Milky Eggs

Lessons from Citadel’s “Market Lens” reports

Citadel Securities, one of the world’s preeminent market-making firms, occasionally publishes short reports as part of an ongoing “Market Lens” series. Although relatively short, they are easy to read and contain interesting and unique analyses which are probably difficult for non-HFT entities to reproduce. For example, they discuss topics such as the effect of tick size on bid/ask spreads, HFT overall on market liquidity, continuous trading vs. frequent batch auctions, and so on. Below, I will briefly highlight several interesting points from each of their publications.

Continuous trading vs. frequent batch auctions

In Why Do Most Markets Trade Continuously Rather Than In Auctions?, the authors present empirical data on the effects of switching between continuous trading and frequent batch auctions. There has been a rich theoretical debate about the benefits of each market type, with some suggesting, for example, that frequent batch auctions might reduce deadweight loss from zero-sum latency competitions between HFT firms (Budish et al., 2015). However, as most exchanges currently operate on a continuous trading basis, there is relatively little empirical data available to help resolve this debate.

Notably, the authors study the Taiwan Stock Exchange, which in March 2020 switched from a frequent batch auction process to a continuous trading model. Overall, they find that the change increased order book depth (especially for the most highly traded stocks), lowered bid-ask spreads, and reduced price volatility, suggesting that continuously trading markets are not just beneficial to highly capitalized trading firms but also to the general investing public.

The authors find that the depth of available liquidity at a fixed distance away from the bid/ask midpoint was much higher after the switch to continuous trading than before. They use the Hong Kong stock exchange as a control, noting that there was no discernible improvement in liquidity depth after March 2020 there. They also find that the improvement in the graph above is even more pronounced for the most highly traded stocks.

Relative to the Hong Kong stock exchange, they also find that the volatility of the Taiwan stock exchange decreased by 18% after the introduction of continuous trading.

Overall, the authors calculate the net benefit to Taiwanese investors (resulting from increased liquidity and lowered bid-ask spreads) as $550 million to $1.36 billion TWD.

Market structure and equities liquidity

In Has Market Structure Evolution Made Equities Less Liquid?, the authors study the evolution of liquidity in the equities market over the course of the 2010s. The article is framed as a response to claims that structural changes, such as regulations curtailing the ability of banks to engage in market-making activities or the rise of electronic, high-frequency trading firms, have caused equities markets to become more fragile and played a role in the resurgence of market volatility.

In general, the authors ask the following question: for a trade of varying size $X, what is the effective spread paid by that trade, if one assumes that the trade is directly executed against all liquidity displayed in the order book at a given time?

At a high level, these “size-adjusted spreads” have not changed dramatically over the last decade either for the S&P 500 or for the Russell 2000. Although the spreads tend to increase commensurately with spikes in the VIX, these data do not suggest any sort of fundamental reduction in the depth of market liquidity. (A comment from me: In fact, perhaps one could argue that the depth of market liquidity is understated by these plots. If high-frequency trading firms have become increasingly dominant over time, and they are very skilled at inserting or cancelling orders at rapid timescales, then it is plausible that the amount of “hidden liquidity” not visible in the order books but still accessible to large, uninformed trades has increased over time.)

The authors go on to analyze several specific equities, for example:

In the case of $BAC (Bank of America), the quoted spread has stayed at approximately 1 cent (the regulatory minimum) throughout the 2010s. Given that the share price has increased by a factor of 6 over that time period, that also means the bid/ask spread in basis points correspondingly decreased by a factor of 6. Commensurate with this reduction in bid/ask spread, we see that the size-adjusted spread for small transactions ($1M or below) has decreased over time, although interestingly this is not the case for $10M transactions.

One can make two interesting observations from this graph. First, there has been a “compression” of liquidity toward the midpoint, with significant benefits accruing to investors trading in smaller size. Second, although the actual size-adjusted spread paid by a $1M transaction has decreased over time, the gap between the size-adjusted spread and the NBBO has actually widened. The authors speculate that this may be one reason why people believe (mistakenly in their view) that liquidity in the markets has worsened. If one looks solely at the amount of size posted in the order books, liquidity may appear to have diminished; however, if one looks at the liquidity available at a fixed distance from the midpoint, liquidity has in fact increased substantially over the last decade, at least for $BAC.

Another very interesting case study is $AAPL (Apple), which performed a 7-for-1 stock split in July 2014. Interestingly, upon doing so, the bid/ask spread fell from 10 cents to the regulatory minimum of 1 cent, which is greater than the 7-fold reduction that one might naively expect to follow from the stock split. The authors speculate that this is because the stock split reduced the total dollar size of a round lot of 100 shares from approximately $70k to $10k, reducing the overall level of risk for market makers when quoting spreads for a round lot. As such, given that the market structure is based on the display of quotes for round lots of 100 shares, extremely high-priced shares may benefit substantially from large stock splits.

One final example the authors study is $NWS (News Corp), which was a randomly selected ticker included in the Tick Size Pilot program run by the SEC from October 2016 to October 2018. The program enforced a minimum tick size of 5 cents, which dramatically increased size-adjusted spreads for trades of sizes as low as $10k to a degree that enormously overshadowed all price-related fluctuation. In a sense, this data may be interpreted as causal evidence that the progressive reduction in quoted spreads previously observed for $BAC (in basis points) was directly responsible for the reduction in size-adjusted spreads over the same time period.

