I am somewhat confused by this double-negative: "No serious market observer disputes the claim that volatility would not be higher without the liquidity provided by high frequency traders."

The author seems to be trying to say that high frequency traders reduce volatility. But I parse the claim differently: it seems to me to be saying that volatility could only be lower in the absence of liquidity from high frequency traders.

As to the rest of the argument, it seems to be structured along these lines:

* More efficient markets with lower spreads between buy and sell are good. I think this is a valid claim, but I don't think it follows from the existence of high frequency trading, but rather from more efficient, automated trading systems.

* High frequency trading helps supply market liquidity, and this liquidity is good. I can buy the first part of this, and the second part seems mostly true.

* Old-fashioned purchasers seem to be annoyed that when they make a large purchase, the price for the last share is higher than the price for the first share, because the market has already reacted to the change in supply and demand. He also makes the argument that were this not so, the sellers of shares would in effect be subsidizing purchasers. His case seems solid enough to me.

* But he then makes another claim that seems to contradict it. He suggests that companies with stocks that have low volume turnover are unduly affected by small purchases, and since high frequency trading increases volume, the impact is reduced.

* Finally, it seems he would like to claim that because "our nation's equity markets are far fairer, more efficient, more liquid and have lower transaction costs for investors than ever before", high frequency trading should claim a substantial portion of the credit.