An Empirical Analysis of Conditional Orders: Which ATSs Prevail in Race Conditions and Offer Unique Liquidity?

Introduction

With over 30 dark pools, 15 exchanges, and several Central Risk Books and SDPs, liquidity is more fragmented than ever. A "parent" order in an execution algorithm is split into tiny pieces across multiple venues, commonly leading to "ships passing in the night" for traders who aim to minimize transactions and execute larger blocks. Conditional orders offer an effective solution for crossing parent orders rather than operating at a "child" order level. They allow algorithms to submit the full parent order (or a substantial portion) to multiple dark pools without the concern of overfill. Conditional orders are essentially IOIs (indications of interest). When two IOIs match from opposite sides, the venue invites the algorithms to place a firm order, giving the algorithms time to cancel other resting orders and submit a “firm” order with large quantity in response to the invitation (i.e., IOI).

In this paper, we analyze which Alternative Trading Systems (ATS) provide the most unique block liquidity using a large, private execution dataset containing conditional orders. We address the challenges of race conditions when utilizing conditional orders and examine which ATSs algorithms choose when they all offer block liquidity in the same stock. Finally, we explore the market share of each ATS in various transaction size buckets, helping to determine the optimal minimum execution quantity.

Race conditions on conditional orders

While conditional venues mitigate the issue of aggregating fragmented liquidity, they can create race conditions. For example, if Algo A sends a sell order for 20K shares to 5 conditional venues, and Algo B sends a buy order for 20K shares of the same instrument to the same 5 conditional venues, they both will receive simultaneous invitations from all 5 venues. However, the sequence of these invites received could differ for Algo A and Algo B.

Algo A might receive the invites in the sequence 1, 2, 3, 4, and 5, while Algo B receives them in a different sequence (2, 3, 1, 4, and 5). This discrepancy could arise due to differences in latency between Algo A and Algo B to these venues. Depending on the logic, Algo A may respond to venue 1 with a firm-up order, and Algo B may respond to venue 2, resulting in no order being executed though both parties were available and willing to execute. Liquidity-seeking algorithms must be designed optimally to address such race conditions.

BestEx Research utilizes conditional orders across its suite of algorithms, including liquidity-seeking algorithms, schedule-based algorithms, and smart order routers. In an analysis of approximately 140K invitations received from conditional orders, we found that 41% of the time there was a race condition—invitations received from at least two venues simultaneously. All invitations arriving within 50 milliseconds of one another are treated as “simultaneous.” This data provides an opportunity to study which dark pools offer unique liquidity—those venues not part of these clusters of invitations. Additionally, this data offers insights on which venues tend to provide a fill when in a race condition.

Unique liquidity and analysis 

For this analysis we look only at those invitations that were not part of a cluster of invitations to identify unique liquidity. The findings provide valuable insights into which dark pools provide unique liquidity distinct from other venues. Interestingly, our findings show that unique liquidity tends to vary based on the size of transactions, and it often does not correlate with the overall market share of these venues.

We categorized transactions according to the following:

• Block transactions: ≥ 5000 shares
• Medium-sized transactions: 1000-4999 shares
• Small transactions: < 1000 shares

Additionally, ATSs are divided into three categories:

• Blotter Scraping Pools: Liquidnet H2O (LIUH), Virtu’s POSIT (ITGI),  Instinet’s BlockCross (BLKX), Luminex (LMNX), and BIDS
• Bank ATS: Goldman Sigma X (SGMT), UBS (UBSA), JP Morgan (JPMX), CitiOne (ONEC), and Barclays (BARX)
• Trajectory Crossing Pools: Purestream (STRM), Level ATS (LEVL)

Key Findings: Unique liquidity by transaction size 

Within each category, we analyze the portion of BestEx Research’s conditional order executions that came from a particular ATS, segmented by size. In the figures below, the vertical axis (blue bars) represents the share of volume executed in a venue in each size category (Block, Medium or Small transactions) in scenarios where this was the only venue offering liquidity. 

