Volatility Skew, Earnings Announcements, and the Predictability of Crashes. Andrew Van Buskirk *

Transcription

1 Volatility Skew, Earnings Announcements, and the Predictability of Crashes Andrew Van Buskirk * Fisher College of Business Ohio State University 2100 Neil Avenue Columbus, OH van-buskirk_10@fisher.osu.edu First Draft: September 2009 This Draft: April 2011 * An earlier version was circulated under the title Implied Volatility and Firm-Level Tail Risk. I appreciate helpful comments from Ray Ball, Jonathan Rogers, Doug Skinner, Eric So, Pietro Veronesi, and workshop participants at the University of Illinois at Chicago, University of Houston, University of Texas at Dallas, and Washington University in St. Louis. Electronic copy available at:

2 Volatility Skew, Earnings Announcements, and the Predictability of Crashes Abstract This paper examines the relation between firm-level implied volatility skew and the likelihood of extreme negative events, or crash risk. I show that volatility skew identifies which firms are likely to experience crashes, but only in short-window earnings announcement periods. The predictive power is incremental to the information in historical volatility, financial reporting opacity, and even the current period s earnings surprise. In contrast, volatility skew does not predict crashes outside of earnings periods, even in regressions with few independent variables, and even when those periods include management earnings forecasts. At best, volatility skew contains modest information about future price declines, but only when looking at cumulative returns over several months. While prior research concludes that volatility skew contains information about future earnings shocks, these results indicate that, outside of quarterly earnings announcements, option investors have difficulty predicting when the adverse earnings news will be revealed. Electronic copy available at:

3 1. Introduction The precise definition of a crash or tail risk is debatable, but the connotation is clear. As The Economist (3/24/2011) puts it, For mere mortals, it has come to signify any big downward move in a portfolio s value. These sudden downward moves (or the risk thereof) have severe implications: firms face an increased risk of litigation following a large stock price drop (Rogers et al. 2010); traditional option pricing models must be abandoned in favor of those explicitly incorporating jump risk (Bakshi et al. 1997); risk-management measurements like Value-at-Risk struggle in the face of severe tail risk (Berkowitz and O'Brien 2002). In the extreme, crashes can disrupt financial markets. Recently, interest in crashes has surged in both the academic and investment communities. Following earlier research focusing on the anticipation of adverse events, such as bankruptcies (Warner 1977) and credit downgrades (Hull et al. 2004), more recent research has focused on understanding the precursors of stock crashes, identifying factors like management equity incentives (Kim et al. 2010a), tax avoidance (Kim et al. 2010b), and financial reporting opacity (Hutton et al. 2009; Bradshaw et al. 2010). In practice, firms such as PIMCO, Deutsche Bank AG, and Citigroup have begun offering funds or securities designed to provide tail-risk protection to clients (Harrington et al., 2010), suggesting the belief that crashes are predictable. This paper examines how options markets anticipate crashes, looking specifically at whether implied volatility skew predicts extreme negative returns. Prior research has demonstrated a positive link between volatility skew and crashes at the market level (Bates 2000; Doran et al. 2007), but has not explored the relation for individual stocks. There is reason to believe that adverse events are more difficult to predict at the firm level than at the market level. At the firm level, investors do not receive a steady and unfiltered flow of news over time, 1

4 especially when the news is bad. Instead, managers frequently delay the revelation of bad news through obfuscation (Li 2008), opaque financial reporting (Hutton et al. 2009), or favoring disclosure of good news over bad news (Kothari et al. 2009). I study the predictability of crashes at the firm level, and, in particular, whether the predictive ability differs between short-window earnings announcement periods and longer-window non-earnings periods, when managers have greater discretion to disclose or withhold information. My results indicate that volatility skew predicts crashes, but only those crashes occurring in earnings announcement periods. For these earnings period crashes, volatility skew demonstrates very strong predictive ability, even after controlling for a variety of factors previously shown to predict crashes, including the reported earnings surprise. In other words, prior to earnings announcements, option markets have information about which firms are more likely to experience a near-term crash. Option prices reflect that information. For crashes outside of earnings announcement periods, the story is different. There is no detectable relation between volatility skew and non-earnings crashes, even for simple regression specifications that exclude many of the traditional independent variables, and even in periods in which earnings news (in the form of management forecasts) is voluntarily disclosed. At best, volatility skew has some information about future negative news, but only when classifying negative news based on cumulative returns measured over several months (rather than sudden downward movements). Even here, the relation is statistically weaker than the earnings period results and is sensitive to the cutoff used to classify extreme negative returns. Outside of earnings announcement periods, it seems that if option investors have information about future adverse news, they do not know how or when that news will be revealed to the market. 2

