The romanticized trader works in a caravan, braving the elements to move property and information between cities. Over millenia, humans have gone from trading physical goods with wagons and ships to trading symbolic contracts with undersea cables and specialized radio networks. Markets’ adoption of communications technology has undoubtedly benefited society. But has it gone too far? Could the benefits of further speed be outweighed by the costs? A lot of people think so. And high-speed networks aren’t cheap; a new cable between Tokyo and London may cost $850M. But while I’ve heard lots of complaints about the cost of improving network infrastructure, I haven’t seen any estimates of the benefit. I will attempt to provide one here. # The “Arms Race” Budish, Cramton, and Shim call further investment in speed “socially wasteful.” They also describe the dynamic between trading firms as a “prisoner’s dilemma,” where firms could increase their profits if they all avoid expensive technology investments. But if one firm “deviates” and improves its speed, it can temporarily increase its profit at the expense of its rivals — until they make their own similar investments. The result is that firms are continually investing in speed, but these expenditures don’t increase industry revenue. Many HFTs, being the supposed prisoners in this dilemma, agree that this process is a waste — for example Mani Mahjouri of Tradeworx: [W]e went from piecing together existing fiber routes to digging trenches across the country to lay straight fiber to now sending signals through microwave towers and laying new trans-Atlantic cables, doing these very, very expensive technological investments… But if you look at it from the perspective of society, that’s a tremendous amount of capital that’s being invested… In my view, maybe that would be better spent making a more competitive price, as opposed to spending it on speed Now, capitalism is supposed to force competitors to invest in order to provide a better service. If an industry complains that high investment costs are squeezing its margins, that’s a sign that competition is working the way it should. The concern is normally the opposite, that competitors are colluding to avoid “defections” from the investment “prisoner’s dilemma.” The question is whether there’s something unique about trading networks that makes the investments worthless to society. I don’t see why there should be. # The Speed of Information and Social Welfare It is obvious that social welfare suffers when communications between markets are sufficiently slow. A revealing example is the experience of a Mediterranean trader (c.a. 1066), who needed to know the price of silk in an away market before he could proceed with his business. He sent the following letter, where he reports that his time awaiting this information will be wasted: The price in Ramle of the Cyprus silk, which I carry with me, is 2 dinars per little pound. Please inform me of its price and advise me whether I should sell it here or carry it with me to you in Misr (Fustat), in case it is fetching a good price there. By God, answer me quickly, I have no other business here in Ramle except awaiting answers to my letters… I need not stress the urgency of a reply concerning the price of silk Clearly, there would have been an economic benefit if the trader had faster communications. In general, how can we estimate the size of this benefit? When prices aren’t synchronized, wealth is arbitrarily transferred between traders — some transactions receive a slightly better price and others a slightly worse price, purely through luck. These wealth transfers are zero on average, so it’d be wrong to say their cost to society is their entire amount. But it’d also be wrong to say that such transfers are completely innocuous because they’re “zero-sum.” Which means that a reasonable estimate of the societal cost of unsynchronized markets is: the volume ($V_{transfer}$) of wealth transfers due to price discrepancies between venues, multiplied by a factor between 0 and 1, representing the economic cost per unit wealth transfer ($C_{transfer}$). Let’s start by estimating $C_{transfer}$. Here are three examples where markets assign a value to the cost associated with random wealth transfers: 1. Insurance: Where customers transfer the risk of bad luck to insurance companies, paying significantly more than expected losses to offload risk. Loss ratios in the insurance industry are generally around 80%. [1] So the insurance market has a $C_{transfer}$ of about 0.2. [2] 2. The equity risk premium: Aswath Damodaran calculates the historical excess return of equities over short-term government debt to be 4.4% globally, and the standard deviation of the difference in returns to be 17.1% (Table 6). This means, roughly, that investors typically demand an additional 4.4% return in exchange for risking 17.1% of their capital — translating to a $C_{transfer}=\frac{0.044}{0.171} \approx 0.25$. Excluding the US, this ratio is 0.2, and in some countries isn’t far above 0.1 (e.g. Belgium or Norway). 