a momentum proxy within each five-minute interval of the trading day, including the market, sector, and industry returns and their betas (see section 2.1 for details). Panel C of Table 1 summarizes the average realized implementation shortfalls (IS) of the seven investment fund managers for all orders in less liquid, medium liquidity, and most liquid investment categories; results are segmented by order size grouping.13 The data reveal a considerable variation in fund managers’ average execution costs. One fund has full-sample implementation shortfall costs of less than 1 basis point; another has IS costs approaching 28bp. Our median fund has IS costs of 11.68bp; not surprisingly, large orders (comprising the top 10% of each client’s empirical order size distribution as measured by dollar volume) have higher costs than all other order size groupings.


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Several questions arise upon inspection of Table 1. First, how much of the variation of different funds’ performance could be attributed to their own price impact versus the price movements independent of own trading size? Second, can fund managers modify their execution strategies to improve their average IS performance by capturing a larger portion of alpha by frontloading (or delaying) their order execution if their intraday return patterns exhibit unfavorable (or favorable) patterns during the trading day? Last but not least, how does the magnitude of potential improvements vary as a function of order size? To prepare the groundwork to address these questions, we will focus in the next subsection on the central subject of the paper – the alpha pattern definition and its properties – and explain how one can obtain the cumulative return alpha pattern net of the market returns and own price impact, which is especially important for the analysis of large order executions.

IDENTIFYING INTRADAY ALPHA PATTERNS The intraday alpha pattern of a fund manager or trader is related to the unique profile of signed average intraday cumulative returns for the securities traded by the fund manager on the days when the manager takes long or short trading positions in those securities.14 As has been mentioned in our discussion of Figure 1, most of our sample fund managers have distinct cumulative return patterns, which may vary by the market segment, direction of the trade, order size, and other attributes. When observing distinct and quite stable return patterns over time, it is natural to associate such patterns with alpha profiles underlying the trades of individual portfolio managers.15 The optimal trading strategies (transaction schedules) are customized with the goal of reducing the implementation shortfall costs taking into account the fund-specific alpha patterns.16 How do we identify the intraday alpha profile of a fund? Whenever possible, we analyze funds separately. All target trades (orders) and the price movements in the corresponding stocks are analyzed before, during, and after their executions. After removing the effects of market, sector, and industry price movements, we split the residual returns of all stocks traded by the fund into the two components: price impact and alpha. Then utilizing the new post-trade framework, the outcomes of various strategies (taking into account the alpha pattern and the impact of those strategies) are simulated and analyzed. Our goal is to search for a consistent, stable trading schedule that is least costly given our best identification of own price impact and the portfolio manager’s alpha profile across multiple trade dates. We make the following assumptions: ¬¬ Filling an order by the end of the day is important; in other words, the fund’s or client’s trading style is strictly non-discretionary. ¬¬ The client’s main objective is to minimize the implementation shortfall (IS) cost. ¬¬ A reasonably stable alpha profile exists for any fund/client under consideration. These patterns can be attributed to differences in funds’ stock selection and trading styles. To achieve these goals, we require that the client’s execution data is granular enough, providing accurate information on the order arrival time, trade time stamps, and fund identifiers. Last but not least, the data must not be sparse: we require at least 800 observations per fund, side, and quarter, with at least a half-year of data.


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THE SET OF POSSIBLE STRATEGIES Our candidate strategy set consists of 25 VWAP-based trade schedules. When ranked by aggressiveness, the median strategy is historical VWAP. The most aggressive strategy trades approximately 20% of the order in the first five minutes of the day; the least aggressive trades roughly 30% in the last five minutes of the day. On a median market volume day, the participation rate of a VWAP-13 order would be equal to the order size divided by ADV; in realization, participation rates will be higher or lower depending on actual market volume. Figure 5 illustrates the family of strategies in volume-time, with each of the five graduations on the X-axis representing 20% of market volume. The Y-axis tracks percent completion of the order. With this presentation, historical VWAP (VWAP-13) is shown as a 45-degree line (in bold). Although the strategies technically run for the entire trading day, the most aggressive strategies finish quite early in the day and the least aggressive delay the onset of trading substantially. The choice of the strategy set is quite important for the measurement of out-ofsample performance of the alpha algorithm. Ideally, the family of candidate strategies should be sufficiently dense within the continuum of all feasible dynamic strategies that could be considered by sophisticated institutional traders. On the other hand, choosing a very large family of strategies would not only be impractical, but also would be prone to in-sample overfitting and, as a result, underperformance of the best strategy of that family out-of-sample. Admittedly, the family of VWAP probe strategies considered in this paper is hardly rich enough to encompass (even approximately) all strategies that can be implemented by institutional traders.17 With this in mind, even though the optimal design of the family of candidate strategies is beyond the scope of the present paper, we demonstrate below that tangible cost savings that can be achieved by the strategies under consideration both in- and out-of-sample within the majority of analyzed scenarios.

OPTIMAL EXECUTION STRATEGY SELECTION PROCESS The target trades (orders) and, specifically, the price movements are analyzed before, during, and after their executions. After removing the effect of market, sector, and industry price movements, the residual intraday returns are split into two components: price impact, which is the expected contribution to returns from own trading, and intraday alpha pattern, originating from the impact of other market participants on the stock price. Then, utilizing our post-trade framework, we simulate the projected price trajectories and costs that would be accumulated from implementation of various strategies from the family of candidate strategies described in section 3.3, taking into account the intraday alpha profiles and the impact of those strategies. The portfolio managerâ&#x20AC;&#x2122;s execution strategy is then modified to reflect the alpha pattern and thereby improve his ex post performance, assuming the proposed modified strategy had been implemented instead of the actual strategy. In real time, all fund-specific strategies chosen for execution need to be re-adjusted periodically. For this reason, we repeat our fund-specific analysis every quarter based on the fundâ&#x20AC;&#x2122;s trading in the most recent six months and identify a set of candidate strategies comprised of the strategy with the lowest dollar-weighted average cost within the recent six months as well as the strategies with average costs within a fixed basis point range of the minimum cost. Finally, we use a regression-based methodology to reduce the candidate strategy set to a single strategy recommendation for each side, liquidity group and size group category; the regression step within the process provides smoothing of strategy recommendation across liquidity and size groupings.


