Prisoner of Speed

by Stubborn Mule on 17 February 2013 · 15 comments

A favourite podcast of mine is known in our household as “Danny’s podcast” in honour of the friend who first put me on to it. The podcast is better known as Radiolab and last week’s episode turned on the theme of Speed. After answering the question, what is the fastest sense, attention turned to high-frequency trading. As the Radiolab hosts are more comfortable with science than finance, they turned for assistance to David Kestenbaum from the Planet Money podcast.

In a past Mule post, I expressed reservations about the merits of high-frequency trading. Just last year, there was talk in the European parliament of enforcing a delay on electronic trading. Some critics argue that high-frequency trading creates instability in financial markets and may have been to blame for the “flash crash” of 2010.

One of the more intriguing aspects of high-frequency trading was brought out in the podcast during an interview with a technologist from the US trading firm Tradeworx. Bemoaning the cost of constantly competing to allow faster and faster trading (millions of dollars are being thrown at shaving milliseconds from the time to send trades to an exchange), he said that high-frequency traders were caught in a prisoner’s dilemma.

The prisoner’s dilemma is a staple of the study of the branch of mathematics known as “game theory“, which seeks to analyse strategic decision-making. Here is a quick overview for anyone unfamiliar with it.

Two criminals are arrested and taken to separate cells to ensure they cannot communicate with one another. The police have enough evidence to send each man to jail for one year. With a confession the police could get a conviction on a more serious charge. So, the police point out to each prisoner that cooperation will help reduce their sentence. If neither prisoner confesses, both will face one year in prison. If one testifies against his partner in crime, he will go free while the partner will get three years in prison on the main charge. But, if they both confess, that cooperation is not worth as much and both will be sentenced to two years in jail.

So, what should each prisoner do? No matter what the other prisoner does, confessing will improve their outcome, either from one year to none if the other does not confess, or from three years to two if the other does confess. So, the only rational thing to do is to confess. If both prisoners follow this logic, they will both get two years. And yet, if they had both kept quiet, it would have only been one year each, which would be better for both of them. The problem is that the “global optimum” is hard to obtain because there is too much of a risk for each prisoner that the other will defect.

The same is true for the high-frequency traders. While it might be cheaper for all of them to call a truce and freeze their technology at its current state, there would always be the risk that one firm breaks the truce and gains an edge. So, they all continue to compete in the speed race.

But the prisoner’s dilemma applies to more players than just the trading firms themselves.

If one of the major exchanges, such as the NASDAQ tried to stop the speed race, then it may well find itself losing business to any other exchange which continued to facilitate faster trading. An exchange without trading does not last long.

Governments too face the dilemma. There is already intense competition between exchanges operating in different countries and no government would want to lose the kudos and, more importantly, revenue that comes with playing host to a major financial centre. Would the UK government, for example, want to put London at a disadvantage to Europe or the US? Unlikely.

The German government is now delaying plans to curb high-frequency trading, in order to “clarify technical details”. I suspect that this will turn out to be a rather long delay.

 

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{ 15 comments… read them below or add one }

1 Mark L February 17, 2013 at 10:03 pm

I like Emanuel Derman’s suggestion of introducing a random delay into trade execution: http://blogs.reuters.com/emanuelderman/2011/08/18/tobin-or-not-tobin/
Of course, this proposal also suffers from the regulatory prisoner’s dilemma.
Cheers,
Mark

2 Ramanan February 17, 2013 at 10:08 pm

And governments also face issues with fiscal policy. Right now due to global imbalances, many government are constrained with fiscal policy (the balance of payments constraint) and hope the rest of the world grows so that exports grow and their fiscal stance can be expanded.

The solution is to coordinate fiscal policy among other things but fiscal policy is incorrectly seen as strictly neutral by most in the economics professional – making it difficult.

3 Stubborn Mule February 17, 2013 at 10:48 pm

@Mark: the random delay is a very elegant solution…if only it could be implemented. Damn that game theory!

4 Emmjay February 18, 2013 at 9:18 am

If trading continues to accelerate, will it reach some terminal velocity ? Could we anticipate stockmarkets being the first entities to go faster than the speed of light ?

But wait… as we approach the speed of light, time slows down. So by extension, if you can trade that fast, you can see what’s happening in today’s market and trade to your advantage …. yesterday…..