5 This study adds to the large and growing body of research related to the causes and predictability of extreme negative events. This area includes the prediction of bankruptcies (Altman 1968), bank failures (Jin et al. 2011a), credit downgrades (Hull et al. 2004), qualified audit reports (Dopuch et al. 1987), and accounting restatements (Jones et al. 2008), not to mention the prediction of natural disasters such as earthquakes and hurricanes outside the financial domain. 1 These and other studies have examined the ability of both accounting-based and market-based signals to predict negative events. I extend the crash prediction literature by demonstrating that firm-level crashes are predictable, albeit in limited circumstances (i.e., in short-window earnings announcements). In addition, this study relates to the broad literature investigating the relation between option and equity markets. In particular, I provide evidence that the previously-documented relation between volatility skew and crashes is sensitive to the event periods used. While prior research suggests that options investors have information about future returns and future earnings (Xing et al. 2010), my results emphasize that having information about future earnings is not the same as knowing when that information will be revealed. This paper also speaks to the topic of market-based regulation. The recent financial crisis has prompted suggestions that market-based measures would allow for more timely (and presumably less costly) regulatory interventions. For example, regulators could use prices on credit default swaps as a signal that banks need to raise capital (Zingales 2010). The success of such proposals would depend upon the market s ability to detect business failure more quickly than regulators. The results in this study suggest that, outside of regular and anticipated public 1 Sornette (2002) discusses the links between extreme behavior in seemingly disparate contexts, such as structural engineering failures, social unrest, natural disasters, and financial crises. 3

6 disclosures, option investors may be limited in their ability to acquire private information before a failure. Finally, this paper adds to our understanding of the role of earnings announcements in providing information to investors. On one hand, researchers have recognized the disciplining role of accounting earnings, in terms of evaluating or confirming the truthfulness of managers prior disclosures (Gigler and Hemmer 1998). On the other hand, we know that earnings announcements provide only a modest amount of information on average (Ball and Shivakumar 2008), raising the question of whether these events are important. The results in this paper are consistent with periodic earnings announcements being useful not because they provide substantial information, on average, but because they discipline managers to disclose adverse information when they might otherwise choose to withhold it. The rest of the paper is organized as follows. Section 2 discusses related research and my hypotheses. Section 3 describes the sample selection and provides some descriptive statistics for the data. I document my primary analysis in Section 4 and extend the analysis of non-earnings periods in Section 5. Section 6 concludes. 2. Prior Research and Empirical Predictions This paper builds upon several topics in both finance and accounting, all of which are substantial in their own right. The following sub-sections reference these topics as they relate to this paper, but are not meant to provide a comprehensive survey of any individual area Crashes 4

7 Many studies have focused on understanding the factors that precede crashes, including hedging strategies (Gennotte and Leland 1990, analyzing the October 1987 market crash), trading-based measures like volume and prior returns (Chen et al. 2001), and negative earnings surprises, especially for growth firms (Skinner and Sloan 2002). More recently, researchers have looked at how managerial actions can lead to stock price crashes. Kim et al. (2010a) find that equity incentives, particularly those of the CFO, are correlated with crashes. Kim et al. (2010b) show that corporate tax avoidance is associated with crash risk, as well. Hutton et al. (2009) find that firms with opaque financial reporting are more likely to experience crashes, arguing that managers stockpile negative news until the revelation of that stockpiled news results in a crash. The Hutton et al. argument is consistent with other evidence that managers frequently obfuscate (Li 2008) or withhold (Kothari et al. 2009) bad news from investors. Bradshaw et al. (2010) extend the Hutton et al. study by investigating the extent to which option markets understand the relation between opacity and future crashes. The Bradshaw et al. study relates to the more general question of how equity and options markets interact Interaction Between Options Markets and Equity Markets Since the development and rapid growth of options markets in the early 1970s, there has been substantial academic interest in the interaction between option and equity markets, with one recurring question being whether options markets anticipate future equity behavior. This question has evolved into two distinct branches of research. The first, based on the idea that privately-informed investors may prefer to transact in options markets rather than equity markets, 2 investigates whether option investors have superior information relative to equity 2 Reasons for this may include lower transactions costs, higher obtainable leverage, or the equity constraints like short-selling. 5