3. Jensen’s analysis of synchronization between fish markets in Kerala: After fishermen obtained mobile phones, they were able to find the nearby market with the highest price for fish, while they were still on the water. This information made it much easier for them to smooth out local fluctuations in supply and demand (see, e.g., Figure IV). Jensen estimates that mobile phones increased fishermen’s profits by 8% and decreased the average cost of fish by 4%. [3] These numbers suggest that the Kerala fish market has a $C_{transfer}$ of at least 0.1. [4] It’s striking that these disparate methods all give approximately the same value. For our calculation, we’ll take $C_{transfer}=0.1$. Now, we just need to estimate the reduction in random wealth transfers, $\Delta V_{transfer}$, for a famous HFT network — The NY-Chicago microwave route seems like a good example. We’ll just make a simple, order-of-magnitude estimate. It’s reasonable to approximate $\Delta V_{transfer}$ with the total executed volume ($V$) for products with multiple important trading centers connected by the route, multiplied by the typical price dispersion ($\sigma_{\Delta}$) prevented by a reduction in inter-market latency. The CME traded over a quadrillion dollars notional in 2015. Some of that volume is “inflated” by contracts with a high notional value (e.g. options, Eurodollars) or may not be tightly coupled with away markets — so let’s cut it by 90% and say that $V \approx \10^{14} yr^{-1}$ is the volume in Chicago that’s highly-correlated with important markets in New York or Europe. [5][6] We can estimate $\sigma_{\Delta}$ by making the usual assumption that price movements are Brownian, so that volatility scales with the square root of time. Let’s just roughly assume that the relevant CME contracts have an annual volatility of 10%. This makes it easy to calculate how much their prices typically move in the ~2.5ms that wireless networks save over fiber (one-way): $\sigma_{\Delta} = 0.1 yr^{-\frac{1}{2}} \sqrt{2.5 ms \cdot \frac{1.6 \times 10^{-10} yr}{ms}} \approx 2 \times 10^{-6}$ [7] So we have that $\Delta V_{transfer} \approx V \cdot \sigma_{\Delta} \approx \10^{14} yr^{-1} \cdot 2 \times 10^{-6}$. In other words, upgrading the Chicago-NY route from fiber to microwave prevents around$200M of arbitrarily transferred wealth per year. Multiplying this by our estimated economic cost per unit transfer, $C_{transfer}=0.1$, gives the societal value of this microwave route: about $20M per year. # Comparing a Network’s Value to its Cost Laughlin, Aguirre, and Grundfest estimate that Chicago-NY microwave networks required around$140M in capital expenditures, with $20M per year in operating expenses. Our estimate of the route’s value is very rough, but still surprisingly close to their (also rough) numbers. And I imagine that some fraction of the costs, which include things like salaries and radio licensing fees, are not a complete loss to the economy. So, it’s quite plausible that these microwave networks are “worth it” to society. There’s also the possibility that the networking technology developed for HFTs will have beneficial applications in other industries, many of which are latency-sensitive. Finance has a history of subsidizing important innovations. According to Rocky Kolb, the first application of the telescope was spotting cargo ships and using that information to trade. Galileo himself described how impressed Venetian leaders were with this application, who rewarded him: And word having reached Venice that I had made one [a spyglass], it is six days since I was called by the Signoria, to which I had to show it together with the entire Senate, to the infinite amazement of all; and there have been numerous gentlemen and senators who, though old, have more than once climbed the stairs of the highest campaniles in Venice to observe at sea sails and vessels so far away that, coming under full sail to port, two hours and more were required before they could be seen without my spyglass. If — in my armchair — I were put in charge of the economy and somebody came to me with a$200M project to cut inter-market latency by 3ms, I really wouldn’t know whether it was a good idea. Sure, I could do a more thorough calculation than we did here. But I bet the best decision for the economy would be based on whether people would actually pay to use the network. That’s what telecoms do already. Capital markets sometimes invest in dead-end projects, but identifying these mistakes, in advance, is rarely easy.

