VWAP is "volume-weighted average price," not "average price". Therefore, to replicate it, you need to participate in line with volume-at-time, not 1/N per time bucket. This requires you to estimate the volume envelope over the time period of interest. (Often a day, or in the case of hedging certain new issue convertible bonds, up to several days.)
Yeah, that's why I said in the extreme case you have to participate in all the volume. Of course randomly trading doesn't prove that you achieve VWAP, but I'm just saying that it's probably not terribly far off.
Many brokers will guarantee an execution at VWAP. It's a competitive business. The last time I put in such an order, I traded a double-digit percentage of the day's volume and paid 10bp commission (0.10%).
Brokers guarantee VWAP only if they also are paid a very healthy commission. They generally lose to VWAP, but makeup for it in premiums.
Plus, if you are dealing with a large broker they may just cross your order with an offsetting order (or their own position, execute nothing in the market and keep the entire premium.
