A growing case law is recognizing private damages claims for market manipulation such as spoofing. A spoofer places orders for an asset while intending  to cancel the orders before they execute. The point is to move the price of the asset rather than to trade. In 2010, Congress outlawed spoofing in the futures markets, leading to criminal prosecutions by the U.S. Department of Justice (DOJ). The Securities and Exchange Commission (SEC) has brought enforcement actions for manipulation in the stock market as well. Private plaintiffs have increasingly pursued manipulation claims. But determining whether a trade occurred at a manipulated price has not always been straightforward.

For many years, government prosecutions and enforcement actions have often focused on the manipulator’s gains rather than investors’ losses. The SEC typically seeks disgorgement, and the U.S. Supreme Court has recently held that the SEC need not show that investors suffered any pecuniary loss to obtain the defendant’s profits. By contrast, private plaintiffs must establish that the manipulation caused them an economic loss, so the magnitude and duration of damages are central questions.

The courts have generally started from a common assumption that the price effect of spoofing is short-lived. In Gamma Traders, a Commodity Exchange Act case alleging spoofing in precious-metals futures, the Second Circuit held that a plaintiff who has not traded in close temporal proximity to the spoofing must plead, “even in general terms, how long it takes for the market price to return to a non-artificial level after a spoof.”

At any moment an observed price path can be significantly higher or lower than where it began for entirely random reasons, even in a random walk with mean zero (like the sum of fair coin flips). Thus, one way to recover the true effect of manipulation is to average across many realized price paths. But over longer horizons an average may be contaminated by unrelated news, and courts have insisted that plaintiffs identify the price impact of each manipulative episode.

In a recent article, I set out two fundamental principles for estimating losses caused to investors by market manipulation. First, price impact is most precisely measured during and immediately after the manipulative activity, making it appropriate to “forward-cast” that price impact as suggested by Ferrell and Saha (2007, 2012) rather than “back-cast” from a later date. Second, because manipulation “sends a false pricing signal to the market,” its price impact is likely to decay and may even disappear once the market fully realizes the falsity of the signal. Because market participants update beliefs as they observe data, the realization that the signal is false may be a continuous process well-approximated by price impact steadily decaying towards the price that would have emerged “but for” the alleged misconduct.

I apply these principles by fitting a decay model to the immediate, short-run price impact, starting at the measured peak of the manipulation relative to the price just before the episode began. I then forward-cast that decay to obtain the but-for price for each asset over time. I fit the decay model to each episode separately, so that the price impact of each is estimated using only information relevant to that episode. This methodology both overcomes the “random walk” problem by not basing price impact estimates on random noise and does not rely on averages.

A manipulator need not account for most of the trading in an asset to distort its price. If he “ignited” other traders to trade, a strategy market regulators call “momentum ignition,” he is causally responsible, in a but-for sense, for the distortion that other traders then extend. The price impact of manipulation thus turns on the liquidity of the instrument being manipulated. A spoofer in an illiquid instrument therefore has reason to bait in only one direction, which is the pattern that prosecutors have alleged in thinly traded assets. An asymmetric price impact of this kind can result in far more persistent price displacement, and thus a far larger class of injured purchasers and sellers, than canceling out on the round trip.

I apply this framework to SEC, CFTC, and DOJ actions whose filings give the times of the alleged manipulation to measure the price impact of the allegedly manipulative activity. Each case is only an example of how one might estimate investors’ losses if the allegations were proven. Of course, the methodological choices are preliminary and based on what has been disclosed thus far, are made for purposes of this rough estimate, and are subject to revision as more evidence is revealed.

For example, in the Patel case, the speed of decay appears to differ from episode to episode. In 170 episodes with an estimable decay curve, half of the distortion disappears within about four minutes in the typical (median) episode. In 16 episodes, the episode’s own curve declines slowly or not at all, and the price remains slightly distorted up to the 90-day cutoff. Investors’ losses in all these episodes come to $61.16 million, far more than the defendant’s gains, with most of those losses arising from the long-run distortion. In another case, SEC v. Shuang Chen, five such episodes account for 99.4% of estimated losses of about $9.47 million, far more than the profits the complaint alleges for the same examples, while the estimated distortion from some episodes fades within minutes. In one episode in Dawson Geophysical, where the price was allegedly pushed down, half of an estimated 1.3% price distortion disappears within about 3.5 minutes of the peak, and the estimated distortion falls below one cent a share about six minutes after the peak. In a case like that, the gains to manipulators may far exceed investor losses.

Where the manipulation’s price impact was fleeting, disgorgement of the defendant’s gains may be preferred to compensating investor losses. Where manipulation was longer lasting, investor losses can exceed the manipulator’s gains many times over, and a remedy measured by gains alone may lead to under-deterrence.

Joshua Mitts is the David J. Greenwald Professor of Law at Columbia Law School. This post is based on his recent article, “Market Manipulation Damages,” available here.