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APPLYING THE ALPHA-ADJUSTED POST-TRADE METHODOLOGY TO THE PERFORMANCE ANALYSIS OF SAMPLE FUNDS As described at the end of section 3.4, the out-of-sample period used for strategy evaluation is comprised of the total dataset available excluding the first two quarters of each funds’ data; these first two quarters are used in estimation of the funds’ alpha patterns. This means that the period for the performance analysis (the out-of-sample period) spans the last two quarters for most funds; one of our funds has a single out-of-sample quarter, while two more have four or five out-of-sample quarters. Table 1 Panels B and C present summary statistics on realized IS costs. In Panel C, we present mean, range and quartile statistics for 18 fund-quarter combinations. Each observation in this sample represents the dollar-weighted mean IS cost for a single fund, during a single quarter within a liquidity-group size-group combination. The top row summarizes the distribution of costs over all 18 fundquarters. Although the distribution of orders across size groups is empirically determined (guaranteeing that all funds have 10% of their orders in the largest size group), the distribution across liquidity groups is not. Although all funds participate in the low-liquidity group each quarter, the number of trades may be low, contributing to extreme values. For nearly all liquidity-size group scenarios, some funds have negative costs; however, median costs are everywhere positive. The summary statistics at the fund level for each of the seven funds analyzed in this paper are presented in Panel B of Table 1. All seven funds exhibit positive average costs (presented in basis points) in aggregate, although one fund exhibits negative costs for its sell orders. In Tables 2 and 3, we present summary statistics on forecasted cost savings when we apply optimal trading strategies. Table 2 presents in-sample results; Table 3 covers the out-of-sample period. We discuss the out-of-sample results here; in-sample results are characteristically similar, but generally exhibit higher savings, as expected. The layout of Tables 2 and 3 is similar to that of Table 1 (Panels B and C), except that our measurement variable is now savings rather than costs. For each order, we forecast the IS cost and subtract it from the order’s realized IS cost. This calculated savings (in basis points) are dollar-weighted across all orders within the liquidity-size scenario for each fund-quarter. As shown in Table 3A, all seven funds exhibit savings from switching to the alphaadjusted strategy, although the gains are far from uniform. The minimum cost saving is less than one basis point; the maximum is over seven. Our median fund shows savings of roughly 4.5 basis points. In Panel B, we examine the savings across 18 fund-quarters and provide more detailed summary statistics broken down by liquidity and size group. The top row shows results aggregated by dollar-volume across all orders; the median savings are 4.11 basis points, with a minimum of 0.57, and a maximum of 10.55bp. Examining the more detailed breakdown presented in the five blocks which follow, we see that savings are somewhat higher for the largest order size group, as expected. It is interesting to note that savings for low-liquidity orders can be negative and rather large. Although the median fund always has savings in these low-liquidity orders, in some fund-quarters, we see evidence of opportunistic trading in illiquid securities.18 Although savings for most fund-quarters are significant, a few are negligible. Furthermore, some scenarios for some funds (such as medium to large trades in less liquid securities) have mixed results. We attribute this to two factors. First, the family of candidate strategies may be insufficient to capture the complex trading decision processes implemented by institutional fund managers. In particular, our reliance exclusively on the impoverished family of VWAP-style strategies would rule out strategies taking into consideration variation in market conditions as well as


12

other factors pertaining to security selection that might constitute private information of the fund manager. As we demonstrate in other studies (in progress), further gains are likely to be attained from adopting genuinely dynamic strategies. Second, the optimal alpha-adjusted strategy is estimated for each fund using a limited evaluation period, so it is subject to significant statistical variation, especially for scenarios with relative sparse observations in the evaluation sample.

FUND-SPECIFIC ANALYSIS OF INTRADAY ALPHA PATTERNS We conclude our discussion with a more granular analysis of intraday alpha patterns and cost savings for one of our sample funds which we refer to as “ZZZ”.19 Fund ZZZ submitted 6036 orders during 2010, with dollar volume totaling $4.8 billion. In Figure 1, we present a graph of ZZZ’s cumulative and market-adjusted intraday signed returns, as well as its signed alpha pattern. We separate buys and sells for this presentation. This fund has positive total signed returns for its buy orders, and negative signed returns for its sell orders; both types of orders involve securities whose prices are rising over the course of the day during trading. However, notice the difference in magnitude. At the end of the day, the average security the fund is purchasing has increased roughly 5 basis points from its opening price; the securities it is selling, however, have increased nearly 70 basis points. After adjusting for market, sector and industry returns, both types of orders have negative marketadjusted returns of 15-30 basis points (as shown by red lines). Both buy and sell orders have negative signed alphas by the end of day of 30 to 40 basis points. These negative intraday signed returns help explain why the fund’s trading costs are already quite low, averaging just over 1 basis point. In Panel B, we aggregate the alpha patterns across order sides and segment by order size grouping. Only small buy orders have positive alpha; the remaining order size groups have negative intraday alphas over 20 basis points. In summary, ZZZ exhibits fairly stable alpha patterns across order size groups, supporting our assumption that funds have a stable alpha pattern across trades. We apply our optimization procedure to the data and identify optimal strategies as discussed in section 3.4. The resulting optimal trading schedules are presented in Figure 6. In Panel A, we show the realized and optimal trading schedules for large orders for the final quarter of data, 2010Q4. The realized buy and sell trading schedules are quite close to a 45-degree line, which would be historical VWAP. The optimal trading schedules in contrast are quite backloaded, as expected considering the negative signed alpha pattern displayed in Figure 1. In Panel B, we show the trading schedules for the smallest orders; although the data is noisier, which is indicative of more immediate executions of small orders, in aggregate the schedules are not far from VWAP; optimal schedules are smoother and somewhat more backloaded. This result is in-line with the signed alpha patterns from Figure 1; recall that the smallest order size group lacked the negative signed alpha pattern of ZZZ’s larger orders. We present cost results broken down by order size and liquidity groups for the out-of-sample period in Table 5.20 The out-of-sample period covers 3228 orders with trading volume of $2.9 billion. During this period, the fund had realized trading costs of 5.21 basis points. Shifting the trading schedule to the far more backloaded schedule suggested by the optimization procedure results in forecasted savings of 4.14 bp21 ( roughly $1.2MM for the last six months of 2010.)