Overall, the authors conclude that there is no evidence that market structure or liquidity have been adversely affected over the 2010s. In fact, their findings suggest that competitive, high-frequency electronic trading, a strong competitive process that drives down quoted spreads, may contribute to better liquidity and lower size-adjusted spreads.

Order cancellation

In Why Restricting Cancel Rates Can Increase Bid-Ask Spreads, the authors discuss the phenomenon of high order cancellation rates by modern, high-frequency electronic market makers. In general, they argue that rapid cancellation is part of a market maker’s risk management strategy ー for example, if the price appears to be increasing substantially, the market maker will wish to cancel their stale asks as fast as possible.

Restrictions on order cancellation rates have occasionally been proposed. However, in the diagram above, the authors illustrate how such restrictions would result in an increase in bid/ask spreads. If a market maker has tight spreads but restricted cancellations (Panel 1), they will effectively end up buying when prices go down and selling when prices go up, resulting in substantial inventory risk and poor expected value. If the market maker then widens their spread, as in Panel 2, we see that the number of trades also declines substantially, resulting in impairment of both price discovery and liquidity. However, if the market maker is allowed to cancel orders without restriction, they can manage to quote a tight spread (Panel 3) without exposure to the adverse selection faced by the market maker in Panel 1.

Two concrete examples are provided to illustrate the relationship between order cancellation and liquidity.

In 2016, the SEC introduced the Tick Size Pilot program, in which randomly selected stocks had their minimum tick size (and, therefore, minimum quoted spread) increased from 1 to 5 cents. Almost immediately, the rate of order cancellations declined by ~20%. (There is a slight lag due to varying start times for different stocks in the program and other such implementation details.) When the TSP was ended, spreads immediately dropped while cancellation rates went back up to the same levels as the control group. Overall, these results suggest that there is a direct inverse relationship between the size of bid/ask spreads and the rate of order cancellations, and that restricting cancellation rates will result in an adverse effect on spreads.

Evofem Biosciences ($EVFM) is presented as a second and particularly interesting test case. Regulation NMS, introduced in 2005, contains a rule known as the “Sub-Penny Rule,” which holds that if a stock trades at $1 or above, its minimum quotable price increment is 1 cent, but if a stock trades below $1, its minimum quotable price increment is 1/100th of a cent. Therefore, when the price of a stock fluctuates above and below $1, its bid/ask spreads may also vary dramatically according to that fluctuation.

In May 2021, the price of $EVFM suddenly dropped from above $1.28 to $0.84 overnight. Immediately upon doing so, spreads collapsed from 80 basis points all the way to 5-10 basis points, while cancellation rates increased ~50%. Subsequently, less than a month later, the price of $EVFM moved back above $1, and cancellation rates quickly returned to their original levels after several days. While the period of time under study is relatively short, these data also support a causal and inverse relationship between the size of a bid/ask spread and the rate of market makers’ order cancellations.

The authors conclude that both of these examples demonstrate the beneficial nature of allowing high order cancellation rates. Doing so enables market makers to quote tight spreads, saving investors substantial amounts of money and improving the market’s price discovery.

Minimum tick size

In Unlevel Playing Field? What 605s Can Tell Us About Tick Sizes, the authors address the question of whether or not the minimum quoting increment should be reduced. They recommend that when stocks are “tick constrained,” i.e. when they are frequently quoted with a one-cent spread, the minimum quoting increment should be reduced to half a penny to allow market participants to quote even tighter spreads.

They also respond to the claim that all stocks, even those with spreads much larger than one cent, should have their minimum tick sizes reduced. The authors claim that this is not necessary, because the limiting factor to tighter spreads for these stocks is not the minimum quoting increment. Using Rule 605 execution-quality reports, the authors supply data to show that off-exchange venues such as Citadel Securities are not unfairly benefiting from an ability to execute “between the ticks” relative to exchanges such as the NASDAQ or NYSE.

When looking at order execution data for all stocks, we see that Citadel Securities offers substantial price improvement to traders, resulting in one of the lowest effective spreads in the industry, resulting in net savings of half a billion dollars for retail investors in the first half of 2022. However, when considering minimum tick sizes, it is more interesting to restrict the data to the top 50 stocks by volume, which generally trade with much greater spreads:

Here, we see that the gap between Citadel Securities and the listed exchanges (in terms of their effective spread) is even more dramatic. Crucially, the ability of exchanges to offer better price improvement is not constrained by the minimum tick size of one penny. For these stocks, Citadel Securities offers nearly 10 cents more price improvement per share than the exchanges; correspondingly, the exchanges have ample room to offer price improvement of far more than 1 cent to compete with Citadel. However, they have not done so, suggesting that factors other than the minimum tick size is not a constraining factor with respect to their offered price improvement.

Overall, even when looking at the subset of the top 50 traded stocks with quoted spreads greater than 20 cents, where spreads are not constrained by the one-penny increment and price improvement is supplied at 5 or even 10+ cents by Citadel, we see that exchanges are unable to execute trades at prices that are competitive with Citadel. As such, the authors conclude that the differences in execution quality arise not from any “unlevel playing field” in which off-exchange venues are able to execute “between the ticks,” but instead due to other factors such as order flow segmentation. Given the risks of lowering the minimum quoting increment where it does not intrinsically limit the quoted spreads, such as “flickering quotes, reduced liquidity, higher transaction costs, and potentially increased fragmentation,” the authors recommend that the minimum quoting increment only be lowered for “tick-constrained” stocks.