Sec. & Exch. Comm'n v. Lek Sec. Corp. (370 F. Supp. 3d 384, 2019)

DENISE COTE, District Judge:

This Opinion addresses the motions of defendants Lek Securities Corporation ("Lek Securities") and Samuel Lek ("Lek"; together with Lek Securities, the "Lek Defendants") to exclude expert testimony to be offered at trial on behalf of plaintiff United States Securities and Exchange Commission ("SEC") by Terrence Hendershott and Neil Pearson, and the SEC's motions to exclude testimony from the Lek Defendants' experts David J. Ross and Alan Grigoletto, offered in rebuttal to the Hendershott and Pearson testimony. It also addresses the SEC's motion to exclude the testimony of Haim Bodek, offered by defendants Avalon FA Ltd. ("Avalon"), Nathan Fayyer ("Fayyer"), and Sergey Pustelnik ("Pustelnik"; together with Avalon and Fayyer, the "Avalon Defendants") in rebuttal to Hendershott and Pearson's testimony. Hendershott and Pearson have analyzed patterns of trading at Avalon, which conducted its trading through Lek Securities. For the following reasons, the Lek Defendants' motions to exclude Hendershott and Pearson as trial witnesses are denied; the SEC's motion to exclude Bodek is granted; and the SEC's motions to exclude Ross and Grigoletto are granted in part.

Background

The SEC sued the Lek and Avalon Defendants on March 10, 2017, principally alleging that traders at Avalon engaged in two schemes to manipulate the securities markets and that they did so through trading at Lek Securities, a broker-dealer based in New York. Avalon is a foreign day-trading firm whose traders are largely based in Eastern Europe and Asia. Avalon is not a registered broker-dealer and relies on registered firms like Lek Securities to conduct trading in U.S. securities markets. The SEC contends that Lek reaped significant commissions and fees from Avalon's trading.

The SEC brought claims for violations of several provisions of the Securities Exchange Act of 1934 (the "Exchange Act"). The claims against the Lek Defendants are primarily for aiding and abetting, in violation of Section 20(e) of the Exchange Act, the Avalon Defendants' violations of Sections 10(b), 17(a), and 9(a) of the Exchange Act. See SEC v. Lek Sec. Corp., 276 F.Supp.3d 49, 57-58 (S.D.N.Y. 2017) (" Lek II").

The same day this case was filed, the SEC obtained an ex parte temporary restraining order ("TRO") against Avalon. An Opinion of March 29, 2017 denied Avalon's motion to modify the TRO. See SEC v. Lek Sec. Corp., No. 17cv1789(DLC), 2017 WL 1184318 (S.D.N.Y. Mar. 29, 2017). Avalon thereafter consented to the entry of an injunction against it. An Opinion of August 25, 2017, denied the Lek Defendants' motion to dismiss the claims against them. Lek II, 276 F.Supp.3d at 57.

Following the completion of discovery, the Lek Defendants moved for summary judgment on August 24, 2018. On the same date, they also moved to exclude the testimony and opinions of Hendershott and Pearson, the SEC's expert witnesses. Those motions became fully submitted on November 2, 2018.

On October 5, the SEC moved to exclude all five of the defendants' expert witnesses including Ross, Grigoletto, and Bodek, who the Defendants intend to call as rebuttal witnesses to Hendershott and Pearson. Those motions became fully submitted on November 16.

This Opinion addresses the motions to exclude Hendershott, Pearson, Ross, Grigoletto, and Bodek. The main threads of the opinions offered by these experts are outlined below, beginning with Hendershott's opinion regarding the phenomenon of layering and Ross, Grigoletto, and Bodek's rebuttals to Hendershott's opinion, followed by an outline of Pearson's opinion regarding the phenomenon of cross-market trading and Ross, Grigoletto, and Bodek's rebuttals to Pearson's opinion.

I. Summary of Hendershott Reports

Hendershott analyzed trade orders, cancellations, and executions made by Avalon traders from December 2010 through September 2016 (the "Avalon Trade Data"). The orders analyzed by Hendershott are limit orders, or "instructions to trade at a price that is no worse than the limit price specified by the trader."

Hendershott analyzed the Avalon Trade Data to determine whether any of Avalon's order and trade activity was consistent with layering. Hendershott defines layering as a trading strategy whereby traders place "visible limit orders ... that they do not intend to execute." They place these orders "to create an artificial appearance of supply or demand to improve the execution of their other orders." Visible limit orders are informative; they are predictive of future price movements. As a result, they can impact trade prices. Among the market participants that rely on data about pending limit orders that are visible to the markets are market makers, high-frequency traders, and investors that use algorithms to implement their trading strategies, such as institutional investors.

As explained by Hendershott, when engaged in layering a trader will place a greater number of visible limit orders on the side of the market where the trader does not intend for the trades to execute and a smaller number of orders on the side of the market where the trader intends for the trades to execute. For instance, a trader will typically place a large number of buy (or sell) orders without intending for those orders to execute in order to increase the perceived demand (or supply) of the stock and therefore influence the price per share or volume of shares the trader is able to sell. A trader will then place a smaller number of sell (or buy) orders that the trader intends to execute. The trader will then cancel the buy (or sell) orders. The side of the market where the trader places the greater number of orders the trader does not intend to execute is referred to as the "Loud" side. The other side of the market, with the smaller number of orders the trader does intend to execute, is referred to as the "Quiet" side.

Using the methods described below, Hendershott concluded that Avalon's order and execution activity was frequently consistent with layering. Using a series of conservative measures, he identified 675,504 sets of trades consistent with layering over a period from December 2010 to September 2016. This trading resulted in Avalon earning more than $ 21 million in revenue, $ 12 million of which was earned in 2015 and 2016. The Avalon trading that was consistent with layering accounted for more than 45% of Avalon's trading revenue, even though it made up less than 5% of Avalon's trading volume.