13

Forecasted savings are highest for large orders; we anticipate savings for the largest order size group (which comprises nearly half of the fundâ&#x20AC;&#x2122;s dollar volume) of over 9 basis points. Savings are not universal across size groupings: the two smallest order-size groupings both show increased trading costs , particular for the fundâ&#x20AC;&#x2122;s small-medium orders. It is interesting to note that the in-sample results (Table 4) predict modest to moderate savings in the two smallest order size groupings; we speculate that fund ZZZ trades these orders somewhat opportunistically in a fashion that cannot be captured outside of a dynamically determined trading schedule. Results for larger order sizes are more consistent when comparing in- and outof-sample results.

CONCLUSION In this paper, we apply a new post-trade TCA model to execution data of seven clients and present empirical evidence of predictable patterns in intraday returns and trading price impact. While there is substantial variation in these intraday patterns across individual investment funds, the patterns under consideration are fairly stable over time, suggesting the existence of identifiable intraday alpha patterns for those funds. These patterns imply that execution strategies can be adopted to reduce trading cost as measured by implementation shortfall. We provide a methodology that identifies ex post optimal trading strategies from a specified set of core strategies, and illustrate how the trading performance can be improved by modifying the fundâ&#x20AC;&#x2122;s execution strategy to better reflect its trading style. The projected out-of-sample gains from adopting the alpha-adjusted trading strategies are substantial, varying between 0.6 and 7.4 bps at the aggregate fund level. These gains are estimated conservatively; enhancement may be possible with expansion of the candidate strategy set to encompass dynamically-determined trading strategies. Furthermore, our results compare realized execution costs from a trading environment where traders can and do avail themselves of block-liquidity; our simulated strategies thus operate at a substantial disadvantage in our framework.


14

REFERENCES Anand, A., P. Irvine, A. Puckett, and K. Venkataraman Performance of institutional trading desks: An analysis of persistence in trading costs. Working paper, 2010. Borkovec, M. and H. G. Heidle The magic of hindsight: Creating a post-trade transaction cost estimate based on realized market conditions. Journal of Trading, 2007. Borkovec, M. and H. G. Heidle Building and evaluating a transaction cost model: A primer. Journal of Trading, 2010. Borkovec, M., K. Tyurin, Q. Fang, and J. Cheng What does it take to work large orders in real time? Introducing ITG dynamic transaction cost model. ITG working paper, 2011. Brandes, Y, and I. Domowitz Alternative trading systems in Europe: Trading performance by European venues post-MiFID, 2010 updated. Journal of Trading, 2010. Breedon, F. and A. Ranaldo Intraday patterns in FX returns and order flow. Swiss National Bank working paper, 2010. Ellis, K., R. Michaely, and M. Oâ&#x20AC;&#x2122;Hara The accuracy of trade classification rules: Evidence from Nasdaq. Journal of Financial and Quantitative Analysis, 2000 Farmer, J., A. Gerig, F. Lillo, and H. Waelbroeck The market impact of large trading orders: Correlated order flow, asymmetric liquidity, and efficient prices. Working paper, 2009 Gomes, C. and H. Waelbroeck Transaction cost analysis to optimize trading strategies. Journal of Trading, 2010 Heston, S.L., R.A. Korajczyk, R. Sadka, and L.D. Thorson Are you trading predictably? Financial Analysts Journal, 2011 ITG Below the Waterline: Uncover Hidden Transaction Costs throughout the Investment Process. ITG Monograph, ISBN 978-0-615-28516-0, 2009 Kissell, R. and M. Glantz Optimal Trading Strategies. ISBN 978-0-8244-0724-0, 2003 Lee, C. and M. J. Ready Inferring trade direction from intraday data. Journal of Finance, 1991 Odders-White, E On the occurrence and consequences of inaccurate trade classification. Journal of Financial Markets, 2000 Perold, A The implementation shortfall: Paper vs. reality. Journal of Portfolio Management, 1988 Sofianos, G Choosing benchmarks vs. choosing strategies: Part 1 â&#x20AC;&#x201C; Execution benchmarks: VWAP or pretrade prices. Journal of Trading, 2006


15

APPENDIX: GRAPHS AND FIGURES Figure 1: Comparison of intraday alpha patterns for fund ZZZ Panel A: Average dollar-weighted cumulative returns and alpha patterns, by order side

Â

Panel A of Figure 1 shows the intraday total and market adjusted cumulative signed returns and alpha patterns for buy and sell orders of fund ZZZ based on the sample of orders traded by this fund between January and December 2010. The realized cumulative signed return patterns are shown (in green) for buy and sell orders along with the realized cumulative signed return patterns net of market, sector, and industry cumulative returns (in red) and the realized net cumulative signed return patterns net of own price impact (in blue). The cumulative market, sector, and industry returns are extracted using the methodology described in section 2.1. Own price impact is determined as described in sections 2.2 and 2.3. All cumulative intraday returns shown on the plots are dollar-weighted averages across all names bought or sold by fund ZZZ on the days that the orders were traded.

Â


16

Figure 1 (continued): Comparison of intraday alpha patterns for fund ZZZ Panel B: Average dollar-weighted cumulative alpha patterns for buy orders only, by order size grouping

Panel B of Figure 1 shows the signed, cumulative intraday alpha patterns for buy clusters of trades by fund ZZZ between January and December 2010. The cumulative return patterns are shown net of market, sector, and industry cumulative returns and net of own price impact. The alpha patterns are reported separately for five relative cluster size categories. The “Small” category includes clusters with the lowest 40% of relative size; the “Small-Medium” category includes the clusters between the 40th and 60th percentiles of relative size; the “Medium” category includes the clusters between the 60th and 80th percentiles of relative size; the “MediumLarge” category includes the clusters between the 80th and 90th percentiles of relative size; the “Large” category includes all the remaining clusters in the sample, which constitute the largest 10% of clusters, by their size relative to MDDV.