8 investors. Studies such as Manaster and Rendleman (1982), Amin and Lee (1997), Xing et al. (2010), Johnson and So (2010), and Jin et al. (2011b) find evidence consistent with this conjecture. Namely, they show that activity in the options markets foreshadows average future equity returns. As these studies focus on the prediction of average risk-adjusted stock returns, they are predicated on some informational inefficiency or differential transactions costs between options and equity markets. 3 The second branch of research focuses on stock price crashes, and stems from a curious, but well-known, pattern in the volatilities implied by observed option prices: when plotted against strike prices, the distribution resembles a smile or a smirk (Rubinstein 1994; Jackwerth and Rubinstein 1996). Implied volatility at extreme strike prices (i.e., for out-of-the-money puts and calls) is higher than for at-the-money options (the smile), and implied volatility is higher for low strikes than for high strikes (the smirk, sometimes called the skew). This pattern is in stark contrast to the fundamental Black-Scholes assumption that expected volatility is independent of the option s strike price, and has been observed in foreign currency and equity options both domestically and around the world (Hull 2006), as well as at the index and individual firm level (Bakshi et al. 2003; Bollen and Whaley 2004). Researchers have offered many reasons for the observed pattern in implied volatilities, including risk aversion (Bakshi et al. 2003), a negative volatility risk premium (Bakshi and Kapadia 2003), and rare event uncertainty (Liu et al. 2005), but perhaps the most straightforward is described by Bates (2000). He argues that volatility skew reflects investors perception that a 3 There is also the possibility that future returns are not adequately adjusted for risk. Yan (2010) shows that jump risk is priced by the market, and that different portfolios formed on the basis of jump risk (measured using option characteristics) yield systematically different future returns. In a related study, Bollerslev and Todorov (2011) conclude that the compensation for rare events represents a sizable portion of the historical equity premium. As a result, risk/return models that omit priced jump risk could indicate that option investors predict future returns even when option participants do not have superior information. 6

9 significant price decline in the underlying is more likely than the lognormal distribution underlying Black-Scholes would suggest. Regardless of why the pattern exists, there is evidence that implied volatility functions contain information about future stock price behavior, specifically crashes. Examples include Bates (1991), who shows that out-of-the-money index puts became especially expensive in the year leading up to the October 1987 crash; Doran et al. (2007), who show that the skew in index-level implied volatility distributions has information content about market crashes; and Bradshaw et al. (2010) who show that firms with greater volatility smirks are more likely to experience a crash in a given year. Whether volatility skew (or other signals) predicts crashes is distinct from the question of whether option investors can predict future abnormal equity returns. 4 In contrast to the prediction of average returns studied in prior research, the idea that volatility skew predicts crashes requires no informational inefficiencies or frictions between equity and options markets; if the probability distribution of the underlying stock is not lognormal, its implied volatilities will vary with the strike price rather than being constant (Hull 2006). As a result, differently-shaped implied volatility functions can be associated with an increased likelihood of a crash even if option market participants and equity participants are on equal footing in all respects a higher likelihood of crashes may be offset by higher returns in non-crash states. Thus, whether and how volatility skew predicts crashes can be viewed as a less restrictive, and more fundamental, research question than whether option investors have superior information relative to equity investors Relation between Implied Volatility and Returns in Earnings Announcement Periods vs. Non-Earnings Announcement Periods 4 See, for example, Chen et al. (2001, 348), who are explicit in their desire to forecast crashes, stating that they are not in the business of forecasting negative expected returns. 7

