Academic CLOB Model

Last week, I commented on the University of Chicago professor Eric Budish et al.'s hedge fund sniping model but neglected a more significant point. To recap, Budish modeled a scenario likened to a Centralized Limit Order Book (CLOB), where liquidity providers (LPs) post bids and asks, and takers then take those orders (link). Assuming several high-frequency traders (HFTs) are posting the bids and asks, for any resting lone bid or ask, a stale quote will generate a race between the lone HFT LP and several HFTs acting as takers. If the race winner is random, the odds are the LP posting the order will lose. This is the latency race deadweight loss. He estimates this symmetric information adverse selection adds 0.4 basis points (0.004%) to the bid-ask spread. When you apply that number to all the stocks traded worldwide, you get $40B. We would save the world $40B if we switched to sequential auctions. In his words, "continuous markets don't 'work' in continuous time." 

The craziest thing about this argument is that he applies this to a novel market mechanism that lowered costs by over 90% after nearly a century of stasis. In the first chart, we see the spread was constant from 1900 to 1990 at around 60 basis points, making some think it was some fundamental equilibrium. The internet enabled an alternative way to trade stocks, the electronic trading revolution from firms like Island, BATS, Archipelago, Instinet, etc. The second chart shows that it fell still lower from 2001 through 2006. The second chart is in different units and breaks it up by size groupings, but the point is the decline continued and was permanent. The current spread is about 3 basis points. 60 to 3.

Jones Trading Costs 1900-2000

Jones, Hendershott and Menkveld (2008)

In that context, advocating a wholesale change in market structure to eliminate a remaining 0.4 basis point of that spread is a classic example of letting perfection be the enemy of the good. This sort of economic ingratitude is standard, as no matter how much GDP grows, someone can point out something wrong and suggest we replace capitalism with a centrally planned economy, one that, unlike any of the past centrally planned economies, will work better than decentralized economies.

In spite of economics as seeming laissez-faire, most economists have been progressives (e.g., founder of the AEA Robert T. Ely, JM Keynes), viewing competitive behavior as wasteful, a criticism shared by industry leaders who appreciate it as a powerful cartelization device. The essence of free markets is private property and liberty. If people can make unfettered decisions about themselves and their property, it promotes prosperity. There is no trade-off between freedom and prosperity; they go hand in hand. Alas, most people, especially academics, don't trust decentralized results. Since Plato's Republic, they have always thought they could design a better world if given the mandate. Hubris and pride were prominent human vices in the Classical and Biblical canon because of their perennial, pervasive, and pernicious nature. It's a constant battle.

Back to Budish's model, he looks at some data circa 2015 on the London Stock Exchange, back when they timestamped in microseconds (now nano) and focuses on trades where several HFTs were taking or canceling a particular offer (e.g., bid for 100 @ 99.32) within 500 microseconds of each other. He figures the takes that got there before the LP canceled were unfairly robbing the poor HFT LP, which happened 90% of the time. Indeed, cancel orders were not recorded most of the time in these races, but if several HFTs tried to take simultaneously, he figured the LP probably wanted to.

This inference is silly for several reasons. First, It depends on who is trading and why. This was highlighted by Holmstrom and Myerson (1981): planners do not know everything in an economy with incomplete information, something economists often forget when looking down at their models like God. Many sniped orders were from retail traders who thought they would post a buy order one tick above the best buy instead of crossing the spread. They get up and go to the kitchen, and when they come back, they are filled, though the market has moved much lower. If the retail trader instead sent a market order and bought at a higher price, they would have a bigger loss. This is not a deadweight loss.

Another type of trader is the HFT, who merely wants to change their inventory, including rectifying a short position (moving from -100 to -90). In that case, they would be willing to cross the spread or post an aggressive limit order; they are not trading for arbitrage, where one tries to buy below the mid, etc. When one posts an aggressive resting limit order above the current best bid, one knows that they are not guaranteed a fill with the price not moving, as otherwise, no one would cross the spread. Marking such resting limit order trades to the mid-price will make it look like a loss to the LP, but it should be marked relative to the alternative, which is crossing the spread.

