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MARKET STRUCTURE BRIEFING NOTES

August 31, 2010

Volume Profiles: A Curve By Any Other Name… Matthew Black 416.594.7576 Kyle Burgess 416.956.6036 The most important factor in achieving the VWAP benchmark is matching the volume profile - if we could perfectly predict the volume profile, we could significantly narrow slippages. The question is how likely are we to accurately forecast the volume profile? Is it even feasible to predict the volume profile accurately by looking at historical trading patterns? Our analysis suggests it may be necessary to accept that one cannot accurately forecast the volume profile based on historical profiles. Specifically, although the average profile may be quite stable, there is a significant amount of noise around this average profile that explains the vast majority of the miss from the VWAP benchmark during execution. Consequently, we find it unnecessary to go through the extra effort of creating stock-specific volume profiles, since a general market-wide U-shape pattern will give results that are statistically indistinguishable.

METHODOLOGY To test, we compared the performance of stock-specific, sector-specific, and market-wide volume profiles. Stock-specific profiles were assembled using the average volume profile for the stock over the last 60 days. Sector-specific profiles were the volume-weighted average across all stocks in the sector over the last 60 days. The market-wide profile was the volume-weighted average across a universe of about 2,000 stocks over the last 60 days.

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EXAMPLE The diagram below compares the stock-specific profile for CM against the sector-specific profile for Financials and the market-wide volume profile. Notice the stock-specific profile is more noisy and steep, as opposed to the smooth and shallow market-wide profile.

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EVALUATION We tested against the 100 stocks with the highest average daily value traded over the last 60 days, because this most liquid set of stocks is most likely to exhibit predictable stock patterns. Less liquid names will be even less predictable. Results were gathered across 11,231 total observations. Specifically, for each volume profile we:

1) assume we execute at the VWAP within each interval1,

2) calculated realized average price over the trading day using the schedule,

3) take the average absolute miss of the realized price above from the actual VWAP for the day.

RESULTS Across the 100 stocks, the average absolute VWAP misses for the different profiles, in basis points, were: Profile VWAP Miss

in bps Standard Deviation

Stock Specific 11.293 ±15.73

Sector Specific 11.567 ±15.90 Market Wide 11.335 ±15.87 The standard deviations are large relative to differences in average performance against VWAP, and we can, with over 95% confidence: - Accept the hypothesis that the stock

specific profile is no better than the market-wide profile, and reject the alternative hypothesis that the stock specific profile is better and results in a lower average absolute VWAP miss

- Accept the hypothesis that the sector specific profile is no better than the market-wide profile, and reject the alternative hypothesis that the sector

1 Assuming VWAP is achieved in each interval implies our micro-order placement is no better or worse than the average trader. This focuses our analysis on the shortfall from VWAP that can be attributed to errors in forecasting the trading schedule

specific profile is better and results in a lower average absolute VWAP miss

- Accept the hypothesis that the stock specific profile is no better than the sector profile, and reject the alternative hypothesis that the stock specific profile is better and results in a lower average absolute VWAP miss

These tests allow us to conclude that no single profile outperforms any of the others with any statistical significance. The more complex stock and sector-specific profiles do not outperform the simpler market-wide profile2. The stock-specific profiles come close to improving on the sector-specific profiles - but not quite; they are essentially equal to the market-wide profile. What if the observations for average VWAP miss were exact with no deviation? What if we rejected the hypotheses and concluded that the stock-specific profiles did outperform the sector-specific profiles by an average of 0.27bps? This still only represents an improvement of 2.4% over the average sector profile miss of 11.57bps - miniscule compared to the large standard deviations. Likewise, if we accepted that the stock-specific profile gave a 0.042bps improvement over the U-shaped market profile, this only represents an insignificant 0.37% improvement.