Speed. It’s a wonderful thing. I think I’ll have some more for morning tea. Such a long time to wait.

5 Iceman February 18, 2013 at 12:32 pm

This industry best resembles sporting franchises…replace Ronaldo with a rapidly obsolete super computer…and bingo

What have the owners tried to do:

– Salary caps (where national competitions exist, e.g AFL, NFL) – nope
– Restrict cross subsidiation, e.g. wealthy owners losing money for pride – maybe in sport but not business

Otherwise

– Coorporation (illegal)
– regulation (why?)

My view – do nothing, these guys are going to wear themselves out and the capital value of HFT firms will approach ZERO with this industry constraint. Sporting teams also would wihtout the kudos of owning a sprorting team.

When the HFT guys start yelling about this problem its time to do nothing – they are feeling the pain. Regulation with only protect these scavengers….leave them alone.

6 dan February 18, 2013 at 4:42 pm

Glad you still like Radiolab Stubby, and happy to have some eponymous credit.

I’m not an HFT maven or anything, but I don’t see this in any way as a “Prisoners Dilemma”. The investment of HFT firms in increasingly expensive bits of technology and software to try to gain some small advantage over their competitors seems to me to be a pretty simple case of market forces.

Lets not think about anything so esoteric as HFT’ers, but rather box manufacturers. Lets call them Visy and Amcor for convenience. Now either Visy and Amcor could invest in increasingly better technology to produce boxes cheaper and faster and thereby gain an advantage in the box market. Or on your logic, “it might be cheaper for all of them to call a truce and freeze their technology at its current state” (noting that “there would always be the risk that one firm breaks the truce and gains an edge.”)

Of course such a freeze, is called collusion. I think the critical difference between what the HFT-ers are doing, and the classic Prisoner’s Dilemma is that the Prisoner inexorably acts to her detriment by following the logic. The HFT-er who spends up big on technology and “gains an edge” has not acted to her detriment, (though there may be a cost/benefit question).

I don’t know any HFT-ers, but one assumes that they know how much they are spending on their computers and wires and stuff, and they also know how much money they stand to make by having faster stuff.

If your argument held water, then Formula 1 cars would still be going round Monaco in just under 2 minutes (http://www.pistonheads.com/gassing/topic.asp?t=852275) because surely that was fast enough, and it wasn’t in anybody’s interest to waste all that time and money “getting an edge”.

7 Stubborn Mule February 18, 2013 at 10:03 pm

@dan you are right that a HFT truce would be collusion. That, however, does not mean that the Prisoner’s Dilemma has nothing to say. Rather it gives some insight into why maintaining a cartel can be very challenging in practice: there is always a significant risk of defection. Note that the prisoner in the dilemma is not so much acting to their own individual advantage (after all, if only one prisoner grasses he gets the best possible outcome), but acting to the detriment of the average of all participants.

There is one important difference between the classical dilemma and the challenges of a cartel. In the case of the prisoners, no communication is allowed. There may be more opportunities for businesses to collude. To quote Adam Smith:

People of the same trade seldom meet together, even for merriment and diversion, but the conversation ends in a conspiracy against the public, or in some contrivance to raise prices.

So, I would not advocate relinquishing any legislative restrictions on collusion in the belief that cheaters will lead to the destruction of any cartel.

8 dan February 19, 2013 at 6:15 pm

I never really thought of a cartel as a Prisoner’s Dilemma (but the venerable editors of the Wikipedia seem convinced so I will defer to them: viz “Long-term unsustainability of cartels” http://en.wikipedia.org/wiki/Cartel.

I can see this with the classic Cartel (I would imagine there would be a temptation from time to time for certain oil producing states to “take the money and run” rather than sticking with their OPEC brethren, particularly during times of “regime change” when the Oil price is high anyway.

But I think Adam Smith hit the nail on the head. The ability to collude is the critical difference.

But perhaps what I had in mind was not so much the Cartel, but the cosy oligopoly and duopoly we love so much downunder. 4 banks. 2 airlines. 3 telcos (sort of). 2 newspapers (?). 2 political parties. I don’t see any of them locked in separate rooms sweating away and taking sub-optimal outcomes because of the relentless logic of assuming the defection of the other. Rather I see a bunch of fairly comfortable incubents (well maybe not the newspaper proprietors) enjoying a great deal of merriment and diversion.