17

Figure 2: Examples of expected values of H distributions for orders of varying size (as a fraction of five-minute interval median dollar volume) in MSFT and ITG under normal market conditions

MSFT: Market Capacity at 130% of 5min binADV (Normal Market Conditions)

Standardized TI

6 5 4 3 2 1 0 0%

20%

40%

60%

80%

100%

120%

140%

Relative Trade Size (% of bin ADV) H (empirical)

Market Orders

ITG: Market Capacity at 253% of 5min binADV (Normal Market Conditions)

4 Standardized TI

H (with Market Capacity)

3 2 1 0 0%

50%

100%

150%

200%

250%

300%

Relative Trade Size (% of bin ADV) H (empirical)

H (with Market Capacity)

Market Orders

Figure 2 shows examples of the relationship between the trade size (normalized by the historical median dollar volume within a five-minute interval under consideration, on the horizontal axis) and the expected contemporaneous standardized trade imbalance (normalized by the historical median dollar volume within the same five-minute interval and then by historical standard deviation of the normalized trade imbalance ratios, on the vertical axis) under normal market conditions for two stocks – MSFT (very liquid, on the left panel) and ITG (less liquid, on the right panel). The blue curves show the globally concave empirical relationships between the two quantities of interest determined from ITG’s Peer Group data. The black straight lines show the expected relationship between the trade size and trade imbalance under the hypothetical scenario where 100% of the trade is executed using market orders only. The expected patterns used in this paper are represented by the “hockey stick”-shaped red curves, which reflect the limited capacity of the market to absorb large trades without impact on the contemporaneous trade imbalance. Specifically, once the normalized trade size exceeds a certain level, the trader would have to rely more and more on market orders to complete execution within the specified five-minute interval. The red curves coincide with the empirical (blue) curves for trade sizes and are parallel to the market order-based (black) straight lines for very large order sizes. The critical levels beyond which the red and black lines become parallel are market condition- and stock liquidity group-dependent.


18

Figure 3: Percentiles of H distributions for hypothetical orders in MSFT and ITG under normal market conditions

MSFT: Market Capacity at 130% of 5min binADV (Normal MC, Trade Size=100% of 5min binADV, i.e. 1.9 mln.shrs)

Standardized TI

8 6 4 2 0 -2 0%

50%

100%

150%

200%

250%

300%

350%

Relative Trade Size (% of bin ADV) mean

1_TIperc5

1_TIperc10

1_TIperc20

1_TIperc80

1_TIperc90

1_TIperc95

ITG: Market Capacity at 253% of 5min binADV (Normal MC, Trade Size=100% of 5min binADV, i.e. 8000 Shares)

Standardized TI

4 3 2 1 0 -1 -2 0%

50%

100%

150%

200%

250%

300%

350%

Relative Trade Size (% of bin ADV) mean

1_TIperc5

1_TIperc10

1_TIperc20

1_TIperc80

1_TIperc90

1_TIperc95

Figure 3 shows the relationship between the trade size (normalized by the historical median dollar volume within a five-minute interval under consideration, on the horizontal axis) and the conditional 5th, 10th 20th, 80th, 90th and 95th percentiles of the distribution of contemporaneous standardized trade imbalances (normalized by the historical median dollar volume within the same five-minute interval and then by historical standard deviation of the normalized trade imbalance ratios, on the vertical axis) under normal market conditions for two stocks – MSFT (very liquid, on the left panel) and ITG (less liquid, on the right panel). All conditional percentile curves are based on the “hockey stick” patterns from Figure 2 and are nearly parallel for large order sizes, reflecting the stylized fact that beyond a certain capacity level further increases of trade size would shift only the conditional mean without affecting the dispersion of the conditional distribution.


19

Figure 4: Expected price trajectories and estimated implementation shortfall costs of orders under alternative execution strategies Panel A: Medium buy order by fund ZZZ in a medium liquidity stock

Â

The top chart of Panel A of Figure 4 shows an example of the expected price trajectories of a medium liquid ticker (HCN) if the medium (2.34% ADV) buy order filled by fund ZZZ during 2010Q1 were executed instead using a series of hypothetical VWAP-based trading strategies as well as the immediate execution (100% of the order traded between 9:35am and 9:40am) and delayed execution (100% of the order traded between 3:55pm and 4:00pm) strategies. VWAP-1 (VWAP-25) is the most front-loaded (back-loaded), executing approximately 20% (30%) of the order in the first (last) five minutes. VWAP-13 is historical VWAP. The bottom chart of the same panel shows the expected implementation shortfall costs of those strategies as well as the realized implementation shortfall cost, in basis points. The instantaneous trading strategy exerts a strong upward pressure on the stock price in the short run, resulting in the expected implementation shortfall cost above 60 basis points. The last-bin trading strategy is the cheapest among the ten strategies considered, resulting in the expected implementation shortfall cost below negative 35 basis points. We attribute this to the negative return this security experiences on the trading day, and the relatively low trading costs at the end of the day.

Â


20

Figure 4 (continued): Expected price trajectories and estimated implementation shortfall costs of orders under alternative execution strategies Panel B: Medium-size sell order by fund ZZZ in a medium liquid stock

Â

The top chart of Panel B of Figure 4 shows an example of the expected price trajectories of a medium liquidity ticker (CPT) if the medium-sized (2.36% ADV) sell order filled by fund ZZZ during 2010Q1 were executed instead using a series of hypothetical VWAP-based trading strategies as well as the immediate execution (100% of the order traded between 9:35am and 9:40am) and delayed execution (100% of the order traded between 3:55pm and 4:00pm) strategies. VWAP-1 (VWAP-25) is the most front-loaded (back-loaded), executing approximately 20% (30%) of the order in the first (last) five minutes. VWAP-13 is historical VWAP. The bottom chart of the same panel shows the expected implementation shortfall costs of those strategies as well as the realized implementation shortfall cost of the order, in basis points. The most aggressively back-loaded VWAP strategy is the cheapest among the ten strategies considered, resulting in the expected implementation shortfall cost below 45 basis points.

Â


21

Figure 5: Cumulative volume profiles of hypothetical trading strategies

Figure 5 shows the average cumulative intraday volume profiles for the menu of hypothetical volume weighted average price (VWAP) strategies of varying degrees of aggressiveness. The most aggressive strategy (VWAP-1) trades approximately 20% of the order in the first five minutes and is represented in the figure by the left-most blue line. The least aggressive strategy (VWAP-25) fills 30% of the order in the last five minutes of the day and is shown as the right-most light blue line. The whole day historical VWAP strategy (VWAP-13) results in a 45 degree line drawn in bold black, reflecting a proportional relationship between the accumulated realized trading volume (on the vertical axis) and the total volume in the same ticker due to executions of all market participants (on the horizontal axis).

