Sudden Demand For Logicians On Wall Street

An anonymous reader writes "In an unexpected development for the depressed market for mathematical logicians, Wall Street has begun quietly and aggressively recruiting proof theorists and recursion theorists for their expertise in applying ordinal notations and ordinal collapsing functions to high-frequency algorithmic trading. Ordinal notations, which specify sequences of ordinal numbers of ever increasing complexity, are being used by elite trading operations to parameterize families of trading strategies of breathtaking sophistication. The monetary advantage of the current strategy is rapidly exhausted after a lifetime of approximately four seconds — an eternity for a machine, but barely enough time for a human to begin to comprehend what happened. The algorithm then switches to another trading strategy of higher ordinal rank, and uses this for a few seconds on one or more electronic exchanges, and so on, while opponent algorithms attempt the same maneuvers, risking billions of dollars in the process."

Comments

Well at least...

[ls671]

Well at least, they seem to start to realize that perpetual growth is impossible to achieve in a finite universe. For us, right now, this means our planet.

We may need to start businesses on other planets until we have conquered the whole universe in order to maintain the illusion that perpetual growth is possible.

Yet, the whole point of investing in the market is more or less (at least it was traditionally) based on a perpetual growth principle where there would always be new markets to conquer thus, rising stocks on average and a perpetually growing economy.

Since they seem to begin to realize that perpetual growth is impossible and that trading is what they have done all their life, they need to keep the profits coming in anyway. So they figured that by using "high-frequency algorithmic trading" they could keep the profits coming in.

Well, at the expense of whom ? How long can this trend be maintained before major problems arise in the economy ?

Re:Well at least...

[sqrt(2)]

And bullshit like high frequency trading (really the entire concept of trading in derivatives, I hesitate to say the entire stock market in general because at its core there is something useful) only makes things worse - and at a faster rate. Every year a bit of wealth from every person in the lower 90% is siphoned off by traders and bankers and given to the top 10% or less. Over the decades a self reinforcing, self perpetuating system has been created, linked with government apparatuses that give it the appearance of legitimacy; this system rewards people who produce nothing of value, make nothing, enrich no one's lives, do not create art, do not expand the sphere of human knowledge, and provide no meaningful service to humanity or the country.

When it's possible to get rich just managing other people's capital and skimming off the top then the way we organize our economy is broken. This house of cards cannot stand forever when you stack more and more of those people on top of the working class, the foundation, that actually produces wealth and knowledge.

Re:Well at least...

[Evtim]

The last book I read about mathematics and physics of human interactions, including economy, was "Critical Mass (how one thing leads to another)" According to the author the best models for predicting the stock market still perform worst than "gut feeling" of an experienced trader.

It seems that the models fail because no one out there plays the game according to the simple rules that are said to define the free market. Or because the system is inherently unstable and prone to collapse. Overall I got the idea that the free market is an illusion, say, like communism. A system that requires people to change themselves first in order to work. Man, such ideologies never work!

Anyway, I totally agree about the growth thingy. I have always advocated that we should self-control our numbers and keep the progress going even if it has to slow down a tad. Restructure our activities in such way as to merge within the natural cycles (like water cycle, carbon cycle and so on) It would mean ever more wealth and possibilities for the everyone. Instead we have a pyramid, a Ponzi scheme. I laughed my head off decades ago when the globalization plans were announced. What, you want to remove the foundation of the pyramid? Make everyone wealthy? Who says that? Oh, the people sitting on top of the pyramid. Right!

T-shirts slogan: "You cannot sustain a progression in a finite Universe moving in cycles"

Re:Well at least...

[alfredos]

I subscribe that and add that the stock value concept is indeed useful but has been twisted beyond recognition. If I try to think about it with a clean sheet, I can't find a real reason why a company that manufactures screws is worth 10% more at noon than at 9 am and then 10% less at market close.

