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Implications of Alternative Trading systems on Price Discovery: Dark Pools

Updated: Dec 4, 2023

In the recent past there has been a growth in alternative equity trading platforms, with dark pools notably increasing in prominence and popularity. The concept priorly disclosed refers to private exchanges or forums where securities are interchanged, exclusively accessible to Institutional Investors. Several factors support the establishment of these alternative trading platforms, including confidentiality, the ability to trade sizable blocks of financial instruments without major market disruption, enhanced pricing, reduced market chatter, and concerns about liquidity. Consequently, it's clear that such an exchange platform is distinct from traditional stock exchanges, often termed "lit pools." This difference arises from the accessibility of these venues to retail investors and the public display of orders and quotes, ensuring transparency for market players. A "lit market" is an exchange inspired by the framework presented by Glosten and Milgrom [1985]. The academics outline a system in which market makers determine bid and ask prices, particularly when there's potential to trade with parties possessing superior information. Their paper, titled “Bid, Ask and Transaction Prices in a Specialist Market with Heterogeneously Informed Traders,” incorporates elements like:

  1. Information Asymmetry.

  2. The establishment of a spread between bid and ask prices by market makers as a safeguard against potential losses from trading with well-informed participants.

  3. Market makers' adjustments to an asset's theoretical value based on the nature of incoming trades.

In a Lit Pool, a risk-neutral Market Maker oversees trades. At the initial stage 0, the market maker sets and pledges to a bid and ask price for the uncertain asset, determined solely by publicly available data. Given the balance of v, there can't be any misquote, so it remains at zero. The ask price and bid price are then, respectively, A(> 0) and −A. Thus, we refer to A/sigma as the “normalized half spread.” Assuming the actual asset value to be sigma, let ye,ye hat, denote the proportions of informed speculators placing "Buy" and "Sell" orders in period 1. Let alphae represent the percentage of uninformed liquidity traders participating in the exchange. Assuming no order splitting across venues, the subsequent reward for the market maker is,

The initial term represents the market maker's profit from the asset, comprising the net earnings from informed traders, yeu-yeu hat , and the net gains from uninformed traders, aeZ--aeZ+ . The subsequent term reflects earnings from the transaction fee (spread) for each trade. If the asset's realized value is −sigma, the market maker's reward will mirror the above due to symmetry. We also denote ye hat as the percentage of informed traders profiting (trading in the favorable direction) and ye as the percentage making losses (trading unfavorably).

The market maker aims to balance out profits and losses over time. That is,

Since EZ+=EZ-=1/2uz, the Market maker’s objective becomes,

Implying that,

By the conclusion of period 1, a closing price,

determined by observed "Buy" and "Sell" volumes , Vb Vs is determined.

In period 2, the market maker's earnings are null since the value of v is already disclosed, and all transactions will occur at the price corresponding to that disclosure.

On the contrary, trading within a Dark Pool involves a pricing system that determines how orders are executed, as well as a mechanism detailing the matching of buy and sell orders. The emphasis is on the midpoint pricing method, wherein the Dark Pool's orders intersect at the bid-ask midpoint in the exchange, previously established as 0. Hence, while traders are subject to transaction costs A on the exchange, in a Dark Pool, this cost is minimized to 0.

We examine a rationing mechanism for order execution. Orders on the shorter side are always executed, while those on the longer side are executed based on probability to equilibrate the market. Given a realization of v as sigma, consider Yd hat and Yd as the proportions of informed traders who trade correctly and incorrectly, and alphad as the portion of uninformed traders in the dark pool. The anticipated execution rates for correct and incorrect trades are:

Where, as we said,

Such execution mechanism reflects an execution risk, a disadvantage of trading in a Dark Pool. In contrast, a Market Maker in the exchange can provide certainty of execution.

Where, as mentioned,

This execution method indicates a risk in execution, a drawback of trading in a Dark Pool. Conversely, a Market Maker in the exchange offers assured execution.

Later in this article, we'll demonstrate that the Dark Pool isn't exempt from information imbalances, indicated by Yd hat > Yd. Consequently, R<R hat, suggesting that orders aligned with the correct trend face a reduced chance of execution compared to those going the opposite way. From this, we deduce the Dark Pool Adverse Selection cost as (R hat-R)sigma, terming (R hat-R) as “normalized dark pool adverse selection cost.”

