In idealized, complete markets, option prices should not convey any new information or contribute to price discovery of underlying assets, but the leverage available to option traders might convince them to forego equity markets. Furthermore, option markets allow relatively easy access to trades based on anticipations of volatility. In this paper we consider whether option markets interpret the implications of firms being named as defendants in class action lawsuits. Our underlying proposition is that markets may underappreciate the dichotomous nature of resolutions to class actions, and we attempt to explore the returns to such a dynamic with option volatility strategies. We find consistent, positive, and frequently significant returns to option straddle and strangle positions held from six months to 1.5 years after a firm is targeted in a class action.

There is a growing literature that studies the general lead-lag relation between option and stock markets. Early work by Manaster and Rendelman (1982) finds evidence that option markets may provide a preferred outlet for informed investors. Easley, OHara and Srinivas (1998) develop a model of an economy where informed traders first choose the option market to trade, causing the option market to lead the stock market. More recent work by Diavatopoulos, Doran, and Peterson (2008), Bali and Hovakimian (2009), Cremers and Weinbaum (2010), Doran, Fodor and Jiang (2013) and Diavatopoulos et al. (2012, 2017) use option information to predict stock returns. The opposing view is that option prices are simply functions of underlying asset prices and do not participate in the price discovery process. DeLong et al. (1990), Chan, Chung and Johnson (1993) and Muravyev et al. (2013) provide support for the assertion that options trading has a negligible impact on stock prices. These studies also suggest options trading introduces excess volatility, reducing pricing efficiency in equity markets.

Relatively little research has considered the explicit trading in option positions to capitalize on the volatility framework expected from certain corporate events. In this paper we propose that markets may underappreciate the dichotomous nature of resolutions to class actions. We construct option straddle and strangle positions in anticipation of a large move in stock price as litigation proceeds toward a conclusion. While testing a range of return horizons, we find consistent, positive, and frequently significant returns to these option positions when held from six months to 1.5 years after a firm is targeted in a class action. Given the long-term nature of

our significantly profitable findings, it is possible that our results are not entirely based on the nature of class actions, but on positions formed preceding large market swings. Using a matched- pair control method, we control for this possibility, and our results remain robust.

The rest of the paper is as follows. In Section 1 we describe the data and methodology, Section 2 discusses our empirical results and Section 3 concludes.

1. Data and Methodology

Our sample begins by taking 3,715 federal securities class action lawsuits (class actions) cataloged in the publicly available Stanford Law Schools Securities Class Action Clearinghouse (clearinghouse) database from 1996 through June, 2015.4 It is well known that empirical test results can be sensitive to the proxy used to identify financial misconduct and the database used to assemble a sample of misconduct observations. Karpoff et al. (2017) posit that each database has a set of first-order features that have implications for financial research, namely; (1) scope of coverage, (2) dates of initial revelation, (3) identification of fraud, (4) omitted events. They also provide a number of suggestions to guide research related to financial misconduct, which we have implemented. Our choice of Stanford's Securities Class Action Clearinghouse is well matched to our research question. Indeed, Karpoff et al. (2017) demonstrate that Stanford's Securities Class Action Clearinghouse data are ideal for analyzing pre/post comparison tests that require good information about the initial public revelation of misconduct. Clearinghouse data notes the exchange where a companys stock trades, and we require NYSE, NASDAQ, or AMEX listings to proceed with our analysis. We ignore privately traded companies and ADR listings. As our intention is to consider the returns of mid-to-long term volatility-based option strategies (straddles and strangles) in the wake of litigation filings, we use the filing date taken from the clearinghouse database as the starting date for tracking option return performance.5 We merge clearinghouse data to the Optionmetrics database and

track strategy returns using the midpoint of the bid-ask spread of contracts at each point to calculate returns (see, e.g., Coval and Shumway (2001); Conrad et al. (2013); Gao et al. (2017)). As the only common linking variable between clearinghouse data and Optionmetrics is the ticker symbol of the sued firm at the time of litigation filing, and because ticker symbols are subject to change, we inspect each observation point to ensure the Optionmetrics company name matches or closely approximates that of the sued firm recorded by the clearinghouse and that the observation is that of a publicly traded company.6 Firms may appear in the sample more than once if they are named in multiple class actions with active litigation periods (from filing date to resolution date) that do not overlap. If active litigation periods do overlap, only the first class actions option strategy results are utilized in our results.7 Option prices, identifying characteristics, strike prices, times until expiration, and open interest levels, as well as underlying stock prices, are gathered from Optionmetrics from 1996 through year-end 2016.