10 Although many studies suggest that crashes are related to earnings information (Skinner and Sloan 2002; Xing et al. 2010; Hutton et al. 2009), the distinction between earnings periods and non-earnings periods is especially pertinent. If opacity leads to future stock price crashes (when the stockpiled negative news is revealed) (Hutton et al. 2009), then predicting crashes is essentially a prediction of when firms will reveal their previously-hidden bad earnings news. Earnings announcements are obvious candidates for when such news would be announced. It is less obvious that managers will be forthcoming with that news outside of their regular earnings disclosures, especially when those managers have been hiding the news previously. In fact, existing research gives reason to believe that earnings announcements are anticipated differently from non-earnings period information events, in general. Patell and Wolfson (1979, 1981) provide early evidence that implied volatilities increase as earnings announcements approach, and that the increases tend to be associated with the magnitude of the earnings surprise. Isakov and Perignon (2001) show similar results and extend this research by comparing the behavior of implied volatility around earnings announcements for positive versus negative earnings surprises. These results are interesting, but not surprising. Earnings announcements are predictable events that feature the issuance of material information to the marketplace. The increase in implied volatilities is a reflection of the anticipated increase in event-period volatility. Significant price changes occur in non-earnings periods as well as earnings periods; Lee and Mykland (2008) confirm this intuitive statement by studying high-frequency trading data for three individual firms and showing the majority of equity price jumps occur with unscheduled company-specific news events. It is an open question, though, whether large stock price changes are predicted by options market participants in non-earnings periods. On one hand, Cao et al. 8

11 (2005) document that call option volume is significantly higher in periods leading up to takeover announcements, indicating that earnings announcements are not the only events anticipated by option markets. On the other hand, Cao et al. (2005) note that option volume is not informative about future stock returns in normal times. Similarly, in their study of management earnings forecasts, Rogers et al. (2009) document very little increase in at-the-money implied volatility prior to the forecast (especially compared to pre-earnings options behavior). Overall, there is good reason to believe that option investors may better anticipate earnings announcement information than information events in non-earnings periods Hypotheses Following from the discussion above, my hypotheses are relatively straightforward. First, I expect that firm-level volatility skew predicts extreme negative returns in earnings announcement periods: H1: Volatility skew is positively associated with the likelihood of stock price crashes in earnings announcement periods. This continues the previously-discussed stream of literature examining the interaction between options and equity markets and is similar in spirit to prior studies of skew and market crashes at the index level (Bates 1991; Doran et al. 2007). However, the focus on individual firms options allows me to control for variation in underlying firm characteristics (e.g., size and leverage) in a way that index-level studies have not. Moreover, as Garleanu et al. (2009) point out, both the shape of the IVF and the demand pattern is different for equity options than it is for index options, which makes it difficult to extend the conclusions drawn from index-level data to individual firms. 9

12 My second hypothesis relates to non-earnings periods: H2: Volatility skew is positively associated with the likelihood of stock price crashes outside of earnings announcement periods. Distinguishing between earnings and non-earnings periods extends the prior crash literature by examining the events that options investors anticipate. Even if we know that option investors have some information about future earnings information (Xing et al. 2010; Hutton et al. 2009), we know little about when that earnings news is revealed to the market. This is especially relevant if managers are actively trying to hide adverse earnings news from investors, either through obfuscating disclosures (Li 2008), misleading accounting numbers (Hutton et al. 2009), or the withholding of bad news disclosures (Kothari et al. 2009). 3. Data and Summary Statistics 3.1. Sample Selection Earnings announcement information comes from the I/B/E/S historical database. I retain announcements for which I/B/E/S reports both an actual earnings value and at least one analyst estimate for the fiscal period being reported. I further require market value, price, and return data on CRSP, and (from Compustat) non-missing book value, total liabilities, assets, current period income, and sufficient data to calculate the opacity measure used by Hutton et al. (2009). Finally, I eliminate observations with stock prices less than $5 prior to the earnings announcement. This process results in 79,630 earnings observations between 1996 and I obtain options data from the OptionMetrics historical option prices database, which includes closing bid and ask prices, option volume, open interest, and the implied volatility and other option Greeks (e.g., delta, gamma, and vega) for puts and calls on the entire listed U.S. equity market. For each earnings announcement, I obtain these variables on two dates: three 10