In our earlier statements, we have aligned with Zhu's (2014) assertion that Dark Pools primarily enhance price discovery, in other words the process of determining the spot price, or the proper price of an asset, is augmented. Despite some academic research presenting opposing viewpoints, as exemplified by Ye (2017), who suggests that in theoretical studies, the inclusion of Dark Pools inherently hinders price discovery. Hence, it is evident that there exist divergent empirical findings that lend credence to these distinct predictions.

From what has been previously stated many advantages as well as disadvantages occurring from the use of Dark Pools can be spotted:

· Advantages:

o Anonymity, long regarded as one of the primary benefits of Dark Pools, enables Institutional Investors to transact significant volumes of securities without divulging their positions to the broader market, thus averting adverse price movements.

o Reduced market impact, owing to the covert nature of dark pools, substantial orders do not have an immediate impact on stock prices, as they remain hidden from public view.

o Potential for improved pricing, as dark pools frequently execute trades at the midpoint between the bid and ask prices, traders have the opportunity to attain more favorable prices compared to public exchanges.

o Cost-efficiency, by bypassing public markets, traders can at times circumvent certain fees and expenses associated with those exchanges.

o Versatility, ensured by Dark Pools, offering distinctive order types and matching rules customized to the preferences of their participants.

· Disadvantages:

o Lack of transparency, Dark pools inherently lack transparency, raising concerns about the potential for unfair advantages among certain traders.

o Uncertain Execution, in other words there is no assurance that orders placed within a dark pool will be executed, as it relies on finding a suitable match within the pool.

o Counterparty risk, the limited transparency can also elevate the risk of trading with an unreliable counterparty.

o Potential for price manipulation, due to the reduced oversight compared to public exchanges, there exists the possibility of price manipulation or other unjust trading practices.

o Adverse selection, as informed traders may also operate in dark pools, creating a risk that uninformed traders consistently trade against those with superior information, resulting in potential adverse selection costs.

o Regulatory concerns, Dark pools are subject to regulatory scrutiny, and there are concerns about their impact on price discovery in public markets.

Types of Dark Pools and Practical examples:

Various categories of Dark Pools exist, each distinguished by distinct objectives and operational characteristics. Specifically, the types include:

1. Broker-Dealer-Owned Dark Pools: These are proprietary exchanges predominantly owned by large broker-dealers, inclusive of their proprietary trading factions. Such platforms determine their pricing based on order flow, thereby incorporating an element of price discovery. The primary rationale behind the establishment of these Dark Pools was to facilitate the matching of orders from the broker's clientele, typically circumventing the need to route orders through public markets. This strategy results in a reduction in exchange fees and diminishes market impact. Consequently, these pools often exhibit a considerable proportion of non-displayed or "concealed" orders and employ sophisticated algorithms to locate liquidity prior to directing the order to the conventional market. Renowned instances of this category include Sigma X, an internal pool of non-displayed liquidity by Goldman Sachs; Citi-Match, Citibank's exclusive pool; and the MS Pool, provided to institutional clientele by Morgan Stanley.

2. Exchange-Owned Dark Pools: These platforms are exclusively owned by established public exchange conglomerates and function in an agency capacity rather than a principal role. The pricing in these pools is directly sourced from established exchanges, employing methodologies such as deriving from the midpoint of the National Best Bid and Offer (NBBO), or orders are executed at VWAP. Consequently, there is an absence of price discovery in these platforms. The primary objective of these specialized exchanges is to furnish clients with conventional trading modalities and functionalities. Through the ownership of such Dark Pools, agencies endeavor to secure a fraction of off-exchange trading volumes. While it might appear that they present matching opportunities akin to Broker-Dealer-Owned Pools, these platforms are more intricately integrated with the systems of public exchanges, affording participants augmented options for order routing and execution. Notable examples within this category encompass Instinet — an agency broker that features CBX, a continuous dark pool, alongside a succession of intraday point-in-time crosses constructed to amass flow at designated intervals. Other prominent instances include Instinet, Liquidnet, ITG Posit, BATS Trading, and NYSE Euronext.

3. Electronic Market Maker Dark Pools: Operated by autonomous electronic market entities, these platforms have operators acting as principals for their proprietary accounts. Unlike the straightforward NBBO-derived pricing in some other pools, these platforms engage in price discovery. Crafted to provide traders with avenues to transact outside traditional public exchanges, they capitalize on the advanced trading prowess of the electronic market maker. This is accomplished through the deployment of intricate algorithms coupled with high-frequency trading techniques. Participants frequenting these pools often prioritize swift execution and might engage in trades where the electronic market maker stands as the direct counterparty. Renowned entities offering these specialized private exchanges include the likes of Getco and Knight.

