The work from 2007 looked at volume curves, the distribution of trading volume over the day which is critical for VWAP strategies. The trade data was from the London Stock Exchange and I published an example for HSBC (HSBA.L) here on gbkr.com. Chart 1 below shows the equivalent distribution of volume for the HSBC listing on HKEx over each day in the month.

This is not a smooth volume curve often shown in broker research. Those smooth curves either ignore variation or reduce it by eliminating outliers. Although the chart may be unfamiliar, the typical shape of trading is apparent, with a rise in volume towards the close and a less pronounced decline in trading after the open.

The variation in volume over the day across the month is also obvious, with noticeably more variation in trading volume during the afternoon session. The blue line shows the median relative volume for each five minutes over the month: this is often taken as the "volume curve" for the listing. The median should be preferred to the mean precisely because of this skew in the distribution. The red line shows the median volume plus two standard deviations of relative volume. Often algorithms assume a one standard deviation tolerance would capture most of the variation.

For an HSI listing the peaks in volume are surprising. On August 15, HSBC traded 498,800 shares from 13:15 to 13:20, and 395,600 shares from 13:25 to 13:30. In the five minutes between those periods 4,388,800 shares traded, or about 17% of the volume for that day, with ten times the number of trades compared to the average. And over four million of those shares traded in just one minute, with 968 trades at a single price.

VWAP strategies that kept to the median curve and failed to participate in that volume missed achieving VWAP.