13 trading days prior to the earnings announcement and three trading days following the earnings announcement (when the earnings information is assumed to have been processed by the market). I refer to the earlier date as the pre-earnings measurement date and the later date as the post-earnings measurement date. Because I am interested in distinguishing between earnings announcement information and non-earnings announcement information in option prices, I retain only those options expiring after the current earnings announcement, but before the subsequent earnings announcement. As a result, the options measured at the pre-earnings date include the impending announcement, but no other, in their horizon. The options measured at the post-earnings date include no earnings announcements in their horizons. In order to eliminate implied volatilities that are likely to be measured with error, I delete observations with the following characteristics: the option s bid-ask spread is negative or greater than 50% of the midpoint of the bid and ask or the option has negative time value (option price is greater than the difference between the strike price and the closing price. Finally, like Bollen and Whaley (2004), I exclude options with absolute deltas below 0.02 or above Descriptive Statistics Descriptive statistics are presented in Tables 1 and 2. As shown in Table 1, there are 61,075 earnings announcements from 1996 through the 3 rd quarter of 2009 for firms that had quoted options prior to the earnings announcement. This population represents approximately three-quarters of earnings announcements with the required I/B/E/S, CRSP, and Compustat data, with the options coverage increasing markedly from 63.7% in 1996 to 88.2% in Not all of 11

14 these observations reflect traded options only 59,513 observations had at least one option series with positive open interest prior to the earnings announcement. I provide more detail about the types of options listed for these firms in Table 2. Following Bollen and Whaley (2004), I categorize options into five groups based on the option s delta, where delta can be thought of as a rough approximation of the probability of the option expiring in the money. The purpose of this characterization is to obtain a distribution of implied volatilities relative to the degree to which the option is in or out of the money. 5 I then average, for each earnings announcement, the implied volatilities for all options in each category. At each measurement date, an earnings announcement observation may have up to five implied volatility measures, depending on the amount and type of options listed on the firm s stock prior to the earnings announcement. Table 2, Panel A, taken from Bollen and Whaley (2004), shows the range of deltas for each category. Category 1 options are those options with the lowest strike prices, including both deep-out-of-the-money ( DOTM ) puts and deep-in-the-money ( DITM ) calls. Category 3 options are approximately at-the-money ( ATM ) options, with deltas ranging from.375 to.625 in magnitude. Category 5 options are those with the highest prices, consisting of deep-in-themoney puts and deep-out-of-the-money calls. Panels B and C present further breakdowns of option availability. Panel B includes all observations with listed options, while Panel C includes only those options with positive open interest immediately prior to the earnings announcement. Consistent with prior research, closerto-the-money options (Categories 2, 3, and 4) are more commonly listed (and traded) than options with extreme strike prices (Categories 1 and 5). For the extreme categories, low strike 5 Grouping options based on the delta is similar to classifying options based on the ratio of strike/current stock price, but takes into account factors such as time to maturity, dividend yield, and underlying volatility that may differ across individual stocks. 12

15 price options (Category 1) are more common than high strike options (Category 5), which is consistent with higher demand for low-probability downside protection, or what Rubinstein (1994) refers to as crash-o-phobia. Relatively few firms have listed options across the full spectrum of moneyness categories. Of the 61,075 earnings announcements with any listed options, only 18,959 (31%) have listed options in each of the five moneyness categories. Panel C shows that only 21% of the 59,513 observations have options with positive open interest in each category The Shape of Implied Volatility Functions I summarize the shape of IVFs in both a graphical and statistical manner. Figure 1 provides the graphical representation, showing the average implied volatility for all options in each moneyness category. The dashed line presents the average implied volatility across all options meeting the stated criteria, with a different number of options in each category. The solid line presents the average implied volatility for only those observations with listed options in each of the 5 categories, made up of 18,959 observations in each category. While both lines demonstrate the familiar skew pattern, the solid line s skew is more pronounced and better reflects the typical firm s implied volatility function. The data underlying Figure 1 is presented in Table 3, Panels A and B. Focusing on the results in Panel B (observations with options in each of the 5 moneyness categories), the average at-the-money (Category 3) implied volatility is 0.50 and ranges from 0.35 at the 25 th percentile to 0.60 at the 75 th percentile. The mean implied volatilities for the next two central groups (Categories 2 and 4) are 0.04 and away, respectively. The two deep-out-of-the-money 13