Â


22

Figure 6: Optimal strategies implied by intraday alpha and return patterns for fund ZZZ Panel A: Cumulative intraday profiles of optimal and actual strategies for large buy and sell orders of fund ZZZ

 Panel A of Figure 6 compares the average cumulative intraday volume profiles based on the intraday trading schedules for buy and sell orders traded by fund ZZZ in the last quarter of 2010 with the average cumulative intraday volume profiles from the optimal strategies selected for fund ZZZ from the family of VWAP-style probe strategies using the intraday alpha patterns for the corresponding group of orders. The plot is for large orders (top 10%, by relative order size). The actual and optimal cumulative volume patterns are shown separately for buy and sell orders. For large orders, the schedules implied by the optimal alpha-adjusted strategies are more backloaded than the realized trading schedules. Optimal strategies for large orders are aggregated across four liquidity groups; buy and sell optimal strategies are not constrained to be similar.


23

Panel B: Cumulative intraday profiles of optimal and actual strategies for large buy and sell orders of fund ZZZ with arrival times between 9:30am and 10:00am EST

Â

Panel B of Figure 6 compares the average cumulative intraday volume profiles based on the intraday trading schedules for buy and sell orders traded by fund ZZZ in the last quarter of 2010 with the average cumulative intraday volume profiles from the optimal strategies selected for fund ZZZ from the family of VWAP-style probe strategies using the intraday alpha patterns for the corresponding group of orders. The plot is for small orders (bottom 40%, by relative order size). The actual and optimal cumulative volume patterns are shown separately for buy and sell orders. For small orders, the schedules implied by the optimal alpha-adjusted strategies are slightly more backloaded than the realized trading schedules. Optimal trade schedules for small orders are aggregated across four liquidity groups, and not constrained to be similar for buy and sell orders.


24

Table 1: In-sample comparison of client executions across different scenarios Panel A of Table 1 shows the summary statistics for executions for seven clients. The sample period is from January, 2010 through September, 2011; individual fund data consists of three to seven consecutive quarters of data. Summary measures are calculated for seven funds; the mean, median, minimum and maximum are reported. The unit of analysis is a â&#x20AC;&#x153;clusterâ&#x20AC;?, which is defined as a set of trades performed by the given client in the same direction, for the same name, and on the same trading day.

Mean Median Min

Number buys

9,114

1,519

44,359

Number sell 9,898 2,954 1,475

49,031

Dol Vol ($ MM) buys

1,147

21,457

Dol Vol ($ MM) sells 3,254 2,323 1,002

21,742

Pct. Trades in illiquid stocks

3.58%

0.07%

0.00%

14.49%

Pct. Trades in low liquidity stocks

20.84%

22.79%

5.49%

39.16%

Pct. Trades in medium liquidity stocks

33.47%

34.72%

20.85%

53.83%

Pct. Trades in high liquidity stocks 42.11% 51.62% 22.50%

59.77%

Avg. Cluster Size in illiquid stocks

14,776

6,633

0

71,114

Avg. Cluster Size in low liquidity stocks

19,333

16,176

6,098

40,974

Avg. Cluster Size in medium liquidity stocks

24,169

23,159

17,943

33,782

Avg. Cluster Size in high liquidity stocks 33,184 32,694 24,013

48,293

3,365

3,181

Max

2,315

Avg Dol Vol/cluster illiquid stocks ($)

267,888

43,298

0

1,612,866

Avg Dol Vol/cluster low liquidity stocks ($)

316,794

301,134

176,556

470,450

Avg Dol Vol/cluster medium liquidity stocks ($)

646,332

648,748

474,952

846,961

1,112,000

969,457

771,611

2,049,074

Avg Dol Vol/cluster high liquidity stocks ($)


25

Table 1 (continued): Realized implementation shortfall costs Panel B presents median, min and max dollar-weighted implementation shortfall costs in basis points for seven funds with trades aggregated across all quarters and clusters; we also present results conditioned on trade side. Panel C presents summary statistics for dollar-weighted realized implementation shortfall costs in basis points. Our sample consists of 18 fund-quarter combinations. The first row presents unconditional results. The following five blocks present results for five order size groupings, further conditioned on three liquidity scenarios (as defined by 20 day historical median daily dollar volume). Panel B: Implementation shortfall costs for seven funds across all orders, all quarters Liquidity Min All orders

Median

3.81

10.72

Max 24.45

Buys 4.98 12.22 24.35 Sells -3.41 5.44 24.55

Panel C: Implementation shortfall costs across 18 fund-quarter combinations Liquidity Mean Min All orders

13.82

0.71

Q1 Median Q3 Max 6.80

11.68

21.23

27.92

Large orders All

21.69 1.85 11.50 17.23 35.23 54.06

High

17.25 -43.47 8.77

Medium

22.57 -16.64 11.77 22.93 40.56 55.70

Low

28.60 -37.81 -0.01 34.62 59.55 73.66

21.25 26.96 55.68

Medium-large orders All

9.78 -7.64 -0.09 13.30 15.61 29.27

High

5.10 -30.91 -0.61 6.63 14.15 29.64

Medium

10.65 -20.65 -4.15 13.56 21.83 34.25

Low

16.43 -29.16 -6.71 24.00 35.89 50.11

Medium orders All

9.62 -5.31 5.18

12.50 14.73 19.29

High

6.99 -15.05 2.01

9.44 11.88 20.06

Medium

10.25 -11.18 4.00

12.99 16.97 26.72

Low

17.05 -23.67 7.40

21.15 28.65 39.07

Small-medium orders All

6.58 -3.44 0.19

7.41 11.44 17.56

High

3.96 -26.63 -1.81 3.50 11.56 26.42

Medium

6.63 -6.44 -2.43 6.55 14.37 18.58

Low

9.33 -27.62 7.99

11.08 18.81 27.75

Small orders All

5.81 -5.84 3.27 5.01 9.49 16.04

High

1.92 -9.09 -3.62 3.33 8.19 14.44

Medium

6.79 -11.37 1.51

8.61 12.67 15.89

Low

14.34 -6.81 5.81

11.53 21.62 43.30


26

Table 2: In sample savings with trade schedule optimization Panel A presents median, min and max dollar-weighted implementation shortfall costs in basis points for the seven funds with trades aggregated across all quarters and clusters. Panel B presents summary statistics for dollar-weighted realized implementation shortfall costs. Our sample consists of 18 fund-quarter combinations. The first row of Panel B presents unconditional results. The following five blocks present results for five order size groupings, further conditioned on three liquidity scenarios (as defined by 20 day historical median daily dollar volume). Panel A: In sample savings for seven funds across all orders, all quarters Liquidity Min All orders

