Sebastian Pokutta's Blog

Mathematics and related topics

Arms race in quantitative trading or not?

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Rick Bookstaber recently argued that the arms race in high frequency trading, a form of quantitative trading where effectively time = money ;-), results in a net drain of social welfare:

A second reason is that high frequency trading is embroiled in an arms race. And arms races are negative sum games. The arms in this case are not tanks and jets, but computer chips and throughput. But like any arms race, the result is a cycle of spending which leaves everyone in the same relative position, only poorer. Put another way, like any arms race, what is happening with high frequency trading is a net drain on social welfare.

It is all about milliseconds and being a tiny little bit faster:

In terms of chips, I gave a talk at an Intel conference a few years ago, when they were launching their newest chip, dubbed the Tigerton. The various financial firms who had to be as fast as everyone else then shelled out an aggregate of hundreds of millions of dollar to upgrade, so that they could now execute trades in thirty milliseconds rather than forty milliseconds – or whatever, I really can’t remember, except that it is too fast for anyone to care were it not that other people were also doing it. And now there is a new chip, code named Nehalem. So another hundred million dollars all around, and latency will be dropped a few milliseconds more.

In terms of throughput and latency, the standard tricks are to get your servers as close to the data source as possible, use really big lines, and break data into little bite-sized packets. I was speaking at Reuters last week, and they mentioned to me that they were breaking their news flows into optimized sixty byte packets for their arms race-oriented clients, because that was the fastest way through network. (Anything smaller gets queued by some network algorithms, so sixty bytes seems to be the magic number).

Although high-frequency trading is basically about being fast and thus time is the critical resource, in quantitative trading, in general, it is all about computational resources and having the best/smartest ideas and strategies. The best strategy is worthless if you lack the computational resources to crunch the numbers and, vice versa, if you do have the computational power but no smart strategies this does not get you anywhere either.

Jasmina Hasanhodzic, Andrew W. Lo, Emanuele Viola argue in their latest paper “A Computational View of Market Efficiency” that efficiency in markets has to be considered with respect to the level of computational sophistication, i.e., as market can (appear to) be efficient for those participants which use only a low level of computational resources, whereas it can be inefficient for those participants that invest a higher amount of computational resources.

In this paper we suggest that a reinterpretation of market efficiency in computational terms might be the key to reconciling this theory with the possibility of making profits based on past prices alone. We believe that it does not make sense to talk about market efficiency without taking into account that market participants have bounded resources. In other words, instead of saying that a market is “efficient” we should say, borrowing from theoretical computer science, that a market is efficient with respect to resources S, e.g., time, memory, etc., if no strategy using resources S can generate a substantial profit. Similarly, we cannot say that investors act optimally given all the available information, but rather they act optimally within their resources. This allows for markets to be efficient for some investors, but not for others; for example, a computationally powerful hedge fund may extract profits from a market which looks very efficient from the point of view of a day-trader who has less resources at his disposal—arguably the status quo.

More precisely, it is even argued that the high-complexity traders gain from the low-complexity traders (of course, within the studied, simplified market model – but nonetheless!!):

The next claim shows a pattern where a high-memory strategy can make a bigger profit after a low-memory strategy has acted and modified the market pattern. This profit is bigger than the profit that is obtainable by a high-memory strategy without the low-memory strategy acting beforehand, and even bigger than the profit obtainable after another high- memory strategy acts beforehand. Thus it is precisely the presence of low-memory strategies that creates opportunities for high-memory strategies which were not present initially. This example provides explanation for the real-life status quo which sees a growing quantitative sophistication among asset managers.

Informally, the proof of the claim exhibits a market with a certain “symmetry.” For high-memory strategies, the best choice is to maintain the symmetry by profiting in multiple points. But a low-memory strategy will be unable to do. Its optimal choice will be to “break the symmetry,” creating new profit opportunities for high-memory strategies.

So although in pure high-frequency trading, the relevance of smart strategies might be smaller and thus it is more (almost only?) about speed, in general quantitative trading it seems like (again in the considered model) that the combination of strategy and high computational resources might generate a (longer-term) edge. This edge cannot necessarily be compensated with increased computational resources only, as you still need to have access to the strategy. The considered model considers memory as a the main computational/limiting resource. One might argue that it reflects the sophistication of the strategy along with the real computational resources implicitly, as limited memory might not be able to hold a complex strategy. On the other hand a lot of memory is pointless without a strategy using it. So both might be considered to be intrinsically linked.

An easy example illustrating this point is maybe the following. Consider the sequence “MDMD” and suppose that you can only store, say these 4 letters. A 4-letter-strategy might predict something like “MD” for the next two letters. If those letters though represent the initial of the weekdays (in German), the next 3 letters will be “FSS”. It is impossible though to predict this sequence solely using information about the past on the last 4 letters. The situation changes if we can store up to 7 letters “FSSMDMD”. Then a prediction is possible.

One point of the paper is now that the high-complexity traders might fuel their profits by the shortsightedness of the low-complexity traders. And thus an arms race might be a consequence (to exploit this asymmetry on the one hand and to protect against exploitation on the other). To some extent this is exactly what we are seeing already when traders with “sophisticated” models, that for example are capable of accounting for volatility skew, arbitrage out less sophisticated traders. On the other hand, it does not help to use a sophisticated model (i.e., more computational resources) if one doesn’t know how to use it, e.g., a Libor market model without an appropriate calibration (non-trivial) is worthless.


Written by Sebastian

September 1, 2009 at 8:38 pm

2 Responses

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  1. the initials of the days of the week are FSSMDMD? in english? seriously?


    October 7, 2011 at 4:54 pm

    • 😀 good point – actually this is the German abbreviation. Totally missed that one!!


      October 7, 2011 at 9:09 pm

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