Reducing latency from 2 weeks to 1 second has obvious benefits to society. Going from 7ms to 4ms is more subtle. [8] But just because progress is incremental, doesn’t mean we should dismiss its value. The economy is big, and our markets process tremendous volumes. A small improvement in price discovery can make a meaningful difference.

[1] Typical loss ratios for property and casualty insurance in 2015 were about 69% (Table 1). For accident and health insurance, they were about 80% (Figures 10 and 11).

[2] Of course, buyers of insurance may be especially risk-averse and willing to pay high premiums to avoid catastrophes. But hopefully competition and regulation keeps exploitation to a minimum.

[3] Jensen estimates that consumer surplus (the welfare benefit to fish-buyers) increased by 6%, a bit bigger than the decline in fish prices.

[4] Also keep in mind that prices were still not perfectly synchronized after the introduction of mobile phones. Perhaps profits would increase and prices decrease even more if fishing boats had automated, low-latency routing. They almost certainly would if new technology made boats faster.

[5] It isn’t just S&P 500 futures in Chicago that are highly-correlated with markets in NY and Europe. You can make obvious arguments to include FX and fixed income futures in this category. Energy pricing is critically important for a wide range of asset markets. Agricultural products and metals also trade around the world, and can provide important trading signals for some equities.

[6] I don’t know whether the current lowest latency route between Chicago and Europe goes through New York. It probably depends on whether Hibernia allows customers to connect at their Halifax landing, and use their own microwave networks to shuttle data between Halifax and Chicago. I’m far from an expert on such things, but Alexandre Laumonier suggests that Hibernia may have restricted connections at a different landing:

Different informants in the industry (and one journalist) told me that Hibernia will not allow (at least for now) dishes at the Brean landing station. I tried to know more about that but the only answers I got were some “neither confirm nor deny” responses. Huh! People know but don’t talk. I wrote an email to Hibernia but I got zero answer (obviously). Then other informants told me Hibernia may finally allow dishes…

It’d be pretty funny if Hibernia let customers connect at Halifax instead of New York or Chicago, but charged extra for the ostensibly inferior service (like airlines do).

In any case, even if there are proprietary wireless networks from Chicago to Halifax, they probably share some towers with the Chicago-NY route. So maybe it’s fair to include Chicago-Europe traffic in our estimate of the economic value of Chicago-NY microwave networks.

[7] Assuming there are ~250 trading days per year, and each trading day is ~7 hours — so there are about $1.6 \cdot 10^{-10}$ trading years per millisecond.

[8] Matt Levine describes (as many do) “a market as a giant distributed computer for balancing supply and demand; each person’s preferences are data, and their interaction is the algorithm that creates prices and quantities.” This analogy may be helpful for understanding high-speed trading. A supercomputer’s performance can depend heavily on its interconnect. If the market is a giant supercomputer, reducing its interconnect latency from 7ms to 4ms could dramatically increase its processing power — for some tasks by 40%. For such tasks, we’d expect a large increase in inter-node traffic when latency is improved. Perhaps we are seeing this increase in modern financial markets, which have far higher trade and message volumes than in the past.

## 8 thoughts on “High-speed Trading Networks and Societal Value”

1. sniperinmahwah

“Hibernia may have restricted connections at a different landing” – I confirm, at least in the UK (no microwave network between the Brean landing station and Slough/LD4).

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2. isomorphismes

The CME traded over a quadrillion dollars notional in 2015. Some of that volume is “inflated” by contracts with a high notional value (e.g. options, Eurodollars) or may not be tightly coupled with away markets — so let’s cut it by 90% and say that $latex V \approx \$10^{14} yr^{-1}$is the volume in Chicago that’s highly-correlated with important markets in New York or Europe. [5][6] I am not getting where your movement$ latex \mathrm{wiggle} \approx \mathrm{notional} \odiv 10 $approximation comes from. This doesn’t seem like the only number that may be more than 1 order of magnitude off. Like 3. isomorphismes Insurance: Where customers transfer the risk of bad luck to insurance companies, paying significantly more than expected losses to offload risk. Loss ratios in the insurance industry are generally around 80%. [1] So the insurance market has a$ latex C_{transfer}\$ of about 0.2. [2]

There are a couple problems with using insurance to estimate social value. Most obvious is wealth effects: a rich person’s life is not “worth more” than a poor person’s, but they are more likely to buy more insurance.

Secondly, externalities are only sporadically accounted for. One may insure one’s children when they are young, but they are unlikely to do the reverse when you are old (again, though, this depends on how much money various family members have). The people who bring the most value to others in their community / family are not the most insured.

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1. Kipp Rogers Post author

Sure, and there are plenty of other reasons (taxes, regulation, lack of competition) to believe insurance pricing might not reflect people’s internal valuation of risk (which as you say could be different from the “true value,” whatever that means). But it’s probably on the right order of magnitude?