Do Dark Pools improve or harm Price Discovery?

As priorly mentioned, the academic realm holds divergent views concerning the influence of Dark Pools of liquidity on Price Discovery. Zhu [2014] was the pioneer in releasing empirical research supporting the notion that such Private Exchanges enhance Price Discovery. This stood in contrast to several central institutions' viewpoints. For instance, the European Commission [2010] noted, “… an increased use of Dark Pools… raises regulatory concern as it may ultimately affect the quality of the price discovery mechanism on the ‘lit’ markets.” Institutions like the International Organization of Securities Commission [2011], CFA Institute [2009], and SEC [2010] express congruent concerns about the detrimental effects of Dark Pools on Price Discovery. Zhu [2014] constructed a strategic venue selection model that caters to informed and liquidity traders. The former aim to capitalize on specific knowledge about the worth of traded assets, while the latter seek to address their unique liquidity requirements. These traders judiciously select between a traditional exchange venue and a private Dark Pool. The exchange showcases a bid and an ask and processes all incoming orders at either the bid or ask rate. The dark pool, on the other hand, leverages exchange prices to match orders within the exchange's bid and ask parameters. However, unlike the exchange, the dark pool lacks market makers to handle surplus order flow, making execution uncertain. Hence, placing an order in the dark pool is a balancing act between potential price gains and the possibility of non-execution.

Zhu [2014] proposes a model where two periods are taken in consideration, t=1, 2. At the end of period 2, an Asset pays an uncertain dividend v that is equally likely to be sigma or -sigma, where sigma is the volatility of the asset value, being displayed at the beginning of period 2. In such model 2 venues operate in parallel, a Lit Exchange and a Dark Pool. Previously it was displayed how the equilibrium status in the Lit Exchange is achieved, taking in consideration a model similar to that of Glosten and Milgrom [1985].

Given what was show above, for both Dark Pools and Lit Exchanges. Zhu [2014] formulates a proposition, that there exists a unique threshold volatility such that:

Some properties characterizing the first equilibria stipulated in proposition 1, found by Zhu [2014] answer two questions on which the academic interrogates, the first aims at determining how do market characteristics vary with the value sigma of private information. While, the second aims at determining how adding a Dark Pool influences market behavior.

Zhu [2014] formulates two further propositions in light of preposition 1:

1. Based on Proposition 1, Proposition 2 states that when volatility (sigma) is less than or equal to a certain level (sigma hat), three outcomes occur: (1) the rate at which liquidity traders participate in dark pools (alphad), (2) the aggregate number of informed traders (u), and (3) the relative exchange spread (S/sigma) all strictly increase as volatility (sigma) increases. Conversely, the rate at which liquidity traders engage with traditional exchanges (alphae=1-alphad) strictly decreases as volatility (sigma) rises. Additionally, the parameters, alpha, u and S not only vary smoothly but can also be differentiated with respect to volatility (sigma). Furthermore, for sigma > sigma hat, the parameters representing the total number of informed traders (u), the product of the informed traders' aggressiveness and their total number (beta u), the positive part of the expected return (r+), and the scaled exchange spread (S/sigma) all show a strict increase with rising volatility. Conversely, the dark pool participation rate of liquidity traders (alpha) and the negative part of the expected return (r-) show a strict decrease with rising volatility. These parameters Beta, alpha d, u, S, r+, r- ,are also smooth functions of volatility and can be differentiated with respect to sigma. In a market without Dark Pools,u and S/sigma still strictly increase with , while the exchange participation rate of liquidity traders (alpha d) strictly decreases. The functions α alphae, u and S maintain continuity and differentiability with respect to sigma.

2. Drawing on Proposition 1 and assuming an equilibrium in a market bereft of Dark Pools, a new proposition suggests that when volatility (sigma) is less than or equal to a specified level (sigma hat), the introduction of a dark pool unequivocally lowers the rate at which liquidity traders participate on traditional exchanges (alpha e) and the aggregate number of informed traders (u). The presence of a dark pool also definitively raises the exchange spread (S) and the combined participation rate of liquidity traders (alpha e + alpha d) across both venues.

Conversely, for cases where sigma > sigma hat the introduction of a dark pool consistently decreases . Additionally, it only increases the exchange spread (S) if certain conditions from the equilibrium described in Proposition 1 are met.

