Earlier quoted context omitted.
But the paper also rightly ends with a further caveat: While we do control for share price levels and volatility in our empirical work, it remains an open question whether algorithmic trading and algorithmic liquidity supply are equally beneficial in more turbulent or declining markets.
Its pretty much a tax; take out all the day traders and whether you gain or lose due to the spread is more or less random; day traders and hft traders narrow the spread, but since whether you gained or lost was random and they are now capturing a piece of that spread, they (err, ashamedly, we) are basically just taxing everyone. A nominal transaction tax would eliminate most of the ultra-high frequency stuff and coul…
Buyers pay the offer, sellers the ask. If you want to save the spread you can leave a resting order and wait for someone to take you out but you have no guarantee of a fill (or at least a timely one).