Can VWAP execute the whole order within a specified time period?

One of the solutions to an EOC question states that ‘Following a fixed schedule as VWAP algorithms do, however, may not be optimal for certain stocks because such algorithms may not complete the order in cases where volumes are low.’

Schweser notes says otherwise, that both VWAP and TWAP ensure that a specified number of shares are executed in a specified time period. A comment on the learning ecosystem mentions that VWAP with no limit price will always get the order done, which is what I thought of as well.

Can anyone confirm if VWAP can fill an entire order (assuming market liquidity is enough to at least absorb it)?

What if nobody likes you and won’t buy your stock?

Then, even TWAP wouldn’t solve the problem, would it?
The question is as follows

Beatrice Minchow designs and implements algorithmic trading strategies for Enlightenment Era Partners LLC (EEP). Minchow is working with Portfolio Manager James Bean on an algorithm to implement a sell order for Bean’s small position in the lightly-traded shares of public company Dynopax Inc. In a conversation with Minchow, Bean states the following:

  • I have no expectations of adverse price movements during the trade horizon and would like to use a scheduled algorithm.
  • I want to minimize market impact, but I’m more concerned about getting the sell order completely executed in one day.

Based on Bean’s comments, Minchow considers three algorithms: POV, VWAP, and TWAP.

Question

Q. Determine which algorithm Minchow is likely to use for the Dynopax sell order. Justify your response.

Determine which algorithm Minchow is likely to use for the Dynopax sell order. (Circle one)
POV VWAP TWAP

Justify your response.