Alex Boulatov and Thomas J. George
Hidden and displayed liquidity in securities markets with informed liquidity providers
Review of Financial Studies | Volume 26, Issue 8 (Aug 2013), 2096–2137

Competitive pressure from dark pools has led securities exchanges to offer a variety of ways by which traders can hide orders that provide liquidity. These are the price-contingent orders (limit orders) that aggregate to the market's supply schedule, and against which orders to trade at the market price (market orders) are executed. Hidden orders account for about 30% of transaction volume on some exchanges, and their proliferation raises questions for exchanges and regulators concerning the effect of hidden orders on market quality. In classic microstructure models, adverse selection arises because informed traders can conceal their market orders among the orders of the uninformed. The intuition from these models suggests that explicitly allowing hidden orders will increase adverse selection and the losses suffered by uninformed traders.

We show that the opposite happens when informed traders can choose between providing liquidity by submitting limit orders and demanding liquidity by submitting a market order. In our model, a market with hidden orders imposes smaller losses on the uninformed and has more informative midquotes than a market in which orders that provide liquidity are displayed. This happens because informed traders are drawn into liquidity provision by the incremental profit associated capturing the bid-ask spread when orders are hidden. When orders are displayed, however, some informed traders are deterred from providing liquidity because display expropriates their informational advantage. Competition is more intense when more traders provide liquidity, so the losses to the uninformed are less and prices are more informative when orders are hidden than when they are displayed.

Our model

Our model resembles Kyle (ECTA 1985) and Kyle (RES 1989). It features M risk-neutral strategic informed traders who each observes vi, a component of the security's payoff v = v1 + … + vM. There is no competitive market maker, however. Instead, liquidity provision is endogenous. The informed traders choose whether to provide liquidity by placing a price-contingent supply schedule into the order book (a bundle of limit orders), or to demand liquidity by submitting a market order that executes against the book. There are also uninformed liquidity traders who submit net market orders of u. All the random variables are mutually independent and normally distributed.

Each informed trader selects his order to maximize expected profit conditional on the order type he chooses. The number of traders who choose to provide liquidity in equilibrium, J*, is such that no informed trader can earn greater expected profit by switching his order type. This structure is novel and, we believe, unique to our model. It allows an endogenously determined number of informed liquidity providers and informed liquidity demanders to coexist in the market. In addition, the model can be solved in closed form for an equilibrium with linear strategies that is unique in the linear class.

We compare the equilibria in two market structures. In the first, orders that provide liquidity are hidden from view. In the second, those orders are displayed to market-order traders who observe the contents of the book before choosing their orders. In both market structures, the informed are drawn into liquidity provision to capture rents to providing liquidity—i.e., to earn the bid-ask spread.

Competition is more intense when orders are hidden

When the book is hidden, these rents draw all the informed into trading as liquidity providers, J* = M. It turns out that competition is more intense among the informed when they trade as liquidity providers than when they trade as liquidity demanders. In the former case, they compete on quantity at every price point, whereas in the latter case they compete on only a single quantity across all prices. As a group, the informed would be better off if some could be constrained away from providing liquidity to limit the intensity of competition. But it is not individually rational for any one of them to forgo the rents to liquidity provision. This implies that across all possible allocations of informed traders to order types, the allocation that arises at equilibrium in a market with hidden orders minimizes the expected losses of the uninformed.

When the book is displayed, liquidity demanders can infer some of the private information possessed by liquidity providers. This expropriates informational rents from the informed who do trade as liquidity providers, which in turn deters some of them from providing liquidity. Informed trader participation shifts away from the liquidity-provision side toward the liquidity-demand side of the market (i.e., J* < M) as depicted in Figure 2 in the paper. This shift reduces competition overall resulting in greater expected losses to the uninformed and less informationally efficient midquotes than if all the informed were to trade as liquidity providers. Consequently, market quality is worse in the market with displayed orders than in the market with hidden orders.

Rents to providing liquidity draw the informed into trading aggressively. Because rents tend to disappear as markets grow, one might expect the difference in market quality between the hidden and displayed market structures to disappear as the market grows—i.e., as M → ∞. However, the differences persist because, as the market grows, traders adjust their trading intensity to account for the size of the market. Display continues to provide a deterrent to liquidity provision, and the differences between hidden and displayed markets remain even when M is large.

The formulas that describe large markets turn out to be quite simple. When orders that provide liquidity are displayed, J* = M – M1/3; whereas J* = M when orders are hidden. This means display deters M1/3 of the population of informed traders from providing liquidity even when the market is large.

Display deters liquidity even when the market is large

This shift away from liquidity provision affects the intensity of competition even though the market is large. Informed traders who provide liquidity in a displayed market submit orders that are only a fraction of the quantity that are submitted in a market with hidden orders. This fraction is approximately equal to 1 / (M – M1/3) in a large market. For example, when M = 100, the informed submit orders to a displayed book that are only 1/95th as aggressive as the orders they would submit to a hidden book.

The impact on market quality is simple to characterize as well. As the market grows large, the magnitude of the expected loss of the uninformed traders grows in both markets, and remains greater by a factor of 2⋅ M1/6 in the displayed market. The uninformed losses arise from transaction prices that deviate from fundamental value. Even in large markets, transaction prices depart more from fundamental value when orders are displayed than when orders are hidden.

Similarly, display discourages the incorporation of information into the midquote through the orders submitted by the informed into the book even when the market is large. We characterize this by the squared correlation (R2) between the market-clearing price and order flow. In a large hidden market, half of the variability in prices is attributable to information impounded into the price schedule by informed orders that provide liquidity. The other half is attributable to the noise from uninformed trading that affects prices through order flow, and R2 = 0.5. In a large displayed market, the aggressiveness of the orders submitted by informed liquidity providers decreases so much that the variability in prices attributable to these orders vanishes. In this case, all the variation in prices is attributable to the informed who trade as liquidity demanders and the noise generated by uninformed trading, and R2 = 1.

The paper closes by demonstrating that the relevance of whether orders are hidden or displayed relies on traders having heterogeneous information. If all the informed observe the same signal, then the orders that provide liquidity are so aggressive that the common signal is fully priced into the order book. In this case, the informed derive no expected profit from their information even when orders are hidden, so there is no deterrent associated with display. The informed still earn expected profit from their role as liquidity providers. However, the equilibrium strategies of the informed and measures of market quality are unaffected by whether information is hidden or displayed.

Bellini (1430–1516): Madonna of the Meadow. Italy, 1500.. Can you imagine a highly reputed drawing and painting workshop in Venice in the 15th century, where the apprentices were busy churning out images of Madonna, under the direction of none other than Bellini? Bellini is considered to be the father of Renaissance painting, creating brilliant shades with the newly-perfected art of oil painting. The Madonna seems psychologically distant from the baby Jesus. This painting hangs in the National Art Gallery in London.

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