The three examples are really to guide the eye. Arguably the equity risk premium is more problematic, since it assumes a 1 year time horizon — and C_{transfer} will scale with the square root of the time horizon (a 4 year horizon will have a C_{transfer} ~twice as large).

But all the estimates are within a factor of 10, and 0.1 is a nice round number.

Also, there may be behavioral finance experiments that effectively estimate C_{transfer} in the context of a game.

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1. isomorphismes

I’d guess maybe half an order of magnitude off but maybe 1 order off.

(Also, this is a really good post; I only wrote criticisms because “Awesome job!!!” sounds like an empty comment. However, awesome job– yeah, I get that the examples are impressionistic.)

I distrust behavioural finance too much personally to even hear this comment — but yeah, there are probably all kinds of reasons to say these might be off. My point was just that since your answer is only 1 OOM difference, we’d like precision 1 or more levels lower to justify the conclusion.

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4. isomorphismes

Matt Levine describes (as many do) “a market as a giant distributed computer for balancing supply and demand; each person’s preferences are data, and their interaction is the algorithm that creates prices and quantities.” This analogy may be helpful for understanding high-speed trading. A supercomputer’s performance can depend heavily on its interconnect. If the market is a giant supercomputer, reducing its interconnect latency from 7ms to 4ms could dramatically increase its processing power — for some tasks by 40%. For such tasks, we’d expect a large increase in inter-node traffic when latency is improved. Perhaps we are seeing this increase in modern financial markets, which have far higher trade and message volumes than in the past.

I would find this more convincing if you could connect continuous-time trading to production decisions — something with a concrete output.

Low latency would make sense if we were talking a farmer’s market. Imagine the egg-laying latency approached zero and so did transport costs & speed. Then instead of riding the bus to market with a guess at how many eggs to bring, the daughter simply calls up Mom when a new customer walks up to the table, asks Mom to tell the chicken to lay a dozen eggs, and immediately fresh eggs are teleported to the customer.

Now let’s take a heterogeneous product. Netflix has been investing a lot of money in original content. NFLX can see how many people stream their stuff right away. So for example, if an ad runs on TV networks 1a, 3b, and 6j at 7:30 pm Pacific after the ___ Show, and NFLX can quantitatively see the traffic spikes from IP’s in those markets, and they have good numbers on how many people watched the ___ Show in 1a+3b+6j, then they can adjust their ad spend. What effect does this fast information have, though, on the films they produce? Here I guess they would still rely on creative, and speed would make little to no difference to whether a program ever gets made, or not.

In financial markets, demand for shares or debt is meant to drive concrete decisions like how many new films Netflix will make; how many staff a publicly traded company will hire; etc. Happy to help researching a post that would look at these kinds of things with respect to latency.

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1. Kipp Rogers Post author

I tend to agree that tiny fluctuations in price don’t usually have an impact on real-world production/consumption. If the price of crude drops by 1 tick, I doubt oil companies really slow down their drilling. But if the price changes by 10 ticks? I don’t know… maybe?

There is a very interesting paper (which I may write more about) by Donier and Bouchaud ( https://arxiv.org/abs/1506.03758 ) which shows that continuous-time (or near-continuous-time) markets have supply/demand curves that vanish near the market clearing price. (The supply/demand curves are locally quadratic, with no linear term. Figure 7 is helpful.) This means that when the price changes by a small amount, we shouldn’t expect much change in supply or demand.

But that seems somewhat separate to the (speculative) supercomputer interconnect argument. E.g. there may be algorithms that transfer information between a banner market like GBP and individual stocks, which only operate in London. So if GBP news from Chicago reaches London a little faster, then the prices of various UK stocks will react a little faster. These changes in turn may have an impact on Chicago markets. Etc. Information may go back and forth and elsewhere many times before markets reach “equilibrium.” So if the Chicago-Europe link is 5ms faster, markets’ news-processing speed could improve by much more than 5ms. If we have “news” occurring in global markets every second, that 5ms could make the difference between markets being able to reach equilibrium before the next news event arrives (i.e. the “global market supercomputer” completes its processing task), and markets being continually behind the news. It’s possible that a faster “supercomputer” results in prices that are different by economically significant amounts. Of course, I’m being somewhat whimsical.

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