Median

1.26

5.80

Max 12.86

Buys -0.43 6.09 17.43 Sells 0.29 5.50 8.50

Panel B: In sample savings across 32 fund-quarter combinations Liquidity Mean Min All orders

5.47

1.00

Q1 Median Q3 Max 3.15

5.30

6.41

12.86

Large orders All

7.58 1.48 4.68

5.87 10.20 19.76

High

9.08 -0.67 4.68

5.74 10.21 44.49

Medium

8.81 -3.08 4.26

5.84 11.67 39.64

Low

2.53 -16.74 -0.95 2.05 7.05 24.80

Medium-large orders All

4.53 -1.05 1.69 4.21 6.05 13.28

High

4.44 -4.67 0.21 2.97 5.86 28.26

Medium 6.25 -1.78 3.07 5.60 7.77 17.09 Low

5.09 -13.57 1.31 3.51 8.57 33.42

Medium orders All

3.82 -2.78 1.61 3.48 5.33 11.66

High

3.49 -8.96 0.83 2.72 5.40 14.88

Medium 4.36 -2.23 2.90 4.19 5.71 12.16 Low

6.22 -4.37 2.04 4.29 6.09 38.15

Small-medium orders All

3.81 -4.52 1.66 3.33 6.83 9.26

High

4.09 -1.63 0.87 2.70 5.72 24.95

Medium 4.48 -8.46 0.42 4.66 6.88 16.68 Low

5.58 -12.69 0.96 4.19 8.85 30.55

Small orders All

4.49 -0.53 0.94 3.89 7.21 16.28

High

2.65 -8.47 0.20 3.27 5.51 14.43

Medium 5.29 -6.06 1.86 4.15 7.01 22.60 Low

9.72 -4.25 5.40

11.02 15.11 19.39


27

Table 3: Out of sample savings with trade schedule optimization Panel A presents mean, min and max dollar-weighted savings in basis points for the seven funds with trades aggregated across all out-of-sample quarters and clusters. Panel B presents summary statistics for out of sample dollar-weighted implementation shortfall cost savings from applying alpha optimized VWAP-based trading schedules. Our sample consists of 18 fund-quarter combinations. The first row of Panel B presents unconditional results. The following five blocks present results for five order size groupings, further conditioned on three liquidity scenarios (as defined by 20 day historical median daily dollar volume). Panel A: Savings for seven funds across all orders, all quarters Liquidity Min All orders

0.60

Median 4.48

Max 7.39

Buys -0.50 3.87 11.70 Sells 0.20 3.06 7.93

Panel B: Savings across 18 fund-quarter combinations Liquidity Mean Min All orders

4.20

0.57

Q1 Median Q3 Max 2.62

4.11

5.85

10.55

Large orders All

6.39 0.77 4.23 5.86 7.97 16.03

High

7.04 -1.14 2.99 4.59 9.19 33.90

Medium 8.30 -1.74 3.48 7.51 9.98 25.94 Low

2.47 -12.19 -1.88 3.52 6.96 14.74

Medium-large orders All

3.40 -2.74 -0.24 4.23 5.25 9.90

High

2.64 -8.04 -1.58 2.75 4.35 12.79

Medium 5.45 -0.79 1.16 6.46 8.31 11.80 Low

6.43 -13.64 -1.73 4.61 11.27 33.17

Medium orders All

3.00 -1.29 0.98 2.84 5.68 8.45

High

3.47 -3.57 0.30 2.52 3.99 21.23

Medium 3.85 -2.98 1.65 3.69 6.66 10.82 Low

5.45 -14.88 -4.14 5.36 11.02 37.27

Small-medium orders All

2.15 -5.88 0.67 2.53 3.68 9.24

High

0.80 -10.63 -0.39 0.79 2.71 8.93

Medium

3.44 -6.40 -0.36 4.26 6.48 16.26

Low

4.38 -13.07 0.60 3.91 8.28 20.50

Small orders All

1.58 -6.09 -1.32 2.62 4.26 7.64

High

0.38 -8.12 -0.64 0.58 3.34 5.23

Medium

2.82 -6.44 -1.88 2.38 5.65 13.92

Low

6.22 -4.11 0.03 6.36 9.02 25.34


28

Table 4: In-sample cost savings using optimized trading schedules We present realized and estimated trading costs and projected savings when applying alpha optimized trading schedules. The sample is 6036 orders executed by client ZZZ from January to December, 2010. All costs and savings are in basis points. Trading volume and dollar savings are in USD millions. Orders are conditioned on order size and liquidity grouping; size groupings are based upon the clientâ&#x20AC;&#x2122;s empirical distribution of orders sizes, with group cutoffs occurring at 40,60,80, and 90th percentiles. Liquidity group cutoffs are based on 20 day historical median daily dollar volume. We further condition results based on trade side, with results for all trades (aggregated) in the left-most results panel.

All Liquidity

obs

Vol ($)

Real

Buy Est.

Savings

Real

Sell Est.

Savings

Real

Est.