16 groups possess the largest values, with a mean of 0.60 for Category 1 (DOTM puts) and a mean of 0.55 for Category 5 (DOTM calls). Following prior literature, I quantity volatility skew based on the difference between Category 2 options and Category 3 options (Bollen and Whaley 2004; Garleanu et al. 2009; Xing et al. 2010). Specifically, I calculate skew as the difference between implied volatilities of outof-the-money puts (i.e., a subset of Category 2 options) and at-the-money calls (i.e., a subset of Category 3 options). The rationale for this choice is that demand for out-of-the-money put options reflects expectations of large stock price drops, and that at-the-money calls serve as an appropriate benchmark for the firm s overall uncertainty. 6 Thus, this measure of skew reflects the perceived likelihood of large stock price drops in excess of what would be expected from the firm s at-the-money implied volatility. Using this measure, skew is available for 30,137 earnings announcements. Table 4 provides descriptive statistics for the firms/earnings announcements that make up this final sample. Not surprisingly, the requirement that firms have listed options results in a sample of disproportionately large firms. The mean market value is $9.1 billion, compared to a mean market value of only $455 million for observations meeting all criteria other than option availability. The mean and median deflated earnings surprises are fairly small (0.04%) and the 3-day earnings announcement period return is slightly positive, with a mean value of 0.5%. Volatility skew, measured before the earnings announcement, has a mean (median) of (0.037). To put that in context, the mean implied volatility for Category 3 options is Approximately 87% of observations exhibit positive skewness (i.e., the out-of-the-money put options have greater implied volatility than the corresponding at-the-money call options.) The 6 Taking a similar approach, Xing et al. (2010) point out that at-the-money calls are an appropriate benchmark for implied volatility as they have the highest liquidity among all traded options. 14

17 degree of skew varies substantially across observations, ranging from at the 25 th percentile to at the 75 th percentile. In Panel B, I present further information regarding the distribution of earnings surprises and earnings announcement returns. These measures, similar to those used by McNichols (1988), characterize the symmetry of the tails of the distribution. Each measure reflects the magnitude of the left tail of the distribution in relation to the right tail of the distribution, with the measures progressively using a smaller part of each tail. 7 In all cases, the variables are negatively skewed, although the skewness is much more severe for the earnings surprises than the associated stock returns. For example, the left half of the earnings surprise distribution is 42% larger than the right half of the distribution, while the left half of the earnings announcement period return distribution is only 4% larger than the right half of the distribution. The difference in skewness between the earnings values and the earnings announcement returns is consistent with both the conservative nature of accounting and with extreme earnings realizations having significant transitory components (Freeman and Tse 1992; Beaver et al. 1979). The negative skewness in both earnings and investor response is consistent with increased risk borne by equity investors during earnings announcement periods. (See, for example, Ball and Kothari (1991) and Cohen et al. (2007).) It seems reasonable that fear of extreme stock price drops is especially strong immediately prior to earnings announcements, and that option prices would reflect this fear. 7 More precisely, each measure is calculated as the ratio of (X percentile 1 st percentile)/(99 th percentile Y percentile), where Y is equal to 100 X. So the 50% tail comparison is calculated as (50 th percentile 1 st percentile)/(99 th percentile 50 th percentile), and the 5% comparison is calculated as (5 th percentile 1 st percentile)/(99 th percentile 95 th percentile). 15

18 4. Empirical Results 4.1. Predictability of Extreme Negative Earnings Announcement Returns My first hypothesis is that implied volatility skew reflects the likelihood of an extreme negative earnings announcement return. This raises the question of how to identify such an event. Prior crash studies have taken a variety of ad hoc approaches. Hutton et al. (2009) and Bradshaw et al. (2010) define crashes based on how frequently firms (market-adjusted) weekly returns deviate by more than 3.09 standard deviations from their mean weekly value. Kim et al. (2010a, 2010b) take a similar weekly-returns-based approach, but use a cutoff of 3.2 standard deviations from the mean. Krieger et al. (2011) define extreme returns based on the highest 3% or lowest 2.5% of equity returns on an annual basis. For the purposes of this study, I define significant negative return observations as those earnings announcements where the firm s stock price declines by at least 15% over the 3-day period surrounding the announcement date. 8 While the definition of a significant return is clearly subjective, I base my definition on the nature of the out-of-the-money put options, as I describe next. For out-of-the-money puts in the final sample, the measurement-date stock price exceeded the options strike price by a mean of 12.9%, with the excess ranging from 8.7% at the 25 th percentile to 16.0% at the 75 th percentile. Framing it differently, the out-of-the-money puts would be exactly at-the-money if stock prices declined by a mean of 11.4% (8.0% and 13.8% based on the 25 th and 75 th percentiles, respectively). Because put options have non-zero payoffs only when the stock price falls below the strike price, out-of-the-money put holders are essentially betting on declines of at least that amount. My definition of extreme negative returns 8 The -15% threshold is a raw return (rather than a market-adjusted return, such as that used by Hutton et al. 2009) because I use a raw measure of volatility skew, like Xing et al. (2010), to predict crashes. 16