Blotter scraping pools dominate block liquidity sourced from conditional orders. For block liquidity, BIDS led in unique liquidity, followed by Liquidnet (LIUH), Instinet’s BlockCross (BLKX), Virtu’s POSIT (ITGI), and Purestream (STRM). Despite Bank ATSs having large overall volumes, they were not dominant providers of unique block liquidity.

Figure 1. Percent of unique liquidity from each venue based on the transaction size, for transaction size > 5000 shares. Source: BestEx Research.

For medium-sized orders, Purestream (STRM) is the clear leader. Among the blotter scraping pools, only BIDS seemed to offer unique liquidity in this category. Goldman Sachs’ Sigma X (SGMT), Liquidnet (LIUH) and UBS (UBSA) were the other three providers in the top 5.

Figure 2. Percent of unique liquidity from each venue based on the transaction size, for transaction size 1000 to 4999 shares. Source: BestEx Research.

Among smaller transactions, banks offered the most unique liquidity. Among the top five, four were the largest banks–Goldman Sach’s Sigma X (SGMT), JP Morgan (JPMX), Barclays (BARX), and UBS (UBSA).

Figure 3. Percent of unique liquidity from each venue based on the transaction size, for transaction size < 1000 shares. Source: BestEx Research.

Unique conditional Liquidity provided by each venue does not correspond with market share. Interestingly enough, the top 5 venues representing more than 90% of the unique block liquidity (highlighted in figure 4) represent less than 10% of ATS market share.

Figure 4. Overall ATS market share based on  total shares traded (all NMS stocks) in Q32024.Source: FINRA.

Determining minimum fill size and liquidity loss

One of the dilemmas in optimizing conditional order execution is setting an appropriate minimum fill quantity. Venues generally support conditional orders sent with a minimum quantity, which is used in their matching algorithms to ensure the fills each party receives are equal to or greater than the specified minimum quantity. Traders can also use this minimum quantity to access selective liquidity. Traders generally prefer a larger minimum quantity to reduce information leakage and to minimize the number of small transactions. However, setting the minimum too high can reduce access to available liquidity. 

To evaluate minimum quantity selection, we analyzed the percent of liquidity within each ATS that belongs to each transaction size category. In this analysis, we include all fills regardless of the ATS being unique or part of a cluster of simultaneous invitations. We introduced a new category called “Mega block” by dividing the block transactions into “regular blocks” (those between 5,000 and 25,000 shares) and “Mega blocks” (those greater than 25,000 shares). 

With the exception of Luminex, which mandates a minimum quantity of 5,000 shares, BlockCross with a minimum quantity of 2500, and Purestream, which mandates a minimum of 1,000 shares, we set a minimum of 500 shares for all other ATSs in our liquidity-seeking algorithms, and 100 shares in our schedule-based algorithms. This ensures that, apart from Luminex, BlockCross and Purestream, comparisons remain consistent and fair across venues.

Key Findings: Determining minimum quantity

1. For blotter scraping pools, most of the volume is in the larger conditional transactions, whereas for bank ATSs, most volume comes from smaller transactions. For example, Virtu’s POSIT, and Liquidnet have more than 75% of conditional liquidity accessible via a minimum quantity of 5,000 shares. On the other hand, for Bank ATSs, only 20%-40% of overall liquidity was accessible in the form of these large block transactions. These findings are illustrated in Figure 5. 
2. Conditional orders offer access to a unique segment of liquidity in each ATS that is larger on average than standard executions. The average transaction sizes using conditional orders within most ATSs are much larger than the averages reported in their public ATS-N filings. See this link for more information. A likely reason for this difference could be that Smart Order Routers ping ATSs in transit before removing liquidity from exchanges, but those IOC orders are unlikely to interact with conditional order flow due to the latency involved. 

Figure 5. Distribution of fills received in a venue varied by transaction size (conditional orders only). Source: BestEx Research

Algorithm preferences during race conditions

Every execution algorithm must be prepared to handle race conditions as multiple invitations can be received at the same time. For Block trades, 29% of the time, a race condition exists (as shown in Figure 6). Most broker algorithms firm up on the first invitation they receive, while others may wait a few milliseconds and then firm up to the most preferred venue among the invitations received. Both approaches can lead to missed opportunities if the counterparty firms up at a different venue.