A. Identification of Layering Loops

Hendershott applied five criteria to identify groups of orders, cancellations, and executions consistent with layering. First, Hendershott considered only instances where a trader places both buy and sell orders in a single stock, because layering is a strategy that involves a trader placing orders on both sides of the market. Second, Hendershott only considered instances where the orders were entirely resolved through cancellation or execution within 60 seconds, even though it is possible for traders to engage in a layering scheme through transactions that last longer than 60 seconds. The parties refer to these groupings as "Loops."

Third, Hendershott required both the number of visible orders and the number of shares in those orders on the Loud side of a Loop to be greater than both the orders and shares on the Quiet side by at least two to one (the "Order Imbalance"). Approximately 2 million Loops from the Avalon Trade Data met Hendershott's first three criteria.

Fourth, Hendershott eliminated Loops where the ratio of executed shares on the Quiet side to the Loud side was less than three to one (the "Execution Imbalance"), even though the Loud-side shares were more numerous. Hendershott contends that considering only Loops with an Execution Imbalance of at least three to one eliminates trading strategies such as market making from the Loops.

Fifth, Hendershott eliminated Loops if a Loud-side order was placed more than one second after the last Quiet-side execution or cancellation. He reasoned that this was consistent with a layering strategy, which typically involves placing Loud-side orders to achieve favorable execution prices for Quiet-side orders. Hendershott explains that, together, these five criteria create a conservative data set reflecting patterns of layering activity. Applying these criteria yielded a total of 675,504 Loops that Hendershott found to be consistent with layering (the "Layering Loops"). Of those, 663,994 occurred after March 12, 2012.

B. Further Analyses

Having identified Layering Loops, Hendershott then conducted four analyses ("Further Analyses") of all or some of the Layering Loops to evaluate whether the Loops did indeed have characteristics consistent with layering and to eliminate the possibility that the activity had occurred as part of a non-layering strategy such as market making. The four Further Analyses were a Cancellation Analysis, Position Analysis, NBBO Movement Analysis, and Realized Spread Analysis.

In the Cancellation Analysis, Hendershott measured how frequently Loud-side orders are cancelled shortly after the Quiet-side orders are executed. He found that 85% of Loud-side orders were cancelled within 3 seconds of the final Quiet-side execution or cancellation, and that 90% of Loud-side orders were cancelled within 4 seconds of the final Quiet-side execution or cancellation. He concluded that this result "is consistent with a layering strategy which tries to minimize the execution rate of Loud-side orders."

For the Position Analysis, Hendershott compared the Order Imbalances in the Layering Loops and the trader's opening position to test whether the Layering Loops might be consistent with trading by market makers. As Hendershott explains, a typical way for market makers to manage risk is to place orders in the opposite direction of any position that they have at the start of a Loop. In contrast, when engaged in layering, a trader is attempting to mislead the market and will place more orders on the side in which the trader already has a position. Having led the market to believe that demand for the stock is higher on that side, a trader engaged in layering will then execute on the Quiet side. The Position Analysis showed that when Avalon's position was long at the beginning of a Layering Loop, the buy side was the Loud side 88% of the time. Similarly, when the position was short at the beginning of the Layering Loop, the sell side was the Loud side 89% of the time. Hendershott concluded that these results "are not consistent with market making, but are consistent with a layering strategy."

For the third and fourth analyses, Hendershott examined only those Layering Loops that occurred in discrete periods of time in three subaccounts identified to him by the SEC. This created a subset of 87,000 Layering Loops.

In his third analysis, which is labelled the NBBO Midpoint Analysis, Hendershott evaluated how often the stock price rose when the Loud side of the Layering Loop was the buy side, and how often the stock price fell when the Loud side was the sell side. According to Hendershott, over intervals such as a minute or less, the average change in the NBBO midpoint is zero and prices should rise or fall on average 50% of the time. Hendershott's NBBO Midpoint Analysis of the 87,000 Layering Loops revealed, however, that in those Loops where the Loud-side orders were purchases, the NBBO midpoint at the time of the Quiet-side sale executions was higher than at the start of the Loop 62% of the time. When the Loud-side orders were sales, the NBBO midpoint was lower at the time of Quiet-side purchase executions than at the start of the Loop 64% of the time. Hendershott concluded that those results were "consistent with Avalon's Loud-side orders contributing to a favorable shift in the NBBO midpoint more often than would be expected by chance."

Finally, Hendershott applied a Realized Spread Analysis to the 87,000 Layering Loops, comparing the profitability of Loud-side and Quiet-side executions. He did so by comparing the price of each execution to the NBBO midpoint 5 minutes after the execution. Under this measure, there is a positive realized spread if a buy order is executed at a lower price than the NBBO midpoint 5 minutes later, and a positive realized spread if a sell order is executed at a higher price than the NBBO midpoint 5 minutes in the future. This analysis of the 87,000 Layering Loops found that the Quiet-side executions had a positive realized spread but the Loud-side executions had a negative realized spread. Hendershott concluded that this result was "not consistent with the Loud-side orders having an economic rationale on their own." Accordingly, the results from the Realized Spread Analysis were "consistent with Avalon impacting the market in order to execute its Quiet-side orders at a more favorable price than would have been available absent its Loud-side orders."

Hendershott also discussed the impact that layering can have on markets generally. He opined that layering can harm markets by creating uncertainty and decreasing market liquidity. He added that layering can also increase the difficulty in executing orders and can degrade market integrity, reducing market participation.

II. Summary of Rebuttal Reports on Layering

The Lek Defendants have moved to exclude the testimony of both Hendershott and Pearson. If they are unsuccessful, the Defendants seek to offer at trial the testimony of Ross, Grigoletto, and Bodek as rebuttal expert testimony. The principal arguments contained in the three defense experts' layering reports are described here.

A. Ross's Opinions on Layering

Ross opines that Hendershott's analysis is "fundamentally flawed" because it does not establish that Avalon acted with manipulative intent when it placed the Loud-side orders in the Layering Loops. Since manipulative intent is an essential component of layering, Ross asserts that Hendershott is unable to "ascertain whether the trading in any specific Layering Loop constitutes layering."

