Ok, I think I understand what you're saying in principle, but I still don't really understand how HFT, or indeed anyone who is only trading on prices, adds liquidity as you have defined it, beyond the addition of their initial capital: it's not having quick trades that makes a market liquid, just having available trading partners with enough capital to complete the trade you want. It strikes me that, if you roughly assume that price-based trading is random, then all that fast trading "really" does is speed up the process by which some people randomly lose their money and others are randomly given that money (those people generally being the price-based traders themselves, presumably, because they will be the ones involved in the majority of the trades).

So my follow-up question is: what is the particular benefit of being able to trade as quickly as possible?

And a related, more specific, question that might be easier to target and explain: I'm sure I've heard people suggesting capping trading frequency (which might be a ridiculous idea, I don't know); how would doing so harm liquidity?

Also, just to clarify my previous question about cost, I was trying to refer to the "cost to the system", rather than direct costs. I'm not sure I can properly define what I mean by that, but I suppose it would be something like if the total revenue going to the HFT firms or similar people was greater than the return to the rest of the system of having their services. I'm not really convinced by market arguments against such cost/benefit inversions taking place, because inertia and changing circumstances can move institutions from being helpful to being unhelpful without markets being in a position to compensate.

If I've made any other bad assumptions, please point them out as well.

The benefit of being able to trade as quickly as possible (as an HFT) is you are able to put more shares/contracts up at each price, ie. provide more liquidity -- this is because anytime the price is going to move against you, you get hit for 100% of your standing bid or offer, and the faster you to cancel those orders are the fewer times this happens. This lets you post more liquidity on average and pull it when the price is no longer good.

Capping trading frequency would lower liquidity. Simply put, the less up-to-date your view of the market is (if orders are only matched every T milliseconds, you could have a view of the market thats up to T milliseconds behind), the more uncertainty there is in your prediction, which will result in you quoting a wider bid-ask spread or quoting smaller amounts at each price. I'd say for T very small (say, T < 5ms), it will make zero difference to liquidity or HFT profits.

I suppose its tough to answer your final question. I'd say liquidity is very useful, and tighter bid-ask spreads help price discovery and help portfolio allocation (the wider the bid-ask spread, the less likely a given portfolio will be allocated in the desired way, since you can only replicate a portfolio modulo transaction costs). Anytime a transaction tax or other regulation is implemented that targets only HFT, liquidity drops, often drastically (e.g. Swedish equity markets in 90s had a relatively high transaction tax that essentially dropped all trading volume on their exchanges to zero, and trading moved to other European exchanges trading equivalent derivatives on Swedish stocks). In addition, HFT industry profits are low -- I'd be surprised if it breaks 5 billion/yr.

Thanks for replying. I like your time averaged argument, that seems to be a good explanation of why it is useful, both to the trading entity and to the market, to be able to change orders quickly.

I think my final question about the balance between total costs and benefits is motivated by the fact that discussion about HFT and similar price-based trading always makes it sound like a lot of effort is being invested in the competition to find profit-making trades, and my wondering whether all that effort could be more productively used elsewhere.

I understand the market motivation behind doing it, which I think yours and others' explanations justify well, however, as I mentioned previously, I remain unconvinced by the allocative efficiency of markets in all situations, and these 'arms race' situations seem like good candidates for market failure (to stress, I mean failure only in terms of the societally-efficient allocation of resources, I don't doubt the local efficiency).

Your note about HFT profits obviously goes some way to addressing this by suggesting that the level of resource allocation isn't that high - I have to confess I didn't realise the profits were quite so low. I do, however, think that revenue is the more important figure, because that will capture the productive effort that we, as a society, are investing in this activity, which we can then usefully compare to the liquidity benefit we get from it.

In case you are interested, I think I have been spurred down this line of thinking by having recently read 'The Collapse of Complex Societies', by Joseph A Tainter, which I can heartily recommend if you haven't already read it. My argument is really his, just applied to the frontier of our times - finance.

And as a personal aside, if you don't mind my asking, you seem to have a good understanding of the realities of this situation, were or are you involved professionally?

Maybe the correct way to look at it is that you can't have a functioning market without market makers (as this article suggests), so once you've accepted the need for them, the natural question to ask is 'who gets to be the market maker?' - whoever can respond/execute the fastest and most effectively. So the question of super fast trading becomes not one of liquidity provision for investors (for whom millisecond timescales are irrelevant), but rather one of competition (and interaction) between market makers. Since spreads have gone down in the HFT era, I suppose the 'cost to the system' in aggregate must be lower than before, unless I'm overlooking something.

I'm not saying any of this with certainty, just sharing my thoughts.

What you've said sounds very reasonable to me. I find it interesting that the line of reasoning you have presented doesn't appear to require super-fast trading. That there has been an "arms race" to become faster and faster fits perfectly, because the competition is over who is the fastest market maker. Given that the skill of people/firms engaged in that race has been to be as fast and smart as possible, it also makes sense that they would be less than enthusiastic about any limitation on their competitive abilities. Neither of those points, however, implies that being able to trade as quickly as possible is actually "useful" to the wider market - only that it is a consequence of that market.

It seems possible that there is a lot of effort being put into that endeavour that is, in some sense, wasted - it is spent on competition rather than "production", and with a judicious rule change the cost of competition could be reduced. The inevitable free market counter-argument is that the market will have already selected the best balance of cost/benefit, but I don't find that convincing at all, even if only because obtaining a sufficiently free market is impossible.

Anyway, thanks for your response, it certainly seems (to a layman such as myself at least) to be a good description of the basis for HFT.