2 bps2996.11123073.15

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We need a 0.29% difference to accept hypothesis with 95% confidence that one method is better than the other

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ANALYSIS From the above profiles we can see that the sector and stock-specific profiles are very close, while the market-wide profile is basically a smooth U-shape. We propose that the use of a general U-shape will perform just as well as stock-specific profiles, and that the vast majority of the observed miss relative to VWAP is the result of unpredictable deviations about the expected profile – at least when previous day’s trading patterns are the basis of prediction. As a specific example we looked at the volume profiles for CM. The ACFs (auto-correlation functions) below describe the historical realized deviations from the stock-specific, sector-specific, and market-wide volume profiles (realized profiles after the respective historical profile has been subtracted). This is done to investigate whether there are further patterns in historical trading data to be exploited. The stock-specific profile, when subtracted from the historical realized volume profiles leaves essentially a white noise pattern, implying that only unpredictable deviations remain. Therefore, the stock-specific profile makes the best use of previous days trading patterns, leaving essentially nothing but unpredictable white noise (which obviously cannot be used in a trading strategy). Note, however, that significant lags do exist in the ACF intraday, i.e. lags less than 78 (see Further Research). The sector-specific and market-wide profiles leave a non-white noise pattern with a noticeable seasonal pattern, implying there are predictable deviations that remain.

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Stock-Specific ACF

This seasonality pattern, however, does not seem to harm performance - in terms of

average absolute deviation or standard deviation of errors - in any significant way. This is because the unpredictable deviations about these patterns account for the vast majority of the realized shortfall from VWAP.

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The stock-specific ACF has only 5 significant lags between interval 78 (one trading day) and interval 200 - no more than would be expected in a random sample (i.e. 5% or 1 of every 20 lags will have a significant correlation in a random sample). This implies that at a 95% confidence level, there are no significant lags beyond 78 (previous day) that could be used to improve our forecast of today’s volume profiles. In this case the stock-specific volume profile had an average absolute VWAP miss of around 13.2bps, +/-63.6bps. By comparison, the sector-specific and market-wide profiles seem to still have some seasonal pattern existing that could be extracted, however, their statistical performance suffers very little, if at all, as a result. The performance of the sector-specific and market-wide profiles in this case are 13.1bps +/- 66.4bps and 11.5bps +/-60.9bps. Given the above average deviations and their standard deviations, for one method to definitively improve performance it must

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improve execution by almost 10 basis points in order to be statistically significant against the 144 daily observations used in this analysis3. None of the profiles vary from the others significantly enough for this to be the case. Once again, even assuming the estimates above are correct, the expected improvement in execution performance of any one method over another is small in percentage terms and miniscule compared to the standard deviations. CONCLUSIONS From this we conclude that a general U-shaped market-wide profile - although seemingly suboptimal - performs just as well as the more involved stock-specific profile, and that random intraday deviation from a general U-shaped pattern is the biggest contributor to negative performance versus the VWAP. Clearly, there is only so much information to gain from using previous days trading patterns to predict today’s trading patterns. Using a basic U-shape (a market-wide profile) is very simple and provides the same performance as sector or even stock-specific profiles. From our analysis of ACFs and actual performance numbers we can see that the majority of the miss from the actual VWAP using any of the above profiles is caused by unpredictable intraday variations in the expected trading profile. For example, even though the market-wide and sector-specific profiles left significant lags in the ACF, this did not hinder their performance.

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bps8.996.114460

=×

We need 0.1% difference to accept hypothesis with 95% confidence that one method is better than the other

FURTHER RESEARCH In the above ACFs, the same-day lags (i.e less than 78 5-minute bars) could have been used to in an attempt to better predict the current day’s volume profile. Therefore, monitoring and updating the profile intraday and adapting to the unpredictable deviations from the expected profile is the best way to gain meaningful improvement in execution performance. This leaves us with three main avenues to explore in order to improve VWAP execution: 1) How to update volume profiles intraday in order to execute closer to the actual volume profile? 2) How much improvement can we achieve by having better order placement logic? i.e. beating the VWAP in each interval? 3) Are there other explanatory variables that can explain deviations from the general U-shape pattern?

THOMAS KALAFATIS Executive Director - Business Strategy | Development (416) 956-6715 thomas.kalafatis@cibc.ca TIM COVEYDUCK Product Director - Client Interface (416) 594-8552 tim.coveyduck@cibc.ca LUKA MARJANOVIC Product Director – Liquidity (416) 594-8397 luka.marjanovic@cibc.ca KYLE BURGESS Product Director – Execution Management (416) 956-6035 kyle.burgess@cibc.ca

ALI LOTIA Viper Development (416) 956-3240 ali.lotia@cibc.ca PHIL SHAM Algorithm Development (416) 956-6032 phil.sham@cibc.ca MATT BLACK Quantitative Analysis (416) 594-7576 matthew.black@cibc.ca

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