19 thus corresponds to the types of returns anticipated/feared by option holders. 9 (I also present results based on cutoffs of -10% and -20%.) Based on this definition, I classify 5.1% of earnings announcements as extremely negative events (10.3% and 2.5% for -10% and -20% cutoffs, respectively). I test my first prediction using a probit regression, with the dependent variable equal to 1 when earnings announcement period returns are less than or equal to -15%, and 0 when earnings announcement period returns are greater than -15%. The regression features standard errors clustered by firm and calendar quarter and includes variables drawn largely from prior literature, defined as follows: Skew: ATM IV: ROE: Log(Market Value): Book-to-Market: Debt-to-Assets: Opacity: Historical Kurtosis: Historical Skewness: The difference between out-of-the-money put option implied volatility and at-the-money call option volatility Implied volatility of at-the-money options Current period quarterly earnings deflated by the prior quarter s shareholder s equity Market value of the firm s common equity Ratio of book value of equity to market value of equity Ratio of total debt to total assets Three year moving sum of the absolute value of annual discretionary accruals (Hutton et al. 2009) The kurtosis of the firm s daily stock return measured over the 365 days prior to the earnings announcement The skewness of the firm s daily stock return measured over the 365 days prior to the earnings announcement 9 For comparison, Hutton et al. (2009) define crashes based on firm-specific (market adjusted) weekly returns more than 3.09 standard deviations below their yearly average. Hutton et al. report that the average crash threshold is an abnormal weekly return of -18% for their sample. 17

20 Historical Volatility: The standard deviation of the firm s daily stock return measured over the 365 days prior to the earnings announcement Historical Turnover: The average daily share turnover measured over the 365 days prior to the earnings announcement Historical Return: The cumulative stock return measured over the 365 days prior to the earnings announcement Deflated Earnings Surprise: Actual earnings minus analyst consensus estimates (both from I/B/E/S), deflated by the pre-earnings stock price Table 5 presents the results of this regression, with the columns including progressively more variables moving from left to right. Skew is the variable of interest, while At-The-Money Implied Volatility controls for the firm s overall uncertainty. The remaining variables in the first column (ROE, Log(Market Value), Book-to-Market, and Debt-to-Assets) capture the relatively immutable firm characteristics used by Hutton et al. (2009). The second column adds Opacity (and its square), while the third column adds the historical stock return distribution characteristics (Kurtosis, Skewness, Volatility, and Return) studied by Chen et al. (2001). In all three cases, Skew is associated with an increased likelihood of an earnings announcement period crash with p-values less than 0.01, which supports the first hypothesis. Most of the remaining independent variables are associated with large stock price drops in unsurprising ways. Firms with greater levels of uncertainty (At-The-Money Implied Volatility) and Historical Turnover are more likely to experience extreme stock price drops, while large firms are less likely to experience such drops. Perhaps surprisingly, firms with greater leverage (Debt-to-Assets) are less likely to experience extreme negative returns, although this could be due to the endogenous relation between a firm s leverage choices and the stability of the firm. Finally, Opacity is positively, but insignificantly related to the likelihood of a crash, which is 18