Savings

Total savings ($)

All orders 3228 2888.07 5.21 -0.59 5.80 4.98 -1.11 6.09 5.44 -0.06 5.50 1,673,990 Large orders All

444 1330.67 7.95 -1.07 9.02 6.11 -4.45 10.56 9.95 2.59 7.35 1,199,999

High 100 455.53 -3.70 -19.33 15.63 -11.26 -31.49 20.23 4.13 -6.73 10.86

711,905

Medium 244 729.53 18.41 10.20 8.21 18.69 12.27 6.42 18.07 7.69 10.38 598,947 Low

100 145.60 -7.99 -0.37 -7.61 -10.67 -11.37 0.70

-6.12 7.27 -13.39

-110,858

Medium-large orders All

370 586.30 6.04 0.92 5.13 16.30 16.47 -0.16 -2.33 -11.77 9.45

300,574

High

80

113,17

184.13 -0.85 -6.99 6.15 17.03 16.73 0.30 -10.46 -19.74 9.29

Medium 196 315.81 3.27 -3.88 7.15 2.87 0.79 2.08 3.66 -8.51 12.18 225,804 Low

94

86.37 30.89 35.34 -4.45 65.56 74.86 -9.29 -1.79 -1.92 0.13

-38,399

Medium orders All

568 525.25 -0.34 -2.72 2.38 -2.43 -7.21 4.78 1.90 2.07 -0.17 125,222

High 98 124.05 0.49 -3.77 4.26 1.18 -0.51 1.69 -0.03 -6.21 6.18

52,859

Medium 332 332.89 -0.32 -1.70 1.38 -2.72 -9.02 6.31 2.60 7.21 -4.61 45,968 Low 138 68.31 -1.93 -5.79 3.86 -6.40 -7.92 1.52 2.84 -3.53 6.36

26,396

Small-medium orders All

496 199.62 -1.78 -3.30 1.52 -5.10 -6.58 1.47 1.86 0.29 1.57

30,322

High

104

49,503

56.97 -7.61 -16.30 8.69

0.22 -9.20 9.42 -19.08 -26.69 7.61

Medium 246 108.70 7.52 7.71 -0.19 7.87 10.12 -2.24 7.17 5.30 1.87

-2,047

Low

-17,133

146

33.95 -21.78 -16.74 -5.05 -60.39 -57.72 -2.68 12.82 19.98 -7.17

Small orders All 1350 246.23 5.85 5.13 0.73 -0.46 -1.90 1.44 12.86 12.93 -0.07 17,875 High

256

33.79 -5.68 -2.47 -3.22 -10.05 -12.29 2.23

0.45 11.32 -10.87

-10,865

Medium 764 194.54 7.85 6.22 1.62 2.13 0.06 2.07 14.03 12.89 1.14

31,578

Low 330 17.90 6.00 7.58 -1.58 -8.91 -1.14 -7.77 19.96 15.75 4.21

-2,836


29

Table 5: Out-of-sample cost savings using optimized trading schedules We present realized and estimated trading costs and projected savings when applying alpha optimized trading schedules. The sample is 3228 orders executed by client ZZZ from July to December, 2010. All costs and savings are in basis points. Trading volume and dollar savings are in USD millions. Orders are conditioned on order size and liquidity grouping; size groupings are based upon the clientâ&#x20AC;&#x2122;s empirical distribution of orders sizes, with group cutoffs occurring at 40,60,80, and 90th percentiles. Liquidity group cutoffs are based on 20 day historical median daily dollar volume. We further condition results based on trade side, with results for all trades (aggregated) in the left-most results panel.

All Liquidity

obs

Vol ($)

Real

Buy Est.

Savings

Real

Sell Est.

Savings

Real

Est.

Savings Total savings ($)

All orders 3228 2888.07 5.21 1.07 4.14 4.98 -0.22 5.20 5.44 2.38 3.06 1,194,851 Large orders All

444 1330.67 7.95 -1.12 9.07 6.11 -4.55 10.66 9.95 2.58 7.37 1,207,554

High 100 455.53 -3.70 -18.79 15.09 -11.26 -30.70 19.43 4.13 -6.46 10.59 687,450 Medium 244 729.53 18.41 10.05 8.36 18.69 11.33 7.36 18.07 8.50 9.57 609,779 Low 100 145.60 -7.99 -1.83 -6.16 -10.67 -9.30 -1.37 -6.12 3.36 -9.48 -89,682 Medium-large orders All

370 586.30 6.04 4.27 1.78 16.30 17.58 -1.28 -2.33 -6.60 4.27

104,322

High

80

-22,085

184.13 -0.85 0.35 -1.20 17.03 19.35 -2.32 -10.46 -9.86 -0.60

Medium 196 315.81 3.27 -1.79 5.05 2.87 1.87 1.00 3.66 -5.41 9.08 159,601 Low

94

86.37 30.89 34.74 -3.84 65.56 73.77 -8.21 -1.79 -2.07 0.27

-33,191

Medium orders All

568 525.25 -0.34 -0.44 0.11 -2.43 -5.56 3.12 1.90 5.00 -3.11 5,631

High 98 124.05 0.49 -5.74 6.23 1.18 -9.07 10.25 -0.03 -3.25 3.22

77,225

Medium 332

-81,745

332.89 -0.32 2.14 -2.46 -2.72 -4.42

1.71

2.60

10.12 -7.52

Low 138 68.31 -1.93 -3.42 1.49 -6.40 -6.13 -0.27 2.84 -0.52 3.36

10,151

Small-medium orders All

496 199.62 -1.78 2.46 -4.24 -5.10 -0.73 -4.37 1.86 5.96 -4.10 -84,685

High 104 56.97 -7.61 -1.90 -5.71 0.22 6.86 -6.64 -19.08 -14.72 -4.36 -32,555 Medium 246 108.70 7.52 12.42 -4.89 7.87 14.29 -6.42 7.17 10.53 -3.36 -53,165 Low

146

33.95 -21.78 -22.09 0.30 -60.39 -67.75 7.35

12.82 18.83 -6.01

1,033

Small orders All

1350 246.23 5.85 7.40 -1.54 -0.46 -1.74 1.28 12.86 17.54 -4.67

High 256 33.79 -5.68 -7.47 1.78 -10.05 -18.78 8.73 0.45 8.42 -7.97 Medium 764

194.54 7.85

9.97 -2.13

2.13

0.83

1.30

14.03 19.86 -5.83

-37,965 6,025 -41,341

Low 330 17.90 6.00 7.48 -1.48 -8.91 6.99 -15.90 19.96 7.93 12.04 -2,648


30

FOOTNOTES 1

See the reviews of recent developments in post-trade transaction cost analysis in ITG (2009) and Brandes and Domowitz (2010).