Ross also contends that Hendershott's criteria for identifying layering is "suspect" because the ratios Hendershott selected for the Order Imbalance and the Execution Imbalance screening criteria are not found in any statute, regulation or peer-reviewed article. Ross points out that there would be many fewer Layering Loops if the ratios were changed to 10 to 1. He also complains that Henderson identifies a Loop as a Layering Loop if his two ratios exist at any time during the Loop instead of measuring the ratios only at the time of the Quiet-side executions. He argues that Hendershott's methodology for identifying layering must be flawed since the Financial Industry Regulatory Authority ("FINRA"), when it provided Lek Securities with a Supervision Report Card for seven months in 2016, only identified one-fifth of Hendershott's Layering Loops as layering activity.

Ross asserts that Hendershott's analysis is flawed due to what he labels as "selection bias," specifically Hendershott's failure to consider Avalon's other trading activity, which constitutes the majority of its trading activity. Because the majority of the Avalon Trade Data does not meet Hendershott's definition of Layering Loops, Ross reasons that "Avalon was necessarily engaged in trading strategies other than 'layering.' " Ross then divides the Avalon Trade Data into six mutually exclusive categories, one of which is Hendershott's Layering Loops. Ross explains how the other five categories are in one respect or another inconsistent with Hendershott's description of a layering strategy. And, because the trading in each of these five categories shares at least some of the characteristics of the trading in the Layering Loops, Ross concludes that this is additional evidence that the Layering Loops are consistent with a non-layering strategy.

Next, Ross examines the Layering Loops. He identifies nine different features of layering activity and measures how frequently they appear in the Layering Loops. For instance, he calculates how often Loud-side orders are cancelled one or more seconds before the first Quiet-side order was entered. He then argues that such cancellations are "inconsistent with the alleged layering strategy because these cancellations necessarily reduced any apparent order imbalance." In addition, Ross offers two further datapoints in a footnote to his report. Ross calculates that Avalon's Loud-side orders had an average duration of 10.18 seconds. He also calculates that 56.5% of Avalon's Loud-side orders were placed "at or inside" the NBBO. According to Ross, these characteristics "increased the likelihood" that the Loud-side orders would execute.

Finally, Ross discusses Hendershott's Further Analyses. For instance, Ross notes that while Hendershott found that all of Avalon's Loud-side orders were cancelled within five seconds of the last Quiet-side execution or cancellation in 93.4% of the Layering Loops, Hendershott found that only happened within one second for 51.8% of the Layering Loops.

B. Grigoletto's Opinions on Layering

Before offering opinions on the layering scheme alleged by the SEC, Grigoletto provides background on the equities and options markets, including a discussion of how trading has evolved since the development of algorithmic trading practices. Among other things, he explains that market makers are the primary source of immediate liquidity for options markets. They are required by exchanges to make a two-sided market by holding themselves out to buy and sell at competitive prices or quotes. In return for providing this service, they receive lower fees and better capital treatment from the exchange and clearing firm. When a trader places an order at a quoted price, it is assigned to a market maker, depending on the rules of the particular exchange.

After providing background information, Grigoletto expresses opinions about Avalon's alleged layering scheme. He begins by noting that, in his view, there is no universally agreed upon definition of layering. Assuming the definition provided by the SEC, however, Grigoletto concludes that Avalon's equity trading was not consistent with layering because Avalon's Loud-side orders were "consistent with the goal for the trades to be executed." Relying on the analysis in Ross's report, Grigoletto explains that Avalon's allegedly non-bona fide orders were "primarily at or inside the NBBO," and that the orders rested in the market on average for over 10 seconds -- what he calls an "eternity" in modern equities markets. Because other market participants could have interacted with these orders, Grigoletto concludes that Avalon's Loud-side orders cannot be deceptive and do not give a false impression of supply and demand.

Grigoletto also argues that traders should not be liable for masking their trading intentions. He claims that placing a limit order in an order book is not a representation that the trader intends to execute it; it is merely a representation that the trader will execute it at the entered price and volume for as long as it is posted. To the extent Avalon's trading strategy harmed other market participants, such as market makers, Grigoletto observes that securities markets are designed to be competitive and opines that market makers should adjust their algorithms to account for Avalon's trading.

Grigoletto also addresses Hendershott's layering report directly. Because he bases his conclusions on Ross's report, his criticisms of Hendershott's analysis largely mirror those discussed above in connection with Ross's report. For example, he claims that Avalon's trades do not always show an order imbalance at the time of the Quiet-side execution, and that Hendershott failed to consider the order of trading events -- e.g., whether the Quiet-side order was placed before or after the Loud-side orders. He also argues that Hendershott's report is skewed because Hendershott failed to consider the vast amount of Avalon's trading that was not included in the Layering Loops. Grigoletto reviewed the trading in an Avalon subaccount in the security Cabela's Incorporated ("CAB"). From that study, which included four of Hendershott's Layering Loops, Grigoletto concluded that Avalon's trading is "not consistent with layering."

C. Bodek's Opinions on Layering

Bodek's report is difficult to understand. It appears to make the following points. Relying on his analysis of eight examples of Layering Loops discussed in Hendershott's reports, Bodek opines that Avalon's trading activity "does not amount to layering as a species of market manipulation," "does not constitute market manipulation more generally because it does not produce an artificial price impact," and "does not violate any laws or regulations specifically referenced by the SEC." Bodek contends that Avalon's trading strategy incorporates a mix of "exploratory trading,"

"market impact," "scalping," and "quasi-market making" strategies. Through these strategies, Avalon "consistently demonstrated the lack of buy and sell interest at particular levels in the market and then took speculative positions at sensible price points." Bodek devotes much of his report to explaining these strategies.

According to Bodek, exploratory trading involves placing orders on one side of the market to assess liquidity on the opposite side of the market. To do this, Bodek explains, a trader may place a series of small, "aggressively-priced" orders on one side of the market. If the orders execute, the trader will suffer an economic loss but will have more certainty that there is liquidity on the opposite side of the market. If the orders fail to execute, the trader will have identified a lack of "contra-side liquidity." In either case, Bodek explains that exploratory trading allows traders to evaluate liquidity and assess the realistic trading range for a particular security.