Possible exception at the moment in the big box hardware space, but that will be short-lived: http://www.smartcompany.com.au/intellectual-property/054103-hardware-fight-gets-nasty-bunnings-registers-masters-business-name-in-new-zealand.html

9 Martin Barry February 19, 2013 at 7:28 pm

HFT is hitting the wall of “diminishing returns”. There is only so much you can invest in lower latency network equipment, tuning of operating systems, honing of code and colocation in the same room as the matching engine, before you are pushing up against Moore’s law and it’s equivalents. At the same time pioneers in this space are finding the “being faster as a winning trading strategy” is becoming a very crowded space. Profits are harder to come by right now and quite a few HFT firms are going broke or getting out.

I think the only thing the regulators and markets need to address is pathological tactics like quote stuffing.

10 Zebra February 22, 2013 at 5:51 pm

I wonder if the randomising solution would work. Randomising the arrival time of information just changes the timing not the order of execution.

Randomising the time of execution of trades would still leave a (decreasing) advantage in being fastest off the block. The buy/sell prices data are already modelled as a random process in which they are seeking a very small signal of information. Unless the prices themselves are replaced by random numbers arriving at random times (so not much of an exchange).

The equivalent prisoners dilemma problem might be to consider a smoky room of prisoners who aren’t sure if the other prisoners have shot yet or due to a randomised gun mechanism when their own bullet will arrive. Being even less sure of their fellow prisoners’ intentions this might make them even more inclined to panic and shoot first! This might lead to more instability, not less.

11 Zebra February 22, 2013 at 6:02 pm

Dan – one of the things I have learnt after several years in banking is that you don’t need to actually collude or have a cartel to mimic its effects. A former colleague of mine (not a contributor to this blog) put it to me thus: “you don’t want to be in an industry where people don’t want to make money”. In other words participants who, for example, bid for jobs will work out that of they alternate high and low bids so will their “competitors” so everybody wins occasionally. As long as the excessive profit, when they do win, is high enough, this stops anybody making more competitive bids the rest of the time. Everybody wins. well except the person who is buying. In the absence of overt collusion it doesn’t break any laws. I think we see something like this happening when banks set mortgage rates, which suggests it is a stable strategy, at least for several years.

12 Zebra February 22, 2013 at 6:13 pm

Iceman – does this mean the Gold Coast Suns rejected your lowball bid? Keep your powder dry my friend. You’ll be able to buy your beloved Roos after this season.

13 Mark L February 22, 2013 at 10:48 pm

Zebra,

Nice analogy. I wouldn’t want to be in that bar!

As you obliquely mention yourself, randomness blunts the advantage of being first so that participants have less to gain by being faster. This means they will invest fewer resources towards it. The degree to which the advantage is reduced increases as the time scale reduces so that the incentive to be faster becomes more and more mild in a smooth way.

For example, consider a simple model of two competitors who chase a single trade opportunity, winner takes it. If the first has a 1 ms advantage over the other she wins 100% market share. But if both suffer independent random trade delays of 0-20ms (uniformly distributed), her market share falls to 54.875%, and she has much less incentive to acquire the 1ms advantage.

The prisoners, who always had more alternative strategies than we were told, will then discover there are other ways out, and turn to more economically (perhaps even socially) useful ways to compete.

Cheers,
Mark

14 Stubborn Mule February 23, 2013 at 4:08 pm

@Zebra you wrote

Randomising the arrival time of information just changes the timing not the order of execution.

but, as Mark L notes, facing a random delay before your order is allowed to enter the message queue will make it possible for the order to change. In Mark’s example of a two-player race, the faster trader still has a bit of an edge (although the drop from 100% to 54.875% is dramatic). Once you allow for a larger number of players the speed advantage falls even further. With enough players, the edge will have almost vanished.

15 Mark L February 23, 2013 at 6:10 pm

Yes, the drop in market share is larger still if there are more competitors. Extending the simple model above to n competitors of which one has a 1 ms advantage over all the others still yields a market share for the fastest of 100% in the absence of random delays regardless of n, but as follows with 0-20ms of random delay:
n=2 54.9%
n=3 38.3%
n=4 30.0%
n=5 25%
n=6 21.7%
n=7 19.3%
n=8 17.5%
n=10 15%
n=20 10%
n=40 7.5%

Cheers,
Mark

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