The ups and downs of the financial markets in these days draw attention to the increasing role of automatic trading, as in earlier episodes of this kind. The use of sophisticated proprietary software has become a major determinant of competitive advantage of fund managers. Many observers believe that this mitigates flaws of human behaviour because robots have no emotions. Software designers can further optimize the algorithms, so that they fully reflect the most advanced knowledge about how financial markets operate and can implement trading with ever increasing speed, scope and reliability.
I dare to question this argument. There is a fundamental problem in designing algorithms in financial markets which reflects Keynes famous argument on the ‘beauty contest’. Further optimizing algorithms would eventually require predicting what competing algorithms do: Think of the financial markets as a system of competing robots, and they face the same problem as humans in Keynes’ metaphor. The robots would need to predict the behaviour of other robots. It seems that today most algorithms treat market data as parametric in the sense that they automatically trigger trades when certain thresholds are reached. Thus, it is argued, similar algorithms start to act in parallel and drive down the market. A sophisticated algorithm would include this effect, which means predicting what other robots do. But is that possible?
A simple answer would be that because the algorithms are business secrets, they cannot predict exactly how others will act. But I think that there is a much more serious problem. Many economists liken the market to a computational system. That would now be distributed across many competing robots. Can we imagine that out of the competition a workable global computational regime would emerge? I think, no. We have strong results in foundational mathematics, basically grounded in Gödel’s theorems, that there are fundamental limits to the capacity of algorithms to mutually predict their actions. The reason is that an algorithm would need to model the other algorithm, including how the other algorithm models itself, and so on. That is exactly Keynes’ problem of the beauty contest! For example, David Wolpert has shown that interacting computational systems cannot predict their behaviour, but only run in parallel real-time.
In other words, I do not think that the growing role of algorithms in financial trading will improve market functionings. To the opposite, the more sophisticated the algorithms become, the higher the probability that the aggregate computational system will collapse in Gödel-Type paradoxes and dilemmas.
At this point, Keynes other famous metaphor comes into play, the ‘animal spirits’. Many people misunderstand this, because they believe it is about the negative consequences of irrational behaviour. But the original meaning was just the opposite: Keynes argued that there is the possibility of rational blockades in the market process, which need to be overcome by activating animal spirits. This is exactly what can happen in a vastly distributed computational system consisting of rationally designed algorithms: Not only literally, but really, a hang-up of the global computation.
Robots don’t have animal spirits. That’s why we need humans on financial markets.
Wolpert, David H. (2001), ‘Computational Capabilities of Physical Systems’, Physical Review E, 65, 016128.