Barclays_Improving VWAP Execution_Jan 2014

Equities

Improving VWAP Execution Using the information ratio for robust intraday volume forecasts

January 2014

Lada Kyj, PhD +1 212 526 8910 lada.kyj@barclays.com Mark Skinner +1 212 526 0887 mark.skinner2@barclays.com

For information purposes only. Recipients should seek appropriate legal, tax or regulatory advice. Not for onward distribution or for distribution to retail investors. More details are available upon request. See back page for additional disclaimer

Equities | Improving VWAP Execution

Executive Summary 

We evaluate the information ratio of intra-day volume estimators and show that the US stock universe has a multi-modal distribution with heavily traded stocks having high information ratios and less heavily traded stocks having low information ratios.



The information ratio is a valuable tool for traders to select between volumeweighted average price (VWAP) and time-weighted average price (TWAP) executions.



We propose and illustrate a methodology of using the information ratio to improve volume forecasts.



Finally, we report the results of the methodology on VWAP execution and show a significant reduction in the standard deviation of slippage.

Introduction Forecasting volume is a major driver in schedule-based automated trading strategies. Daily volume is not static, and therefore estimates used in automated trading strategies should be updated daily to account for changes observed in daily volume. In contrast, daily changes in the distribution of volume across the trading day (i.e. volume profile) are sometimes overlooked with the result that trading strategies rely upon static or poor estimates. Intraday volume distributions should be symbol specific and updated frequently enough to capture the heterogeneity across different symbols and the volume distribution changes observed over time. We will show that misspecification of the intraday volume distributions results in substantially poorer execution performance. We will also develop a metric to measure the informational content of intraday volume estimators, and how to use this metric to improve volume forecasts, and in turn VWAP execution. Of greatest practical interest, we suggest how this information can help decide when to choose TWAP instead of VWAP for stocks with poor intraday volume estimates.

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Intraday Volume Properties The diurnal pattern of intraday volume is well known and VWAP strategies attempt to schedule executions in line with this pattern1. The pattern is not the same across the universe, and there is substantial variation between stocks. This feature motivates cluster based, or even stock-specific, volume curves. The cross-sectional variation and dynamic changes in intraday volume suggest that symbol-specific, rolling window estimators such as Exponentially Weighted Moving Average (EWMA) are suitable estimators for intraday volume. Specifically let i denote the index of trading minutes within a day t. Define:

The EWMA estimator for expected volume

is given as:

where λ is set to 0.95, which is consistent with the standard parameterization of daily price returns2. The advantage of the EWMA is the ease of computation, but this estimator may not be robust to outliers. Specifically, the distribution of volume by minute is both skewed and heavy tailed, and as a result the mean of the distribution may not be representative of median outcomes. This raises a legitimate concern about the informational quality of intraday volume curves derived from EWMA, which is more commonly expressed as:

Information Ratio of Intraday Volume We describe a method for evaluating the information ratio of intraday volume estimators and show how to use this metric to improve volume forecasts and VWAP execution. This approach can be viewed as a regularization procedure to address robustness concerns for heavy tailed data. We believe that it has minimal computational overhead, is simple to explain to non-technical users, and provides substantial performance gains for VWAP execution. VWAP is defined as

Where

1

is the density of intraday volume defined as:

Brownlees, C., Cipollini, F., and G.M. Gallo. (2011) 489-518.

-day Volume Modeling and Predictio

Journal of Financial Econometrics, 9,

2

2


We denote the variation of the intraday volume density as:

Where

is the square root of the EWMA of the variance of volume:

We define the information ratio as:

the truncated average ratio of the signal over the distortion at each time index i.

Analysis of Information Ratio Exhibit 1 shows the distribution of the information ratio for three indexes and over the entire universe of US equity from November 2011 to August 2012. The entire universe appears multi-modal, with a cluster centered on 0.7, a second cluster centered on 0.3, and a third, more concentrated cluster centered around 0.1. Of note, this analysis differentiates high information stocks as those with > 0.5. Exhibit 1 Information Ratio by Index Membership

Source: Barclays analysis.

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The S&P 500 is representative of the most heavily traded stocks within this universe. Most of the stocks in this set have estimates of ω that are close to 1, with a mean of 0.79, the 25th percentile is 0.74, and the 75th percentile is 0.86. This is consistent with expectations that heavily traded names have a high information ratio and that a high quality volume schedule signal can be estimated for this set. Nevertheless, there are a handful of stocks such as Washington Post (WPO) and Hudson City Bancorp, Inc. (HCBK) that have low information ratios (< 0.5). This indicates that clustering by attributes such as market capitalization or average daily volume (ADV) may offer a misleading sense of quality of volume curve forecasts. The ETF 50 is defined as the 50 largest ETFs by 20-day trading volume and represents another set of heavily traded stocks. Summary statistics for this set are as follows: the mean is 0.76, the 25th percentile is 0.67, and the 75th percentile is 0.82. In contrast, the Russell 2000 (R2000) represents a more diverse set of stocks in terms of trading activity and includes high and low ω stocks. The distribution appears multi-modal with modes at 0.125, 0.275, and 0.625. This is consistent with expectations that less frequently traded stocks in general have a lower ω score. Moreover, this legitimizes concerns about the informational quality of intraday volume curves derived from EWMA. Low information stocks might achieve lower VWAP slippage by trading a flat profile instead of a non robust volume profile. As an alternative to adopting TWAP, we show that ω can be used to improve the cross-sectional quality of intraday volume curves. To investigate the relationship between the information ratio across symbols we perform regression analysis on a set of trade features. We define the following variables: 

adv is the 30-day average daily volume



turnover is the total value of all shares traded that contribute to VWAP calculation



num_trades is the number of trades that contribute to VWAP



volatility is the 30-day price volatility



spread is the average of all bid-ask spreads taken as a percentage of the mid price

Exhibit 2 Correlation Structure of Symbol Attributes and Information Ratio

w w adv

adv 1

Price

num_trades

volatility

spread

turnover

0.5

0.46

0.63

-0.15

-0.57

0.75

1

-0.18

0.89

0.1

-0.26

0.68

1

-0.04

-0.47

-0.56

0.52

1

0.07

-0.35

0.81

1

0.46

-0.25

1

-0.6

price num_trades volatility spread turnover

1

Source: Bloomberg, Barclays analysis.