Our underlying proposition is that markets may underappreciate the dichotomous nature of resolutions to class actions, and we attempt to explore the returns to such a dynamic with relatively straightforward strategies. Thus, we do not attempt to forecast the type of resolution that concludes a lawsuit, nor do we try to predict the relative magnitude of the potential damages that a class action might inflict upon the firm.8 Instead, we create three, similar-type option strategies all designed to benefit from any large movement in underlying stock price, whether positive or negative, as litigation proceeds toward a conclusion. In each of our option strategies, positions match together long call and put contracts of identical expiration dates in order to attempt a volatility-based investment approach. We first form closest to at-the-money (ATM) straddle positions in which accompanying call and put options have identical strike prices. In these straddles we utilize the available strike price closest to the current underlying strike price. Thus, one of the call or put options in the straddle is usually out-of-the money (OTM) while its matching contract is in-the-money. Secondly, to allow for potentially lower costs to the willing investor, we form strangle positions in which the OTM call and OTM put closest to ATM status are paired together (OTM1 strangle or OTM1). Finally, when additional contracts are

available, in order to consider even lower initial investment costs, we form further strangle positions in which the OTM call and OTM put next closest to ATM status are paired together (OTM2 strangle or OTM2).9 For robust consideration of liquidity constraints we consider minimum open-interest threshold requirements of 10, 50, or 100 Optionmetrics call and put contracts in our analysis. This need for liquidity of mid-to-long term options, and the scarcity of such liquidity amongst most small-to-mid size firms, reduces our effective sample to 1,089 non- overlapping, firm-class action observations. Summary statistics recapping the full clearinghouse and final, effective samples are shown in Table 1. The median length of time until resolution of a litigation is 717 days for thoseobservations resolved by the time of our analysis.10 Our focus is on a mid-to-long term volatility- based investment strategy, for we do not attempt to pinpoint the probability of any specific lawsuit being resolved under any particular timeframe. For robustness, we consider various horizons for holding our option strategy positions, spanning from lengths of one month to over two years.11 For additional robustness, we consider creating these one-month to two-plus-year returns by buying our long ATM, OTM1, and OTM2 positions based on options available with a variety of times available until maturity. For example, we consider forming long positions based on options with over two years until maturity (and qualifying open interest) and tracking one- month through two-year return performances. Additionally, as another example, we consider forming long positions based on options with between 1 and 1.5 years until maturity (and qualifying open interest) and tracking 1-month through 1.5-year return performances, etc. In cases where more than one eligible position might be created we utilize only option pairs with the longest time remaining until maturity.

While our initial long straddle (ATM) and strangle (OTM1 and OTM2) return results consider the profitability of investments in dichotomous option positions, the recorded return levels and their statistical significances (relative to a return of zero) do not consider contemporaneous market conditions. As seen in Table 1, the option positions formed span many years and cover booming, stable, and slumping markets. Thus, we conclude our analysis with a matched-pair approach which calculates returns and significance levels of ATM, OTM1, and OTM2 positions on a relative basis. For each class action observation in the sample, on the day of the class action (on which we have constructed initial ATM, OTM1, and OTM2 positions) we consider all Optionmetrics firms with at least 100 call and put contracts available of identical time until expiration as the class action firm. Because data for matching firms is typically available amongst larger firms, we provide only results requiring an open interest level of at least 100 for both sample and matched, control firms.

