Economic calculation and high-frequency trading. Can a computer economically calculate?

Economics Economics Questions
1

I’m leaving this as an open discussion because I’m working on some preliminary study for this topic as a potential masters thesis. Anyways, the reason why I ask this question is due to the two flash crashes in the last two years I’ve read about. The first happening in May of 2010 and the most recent one happening this July. I find the flash crashes troubling because in both instances it was due to the algorithms utilized to trade which caused them and not due to direct human intervention. For me, this made me realize that there was something missing from the use of algorithms and computers in trading: the ability to measure economic value of the goods traded.

It may seem trivial to some that one could easily assume if some good has a price, that it must have a constant economic value, but that isn’t true if one considers the fact that goods are always purchased/sold on the margins of the benefits in buying/selling them. And it is this particular issue of marginal utility that can’t be captured in a price. There are other ways to measure the good excluding its price. What this means for designing algorithms is that there is no easy way (or perhaps no way at all) to form non-arbitrary parameters from which we can create the algorithms themselves.

Algorithms in this context require a definite set of problems that are uniform in nature with an equally definite set of solutions to the problems which are also uniform. One cannot create an algorithm that gives solutions which are wrong (this contradicts the definition of an algorithm). Nor can one create an algorithm which has variable steps (they must be finite). Nor can the algorithm run for an indefinite amount of time (it must have some finite upper limit to its runtime). This means there’s two possibilities for the problems regarding high-frequency trading at present: the algorithms are not solving problems regarding the trading of goods (they’re arbitrary in their calculations) or they fail to capture the parameters of the trades they’re issuing (they’re incomplete in their calculations). In either case, I think there are terrible flaws in the use of computers in absence of human beings when it comes to trading goods (beyond automation of human issued trades).

The things I’m missing to make this a strong argument is a theoretical background from both economics and computer science (I have the latter down from researching effective methods and the Church-Turing thesis) and some empirical research to back up the theoretical background (I’m writing up some random scala programs to capture market data from firms known to regularly utilize HFT). If anyone here has any ideas where to look in terms of the economic theory for this, please post what you know or any good journal papers I can dig up at my university library. Thanks in advance.

2

The word “calculation” in Misesean terminology has no relationship to the calculation that a computer performs. Economic calculation is the assessment of whether one is better off or worse off after exchanging than he was before exchanging. If I had one goat and two pigs but now I have one pig and three chickens, am I better off or worse off than I was before? Money permits the comparison of unlike things, that is, it rationalizes calculation so that my assessment of whether I am better off or worse off is not solely the result of my own subjective valuation but is also informed by the valuations of others through the market price.

I think it is a mistake to think of computer automated trading as having something to do with economic calculation. Instead, computers that automate trading are commoditizing the brokering profession. One hundred years ago, JP Morgan could have sent a telegram to his broker to the effect “Sell STANDARD OIL @ $3.50 unless WHITE-WESTINGHOUSE is above $5.00.” The decision to sell at $3.50 was made on the basis of his own ideas about where the stock price was going and the connection between the price of Standard Oil and the price of White-Westinghouse reflects some unknown theory in Morgan’s head. Algorithmic trading just consists of large sets of such buy and sell orders that are chained together through if-then conditions. While computers react faster than brokers could have, they are not doing anything different. The computers are not “thinking up” their own algorithms. The failures of these algorithms only illustrate the fact that being wrong in the market means losses… being wrong very fast and very many times means massive losses.

Clayton -

3

This still doesn’t resolve the issue of producing proper mappings of problems to solutions. If, at any time, your algorithm doesn’t map a problem to a solution or doesn’t do it correctly, it ceases to be an algorithm. If anything, my thesis depends upon the fact that we can’t encapsulate all the factors involved in a trade. In your own example of the person telegramming trade orders has to make calculations based on expectations of the future versus the present. Such things can’t be properly mapped in a computer since the very idea of meaning is never mapped at the beginning (so it could be said that because of this alone no computer could ever think, let alone trade with other humans).

And this is even further bolstered by the Misean use of calculation for economics versus calculation in mathematics (as computer science). Humans in the proper sense simply don’t calculate, they don’t use equations in their head at the time of judging which action to do. Which is why I think there’s issues with utilizing HFT (or any equivalent computer aggregation).

