A Quick Note About the FCA Occasional Paper on “Latency Arbitrage”

Aquilina, Budish, and O’Neill (ABO) today published a paper on the “HFT Arms Race” with the headline that estimates a “latency arbitrage tax” on global investors of $5B/yr. The paper shows some interesting statistics on a unique dataset, raw messages sent to the LSE which are captured and timestamped by one of LSE’s TAPs. Unfortunately, I don’t see how the activity measured in the paper resembles anything approaching a “tax”. I’ve only had a short time to read the paper, so I apologize if I’ve made any errors. And the paper does not necessarily reflect the views of the FCA.

Essentially ABO measure messaging activity that occurs in short bursts, particularly batches of marketable orders — possibly accompanied by cancel-requests — where some of the later orders or cancel-requests fail because an earlier message succeeded. E.g. if 3 marketable orders (from different trader IDs) are sent in short succession when the order book only has the quantity available to fill one of them, then that is identified as a “race” which the first order wins and the later 2 orders lose. Similarly, a “race” is also identified if the LSE receives marketable orders shortly before it receives cancel requests for the matched resting orders. In this case, the failed cancel-requests are the losers of the “race”. The authors provide event counts, volume, and estimated profit for race-winners — where they vary the duration window to identify a “race”, as well as other parameters such as race-type. The headline number of a 0.42bp “tax” is the race-winners’ estimated profits as a share of total volume, where the race window is set to 500us.

Figure 5.1 is a histogram (truncated at 500us) of the time-differences between the first successful message in a race, and the first message to fail (either by being too late to cancel, or trying to trade with liquidity that’s already gone). It’s no surprise that the distribution is highly-skewed, with a mode of 5-10us and a 90th percentile of about 200us. And Figure 4.1 shows reaction-times on the LSE for a different type of event, which the authors use to estimate LSE latency at around 29us. Tables 5.5, 5.6, and Figure 5.3 also show the midpoint price trajectory after race events. The authors do a very nice sensitivity analysis that shows how the numbers vary if you change the race window and other parameters. It’s important to note that the longer the race window, the more it will blend messages stemming from different market events. The 500us window selected could help include failed messages sent across Europe on slow networks, but it also includes ~15 roundtrip times from the LSE — enough time for order books on correlated products to react and refill multiple times. One noteworthy measurement is in Table 6.3, which gives an idea of the volume that market-makers perhaps wish they could avoid by being faster: the approximate “profit” that marketable orders make from trading with someone who tried-and-failed to cancel within 50us. This number is very low, about 0.03bp, an indicator of a pretty efficient market where market-makers are not getting “picked-off” very often.

Now, it’s very interesting to see statistics on these types of events, but I don’t see how they can be considered a “tax” in any way. All they show is that trading is competitive, and that traders may send messages even if there’s a low probability of success. As a real-world example, consider America’s favorite holiday, Black Friday. Perhaps your local toy store is selling the new Nintendo for $100 off, but they only have 10 available with the discount. You know it’ll be a long shot, but you really want to catch some Pokemon, so you get up early and head to the store. You get there just in time to be 10th in line. A bunch of people arrive a few minutes later, but they all have to pay full price.

Did you levy a tax on them? It’s hard to see how. You got there first and you got the reward. Your time and transportation cost were arguably wasted. But in financial markets, investments in network infrastructure which ensure the law of one price have significant economic value. I suppose Nintendo could forbid discounts, and maybe everyone else could get 0.004% off, but Nintendo gets to decide how to sell their wares. It’s a silly analogy, but maybe stocks aren’t so different. If a shareholder prefers to disengage from this type of race, she can sell her stock in an auction if she likes. And the paper appears to suggest that a way to avoid the “tax” is to have everyone trade in auctions, referring to the batch auction proposal from Budish, Cramton, and Shim (BCS):

BCS showed that even information seen and understood by many market participants essentially simultaneously — e.g., a change in the price of a highly-correlated asset or index, or of the same asset but on a different venue, etc. —creates arbitrage rents too. These rents lead to a never-ending arms race for speed, to be ever-so-slightly faster to react to new public information, and harm investors, because the rents are like a tax on market liquidity. BCS showed that the problem can be fixed with a subtle change to the underlying market design, specifically to discrete-time batch-process auctions; this preserves the useful function of algorithmic trading while eliminating latency arbitrage and the arms race.

Of course, auction prices are still partly set by proprietary traders, sometimes in a latency-sensitive way. The BCS proposal claims to eliminate “latency arbitrage” by having auctions every 100ms or so, with only price priority and ties broken randomly. To further prevent “latency arbitrage”, BCS proposes no pre-auction transparency. Normal exchange auctions have a long period of transparency before the final match occurs, in order to attract liquidity and ensure a sensible price. This transparency often takes the form of a partly displayed order book (e.g. on many futures exchanges), or indicative pricing and order imbalances (e.g. on many equities exchanges). Pre-auction transparency does make trading somewhat latency-sensitive, but exchanges in the real world know that having an auction blind can result in chaotic pricing — even when auctions occur once a day on highly liquid products. Holding blind auctions so frequently that they have only 0 or 1 orders of natural liquidity, and where traders are rewarded with priority for aggressive pricing, is a recipe for disaster. Prop traders would probably make a lot of money off of the ensuing chaos, but the uproar might be so intense that few of them would recommended it.

More generally, there is a tradeoff between immediacy and liquidity. If you want to have liquid auctions, they probably can’t be very frequent. Donier and Bouchaud suggest that for batch auctions to improve liquidity they should occur on the order of once per hour. I think most traders like auctions — BCS is right about that. And since we’re discussing pet market structure reforms with no chance of happening, I may as well suggest one that would give us more auctions and could save something of far more significant value: people’s time. The industry currently spends a lot of time keeping markets open when they probably don’t need to be. We could reduce that time, which currently has many professionals in the office for 11 hours a day. Stock exchanges could hold 2-4 sessions per day, each around 30-60 minutes long and overlapping with market hours in other major financial centers. This schedule could encourage working from home and a more clear demarcation of business hours between offices in different timezones.

I enjoyed seeing the statistics in ABO and wish regulators would publish more statistics on raw market data. The “tax” claim seems a bit strange though.

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