Class-action litigation for fraud on the market typically focuses on purchasers and sellers of stock. Yet those that traded in options on the shares can also be harmed. In a recent paper, we draw from experience in In re Apple, Inc. Securities Litigation (N.D. Cal. 2022) to describe the issues related to including options in a certified class in the face of substantial opposition from defendants.

In the Apple case, plaintiffs claimed that the company had inflated its share price in early November 2018 with misleading statements about demand for its products in China. In February 2022, the district court certified a class consisting of purchasers of stock during the relevant period. Yet it also sought testimony on the efficiency of the market for Apple options for purposes of invoking the “fraud on the market” doctrine and determining the feasibility of a common methodology for calculating damages for options traders. In March 2023, based on the testimony of expert witnesses Don Chance and Steven Feinstein, the court modified its class certification order to include purchasers of call options and writers of put options during the class period. The result was a $490 million settlement of the case in March 2024.

Options Market Efficiency

Since the Third Circuit’s decision in Deutschman v. Beneficial Corporation,[1] securities class actions have often included options traders alongside purchasers and sellers of stock. In considering whether options traders may invoke the “fraud on the market” presumption of reliance under Erica P. John Fund v. Halliburton,[2] one must recognize that a stock option is designedto move in response to a change in the underlying stock price. For example, market makers generate quotations for exchange-listed options by deriving their value from real-time stock prices and five additional factors: exercise price, the risk-free interest rate, time to expiration, volatility of the stock, and dividends. The widespread use of option deltas (the ratio of the change in option price to the change in stock price) for hedging likewise evinces acceptance of a quantifiable cause-and-effect relationship between stock and option prices.

Many courts thus take judicial notice that claims of “options-holders and stockholders are in most cases sufficiently similar that they should be consolidated ‘in form and in fact.’”[3] Other courts have required litigants to establish the informational efficiency of options markets independently of the underlying stock market. The methodologies that courts commonly employ to gauge stock market efficiency, however, do not map neatly on options markets. In Cammer v. Bloom, the court identified five indicators that it found probative of market efficiency for common stock: high trading volume, analyst coverage, listing/market maker coverage, Form S-3 eligibility, and an observable cause-and-effect relationship between company announcements and security price movements.[4] Unger v. Amedisys[5] and Krogman v. Sterritt[6] recognized three additional factors: market capitalization, public float, and narrow bid-ask spreads.

In Apple, the district court sought expert testimony from plaintiffs about the application of the Cammer-Krogman factors in assessing options market efficiency. As an example, the Apple defendants disputed plaintiffs’ claim that Apple options traded in an efficient market because they exhibited a low average volume per series (total volume among all option series divided by the total number of option series available for trading). Chance explained that options do not need high trading volume or a substantial number of market makers to trade efficiently because option prices are structurally bound to stock prices and the relationship is enforced by arbitrage. Low volume is thus not indicative of inefficiency of the entire market for options on a given stock – or even for any individual option series.

Likewise, the Apple defendants observed that the bid-ask spreads for Apple options were substantially higher (as a percentage of price) than the bid-ask spreads for the underlying stock. Chance found this argument unavailing: Options prices and volume are generally lower than stock prices and volume, respectively, and therefore market makers must charge higher percentage spreads on options trades to generate a reasonable return. Other factors, such as analyst coverage, Form S-3 eligibility, market capitalization and public float, relate to the efficiency of the market for the stock underlying an option and not trading in options themselves. By contrast, Chance asserted that movements in bid and ask prices for Apple options provided strong evidence of efficiency: For example, one study found that Apple option bid and ask prices update over 9,000 times per second.[7]

To demonstrate the cause-and-effect relationship required under the last Cammer factor, Feinstein conducted an event study to demonstrate that Apple stock responded to Apple’s earnings announcements. He then extended the methodology to options by calculating a synthetic stock price from Apple options using European put-call parity. Feinstein found that the synthetic stock price reacted significantly to Apple’s earnings announcements three out of four times in the 2018 sample year – the same frequency of significant reactions as exhibited by the underlying Apple stock. If the synthetic stock price implied by option prices reacted significantly to Apple’s earnings announcements, the option prices themselves must have been reacting to Apple’s earnings announcements.