2

ITG’s Peer Group database contains execution details for more than 25 mln. orders by more than 160 institutional clients within the two-year time period 2009−2010.

3

Cumulative returns are conditional on direction of orders and weighted by dollar-value of trading.

4

The initiator (“aggressor”) of each transaction can be identified from client execution data. If the client execution data is unavailable, it is possible to approximate trade imbalance by the popular Lee–Ready algorithm (Lee and Ready, 1991) or one of its variations (for example, Odders-White, 2000, Ellis et al., 2000, etc.) For more discussion and empirical evidence on the importance of these real-time “Smart Indicators” we refer to the paper Borkovec et al. (2011).

5

6

Farmer et al. (2009) obtain this property from a theoretical model and confirm it empirically for several liquid LSE-traded stocks. There might be a legitimate concern that the coefficients of F and G functions estimated from the entire Level 1 data may be different from the coefficients of those functions estimated using only the securities and dates chosen by the clients for trading. We confirmed that this is not the case. Even though we observed a moderate variation in the estimated coefficients across funds, the estimated fund-specific coefficients of F and G have very similar patterns across funds. In other words, the variation between the coefficients of F and G estimated on the fund-by-fund basis does not lead to significant differences in the pre-trade optimal trading schedules or costs between funds.

7

8

It is important to keep in mind that, in spite of this assumption, the unconditional distributions of F and G within the same time interval are not independent of each other. By the same token, the conditional distributions of F and G in the same time interval given the realized contemporaneous trade imbalance are not assumed to be conditionally independent, since they rely on the common vector of market conditions.

9

The implicit assumption is that the liquidity providers and demanders do not change their behavior if the trader attempts the number of shares smaller than the actually observed trade size. If the hypothetical trade size is so large that the individual trade virtually becomes the market then the standardized trade imbalance distribution implied by the H function becomes asymptotically more concentrated around the mean. If the hypothetical trade size is so large that the individual trade virtually becomes the market then the standardized trade imbalance distribution implied by the H function becomes asymptotically more concentrated around the mean.

10

By construction (and in contrast to traditional pre-trade models), the cost model framework separates the impact of one’s own trading on the overall order flow (captured by the H function) from the impact of the overall order flow on the execution price dynamics (captured by F and G distributions); there is no direct impact of one’s own trade size on prices, but rather an indirect impact on prices through the effect of one’s own trading on the trade imbalance in the market. The modeling is performed for each interval j of the day separately, thus capturing a systematic variation of properties of H, F, and G distributions through the course of the day. The proposed approach is more flexible and can be viewed as a simplified Bayesian network.

11

We divide stocks into four liquidity groups based on 20 day historical median daily dollar volume (MDDV). Cutoffs change over time with market price levels and trading volumes. At the end of September, 2011, liquidity group 1(2,3) included stocks with MDDV less than 1.3 (13.8, 58.4) MM USD, with remaining securities assigned to liquidity group 4. Many fund-quarters in our sample have no trading in the smallest liquidity group; our most-active fund in liquidity group 1 trades less than 1% of its dollar-volume within this group of stocks. Consequently, we omit this liquidity group from disaggregated results, although they are included in aggregated results at the fund level designated as “all trades”.

12


31

13

Each client’s orders are divided into size categories based on the client’s individual empirical order size distribution. The bottom 40% of orders comprise size group 1, referred to as “small orders”. The remaining cutoffs occur at percentiles 60,80 and 90 of the distribution.

14

While we remain agnostic about the origins of client’s alpha patterns, they may be attributed, at least in part, to the fund manager’s skill in security selection, trader’s timing ability, as well as predictable intraday patterns in equities’ and other assets’ returns (Heston et al., 2011, Breedon and Ranaldo, 2010).

15

Anand et al. (2010) document persistence of institutional trading desks’ relative performance over prolonged periods, which may be attributed, at least in part, to persistence of their trading styles and alphas.

16

Customization of trading schedules based on post-trade transaction cost analysis is also discussed in Gomes and Waelbroeck (2010).

17

In fact, for some scenarios considered in sections 3.5 and 3.6, the average actual trading costs happen to be lower than the average costs of all probe strategies from our family.

18

As an example, imagine a fund that chooses to trade illiquid securities only when it can do so as a liquidity provider. The fund may realize very low trading costs with a strongly front- or back-loaded strategy, or as the result of a block trade. Any of our VWAP strategies is likely to underperform in this situation and partially motivates our nondiscretionary trading assumption. To the extent that a portfolio manager can choose to depart from optimized VWAP strategies when block market opportunities exist to the same extent as she has done so previously, our forecasted savings introduce a conservative bias to our results.

19

In order to provide an illustrative case study, we discuss an analysis of now-defunct fund “ZZZ”. Our data aggregation schemes elsewhere in this paper are motivated by a desire to illustrate results as clearly as possible while protecting client data confidentiality.

20

In-sample results are presented in Table 4 and are characteristically similar to out-of-sample results.

21

The range of forecasted costs across clusters is similar to those for realized costs. For example, for medium sized orders in medium liquidity stocks, actual costs (bp) have median and 95th percentile values of -1.9 and 78.3, respectively. Using the optimal strategy, the hypothetical median and 95th percentile values are -5.9 and 61.6. For large orders in high liquidity stocks, realized costs have median (95th percentile) costs of 1.9 (77.3); for hypothetical costs using optimal strategies we predict 16.5(81.6).

© 2011 Investment Technology Group, Inc. All rights reserved. Not to be reproduced or retransmitted without permission. 42012-22199 These materials are for informational purposes only, and are not intended to be used for trading or investment purposes. 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. 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. 283940 (“ITGL”) and/or Investment Technology Group Europe Limited, registered in Ireland No. 283939 (“ITGEL”) (the registered office of ITGL and ITGEL is Georges Court, 54-62 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. 100138-1), and ITG Australia Limited (ACN 003 067 409), a market participant of the ASX and Chi-X Australia (AFS License No. 219582). All of the above entities are subsidiaries of Investment Technology Group, Inc. MATCH NowSM is a product offering of TriAct Canada Marketplace LP (“TriAct”), member CIPF and IIROC. TriAct is a wholly owned subsidiary of ITG Canada Corp

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