A continuous market price is an illusion; let's not forget that. Every market is made up of trades, which are discrete, and every price has an unstated amount of uncertainty, which may be large by any standards. You can't know from first principles whether a change in quoted price is even a change in the market, because it could be within the +/- range that's implicit. Apple is quoted to the nearest penny, at least, but the idea that the current price is accurate to within 0.004% is ridiculous.
Edit:
"Fischer Black famously defined an efficient market as “one in which price is within a factor of 2 of value, i.e., the price is more than half of value and less than twice value,”
...I hadn't heard this before Matt Levine mentioned it, but I was like "yeah, obviously, why haven't most people gotten the message?"
But: "BNP Paribas...said [Saudi] Aramco was worth exactly $1.424394 trillion."
I wonder which particular millisecond that held for.
Edit Edit: The market has a whole (mostly) unseen dimension other than uncertainty, which is depth. You can only buy or sell so many shares at the instantaneous market price. Further away, there may be orders, but the price of the whole company is going to be way outside of that. The shorter the timescale, the shallower the "market" so you can't just say we're making progress by doing things faster. It's like when research lasers are said to make unbelievable power, but it's like for a femtosecond or something. Liquidity, in my mind, requires depth, just as with water.
And to address your concerns about depth, I believe that's where market makers (which are related to HFT) come in.
Look at gas stations. If people are spending $1 driving around to save $0.10, then that's not good and at least public policy shouldn't encourage it.
The faster the price discovery, the shorter the validity time. This means a more accurate price.
> If a few milliseconds can change the value of a financial instrument then we have to accept that waiting a second or two will allow a lot more traders to reevaluate and offer a fair price.
You're making the mistake of assuming the price is static. If I have to quote you a price on an instrument that's valid for the next 5s, I have to be more conservative than if I'm quoting for the next 5ms. Which means you get a worse price.
> The HF in HFT looks like a play to reduce the number of traders who can act on information, which means the buyer/seller is probably getting scalped. HFT traders are making money arbitraging the speed of information dissemination, which indicates that other traders would offer different (/better) prices if the market waited a half-second or so to let everyone gather all the relevant data.
There's literally nothing stopping or limiting the numbers of players operating at this speed. What the race actually results in is all market participants getting smaller spreads and better prices.