4

But I think you’re missing my point. Just as the broker doesn’t need to know why Mr. Morgan wants to sell under those conditions, only that he wants to sell under those conditions, so the computer does not need to know why, only that. There is a separate question which is: how well are computers really commoditizing brokering? I think the answer is that they’re doing about as well as in every other white-collar industry. In my line of work (computer engineering), we have ranks of engineers - whole business units - that are attempting to commoditize the engineering work itself. Apart from the aggravation of constantly having to point out how retarded this is, it is actually quite humorous to watch. You cannot commoditize general-purpose problem solving with special-purpose algorithms. It just doesn’t make sense. And even if/when we build something that looks/acts like a general-purpose algorithm, we will only have succeeded in commoditizing the human brain, that is, we will simply be multiplying the human problem-solving ability just as computers today are multiplying the ability of an individual to manage far more expansive bureaucratic decision-making processes than he can manage with pen, paper, typewriter and file-drawers.

Clayton -

5

I think you need to realize that HFT doesn’t work like you think it does. It’s not mere automation of existing trade orders. It’s actually a predictive system where it decides when and what to trade. That means the computer is acting both as the man who telegrams the trade and the broker house who takes the orders and issues them to other brokerages. Which is the problem that I see with HFT, it’s designed to take out the human element completely.

6

All trading software does is interpret existing price patterns and make predetermined choices based on what it believes is the current stage in a pattern. There must already be a price history for it to work. It works until something exceptional happens. Which is why it is only good for HFT. Berkshire Hathaway uses this, btw.

7

Mayhaps this will help. It’s dense, but by golly did I learn some **** when I read it. Turns out that the Flash Crash had less to do with “Economic” calculation and more to do with bandwidth limitations in the current exchange infrastructure.

8

@ladyattis: My point still stands that I think the characterization of HFT algorithms as something more than conditional buy/sell orders is the root of the problem. The attempt to commoditize general-purpose decision making (Mr. Morgan’s thought processes) with special-purpose algorithms is clearly futile. It is directly analogous to the attempts within the company I work for to commoditize engineering.

By the way, mathematicians already plumbed the depths of this problem a long time ago (you might be familiar with this given your study of comp sci). This lecture by mathematician Gregory Chaitin on the subject is very enlightening.

Clayton -

9

I don’t think we’ve seen the entire issue discussed in a larger context where HFT which is based on the idea that most of the trading inputs are from human beings and not other HFT algorithms/systems. What if all trades tomorrow become the subject of HFT systems with no direct intervention from human beings? That’s a question that hasn’t been asked because it seems impossible, but that is still what some firms are betting on.

10

There is probably already an overload by now or there will be soon. Yet, there will always be gamblers, urgent trades, etc. to feed them.

11

It’s not really a matter of bandwidth. Lets just say we have unlimited bandwidth and unlimited memory. Holding those constant, can algorithms built around human input produce the correct mappings to solutions when the inputs are from other algorithms?

12

I don’t see how there can be a correct “solution” to the “problem” of when to buy/sell X amount of Y stock.

13

Bingo, autolykos! That’s part of the problem right there.

14

Thanks.

I think another aspect to the problem is that the HFT algorithms probably can’t integrate as much market information as people can (and do). For example, did the HFT algorithms factor in the Japanese tsunami when evaluating the stock prices of corporations that do business in the nuclear-power industry? Although I’m by no means an expert about HFT algorithms, I doubt that any of them did.

15

An event like that is what you would consider for a buy and hold strategy. This is more about making that 1 cent spread from one minute to the next.

16

You’re right. But the HFT algorithms are running constantly, aren’t they? So essentially, they’re not taking the “bigger picture” into account. That can cause problems when the “bigger picture” changes.

17

“It’s not really a matter of bandwidth. Lets just say we have unlimited bandwidth and unlimited memory. Holding those constant, can algorithms built around human input produce the correct mappings to solutions when the inputs are from other algorithms?”

