> If you're winning a race by milliseconds, you are trying to interpose yourself into a trade that was already going to happen that day.

This is an inaccurate framing of how high frequency trading propagates liquidity in an otherwise illiquid (or strictly less liquid) market. The claim is not that liquidity is contributed on a strictly trade by trade basis, but rather than the low-latency activity has meta-reactive effects owing to enhanced price discovery that increase overall participation by drawing in other traders at different time resolutions. For example, where there may a stagnant order book on one equity (and consequently, few human traders able to fulfill orders without significant pricing penalties), the same order book may draw in competing market makers. They attempt to predict the next price movement - some win and some lose on the immediate sequence of trades, but the consequent activity narrows the bid/ask spread by heightening local participation in the order book and improving the pricing confidence. This has practical ramifications for "human" time resolutions, because the human traders now have a better opportunity to fulfill orders without overpaying. This in turn reduces overcautious traders from participating, and so on and so forth.

For what it's worth, your line of argument has been rehashed for years now on Hacker News, going back to when Chris Stucchio wrote his HFT apologia. Instead of lazily linking to that thread, I'll do one better by walking through research on the subject. Fortunately there is a handy paper that explicitly examines the question, "how does the interaction of these traders in the millisecond environment impact the quality of markets that human investors can observe?"[1] The data is constructed using NASDAQ TotalView with equities in the S&P500 in periods of varying volatility. Both reactive and periodic trading algorithms are reviewed.

Here are a few critical passages:

By tracking submissions, cancellations, and executions that can be associated with each other, we create a measure of low-latency activity. We use a simultaneous equation framework to examine how the intensity of low latency activity affects market quality measures. We find that an increase in low-latency activity lowers short-term volatility, reduces quoted spreads and the total price impact of trades, and increases depth in the limit order book.

IV.B. Results
Panel A of Table 4 presents the estimated coefficients of the pooled system side-by-side
for the 2007 and 2008 sample periods. First we note that the two instruments have the
25 expected signs and are highly significant. Specifically, the coefficient a2 indicates that
when liquidity off NASDAQ is higher, our NASDAQ market quality measures show
higher liquidity and lower volatility. Similarly, the coefficient b2 is positive in all
specifications, indicating that higher low-latency activity in a specific stock in an interval
is associated with higher low-latency activity in other stocks on the NASDAQ system.
Second, the estimated b1 coefficients tell us that low-latency activity is attracted to more
liquid and less volatile stocks.

The fact that low-latency trading decreases short-term volatility and
contributes to depth in the 2008 sample period where the market is relentlessly going
down and there is heightened uncertainty in the economic environment is particularly
noteworthy. It seems to suggest that PA activity creates a positive externality in the
market at the time that the market needs it the most. Panel B of Table 4 presents roughly
similar results from the estimation of the system with SpreadNotNasi as the instrument
for market liquidity.

It is possible, however, that the impact of low-latency trading on market quality
would differ for stocks that are somehow fundamentally dissimilar, like small versus
large market capitalization stocks. Table 5 presents system estimates in subsamples
consisting of four quartiles ranked by the average market capitalization over the sample
period.22 There is not much pattern across the quartiles in the manner low-latency activity
affects short-term volatility in the 2007 sample period. The picture in the 2008 sample is
different: It appears that during more stressful times, low-latency activity helps reduce
volatility in smaller stocks more than it does in larger stocks.

Lastly, Table 6 shows summary statistics for the stock-by-stock estimations. The
results suggest similar conclusions concerning the effect of low-latency trading on market
quality. In particular, an increase in low-latency activity decreases short-term volatility,
decreases quoted spreads, and increases displayed depth in the limit order book. This is
true both in the 2007 and 2008 sample periods.

_______________

1. http://people.stern.nyu.edu/jhasbrou/Research/Working%20Pape...