Chance further examined Feinstein’s synthetic stock price test and found that over the sample period the synthetic stock price implied by the Apple options had a near-perfect correlation with the actual stock price. He adduced additional empirical evidence of the link between option prices and the underlying stock through an examination of the response of option bid and ask prices to stock price changes. Using available Apple options data, he also measured the midpoint of the bid-ask spread for over 150,000 calls and puts to determine whether the midpoint moved in the correct direction when the underlying stock price changed. The correct change occurred more than 80 percent of the time for calls and more than 79 percent of the time for puts – a statistically significant outcome.

Chance also examined a sample of deep-in-the-money calls and puts. He found that more than 97 percent of the time for calls and more than 98 percent of the time for puts, the midpoint of the bid-ask spread moved in the correct direction given the stock price change. Moreover, because deep-in-the-money options are very likely to be exercised, they should have a delta very close to 1 for calls and –1 for puts. Chance found that the empirical delta during the class period was 0.960 for calls and –0.939 for puts. These results were notable in that deep-in-the-money options accounted for less than 2 percent of all trading volume in the sample, thereby demonstrating that low volume does not indicate inefficiency.

Common Damages Methodology

Class action plaintiffs must also allege that the material misrepresentations or misleading omissions artificially inflated the price of the stock or call option (or depressed the price of a put option), such that plaintiffs’ loss is caused when the price declines following a corrective disclosure or when the truth becomes more generally known. Comcast Corp. v. Behrend further requires plaintiffs to propose a methodology for calculating damages common to the class.[8] Securities class action plaintiffs generally propose an event study to estimate how much artificial inflation was (i) triggered when the misinformation was disseminated or (ii) dissipated when disclosures ultimately corrected the misinformation. Plaintiffs’ experts may also propose valuation analyses to estimate what the security price would have been “but for” the alleged misstatement or omission.

As a common methodology for calculating option damages, Chance and Feinstein proposed using the Cox-Ross-Rubinstein binomial option pricing model,[9] with technical adjustments, to reprice each option position when opened and closed to eliminate the effect of the fraudulent inflation in the stock price. To limit damages to the inflation dissipated by corrective disclosures, as required by Dura Pharmaceuticals v. Broudo,[10] they further proposed to apply this methodology to a period  surrounding each corrective disclosure rather than to measure the change in inflation over the investor’s entire holding period.

ENDNOTES

[1] 841 F.2d 502 (3d Cir. 1988), cert. denied, 490 U.S. 1114 (1989).

[2] 563 U.S. 804 (2011).

[3] In re MicroStrategy Inc. Sec. Litig., 110 F. Supp. 2d 427, 440 (E.D. Va. 2000) (quoting In re Orbital Sciences Corp. Sec. Litig., 188 F.R.D. 237, 240 (E.D. Va. 1999)).

[4] 711 F. Supp. 1264 (D.N.J. 1989).

[5] 401 F.3d 316 (5th Cir. 2005)

[6] 202 F.R.D. 467 (N.D. Tex. 2001).

[7] See Torben Andersen et al., A Descriptive Study of High-Frequency Trade and Quote Options Data, 19 J. Fin. Econometrics 129-177 tbl. 3 (2021).

[8] 569 U.S. 27 (2013).

[9] J.C. Cox, S.A. Ross, & M. Rubinstein, Option Pricing: A Simplified Approach, 7 J. Fin. Econ. 229 (1979).

[10] 544 U.S. 336 (2005).

This post comes to us from Don Chance, the Norman V. Kinsey Distinguished Chair in Finance at Louisiana State University; Steven Feinstein, an associate professor of finance at Babson College and the founder, president, and senior expert of Crowninshield Financial Research; and Onnig H. Dombalagian (who did not participate in In re Apple Securities Litigation), the John B. Breaux Chair in Law and Business and the George Denègre Professor of Law at Tulane University. It is based on their recent paper, “The Class Certification of Exchange-Listed Options in Securities Class-Action Litigation,” available here.