Bodek's report further explains that an exploratory trading strategy may include a market-impact component, which Bodek sometimes refers to as a "pressure strategy." He admits, however, that market impact is typically considered a cost to traders, since the very act of consummating a transaction usually pushes market prices in an adverse direction.

Although Bodek admits that Avalon's trading strategy pushed prices in the direction of Avalon's Quiet-side orders, he claims that this strategy is not manipulative. According to Bodek, this is because Avalon's Loud-side orders "typically improved over" (i.e., were "inside") the NBBO. He explains that this means the Loud-side orders were likely to execute, and "result[ed] in a likely correction of the prevailing market price rather than an artificial price impact."

Bodek next argues that Avalon's orders on the Quiet side represented a quasi-market making strategy. He explains that after Avalon's exploratory trading and market-impact strategies "improv[ed] the market price" and exposed a lack of "contra-side liquidity," Avalon "place[d] larger orders with hidden or reserve size that provide[d] liquidity at the upper and lower bound of Avalon's trading range." According to Bodek, these Quiet-side orders helped "make a market" in part because they "provide[d] potentially significant liquidity to other market participants." Once Avalon executed its Quiet-side orders, Bodek explains that it was rational for Avalon to cancel its outstanding orders on the Loud side. According to Bodek, this is because Avalon is a "two-sided quasi-market maker." Thus, while it was "natural" for Avalon to cancel Loud-side orders after entering into a short position on the Quiet side, Bodek claims that Avalon "would have undoubtedly had a different response if it had established a long position" through its Loud-side orders. Bodek concludes that "[t]he conditional nature of Avalon's orders as a two-sided quasi-market maker" renders Avalon's trading activity legitimate and non-manipulative.

III. Summary of Pearson Reports

As described in his principal expert report, Pearson reviewed two sets of trading activity by Avalon traders. The first was Avalon orders, cancellations, and executions in stock and options through Lek Securities from November 2010 through September 2016. The second set was Avalon orders, cancellations, and executions in stocks and options through Lime Brokerage between April 1, 2013 through April 12, 2013. The two sets of trading activity involved both put options -- contracts that give the holder of the option the right to sell the underlying stock at a set price on or before a set date -- and call options -- contracts that give the holder of the option the right to buy the underlying stock at a fixed price on or before a set date. See generally Olagues v. Perceptive Advisors LLC, 902 F.3d 121, 123, 126 (2d Cir. 2018).

Pearson examined this Avalon trading activity to determine if there were patterns of orders, cancellations, and executions consistent with what the SEC has termed the "Cross-Market Strategy." In this scheme, a trader manipulates the prices of options through trading in the corresponding stocks. First, the trader buys or sells a stock to impact the stock price and cause the stock to trade at an artificial price. Because options prices are related to stock prices, a movement in a stock's price also affects the price of the options in that stock. Second, the trader establishes an options position that will benefit from the underlying stock returning to its price before the trader placed the stock trades. Third, the trader begins to liquidate the stock position, which moves the stock price back to its initial level, which generally allows the trader to close out the options position at a profit. Typically, the trader loses money on the stock transactions but more than offsets any losses through the profits made on the options transactions.

A. Identification of Cross-Market Loops

Pearson first used three criteria to identify patterns of trading -- referred to as "Loops" -- that were potentially consistent with a Cross-Market Strategy. First, an Avalon trade group had to place orders and trades in both a stock and the corresponding option. Second, there could not be any overnight positions. Third, the Loop had to have both stock and option orders or positions open at the same time. Pearson identified 796 Loops that fit these initial criteria, which represented 95% of Avalon's option trading volume.

Pearson divided the Loops into three patterns: One-Directional Loops, Multi-Directional Loops, and Overshoot Loops. In One-Directional Loops, the trader's stock position was only or predominately long (or short). To be predominately long or short, the position had to be more than four times greater than the largest inverse (short or long) position. In Multi-Directional Loops, the trading activity included both long and short stock positions and the largest long or short position was four times or less than four times greater than the largest inverse (short or long) position. Overshoot Loops are Multi-Directional Loops where the trader traded options only in one direction -- either buying puts and/or selling calls or selling puts and/or buying calls, but not both.

Next, Pearson analyzed the "nature and timing of the purchase or sale of options relative to the trading in the stock" in each of the Loops to determine if the trading patterns were consistent with a Cross-Market Strategy. To do so, Pearson defined the maximum stock position, either long or short, in a Loop as the Equity Peak. He then applied screening criteria to each Loop type.

In One-Directional Loops where the Equity Peak was long ("Long One-Directional Loops"), Pearson concluded that Avalon's trading was consistent with the Cross-Market Strategy if two additional criteria were satisfied. First, the loop had to involve "either a purchase of puts and/or a sale of calls when the stock position is within 20% of the maximum long stock position." Second, the options positions had to be one-sided, meaning the largest position in purchased puts or sold calls was more than four times as large as the inverse position (sold puts or purchased calls). According to Pearson, Loops that satisfy both criteria are consistent with the Cross-Market Strategy because "the options trades to open the options position occur at a point when the puts are artificially cheaper and the calls are artificially more expensive as a result of the long stock purchases."

Pearson applied the opposite two criteria to One-Directional Loops where the Equity Peak was short ("Short One-Directional Loops"). For a Short One-Directional Loop to be consistent with the Cross-Market Strategy, Pearson required "a purchase of calls and/or a sale of puts when the stock position is within 20% of the maximum short stock position." Additionally, "the largest position in purchased calls and/or sold puts [had to be] more than four times as large as the largest position sold calls and/or purchased puts." Pearson explains that Short One-Directional Loops that satisfy these two criteria are consistent with the Cross-Market Strategy because "the options trades to open the options position occur at a point when the calls are artificially cheaper and the puts are artificially more expensive as a result of the short stock purchases." Applying these criteria, Pearson identified 497 Long and Short One-Directional Loops consistent with the Cross-Market Strategy.

Pearson applied similar criteria to identify which Multi-Directional and Overshoot Loops were consistent with the Cross-Market Strategy. Applying those criteria yielded 36 Overshoot Loops and 103 Multi-Directional Loops that he concluded were consistent with the Cross-Market Strategy. Together with the One-Directional Loops, Pearson identified 636 Loops, which are termed the Cross-Market Loops, consistent with the Cross-Market Strategy.

