A broker must buy Rs 50 crore of a stock through the day, and the volume profile is U-shaped: 30% in the first hour, 20% in the last. Build TWAP and VWAP schedules and compare their tracking risk against the day's VWAP.

VWAP buys 15, 7, 5, 4.5, 8.5 and 10 crore by hour; TWAP buys 8.33 crore every hour. VWAP keeps participation at a steady 10% and tracks the benchmark except for errors in the volume forecast, about 5 bps on a plausible miss. TWAP's weights differ from the market's, so any intraday drift moves it off the benchmark: about 15 bps, or Rs 7.4 lakh, one standard deviation. It also trades 18.5% of volume at midday.

TWAP is the simple one: Rs 50 crore over six hours is Rs 8.33 crore an hour, whatever the market is doing. VWAP buys each hour's share of the day's volume: 30% of Rs 50 crore in the first hour is Rs 15 crore, then 7, 5, 4.5, 8.5 and 10. Because the order is 10% of the day's volume, the VWAP schedule is always 10% of whatever trades in that hour, while TWAP's participation swings from 5.6% at the open to 18.5% at midday. Think of two people filling buckets from a tap that runs fast, then slow, then fast: one takes a fixed cupful every minute, the other takes a fixed share of whatever is flowing.

The VWAP benchmarkThe average price of the day weighted by the volume traded at each price. An order that buys in the same proportions through the day pays the same average. is the day's prices weighted by the day's volume. If your weights match the market's, your average price equals the benchmark whatever the path. If your weights differ, what matters is how much of the order is still unbought when the price moves. After the first hour TWAP has bought 16.7% against the market's 30%, so 13.3% of the order is exposed to every move from there on; that exposure shrinks through the day and turns slightly negative after 13:15.

For this benchmark, mostly yes, with two limits. A VWAP schedule is only as good as its volume forecast: if the day's volume comes in at 26, 15, 11, 10, 16 and 22 instead of the historical profile, the schedule still drifts about 4.8 bps from the benchmark. And VWAP concentrates buying at the open, when spreads are often widest and the price is still finding its level. The cost side modestly favours VWAP too: with impact rising with the square root of participation, TWAP's uneven participation costs roughly 7% more impact than a flat 10%.

Close by tying the choice to the client. A client measured against the day's VWAP wants the VWAP schedule, updated during the day as actual volume arrives. A client who wants the order done quickly, or has information that the price will rise, should not be benchmarked to VWAP at all, because the benchmark rewards patience. The schedule follows from the benchmark, not the other way round.