The company in my example behaves like most companies. They are going to open the next day and sell a bit more or a bit less, manufacture about the foreseen number of screws, some employees are going to get hired, others fired, others retire... Yet the swing in value of the whole company is based around news and rumours. Traders will "discount" this or that news on stock price of our happy screw manufacturer without even bothering about the steel stock or last month's sales. Some will buy stock and make a profit by noon if they are lucky, or loss at close if unlucky.

Now, what does all this have to do with manufacturing screws? Isn't there much more in common with Casino Royale than with industry and people building things and making a living out of creating something of value?

I attended a conference two years ago where an accountant explained that the concept of stock worth is fatally wounded. His theory, which I also agree wholeheartedly, is that stock should benefit the stockholder with dividends, i.e., with the net value generated by the company's activity. Not by the increase in the value of stock itself in the short term. Now there is a place for investors, he also said, who invest in stock and sell the stock. But that kind of operations ought to be separated by months or years, when actually the stock reflects the increase in the value of the company. Not by minutes, when the increase in value is nothing more than a throw of dice, even if you attach fancy and serious names to it.

Re:Well at least...

[metacell]

There is no reason better production methods should lead to unemployment in the long run. When production becomes more efficient, resources (like labour, capital and natural resources) are freed up to do other things, and so far, humanity has showed an incredible ingenuity in coming up with new things to produce and consume.

Three or four hundred years ago, the majority of the population worked in agriculture. Today, we produce more food than ever, with only a few percent of the population tied up in agriculture. If we had said back then, "We must stop the industrialisation of agriculture, or the farmers will lose their jobs!", there would have been no one to work in the factories and produce the cars, toys, medical equipment, cheap clothes and furniture, and all the other things we have become used to today.

The problem with unemployment is not that we have become too efficient in producing goods and services, but rather, that we have become worse at letting new, innovative providers of goods and services establish themselves on the market. Large corporations effectively block out competitors through patents, anti-competitive behaviour and friends in high places. Governments watch the backs of large corporations because they are afraid that they will go out of business and a large portion of their voters would lose their jobs - not realising they are at the same time helping the corporations stunt the growth of new businesses and new jobs.

Re:Well at least...

[seyfarth]

...When it's possible to get rich just managing other people's capital and skimming off the top then the way we organize our economy is broken. This house of cards cannot stand forever when you stack more and more of those people on top of the working class, the foundation, that actually produces wealth and knowledge.

I think we need a federal stack exchange tax. If every trade is taxed, then the millisecond trading scheme will disappear. Instead people will think long and hard about investments and invest for long enough periods to make more profit than the initial tax. Of course if they were taxed as heavily as the sales tax I have to pay on food, then they might be investing for dividends rather than profits.

Is there any better way to convert our casino-like stock exchange into a real investment system?

Wouldn't this help with our federal deficit?

Re:Well at least...

[radtea]

The casino doesn't produce any "real" wealth - it just distributes it.

Sorry, stopped reading at that point, as your ignorance of economics is obviously profound. How wealth is distributed has an enormous effect on a society's ability to produce new wealth. Many dirt-poor native tribes in Canada, for example, are "wealthy" on paper, but the ordinary people have no access to that money, only the band council does. A financial system that allowed ordinary people access to that money would make everyone but a few assholes at the top enormously richer.

Likewise, systems that attempt to "spread the wealth" uniformly across all individuals, the way Sarah Palin's socialist Alaska did with oil revenues, are also vastly less productive than systems with moderate gate-keepers that try to ensure capital is deployed in somewhat productive ways.

Learn a tiny bit of economic theory and--far more importantly--economic history before making up lame analogies, please.

Re:Well at least...

[DerekLyons]

The reason price fluctuates throughout the day is not internal to the company, but external.

That's pretty much his point - which seems to have gone whooshing right over your head. The value of a stock is (theoretically) tied directly to the value of a company, yet the price varies even when the value doesn't - and he doesn't see why that should be. I tend to agree with him, the stock market has increasingly become an abstract game unrelated to the underlying real world it's (theoretically) based on.
 