B. Further Analyses

Pearson then applied seven Further Analyses to all or some of the Cross-Market Loops to determine "whether the stock price movements and returns" during the trading in the Cross-Market Loops "are consistent with the Cross-Market Strategy." These analyses were the Stock Return Analysis, Trading Volume Analysis, Return Reversal Analysis, News Analysis, Cancellation Analysis, But-For Analysis, and Sensitivity Analysis.

For the Stock Return Analysis, Pearson examined stock price movement during the One-Directional and Overshoot Loops. Pearson measured stock price in three periods: between the beginning of the Loop and the Equity Peak, between the Equity Peak and the Equity Liquidation, and between the Equity Liquidation and the end of the Loop. Pearson analyzed both the average return and the market-adjusted return to control for market-wide movements in stock prices. For both types of return, the mean return for long Loops was positive from the Loop start to the Equity Peak, negative from the Equity Peak to Equity Liquidation, and negative from the Equity Liquidation to Loop end. For the short Loops, the mean for both types of return was negative from Loop start to Equity Peak, positive from Equity Peak to Equity Liquidation, and positive from Equity Liquidation to Loop end. Pearson concluded that these results are consistent with the Cross-Market Strategy and that it is "extremely unlikely -- essentially impossible -- that the average returns from Loop Start to Equity Peak occur by chance."

The Trading Volume Analysis compared Avalon's share of a stock's total trading volume between the Loop start to Equity Peak of each One-Directional and Overshoot Loop to determine if Avalon's trading patterns were large enough to impact stock price. First, Pearson determined Avalon's share of the stock's total trading volume during each Loop. For long Loops, Avalon's trading between Loop start and Equity Peak represented, on average, approximately 48% of the total trading in the stock. For short Loops, Avalon's trading between Loop start and Equity Peak made up, on average, approximately 52% of the total trading in the stock. Pearson concluded that, for both long and short Loops, Avalon's share of trading volume was "more than sufficient to impact stock prices." Pearson then used a regression analysis to estimate the relationship between Avalon's trading volume and the market-adjusted returns from the Loop start to the Equity Peak. Pearson explains that this analysis showed that "the magnitudes of the returns from Loop Start to Equity Peak are explained by the trader's share of market trading volume during the same period." Finally, Pearson examined Avalon's share of each stock's daily trading volume and found that this averaged roughly 2.9% of the daily trading volume in long Loops and 2.8% in short Loops. Pearson explained that these percentages are substantial and also sufficient to impact market prices.

Next, in the Return Reversal Analysis, Pearson analyzed whether movements in stock prices during the Loops could be explained by new information entering the market instead of by the stock trading activity. First, he assessed whether the changes in stock price between Loop start and Equity Peak reversed themselves by the Loop end. If the price changes between Loop start and Equity Peak reversed between Equity Peak and Loop end, Pearson explains, that makes it unlikely that the price changes were due to new information, which tends to have a longer impact on prices. Pearson found that the price changes did reverse themselves and that this result was unlikely to occur by chance. Second, Pearson examined a subset of 20 randomly selected One-Directional Loops to determine whether news had been published about the relevant stocks on the day of the Loop that could have affected stock prices. He concluded that no news that would have affected prices was released on the day of any of the 20 Loops he reviewed.

In the Cancellation Analysis, Pearson examined One-Directional and Overshoot Loops to determine when during each Loop Avalon cancelled outstanding orders to buy or sell stock. His review showed that around the Equity Peak, the average number of equity order cancellations increased and the average equity order balance decreased to close to zero. He concluded that this is "consistent with the Cross-Market Strategy because the trader's initial stock trades and orders are intended to move the stock price" until the Equity Peak, at which point the trader establishes options positions and cancels outstanding orders to "allow[ ] the stock price to return toward its pre-existing level."

The But-For Analysis considered whether the stock trading in 20 randomly selected Cross-Market Loops affected the prices of the related options. Pearson first compared the net revenue that Avalon actually made on its options trades to what the net revenue would have been had the initial options trades taken place at the prevailing prices for the options before each Loop began. He found that Avalon's actual revenue from the 20 Loops was positive $ 224,231, but that, had the initial options trades occurred at the prices prevailing before the stock trading, the revenue would have been negative $ 411,429. In a second But-For Analysis, Pearson compared the actual trading revenue for the 20 Loops to what the revenue would have been if Avalon had established options positions at prices prevailing before each Loop and if Avalon had closed its options positions at the time it began liquidating its stock positions. In the hypothetical scenario, the 20 Loops would have resulted in a net loss of $ 1,600,164, whereas the actual revenue for those 20 Loops was, as noted above, positive $ 224,231. Pearson explained that these measures indicate that Avalon's options trading was only profitable because Avalon's stock trading artificially impacted the prices of options.

Finally, Pearson conducted a Sensitivity Analysis to determine whether his results were sensitive to the specific parameters he used to define Cross-Market Loops. Pearson varied the criterion that requires options trades to have occurred within 20% of an Equity Peak to criteria of cut-offs between 0% and 100% of the Equity Peak. He found that the number of Cross-Market Loops did not change significantly even when this parameter changed. He also varied the ratio used to differentiate types of Cross-Market Loops and found that changing the definition of Multi-Directional Loops from a one-to-four ratio (between the longest or shortest stock position and the inverse position) to a one-to-ten ratio did not significantly change the number of Cross-Market Loops.

C. Additional Opinions

Pearson also opined that the Cross-Market Loops did not have a legitimate economic rationale. Pearson first observed these Loops were only profitable due to the change in options prices achieved by the trader's stock transactions. He then considered whether the Loops could be explained as a stock trading strategy, as an options trading strategy, or as a method of learning about market liquidity. He concluded that the first two explanations are untenable because the stock transactions, in isolation, are unprofitable, and because the options trades occurred after stock trading had already occurred, which is inconsistent with a delta-hedging strategy. He additionally rejected the explanation that the Loops are explained as a method of determining stock liquidity because, in his view, the significant size of the stock trades relative to total trading activity and the impact the trades had on stock prices are inconsistent with this explanation. Finally, Pearson opined that the Cross-Market Strategy harmed other market participants by causing other participants' stock and options trades to occur at artificial price levels created by the Avalon traders' manipulation.