It is sufficient (but not necessary) that:

After postulating such propositions, Zhu covers the implications of Dark Pools on price discovery, in other words the extent to which announcements made in period 1 (P1, Vb, Vs) are informative of the fundamental asset value . Given the fact that the Market Maker observes the volume (Vb, Vs) , the closing price is

Given the fact that v is binomially distributed, the conditional distribution after period 1 trading is completely determined by its conditional expectation.

Which explains that all period 1 public information that is relevant for the asset value is conveyed by the closing price . What will be pointed out later is that the “closer” is P1 to v the better the price discovery.

P1 is solely determined by the log likelihood ratio,

Where, the probability mass function of Z+ and Z- is denoted as o. Whereas, (P = +sigma) and (P=-sigma) are equal to 0.5. Given , the market maker sets the period 1 closing price

Given P1 a non-trader assigns the probability that the value of the asset is high,

Assuming v=+sigma for simplicity, we consider price discovery to be definitively enhanced if the likelihood of R1 increases according to first-order stochastic dominance. The full revelation of v=+sigma would imply that R1=infinite with certainty. To precisely determine R1, P1, and Q1, we must understand the specific nature of the probability density function . Nonetheless, given that the distributions of Z+ and Z- are infinitely divisible, they can be represented as the sum of independent and identically distributed random variables. Moreover, for illustrative purposes, if we assume that uz and sigma^2z are sufficiently large, by the central limit theorem, the pdf can be approximated by a normal distribution N(0.5uz, 0.5sigma^2). By inserting the log likelihood ratio into this normal distribution, we obtain an approximate value for R1:

In this context,

represents the "signal-to-noise" ratio. This ratio is a measure of the quantity of informed trading activity on the exchange (the "signal") relative to the volatility of the liquidity order imbalance (the "noise"). The "signal-to-noise" ratio I(Beta, alphae) increases alongside the scaled exchange spread S/sigma.

The prior figure illustrates the effects of a dark pool on the distribution of R1, showing that its introduction raises the scaled spread S/sigma and the signal-to-noise ratio I(Beta, alphae), thus affecting price discovery. Generally, a dark pool increases the mean and variance of R1's distribution, leading to more accurate valuation estimates. However, in cases of low R1 values, it can impair price discovery.

Whereas, such figure further demonstrates that a dark pool typically improves price discovery by shifting the probability density function of Q1 to the right, except in rare instances of extremely low Q1 values caused by significant opposing liquidity orders, which could mislead asset valuation. Dark pools usually enhance price discovery for frequent, short-term information but may also cater to the needs of long-term investors differently than traditional exchanges.

Whereas Ye (2017) shares a perspective common to various commissions and central banks about the detrimental effects of Alternative Trading Systems (ATSs) on Price Discovery.

His study details the rise of ATSs after the introduction of the SEC's Regulation National Market System in 2005, with a particular focus on dark pools, which by 2015, represented a considerable share of market trades.

Ye's research examines the dual nature of dark pools: they provide anonymity that guards against price impacts during large-volume trades but conversely cloud the price discovery process.

The study uses M&A rumors to analyze dark pools' influence on price impact, opting for rumors over official announcements to better gauge dark pools' unexpected effects. It looks at the link between dark pool trading volume and market indicators such as returns, volatility, and spreads when rumors circulate.

Ye concludes that while dark pool trading volumes are associated with price discovery within these platforms, they do not align with the veracity of rumors or the intrinsic value of the firms. In open markets, however, price discovery is influenced by these factors, indicating that dark pools' reaction to information might be inconsistent, likely due to liquidity challenges. The study also observes trading patterns across dark and open markets, noting that an increase in dark pool trading volume enhances its role in price discovery.

In conclusion, the debate on whether dark pools harm or improve price discovery is complex and multifaceted, with compelling arguments presented from both sides. Without endorsing either viewpoint, it is clear that the role of dark pools in financial markets is nuanced and perhaps not amenable to a definitive judgment. The impact of dark pools seems to vary based on market conditions, the nature of the information being traded, and the behavior of market participants. As the financial landscape evolves with technology and regulation, the influence of dark pools on price discovery will undoubtedly continue to be a critical topic of discussion among academics, traders, and regulators alike. The ongoing challenge for the financial community is to balance the need for privacy and efficiency in trading large blocks of securities with the overarching goal of maintaining transparency and fairness in the markets.


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