One has only to watch the afterhours sessions for the ES to see how well algos trade with eachother. Block orders in the tens of thousands hit the ticker periodically only to be pulled once the NBBO starts creeping up (or down) towards the same range. That has nothing to say towards their ability to discern “true” value (they clearly have none as they mostly do latency arbitrage between incoming bids and asks) but that condition in and of itself does not precipitate flash crashes. Quote dissemination backlogs on the exchange side do. ie: insufficient bandwidth. Per Nanex:

"Beginning at 14:42:46, bids from the NYSE started crossing above the National Best Ask prices in about 100 NYSE listed stocks, expanding to over 250 stocks within 2 minutes (See Chart 1-b). Detailed inspection indicates NYSE quote prices started lagging quotes from other markets; their bid prices were not dropping fast enough to keep below the other exchange’s falling offer prices. The time stamp on NYSE quotes matched that of other exchange quotes, indicating they were valid and fresh.

With NYSE’s bid above the offer price at other exchanges, HFT systems would attempt to profit from this difference by sending buy orders to other exchanges and sell orders to the NYSE. Hence the NYSE would bear the brunt of the selling pressure for those stocks that were crossed.

Minutes later, trade executions from the NYSE started coming through in many stocks at prices slightly below the National Best Bid, setting new lows for the day. (See Chart 2). This is unexpected, the execution prices from the NYSE should have been higher – matching NYSE’s higher bid price, unless the time stamps are not reflecting when quotes and trades actually occurred.

If the quotes sent from the NYSE were stuck in a queue for transmission and time stamped ONLY when exiting the queue, then all data inconsistencies disappear and things make sense. In fact, this very situation occurred on 2 separate occasions at NYSE: October 30, 2009, and again on January 28, 2010. (View Previous Occurrences).

Charting the bid/ask cross counts for those two days reveals the same pattern as 5/6! Looking at the details of the trade and quote data on those days shows the same time stamp/price inconsistencies. The NYSE stated that during the same intervals, they were experiencing delays in disseminating their quotes!

In summary, quotes from NYSE began to queue, but because they were time stamped after exiting the queue, the delay was undetectable to systems processing those quotes. On 05/06/2010 the delay was enough to cause the NYSE bid to be just slightly higher than the lowest offer price from competing exchanges, but small enough that it was difficult to detect. This caused sell order flow to route to NYSE – thus removing any buying power that existed on other exchanges. When these sell orders arrived at NYSE, the actual bid price was lower because new lower quotes were still waiting to exit a queue for dissemination.

This situation led to orders executing against whatever buy orders existed in the NYSE designated market maker (DMM) order book. When an order is executed, the trade is reported to a different system (CTS) than quotes (CQS). Since trade report traffic is much smaller than quote traffic, there is rarely any queueing or delay.

Because many of the stocks involved were high capitalization bellwether stocks and represented a wide range of industries, and because quotes and trades from the NYSE are given higher credibility in many HFT systems, when the results of these trades were published, the HFT systems detected the sudden price drop and automatically went short, betting on capturing the developing downward momentum. This caused a short term feed-back loop to develop and panic ensued.

Some trading firms have stated that they detected a problem with the accuracy of the data feed and decided to shut down which further reduced liquidity. We think the delay in NYSE quotes was at the root of this detection."

http://www.nanex.net/20100506/FlashCrashAnalysis_Part1-1.html

18

Nor can one create an algorithm which has variable steps (they must be finite).

Maybe I’m just picking, but there are algorithms which work on infinite, on-line data and never have an end but constantly improve something they calculate.

19

Nope, information is still finite. You seem to be confusing physical infinity for mathematical infinity. They are not the same due to one being about physically unbounded or uncountable number of things/states/etc in the known universe and unknown universe, but when we’re considering mathematical infinity we’re considering the literal unboundedness of all countable units. In this case, the closest you could probably come to infinity in mathematics that you can get your head around is the infinite precision of real numbers(1.0 1.00 1.000 1.0000 1.00000… just for an example), which are infintesimals. So, even in computers we round or make everything integer-like as possible (even our real number equivalents such as floats and doubles). That includes realtime data.

20

But since we’re calculating the physical infinity, isn’t that enough to satisfy our demands?