IV. Summary of Rebuttal Reports on the Cross-Market Strategy

Ross, Grigoletto, and Bodek have proffered testimony in rebuttal to Pearson's analysis of the Cross-Market Strategy. Their principal arguments are described here.

A. Ross's Opinions on the Cross-Market Strategy

Ross's report addressing the Cross-Market Strategy principally makes the following points. Ross complains that Pearson's analysis is overbroad since it does not require Avalon's transactions in the Cross-Market Loops to fit the pattern of trading described in the SEC's complaint. In making this assertion, Ross does not acknowledge that the single pattern to which he refers was described in the complaint as an "example" of various cross-market trading patterns.

Ross additionally argues that Pearson's analysis is unreliable because it suffers from what he labels as "selection bias." Ross asserts that, because Pearson considered only Loops where Avalon acquired both stock and options positions but not Loops where Avalon acquired only a stock position or only an options position, Pearson analyzed only a fraction, indeed a small fraction, of Avalon's trading. Ross contends that because Cross-Market Loops are not representative of all of Avalon's trading, there is likely a "legitimate economic rationale" for the trading activity in the Cross-Market Loops.

Ross also argues that, without evidence about Avalon's intent, there is no basis to find that any impact on prices was "artificial" as opposed to an impact caused by "legitimate, non-manipulative trading." Ross suggests, for example, that Avalon traders may have expected a stock's price to change in a particular direction and traded accordingly.

Ross also asserts that Pearson's Cancellation Analysis is not probative of Avalon traders' intent because order cancellations naturally accompany the attainment of an Equity Peak. Ross next asserts that the But-For Analysis is fundamentally flawed because it measures the wrong things. Ross additionally claims that Pearson inaccurately characterized the profitability of the stock and options transactions that made up the Cross-Market Loops because Pearson only reported the total of the revenue and the average revenues for Cross-Market Loops, by category. Ross disaggregated the data and showed that some of the Loops did not fit the typical pattern.

Finally, Ross challenges Pearson's conclusion that the Cross-Market Loops lacked a non-manipulative economic purpose. Ross contends that Pearson failed to consider that the Avalon trading was the result of a dynamic trading strategy, where trades were placed for legitimate economic reasons, and then the direction of the trading changed in response to new information or changes in market conditions.

B. Grigoletto's Opinions on the Cross-Market Strategy

Grigoletto states his opinions on Avalon's alleged Cross-Market Strategy in eight paragraphs of his report. He principally makes the following points.

First, Grigoletto explains that Avalon's options trading was legitimate because it was "consistent with a desire to seek profit from options Market Makers offering more liquidity than the Market Makers were able to profitably hedge." Citing primarily to a complaint that Citadel Securities filed with the SEC, Grigoletto opines that market makers exposed themselves to unnecessary risk by "delta hedging" their options positions in the corresponding equities markets. According to Grigoletto, "Avalon captured the liquidity difference between the options markets and the equities markets," which he asserts is "consistent with legitimate trading."

Second, Grigoletto asserts that Avalon's stock trades were not designed to decrease the price of the options that Avalon acquired. Instead, he contends that Avalon's stock trading is consistent with at least two alternative purposes: to evaluate whether market makers were quoting too much liquidity in the options markets relative to the equities markets, and to serve as a partial hedge in case Avalon executed options transactions in the corresponding stock. To support this conclusion, Grigoletto points to Ross's rebuttal report, which highlights stock transactions that Avalon executed without corresponding options trades and which purports to demonstrate that, in some cases, Avalon's equity trades did not impact the stock price as expected. He also points to his own experience, arguing that traders do take positions to hedge anticipated trading and that traders may test for market liquidity with large, executable orders.

C. Bodek's Opinions on the Cross-Market Strategy

Again, Bodek's report is difficult to decipher. Bodek appears to acknowledge that Avalon is engaged in cross-market trading but asserts that it is not manipulative. Instead, he contends that Avalon's equities and options trading consists of a combination of two legitimate strategies: a "market impact" strategy in the equities markets and a "liquidity arbitrage" strategy in the options markets.

A market impact strategy, Bodek explains, involves placing a series of orders on one side of the market (buy or sell) to discover liquidity limits at the upper and lower ends of a security's trading range. Bodek contends that Avalon used this strategy to build a speculative position in the equities markets. Bodek admits that market impact orders are "intended to" and "of course have price impact" in the underlying stock, and he admits that this price impact may harm other market participants. Nonetheless, Bodek opines that Avalon's market impact orders do not produce artificial price impact because the strategy uses "bona fide" orders that execute against real market participants. Any increase (or decrease) in price, he argues, results from the depletion (or addition) of liquidity on the opposite side of the equities market. Moreover, although Avalon's market impact strategy regularly resulted in substantial losses in its equities trading, Bodek concludes that the strategy did have a legitimate economic rationale because it was profitable when combined with Avalon's liquidity arbitrage strategy in the options markets.

A liquidity arbitrage strategy, according to Bodek, involves capturing a profit from price disparities in the equities and options markets. As a result of Avalon's market impact strategy, Bodek explains that the "liquidity premium" -- i.e., the price of liquidity in the market -- becomes high in the equities markets but low in the options markets, where market makers react by quoting excessive liquidity. According to Bodek, this cross-market mispricing creates an opportunity for Avalon to "cover" or "reverse" its established position in the equities markets. To do so, Bodek explains that Avalon engages in a "liquidity arbitrage"

by purchasing options at a liquidity premium lower than that available in the equities markets. After establishing its options position and exiting its equities position, Avalon ultimately closed out its options positions for a profit. Bodek claims that this pattern of trading -- namely, "exploiting oversize [sic] liquidity in options markets" -- is not deceptive or manipulative because it is executed through bona fide orders.