Each potential control firm is ranked based on closeness to the market capitalization (size) of the class action firm on the class action date (with 1 being the potential control firm closest to the class action firms size). Each potential control firm is also ranked based on closeness to the average implied volatility of ATM calls and puts of the class action firm on the class action date (with 1 being the potential control firm closest to the class action firms ATM call and put average implied volatility).13 The potential control firm with the smallest sum of ranks is declared to be the matched-pair control firm for the class action observation. Abnormal returns for class action firm option strategies ATM, OTM1, and OTM2 for various holding periods are subsequently calculated by subtracting the analogous, respective ATM, OTM1, and OTM2 returns of the matched-pair control firms. Significance levels, relative to a return of zero, are calculated based on these abnormal returns.

2. Empirical Results

Table 2 presents raw return results. We note a right-skewed distribution of returns as mean returns throughout Table 2 are of a positive sign, while median returns throughout the table are negative. Our focus is on mid-to-long-term straddle and strangle performance as the

expectation is for some time, ranging from months to years, is typically necessary for a class action to be resolved. For robustness, we consider a variety of times until options expire, and we track the performance of holding our three strategies (ATM, OTM1, and OTM2) for times ranging from a month to 1.5 years. Because of open interest minimum requirements and the tendency of investors to eschew long-

term options, sample sizes are largest (smallest) in Panel C (Panel A) of Table 2, where we consider straddles and strangles with 0.5-1 years (1.5-2 years) until expiration.

Certain tendencies emerge amongst the returns data of Table 2. Mean returns are not only predominantly positive, but are significantly positive in many combinations of option time until expiration and the times we consider holding the various strategies (ATM, OTM1, or OTM2). The profitable returns to straddles and strangles generally appear highest when positions are held for at least a few months, as in many cases no clues toward a class actions resolution would have emerged in the first few months following filing. Most results for ATM, OTM1, and OTM2 holding periods under six months are insignificant (though positive) in our results, while holding periods of six months and longer see many more significantly positive returns. We also find the cheaper, OTM2 positions, which require bigger underlying stock price movements in order to be profitable, to have generally the highest average returns, but these depend on the large returns to a small number of strategies, for median OTM2 returns are generally lower than ATM and OTM1 median returns. Finally, we note that larger open interest requirements, within the scope of our considerations, do not seem to result in markedly worse mean returns.

Specifically, we begin finding more significant, positive position returns with holding periods of at least six months, even though sample sizes decline from shorter-term holdings. For example, in Panel A of Table 2, with the lowest open-interest minimum requirement of 10 call and 10 put contracts, we note six-month straddle returns of 4.1%, significant at the 5% statistical level. Less expensive strangles (OTM1 and OTM2) are even more profitable, on average, with 9.2% and 9.9% six-month returns, respectively. When open-interest requirements increase to 50 (100) call and put contracts to form positions, ATM, OTM1, and OTM2 returns increase to 4.7%, 9.9%, and 10.4% (5.9%, 11.2%, and 12.3%), respectively.

Raw returns to straddles and strangles in Panel A of Table 2 increase with longer holding period returns of nine months or one year, but the increased opportunity costs of longer holding

times do not seem to offset the additional gains. The longest possible holding times of strategies seen in this study, the 1.5-year holdings of Panel A, see the largest raw returns of all. For example, with the highest open-interest minimum requirement of both 100 calls and 100 puts needed to form positions, ATM, OTM1, and OTM2 returns are highly significant 10.6%, 11.1%, and 20.7%, respectively.

The straddle and strangle mean returns seen in Table 2 are impressive initial evidence that simultaneously betting on both large future upswings and downswings in stock prices, via straddle and strangle option strategies, can prove highly profitable. The market does not appear to fully appreciate the large future movements often commensurate with a publicly traded firms status as a class action defendant.

Question

A straddle consists of a long call and a long put. A large straddle return must come from either the long put or the long call. Which position is more likely to explain the very large returns of the straddle strategy? If you can find evidence in the reported tables in the paper to support your argument, explain the evidence. If not, support your argument with economic reasoning. (500 words)