Another significant problem in his model is that this is not so much an exogenous cost born by HFT LPs, just an intra-HFT transfer. Only a dozen firms dominate HFT, as is usual in elite competitions. Those playing the game are taking and posting resting limit orders probabilistically. Such an order may be taken by a retail rube immediately, sniped by an HFT, and sometimes, their bid will sit there, and the price will move, and then they will become the top of a large queue, the perfect place for a positive expected value order. If you only count those times they get picked off as a loss and consider that an exogenous expense to be eliminated, you are simplifying the game in a way that mischaracterizes it completely.

His batch auction alternative is efficient when one thinks about a one-period scenario where people have private valuations for an object. With repeated auctions for equities, we must incorporate the complexity of updating valuations based on other valuations, inventory situations, and time preferences. As the other players are doing the same thing, we must update the priors of other people's priors, ad infinitum. There is also the possibility of collusion, like playing poker with two players sharing information, which would radically alter one's interpretation of market orders. His simple model is an excellent way of illustrating a particular problem, but to presume this is sufficient justification for a policy suggestion, let alone a radical new regulatory mandate, is absurd. The state space quickly becomes beyond any closed-form solution.

He also says the market can't fix itself like it's stuck in the bad Nash equilibrium and mentions two examples. First, he objects to letting the broker get two cents for their trades from an HFT who processes the orders rather than an explicit two-cent fee charged to the retail trader. The broker gets two cents in either case, but the trader may feel like he is getting a better deal. Retail flow is considered uninformed, as it will always have high latency, so HFT LPs can assume it is not filled with adverse selection and charge a lower spread, creating positive gains from trade. Allowing the broker to swap an explicit fee for an implicit fee via the rebate given by HFTs is an efficient way to capture this. His example of an HFT problem is the sort of fix markets make.

Budish also mentions co-location as a cost of HFTs because many millions are spent by HFTs wishing to be the fastest. This is perverse because providing privileged but open access, where everyone is treated the same, down to a couple of nanoseconds, is undoubtedly more efficient than distributing this privilege off the books. The latency advantage will exist in any modestly continuous market, so the question is how to administer this. Backroom deals encourage corruption and are cancerous. What Budish presents as a problem and something markets cannot fix is actually an efficient market solution. He has it backward.

During the 90 years of bid-ask stasis, the country was transformed by the telephone, radio, and TV, which radically altered the speed of information flow across the country. Yet it was only with the internet that outsiders could create an alternative to the closed, heavily regulated specialist equity trading system. Consider the NYSE's alternative, Nasdaq, was found to collude, quoting highly liquid stocks in ¼, ½, etc., but rarely, 1/8, 3/8, etc., artificially increasing the bid-ask spread. There were more Nasdaq dealers competing for quotes than on the NYSE, but the NYSE was a more efficient mechanism. Those just counting the number of players, as many naively do (Herfindahl index, Nakamoto number), would have never guessed that. Such are the game theoretic equilibria in complicated real-world games.

Instead, Budish emphasizes state coercion, ignoring the precedent of a 90-year regulatory-enforced inefficient market. In his paper, Will the Market Fix the Market, he favorably quotes a top regulator for writing, "Without changing [the] incentives, we cannot and should not expect the market to fix the market." This naïve and hubristic view is natural because big institutions are not going to fly him around to tell them that markets are doing well, though there's an edge case where you get adverse selection without asymmetric information. He created a model that theoretically proved a new inefficiency exists, and he also empirically proved billions of dollars in waste. 

Luckily, this policy does not look like it is gaining ground, as Taiwan recently moved away from a batched auction market to a standard CLOB. A simple solution, liberty, implies its best if we generally ignore economists when they come up with specific policies.