Discussion

Federal Rule of Evidence 702 governs the admissibility of expert testimony. It provides:

A witness who is qualified as an expert by knowledge, skill, experience, training, or education may testify in the form of an opinion or otherwise if:

(a) the expert's scientific, technical, or other specialized knowledge will help the trier of fact to understand the evidence or to determine a fact in issue;

(b) the testimony is based on sufficient facts or data;

(c) the testimony is the product of reliable principles and methods; and

(d) the expert has reliably applied the principles and methods to the facts of the case.

Fed. R. Evid. 702.

The proponent of expert testimony carries the burden of establishing its admissibility by a preponderance of the evidence. United States v. Williams, 506 F.3d 151, 160 (2d Cir. 2007). Expert testimony admitted under Rule 702 must be relevant and rest on a reliable foundation. Daubert v. Merrell Dow Pharm., Inc., 509 U.S. 579, 597, 113 S.Ct. 2786, 125 L.Ed.2d 469 (1993) ; Williams, 506 F.3d at 160. An expert's opinion is relevant if it will "help the trier of fact to understand the evidence or to determine a fact in issue." Fed. R. Evid. 702 ; see Daubert, 509 U.S. at 591, 113 S.Ct. 2786. Expert testimony that usurps the role of the fact finder, however, must be excluded. See United States v. Lumpkin, 192 F.3d 280, 289 (2d Cir. 1999).

An expert's opinion must have "a reliable basis in the knowledge and experience of his discipline." Daubert, 509 U.S. at 592, 113 S.Ct. 2786. In general, a court should consider "the extent to which the expert's theory has been subjected to peer review and publication, whether the technique is subject to standards controlling the technique's operation, the known or potential rate of error, and the degree of acceptance within the relevant scientific community." United States v. Ulbricht, 858 F.3d 71, 116 n.50 (2d Cir. 2017) (citation omitted). This " Daubert reliability assessment" is a "flexible" inquiry, however, and " Daubert is not a definitive checklist or test for the reliability of expert testimony." Id. (citation omitted). "[W]hether Daubert's specific factors are, or are not, reasonable measures of reliability in a particular case is a matter that the law grants the [court] broad latitude to determine." Id. (citation omitted).

There is no requirement that all expert testimony express opinions or conclusions that have been "established to a degree of scientific certainty." Restivo v. Hessemann, 846 F.3d 547, 577 (2d Cir. 2017). All experts, including "economists[,] may express professional opinions that fall short of definitive proof" as long as their "testimony [is] reliable under Rule 702." Id. at 576 (citation omitted). Instead, a court must "assess whether the expert employs the same level of intellectual rigor that characterizes the practice of an expert in the relevant field." Id. at 577 (citation omitted).

"[A] trial judge should exclude expert testimony if it is speculative or conjectural or based on assumptions that are so unrealistic and contradictory as to suggest bad faith." Zerega Ave. Realty Corp. v. Hornbeck Offshore Transp., LLC, 571 F.3d 206, 213-14 (2d Cir. 2009) (citation omitted). "[N]othing in either Daubert or the Federal Rules of Evidence requires a district court to admit opinion evidence that is connected to existing data only by the ipse dixit of the expert." Gen. Elec. Co. v. Joiner, 522 U.S. 136, 146, 118 S.Ct. 512, 139 L.Ed.2d 508 (1997). When evaluating the reliability of expert testimony, "it is critical that an expert's analysis be reliable at every step." Amorgianos v. Nat'l R.R. Passenger Corp., 303 F.3d 256, 267 (2d Cir. 2002). "[A]ny step that renders the analysis unreliable ... renders the expert's testimony inadmissible. Id. (emphasis omitted).

A contention that an expert's assumptions are unfounded, however, may "go to the weight, not the admissibility, of the testimony." Restivo, 846 F.3d at 577 (citation omitted). "A minor flaw in an expert's reasoning or a slight modification of an otherwise reliable method" does not itself require exclusion; exclusion is only warranted "if the flaw is large enough that the expert lacks good grounds for his or her conclusions." Amorgianos, 303 F.3d at 267 (citation omitted). This is because "our adversary system provides the necessary tools for challenging reliable, albeit debatable, expert testimony." Id."[V]igorous cross-examination, presentation of contrary evidence, and careful instruction on the burden of proof are the traditional and appropriate means of attacking shaky but admissible evidence." Id. (quoting Daubert, 509 U.S. at 596, 113 S.Ct. 2786 ).

I. The Lek Defendants' Motion to Exclude Hendershott

The Lek Defendants principally argue that Hendershott's expert testimony should be excluded because his methods are novel and unreliable, and because his analysis suffers from what they label as "selection bias." For the following reasons, their motion to exclude his testimony is denied.

The Lek Defendants first assert that Hendershott's testimony is inadmissible because his multi-step filtering process to locate Layering Loops has never been published, and he has not cited any basis in "law, regulation, practice, or academic literature" for it. They argue as well that the process he used appears to be different from the criteria used by FINRA and BATS Global Markets, Inc. ("BATS") to identify layering.

The Lek Defendants do not challenge Hendershott's expertise. Nor could they reasonably do so. His area of expertise bears directly on the issues on which he is opining in this case. His research focus is the field of market microstructure, including strategies employed in high-frequency trading and how those strategies affect securities prices. There is broad agreement among the parties (and regulators) about what trading conduct constitutes layering. The methodology Hendershott employed to locate Layering Loops, which he identified as trading activity consistent with layering, springs directly from that well-accepted description of the phenomenon of layering. His methodology is a conservative construct with objectively-defined steps that can be applied by any expert to any body of trades. Those steps, and the criteria implied in them, are reasonably related to the academic and regulatory definitions of layering cited by the parties. Hendershott has explained the bases for the criteria he used, and the Lek Defendants have not shown that any step he employed is in tension with the literature in the field. Moreover, Hendershott designed a series of Further Analyses to confirm the reliability of his methodology.

