Trading Speed Competition: Can the Arms Race Go Too Far?

Trading Speed  –  Abstract:

We analyze the likelihood of arms race behavior in markets with liquidity provision by HFTs. Liquidity providers (makers) and liquidity consumers (takers) make costly investments in monitoring speed. Competition among makers and takers induces arms race behavior. However, trade success probabilities increase in monitoring speed, giving rise to complementarity externalities between makers and takers. This counters negative arms race effects. Whether arms race effects materialize crucially depends on how marginal gains from trade depend on transaction speed. With the common (often implicit) assumption of constant marginal gains from trade, complementarity effects mostly dominate and market participants tend to under-invest in technology. However, with marginal gains from trade that decline in transaction speed, arms race behavior is much more likely. We provide micro-foundations for declining marginal gains from trade by a dynamic portfolio optimization problem with random rebalancing opportunities.
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Trading Speed  – Conclusion

In this paper, we have explored whether competition on speed among stock market participants is likely to trigger arms races, leading to socially wasteful investments. We highlight two opposing economic channels that influence such effect in opposing and partially offsetting ways. Competition among makers as a group and among takers as a group may indeed trigger arms races in the classical sense. However, a complementarity between the two sides, the increased success rate of trading, may offset this competition effect if the gains from trade are large enough. Therefore, the likelihood of arms races depends on how gains from trade depend on transaction frequency. Using a portfolio rebalancing model, we show that gains from trade are likely to be concave in transaction frequency. Intuitively, the gains realized in a trade shrink the smaller the time interval in between subsequent trades. Under this new more realistic speci- fication, arms races are more likely to occur than under the standard paradigm in the literature (featuring gains from trade that are independent on the time interval in between subsequent trades).
While providing important insights, our model does make some concessions to reality. A potential concern is that it does not allow for the dual role of participants in modern limit order markets. Yet, in fact this concern is not as grave as one would think. After all, there is a group of market participants that are likely to show a net demand for liquidity. Moreover there is a group that on net will be providing liquidity. This is what in the end generates the welfare gains. Trades among makers, which currently are very common, are zero sum within the group of makers (one maker could have been the only intermediary rather than a whole chain). The single role assumption massively simplifies our problem, leading to better tractability.
Another comment to make on the results of the model is that competition in speed may have positive externalities in the sense that it boosts technological progress and knowledge. Other industries may benefit from this progress in unanticipated ways. As an example, the internet was developed for internal and largely military purposes, but in an unanticipated way massively improved productivity and living standards across the globe. Unfortunately, incorporating such effects is notoriously difficult due to the unanticipated and uncertain nature of such effects. The model could be adjusted for such effects in reduced form, but conclusions would depend crucially on parameters and probability distributions that are very hard to calibrate.
Trading Speed pdf below