One result is that we take the market to be something it isn't - an accurate reflection of the underlying structure, despite the fact that the two increasingly bear no relationship to each other.
 
The other (and more dire) result is that we increasingly hold CEO's responsible for matters they have no control over - which leads to them indulging in all manner of what are regarded as reprehensible activities in a vain attempt to raise the value to meet the price. (The whole 'nothing but next quarters bottom line' mentality so often derided.) This also happens at the other extreme, if for some reason everyone decided GE was worth (priced on the market) 30% less at the close of trading today than at the start - the CEO of GE would be held responsible even if absolutely nothing had changed regarding the value of the company.

Re:Well at least...

[Anonymous Coward]

I recently worked as a developer writing exchange gateways for a high frequency trading firm that traded with their own money, not other people's.

They were designated as a Market Maker, and their supposed purpose was to provide quotes on financial instruments.

Theoretically, the price for the same instrument should be the same on all exchanges, but in reality, there is lag. So, this company would pay for the fastest possible connection to each of the markets, and then sit and watch. Although What their real bread and butter was arbitrage, and they have automated systems that take advantage of lag between updates of the same instrument (usually derivatives) on different markets.

Basically, they'd see an instrument raise a fraction of a cent on one exchange, and they'd then buy a TON of it on another exchange and sell it back to the first exchange, all within a few milliseconds. Dumping all this would then cause the price to drop on the exchange they just sold it on, because the buy they executed on the second exchange would sometimes take a while to get back to the first exchange. Once all this instability started happening, it'd spur other people to start buying and selling - and they'd have an even greater opportunity to take advantage...

The whole system was very "clever" - but completely devoid of adding any real value to the market.

The company was investigated for some criminal behavior, but because they were very careful not to break the letter of the law in what they were doing - the law couldn't touch them.

I could give more details, but I'm afraid I've already said too much - because I certainly do not want to be identified by the company for fear of some kind of retaliation, either above or below the table

Self regulating?

[dna_(c)(tm)(r)]

So, the next global financial crisis will happen a lot sooner? This is not a good thing. They invest in speculation instead of companies.

Re:Self regulating?

[aquabat]

If only the circuit breaker worked as quickly as these trades do, then we might avoid destroying a trillion dollars because of a typo.

That trillion dollars wasn't destroyed; it just got redistributed to people that are not me.

Practical Joke?

[the_povinator]

I am wondering whether this story is some kind of practical joke.

As someone who understands math to at least a certain degree (I publish in what is effectively applied mathematics), I know enough to say that this is bogus. The Wikipedia page on ordinal collapsing functions (http://en.wikipedia.org/wiki/Ordinal_collapsing_function) shows that they relate to transfinite numbers (various orders of infinity). It is, to me, beyond plausibility that this could have any practical application in trading-- unless it's some kind of weird fad that only the mathematicians understand is a joke. I think someone needs to dig down further into this source.

Re:Practical Joke?

[Anonymous Coward]

IANAST (set theorist), but my guess is that there are uncountably many trading strategies that don't allow for response to the other players strategies, but they can be indexed by ordinals (assuming choice). Furthermore, there is probably some kind of ordering on them so that a< b if b beats a. Transitivity would not be obvious (you probably would get somewhere if you restrict to some "good" subset or use some weaker sense of "beats"). Anyway, assuming that there are \kappa such strategies, and assuming that \kappa has infinite cofinality you choose one strategy, and then someone else chooses a strategy that beats yours, so you use a larger ordinal (which then beats the other strategy). To index these larger ordinals you would need a way to represent them with finite data, hence the ordinal collapsing function. Terrifying. Set theory gives me nightmares.

Re:Practical Joke?

