Dark pools are Alternative Trading Systems (ATSs) that do not provide their best-priced orders for inclusion in the consolidated quotation data. They offer subscribers venues where anonymous, undisplayed orders interact away from the lit market yet execute at prices no worse than the National Best Bid Offer (NBBO). Dark pools today represent a considerable fraction of volume (Fig. 1). In the U.S. there are over 50 dark pools, and the 19 of them for which data are available (from Rosenblatt Securities Inc.) account for more than 14% of consolidated volume. In Europe the 16 dark markets which report to Rosenblatt account for approximately 4.5% of volume, and in Canada they represent 2% of volume. The most active types of dark pools in the U.S., Europe, and Canada are Bank/Broker pools followed by Independent/Agency pools (Fig. 1). The Bank/Broker pools are operated by banks and are used both for agency and proprietary trading. These pools generally offer continuous execution and execute at prices derived from the NBBO. The Independent/Agency pools, like ITG POSIT, are instead operated by agency brokers and offer periodic executions at the midpoint of the NBBO. In Market Maker pools, liquidity can only be provided by the manager of the pool. Consortium-Sponsored pools are owned by several banks which already own their dark pool and use the Consortium Sponsored pools as trading venues of last resort. Finally, Exchange-Based dark pools are owned by exchanges and offer continuous execution.
The rising market share of dark trading recently prompted three major U.S. exchanges to publicly urge the Securities and Exchange Commission (SEC) to put rules in place to curb dark pool trading. Exchange officials are concerned that dark pools divert volume away from lit venues, rather than attracting new order flow to the market. With declining trading volumes worldwide, such a diversion of order flow is a real threat to exchanges’ bottom lines. Consequently, it is important for exchanges to understand which factors cause order flow to go dark, and under what circumstances dark pools are likely to primarily divert volume away from lit venues as opposed to create more opportunities for trades to take place. Regulators are concerned about the effects of dark trading on market quality and welfare. Order migration away from lit markets to dark pools may adversely influence the incentive for traders to provide liquidity in the lit market, potentially resulting in higher trading costs. Dark pools may also affect the distribution of welfare between retail and institutional investors, as dark venues are primarily used by institutional traders.
In this paper we build a theoretical model that enables us to address the concerns raised by exchanges and regulators in a realistic market setting. Specifically, we populate our model with fully rational traders who form their optimal trading strategies based on their private valuations. All traders in our model can choose to submit a one-share market or limit order to a transparent limit order book (LOB) with a discrete price grid. In addition, some traders may submit orders to a dark pool. If sufficient two-sided trading interest is routed to the dark pool, orders are executed at the midquote of the prevailing NBBO. The dark pool executes orders continuously, meaning that traders with access to the dark pool can simultaneously access the lit and the dark markets. To model this simultaneous access, we introduce an additional order type, Immediate-orCancel (IOC) orders. These orders are first routed to the dark pool, and if they do not execute are routed back to the lit market as a market order. Our model closely resembles real world order book markets competing with Bank/Broker dark pools, and this group of dark pools executes 57%, 67%, and 87% of dark volumes in the U.S., Europe, and Canada, respectively (Rosenblatt Securities Inc.,2012). We use this rich setup to address the concerns raised by exchange officials and regulators, market participants, and media about order migration, market quality, and welfare.
Our theoretical model builds on Parlour (1998), but in the spirit of Buti and Rindi (2013) we extend her model to include a price grid, a dark pool, and additional order types. We also differentiate between traders with and without access to the dark pool. We start by modeling a benchmark LOB where traders decide whether to submit a market order, a limit order, or to refrain from trading based on the information they infer about future execution probabilities from the current state of the LOB. The model runs for four periods, and the LOB starts empty. We then introduce a dark pool which also starts empty, accepts orders from traders with access, and attempts to execute submitted orders continuously at the prevailing LOB midpoint. Note that the opacity of the dark pool effectively works as a friction in that it adds an inference problem to the traders’ optimization problem. Traders with access cannot see orders resting in the dark pool, and also do not know what the execution price will be for an order sent to the dark pool as it depends on the state of the future LOB. Hence, traders use the lit LOB to make inferences about the potential price improvement (midquote price) and the execution probability in the dark pool compared to the trading opportunities on the LOB.
By comparing results from the benchmark LOB model without a dark pool to the results from the model with a LOB competing with a dark pool, we are able to address the concerns raised by exchange officials and regulators discussed above. We show that the introduction of a dark pool to a LOB market results in higher consolidated fill rates, but also higher LOB fill rates. We also show that the higher LOB fill rates are associated with wider LOB spread and lower LOB depth. The intuition for this result is that the consequences for LOB fill rates and market quality of the introduction of a dark pool depend on whether it is predominately traders that would have used limit orders or market orders that go dark. When the LOB starts empty traders are more likely to use limit orders, and it is therefore predominantly limit orders that migrate to the dark venue. Moreover, everyone knows that the dark pool traps market orders submitted to the lit market, and since this means that the execution probability of limit orders in the LOB declines, traders remaining in the lit market on the margin switch from limit to market orders. As a result of both these effects, LOB liquidity supply declines and LOB fill rates increase causing spreads to widen.
It follows that our model suggests that exchanges are actually better off in the presence of dark pools because the higher fill rate allows them to harvest additional trading fees. However, since the increase in fill rates is associated with a wider LOB spread and lower LOB depth, the concerns raised by regulators that dark trading may undermine the liquidity of the lit market book are warranted. Note that the reason for lit market depth to decline and spreads to widen is that traders use more marketable orders, resulting in higher fill rates. Our model therefore illustrates that there is a trade-off between displayed liquidity and trading volume. Ultimately, the question then becomes whether traders are better or worse off. We find that while the fill rate increases, this occurs at worse trading conditions and as a result welfare both for traders with and without access deteriorates.
We derive cross-sectional predictions for our model by varying the model parameters. Dark pool activity is decreasing in the dispersion of valuations around the common value of the asset, and the effects of dark pool activity on LOB and consolidated fill rates, market quality, and welfare are weaker when the dispersion in traders’ valuations is larger. Not surprisingly, dark pool activity is increasing in the proportion of traders with access, and dark pool activity is associated with a stronger positive effect on LOB and consolidated fill rates, but also a stronger adverse effect on spread and depth when more traders have access to the dark pool. Finally, dark pool activity decreases when the stock price is higher and therefore the relative tick size is smaller, and the effects of dark pool activity on LOB and consolidated fill rates, market quality, and welfare are weaker when the relative tick size is small.