Figure 6. % of invitations that have race conditions after the algorithm has resting conditional orders, varied by the size of conditional order. Source: BestEx Research

To avoid missing liquidity opportunities, our execution algorithms adopt a strategy of "spraying"—firming up at as many venues as possible, simultaneously, while respecting the minimum execution quantity specified in our order. For example, if we submit conditional orders for 12,000 shares across 10 venues with a minimum quantity of 5,000 shares, and receive three simultaneous invitations, our algorithm will allocate 6,000 shares to two of these venues. This approach maximizes our hit rate. Additionally, our private dataset allows us to evaluate which venues are preferred by algorithms when simultaneous invitations are received. The data can also be used to rank venues, ensuring that if an algorithm cannot firm up to all venues, it can prioritize the one most likely to have the counterparty’s firm order.

Key Findings: Conditional WinMatrix

The results of our algorithm preferences analysis are presented in the WinMatrix in Figure 7, below. Here, we evaluate only the largest block crossing networks. For each pairwise combination of venues, the value in the corresponding cell indicates the percentage of times the venue in the row got a fill when the venue in the column didn't. For example, focusing on the row STRM (Purestream) and column BLKX (Instinet’s BlockCross), in the event where BestEx Research sprayed firm-up orders to multiple ATSs including STRM and BLKX and received a fill from either STRM and BLKX or both, STRM was one of the venues that provided a fill 83% of the time whereas BLKX was one of the venues that provided a fill 17% of the time. The last column represents the average winning percentage (against all other venues) for the designated row. Purestream (STRM) leads the chart followed by Liquidnet (LIUH), whereas Instinet’s BlockCross (BLKX) had the fewest fills in race conditions, indicating weaker performance in competitive scenarios. 

Figure 7. WinMatrix that captures how often a venue (row) fills an order over the other venue (column) when in a race condition for order sizes > 5000 shares. Source: BestEx Research

Conclusion

The analysis of unique liquidity and race conditions using our private data set of conditional orders reveals several key insights. First, blotter scraping pools like BIDS, Liquidnet, and Instinet’s BlockCross are particularly effective for sourcing unique block liquidity, especially when using conditional orders. Trajectory crossing pools like Purestream have more unique liquidity in medium-sized transactions, while major bank ATSs have more unique liquidity in smaller trades.

In addition, we find that unique liquidity often does not align with market share—venues with unique liquidity may represent a small portion of overall ATS volumes. This highlights the importance of a data-driven empirical approach that looks beyond market share alone to assess each venue's suitability for various transaction sizes.

Because race conditions exist frequently, as detailed above, effective management of race conditions and efficient use of conditional orders is crucial for seeking liquidity. Our “spraying” strategy, which involves firming up at multiple venues simultaneously, maximizes hit rates and minimizes missed opportunities, particularly in these competitive scenarios. Consistent updates to venue rankings based on their performance during race conditions is also critical; we evaluate this using the  competitive analysis shared in the WinMatrix above. 

BestEx Research uses empirical analysis of its private execution data to continuously enhance liquidity-seeking and schedule-based algorithms, ensuring that each maximizes interaction with natural liquidity and minimizes information leakage appropriately to provide optimized execution to our clients.

Appendix

The table below shows the names of the ATSs used in our analysis and their corresponding abbreviations:

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At BestEx Research, we care how you fill. We know from experience that systematic, quantitative decision-making around algorithm design contributes to globally optimal execution and results in significantly reduced execution costs. Reach out to us with questions at research@bestexresearch.com or learn more about us at bestexresearch.com. 

This research paper reflects the views and opinions of BestEx Research Group LLC. It does not constitute legal, tax, investment, financial, or other professional advice. Nothing contained herein constitutes a solicitation, recommendation, endorsement, or offer to buy or sell securities, futures, or other financial instruments or to engage in financial strategies which may include algorithms. This material may not be a comprehensive or complete statement of the matters discussed herein. Nothing in this paper is a guarantee or assurance that any particular algorithmic solution fits you, or that you will benefit from it. You should consider whether our research is suitable for your particular circumstances and needs and, if appropriate, seek professional advice.

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