[NeutronCowboy]

I've done a bit of googling, but nothing else comes up. What did come up, however, was David Li and his copula function. I can barely follow the copula function, and set theory is completely beyond me. However, what I will believe in a heartbeat is that hedge funds will throw million-dollar salaries at people to come up with a mathematical function that will tell them whether to sell or buy or something, regardless of whether they have any clue what the function actually means or does.

Again, I can't tell if this particular story is true or even makes sense. But the basic premise has already been proven.

Re:Practical Joke?

[cobaltnova]

The point would be that anyone who isn't playing the game this way would be playing the game according to a strategy for some fixed kappa. Then you beat them automatically. I'm not sure such a well-ordering of strategies exist. Ostensibly, this is probably what the mathematicians are being recruited to determine.

Re:Practical Joke?

[SamSim]

It is, to me, beyond plausibility that [transfinite numbers] could have any practical application in trading

...The terrifying alternative, of course, being that Wall Street has discovered a way to create a literally infinite quantity of money, and a year from now, the only way to tell who is richer than whom will be by comparing the size of two transfinite ordinals.

(It makes bank transfers insanely difficult because there's no consistent way to perform ordinal subtraction. If I have $^2 and I owe you $ then either I still have $^2 left over afterwards, or I can't pay you at all!)

has anyone taken into account

[nimbius]

many stocks are valued entirely on speculation? how does one apply logic to that? what about crap like derivatives trading? effectively a "dont ask, wont tell" sort of thing based entirely on what you "think" the value of something that has no value might become?

Re:And the moral is:

[Inzite]

There's a long-running joke among financial types....

If things are gonna get worse, buy bonds.
If they're gonna get much worse, buy gold.
If you're still worried, buy canned food, ammunition, and land in New Zealand.

Lies, Damn Lies and Theft!

[Iffie]

Complexity in these algorithms is only to hide the fact that the are FRONT RUNNING trades, they have servers that are directly next to the ones performing normal trades and using the speed that affords they put themselves between buyers and sellers. Goldman Sachs steals 100 million USD every day. To hide this theft they claim sophistication. Same story with derivatives, they are FRAUD. to hide the fraud they are made 'complex' using the work of so called Quants. It is thieving and it is nonsense.

Re:Lies, Damn Lies and Theft!

[ortholattice]

Micro-timing has no purpose other than to take advantage of ordinary investors who don't have access to this information. It basically amounts to a kind of insider trading.

I would propose that ultra-short-term profits should be taxed at a punitive rate, perhaps approaching 100%, to discourage this kind of cheating of ordinary traders.

Already, short-term capital gains are taxed at a different rate than long-term gains, in order to encourage long-term investment. Micro-timing is short-term trading taken to an extreme, so why not tax it accordingly?

There is no valid reason why anyone should trade a stock multiple times per day - either it is pure gambling or there is some inside information behind it. Companies report their revenues and profits on a quarterly basis, not microsecond by microsecond. (Of course news stories may affect a stock, but even news stories rarely change more than once per day.)

The markets need to be forcibly civilized.

[Cordath]

Margaret Atwood once described civilization as the judicious trading of "freedoms to" for "freedom from". e.g. You trade the freedom to murder anyone you like for freedom from being murdered yourself. While a rather distressingly large percentage of Americans would scream "COMMIE PINKO!!!" at me for daring to suggest this, I feel that the stock markets could stand to be civilized a tad.

What is the purpose of the stock markets? Are they meant to be a video game played by A.I.'s for big cash prizes, or a way of facilitating investment and trade? It's time to find ways of restricting high frequency traders. While cumbersome regulations are one option, perhaps a per-trade tax or user-fee would be better. A tiny one, percentage wise, that will only have a significant impact on high frequency traders. Cuts to other taxes could be made to offset them for average frequency traders and perhaps even benefit low frequency traders.

There are, naturally, many other ways to approach this. All it takes is resolve and, in the U.S. at least, thick skin.