Hendershott was not required to design a methodology that would identify the same sets of layering as a regulator. There is no requirement that experts use only those methodologies used by exchanges or regulators. Exchanges and regulators are performing different functions than trial experts, and they may be using different data sets and more easily applied tests to perform their tasks. Daubert and its progeny supply the test that applies to the admissibility of expert testimony at trial. Daubert requires that the expert employ "the same level of intellectual rigor that characterizes the practice of an expert in the relevant field." Restivo, 846 F.3d at 577. Hendershott's methodology falls comfortably within that parameter.

The argument that Hendershott's testimony is inadmissible because of selection bias fares no better. The Lek Defendants use the term selection bias to refer to their argument, generally, that Hendershott failed to consider most of Avalon's trading -- that is, all of the trading outside the Layering Loops. That argument proceeds from a false premise.

The concept of selection bias in scientific studies most commonly refers to a sampling error where the sample selected is "unrepresentative of the general population to which inferences are to be made." 1 Faigman et al., Modern Scientific Evidence § 4:16 (2018). Hendershott's report does not reflect selection bias. Using the objective criteria outlined above, his methodology located 675,504 Layering Loops. Together, these Loops account for only about 4.5% of Avalon's total equity trading volume, but almost half of its total equity trading revenue. The methodology is not scientifically unsound because so much of the Avalon trading fell outside the series of screening tests. Nor is it unsound because Hendershott did not undertake separately to analyze and characterize the portion of Avalon's trading that did not survive the conservatively constructed screening tests. As Hendershott has observed, the remainder of Avalon's trading may indeed include additional layering activity. The SEC has decided to proceed to trial, however, on only those trades that formed the Layering Loops. The SEC has no obligation to separately analyze the remainder of Avalon's trading that fell outside Hendershott's analysis to understand its characteristics and/or to exclude the possibility that it also contains trading consistent with layering.

II. The Lek Defendants' Motion to Exclude Pearson

The Lek Defendants contend that Pearson's testimony is inadmissible because it is unreliable. They assert that Pearson's methodology is crude and novel, suffers from selection bias, and lacks probative value. For the following reasons, the motion is denied.

Pearson constructed a set of screening tests to identify instances of linked equity and options trading. He broke that trading down into groups that shared characteristics, and then, using conservative criteria, located Loops of equity and options trading that formed patterns consistent with a Cross-Market Strategy that created profits by manipulating prices. He tested the reliability of his methodology through a series of Further Analyses, repeatedly citing to authority in the field for the tests and analyses that he employed. He explained the basis for his findings that the Cross-Market Strategy was deceptive and harmful to other market participants. His analysis was objective, detailed, well-supported by reference to academic research, and thorough. There is no basis to exclude it from the trial.

The Lek Defendants first contend that Pearson's methodology is too crude and not carefully tailored to identify only Loops that are consistent with the Cross-Market Strategy. For example, they point out that Pearson's model identifies Cross-Market Loops where the first trade is an options trade, as opposed to a stock trade. This, and other examples of individual trades which the Lek Defendants contend were improperly captured in the Cross-Market Loops, fails to undermine the admissibility of Pearson's testimony about his model and the Cross-Market Loops identified by his model. The Lek Defendants have not shown that, when the entire pattern of trading in a Loop is examined, the model has failed reliably to identify Cross-Market Loops consistent with manipulative trading. The Lek Defendants have offered no basis to find that manipulative cross-market trading may only exist if a trader strictly adheres to a circumscribed set of steps in placing trades. Nor have they pointed to any material variations from the parameters established by the model that might undermine the model's reliability. Variations in trading that would naturally occur when trading is conducted by different individuals over time do not undermine the utility of Pearson's model, which is constructed with a series of conservative screening tests.

The Lek Defendants also assert that Pearson's testimony is inadmissible because his model is novel and developed for this litigation. Pearson is an expert in the field of derivative financial instruments and used a commonly employed method for identifying and analyzing trading strategies in that field. He identified the characteristics of a manipulative Cross-Market Strategy, created screening tests to locate the Avalon trading consistent with that strategy, and then further analyzed the trading to confirm that the screening tests had indeed located trading that was consistent with a Cross-Market Strategy. As described above, having identified a universe of trading that bore the characteristics of a Cross-Market Strategy, Pearson tested his hypothesis that the trading was indeed manipulative with a series of inquiries. Many of the analytical tools he employed in that process are far from novel. They are tools described and employed in articles appearing in peer-reviewed journals. Much of his report is supported by citations to published works in the field of economics. A methodology may be reliable even if novel. The Lek Defendants have not shown that Pearson's model lacks the reliability required by Daubert and its progeny.

The Lek Defendants next argue that Pearson's testimony should be excluded because his entire analysis suffers from selection bias. The Lek Defendants explain that the trading in the Cross-Market Loops represents only a miniscule amount of the trading done by those traders, who largely traded stocks with no related options trading. They complain that Pearson did not analyze these traders' unrelated stock trades to discern their more general trading strategies. As was explained in connection with the motion to strike the Hendershott testimony, this is a misuse of the term selection bias. Pearson does not offer opinions about the entirety of Avalon's trading or about stock trading unconnected to options trading. He does not claim that the Cross-Market Loops are representative of the trading activity of any set of traders. Thus, Pearson was not required to apply his analysis to a random sample of the entirety of the Avalon trading data. Accordingly, the Lek Defendants' motion to exclude Pearson's testimony is denied.

III. The SEC's Motion to Exclude Ross

The SEC moves to exclude Ross's expert testimony, which the Lek Defendants seek to introduce to rebut testimony from Hendershott and Pearson. The SEC contends that Ross is unqualified to give his proposed testimony and that his opinions are unreliable and would confuse the jury. The SEC is largely correct and its motion is granted, with the exceptions identified below.

A. Ross's Expertise

Ross is unqualified to give an opinion about the phenomena of layering and cross-market manipulation or about high-frequency trading practices more generally. Nothing in his educational background, his work experience, or even his prior work as an expert gives him the necessary expertise to opine on these matters or to critique other experts' opinions on these topics.

To testify as an expert witness, an individual must be "qualified as an expert by knowledge, skill, experience, training, or education." Fed. R. Evid. 702. "To determine whether a witness qualifies as an expert, courts compare the area in which the witness has superior knowledge, education, experience, or skill with the subject matter