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Exhibit 2 shows that with the exception of volatility, most of the variables show strong correlation with the information ratio. Turnover is a function of adv and price, and is strongly correlated with number of trades.

Given the strong correlation structure, a reasonable parsimonious model is : = ln(turnover) + spread, with turnover and spread as explanatory variables for the information ratio . Exhibit 3 shows the results of the regression analysis. Consistent with intuition, the information ratio increases with the ln(turnover) and decreases with spread. Both variables are statistically significant and the goodness of fit is 84%. Exhibit 3 Regression Analysis

Variable Estimate Std. Error t value Pr(>|t|) ln(turnover) 0.02577 0.00029 88.87 <2e-16 spread -0.70057 0.02920 -23.99 <2e-16 Multiple R-squared: 0.8373, Adjusted R-squared: 0.8371 F-statistic: 4801 on 2 and 1866 DF, p-value: < 2.2e-16 Source: Barclays analysis.

Exhibit 4 illustrates the interaction of daily turnover and spread on the estimate of information ratio. High ω scores are concentrated to low spread and high turnover stocks, but low ω scores are distributed across the spectrum of spread and turnover. The 3D plot shows an inverted cornucopia-like shape. Conditioning on spread, we see that the ω score increases with turnover. Conditioning on turnover, we see that the ω score decreases with increasing spread. From a market microstructure perspective the lower information ratio with increasing spread is consistent with relatively lower opportunity cost in delayed execution. Exhibit 4 Information Ratio with respect to Daily Turnover

1

weight

0.8 0.6 0.4 0.2 0 0.4

25 0.3

20

0.2 15

0.1 spread

0

10

log(turnover)


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Application to Intraday Volume Schedule We discuss an application of the information ratio to improve volume EWMA forecasts for VWAP execution. Shrinkage is a popular methodology for improving estimation of covariance matrices in portfolio applications. 3 We start with the EWMA estimate of intraday volume. The premise is to identify an idealized target behavior and balance the advantages of the target with the need for specificity. First, we generate a dictionary of idealized volume profiles which are constructed by clustering the universe of stocks into self-similar subsets. These dictionary entries contain average percentages of daily volume per minute, and can be scaled by stockspecific ADVs to generate stock-specific volume curve estimates. The dictionary curves are idealized in that they are smooth and robust to outliers. Subject to a distance error metric, we optimally choose a dictionary entry per stock. Next, we state the Robust Volume Estimator (Rbst) as a weighted average of the EWMA and Target curves where the weights are subject to the information ratio of the EWMA profile. Robust (Rbst) = (1- )*Target + where if(

<=0.5) then set

*Original;

to 0.

The resulting estimator limits distortions due to non-systematic volume observed in low information ratio stocks (e.g. S.N, SIRI.OQ, and AAXJ.OQ), while preserving specific volume schedules of high information ratio stocks (e.g. SPY.P and BAC.N). The details of the procedure are illustrated in Exhibit 5.

3

The Journal of Portfolio Management, 30, 110-119.

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Equities | Improving VWAP Execution Exhibit 5 Illustration of Process of Applying the Information Ratio to Create a Robust Intraday Volume Schedule

Overlay the intraday information ratio

The Robust Volume Estimator weights the EWMA and Target curves as a function of the information ratio


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Trading Implications of Intraday Volume Schedule Specification We evaluate the performance of intraday volume schedules by comparing the slippage of the estimator with respect to VWAP. Assume that the schedule is sampled at oneminute intervals, and execution within that interval is at the interval VWAP price. As each allocation has VWAP execution, parent order-level VWAP slippage is due to scheduling errors. We consider the 6500 most heavily traded stocks from November 2011 to August 2012. Daily VWAP slippage of both buys and sells are aggregated per symbol.

Considering both buy and sell full-day trades the deciles of standard deviations are presented below in Exhibit 6 as the difference between standard deviation of slippage using EWMA versus using the Robust Estimator. The results show a reduction in tail behavior as the median standard deviation of slippage is smaller for the Robust Estimator than for EWMA. A closer evaluation of the deciles of the difference of standard deviation of slippage confirms the performance benefit. Focusing on the extreme tails, we see an improvement of 3.94bps overall, 2.26bps for Russell 2000, 1.32bps for ETF50, and 0.4bps for SP500.

Exhibit 6 Difference in Standard Deviation of Slippage Between EWMA and Robust Estimator (bps)

Deciles

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

All

-2.80

-1.08

-0.47

-0.11

0.05

0.34

0.77

1.58

3.94

SP500

-0.55

-0.27

-0.14

-0.08

-0.02

0.02

0.07

0.18

0.40


Conclusion We discussed a method for evaluating the information ratio of intraday volume estimators. This metric can be used to identify stocks that are difficult to trade using VWAP, and suitable for switching to TWAP execution. Our analysis examined stock characteristics that are correlated with low information ratios and in turn identifies stocks for which volume curve forecasts are not robust. We introduced a procedure that uses the information ratio to improve volume forecasts and performance of VWAP execution.

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Barclays_Improving VWAP Execution_Jan 2014

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