What the study does say is that HFTs are profitable and they make profits as a group from every other kind of trader—retail investors, institutional traders, hedge funds and market makers. It also shows that successful HFTs are persistently successful, which leads to market concentration and implies that some HFTs are better than others.
But because the study is limited to HFT profits, it doesn't take in account the value of liquidity provision. This is not a flaw in the study—it's just a limitation. Investors of all sorts benefit from additional liquidity. In order to know whether HFTs hurt investors on net, you'd have to measure the benefits against the costs.
There is at least some evidence that suggests HFT are a net cost to other investors. That evidence comes from a surprising place: the so-called Quant Bloodbath of 2007.
Here's how the Wall Street Journal described 07:
The trouble started Aug. 3, when stocks started moving not only in ways that commonly used models didn't predict, but in precisely the opposite direction from what was expected. Equally troubling, the moves were far more volatile than models based on decades of testing assumed were likely. Those relatively minor anomalies escalated quickly this week, exploding into a global rout for quantitative funds by Wednesday.
This led to the head of quantitative trading at Lehman Brothers to say: "Events that models only predicted would happen once in 10,000 years happened every day for three days."
The quants experienced this as severe pain. But it wasn't really all that extraordinary of a time for most investors. Stocks went up and stocks went down. The market ended the week a bit below where it started.
But, tellingly, the S&P rose on the days that were supposedly the worst for the quants. The reason why that is significant is that we've since learned that one of the things that made the situation so bad for the quants was a sudden loss of market liquidity.
And what caused the loss of liquidity? Well, it appears that one big factor was the flight of high-frequency traders from the market. The algos of the quants just didn't work well when the HFTs refused to provide liquidity. .
The point here, however, is not about the quants versus the HFTs. It's about what a rising market in the absence of HFTs may indicate. If high-frequency traders are a net benefit to investors, their exit should cause valuations of stocks to fall. If stocks rise while they exit, this at least suggests they may be a net cost.
This isn't decisive evidence against HFT, of course. It's always perilous to read too much into market movements. But it is one of the few natural experiments we have had in taking high-frequency traders out of the market.