21 consistent with the annual crash predictions documented by Hutton et al. (2009) and Bradshaw et al. (2010). 10 The fourth column adds an additional independent variable, Deflated Earnings Surprise, to help gauge the nature of information in volatility skew. If volatility skew reflects investor knowledge of forthcoming earnings (as in the recent SEC allegations against Galleon Management and Raj Rajaratnam), the skew would not provide incremental information after controlling for the earnings surprise. The results in column four reveal that this is not the case: the association between Skew and crash risk continues to be positive and significant. (Obviously, a large negative earnings surprise also increases crash risk.) Again, the association between Opacity and crash risk is not statistically significant after controlling for the announced earnings surprise. If financial reporting opacity predicts crashes, it appears to do so only by predicting future negative earnings surprises. In contrast, volatility skew s predictive ability goes beyond the information in the current quarter s reported earnings. Panel B of Table 5 repeats the analysis shown in the fourth column of Panel A, but uses different thresholds to identify extreme negative events. The results are not affected by using either a looser or more stringent definition of crashes. Volatility skew continues to predict earnings crashes regardless of whether the cutoff is -10%, -15%, or -20%. The observed relation between volatility skew and extreme earnings-period returns is consistent with extant literature documenting that options markets impound earnings-related information prior to the earnings event (Amin and Lee 1997; Ni et al. 2008; Xing et al. 2010). The next section tests my second hypothesis, which asks whether volatility skew contains information regarding non-earnings announcement events. 10 The Opacity result is somewhat sensitive to the threshold used to identify crashes. Opacity is significantly associated with the likelihood of a crash in the first three specifications when crashes are defined as 3-day returns less than -10%, but not when using -15% or -20% thresholds. 19

22 4.2. Predictability of Extreme Negative Events in Non-Earnings Periods Using the process described earlier, I measure Skew three trading days after the firm s earnings announcement, including only those options expiring no later than three trading days prior to the firm s subsequent earnings announcement. By construction, any information in implied volatility skew relates to the immediate non-earnings announcement period and not to the potential for tail risk in future earnings announcement periods. Both implied volatility and volatility skew measured after the earnings announcement are smaller, on average, than the respective pre-earnings levels, a pattern consistent with prior research. Specifically, implied volatility tends to increase prior to scheduled events and decrease thereafter (Patell and Wolfson 1981; Ederington and Lee 1996; Rogers et al. 2009). However, the declines in volatility and skew in this sample are modest. For observations with both pre- and post-earnings open interest, at-the-money implied volatility declines by a mean of 0.027, relative to a starting mean value of for the same observations prior to the earnings announcement. Volatility skew declines by a mean of 0.001, compared to the mean skew of prior to the earnings announcement. While more than twothirds (68%) of the observations exhibit a decline in at-the-money implied volatility, only 52% of the observations show a decline in volatility skew following the earnings announcement. Overall, the data show that much of the pre-earnings skew persists into the non-earnings period, even when there are no earnings announcements in the option horizon. Given the persistence of the volatility skew and the predictive power shown in the prior section, it seems plausible that the skew conveys information about returns and, specifically, crashes in non-earnings periods. 20

23 I test this prediction using a probit regression similar to that described earlier. The two differences between this regression and the regression summarized in Table 5 are: 1) Skew is measured three trading days after the earnings announcement, and 2) the (binary) dependent variable indicates the occurrence of a significant negative return in the non-earnings period. A significant negative return is defined as a cumulative -15% return (or worse) in any 3-day period between earnings announcements. As before, I present results using the -10% and -20% cutoffs, as well. The results of the regression are shown in Table 6, which is structured similarly to Table 5. Panel A presents four columns of regression results, each including progressively more independent variables. In none of the four regressions is volatility skew associated with crash risk. Even in the reduced-form regression in the first column, the t-statistic on Skew is less than 1.2. Thus, the earnings period predictability documented in Table 5 does not extend to nonearnings periods, which fails to support my second hypothesis. The same is true of financial reporting opacity; Opacity is significantly associated with crash risk in only one specification (Column 2) and then only at the 10% statistical level. As with Table 5, Panel B of Table 6 shows that the results are fairly insensitive to the crash threshold. Skew is not associated with crash risk at any of the three cutoffs, while Opacity is associated with non-earnings announcement crash risk only when a crash is defined based on a -20% cutoff. In all cases, the strongest predictors of crash risk are overall uncertainty (ATM Implied Volatility) and the future earnings surprise (Deflated Earnings Surprise). The combined results from Tables 5 and 6 emphasize the importance of distinguishing between earnings announcement periods and non-earnings announcement periods. The next 21

24 section explores some possible explanations for why the earnings-period predictability would not extend to non-earnings periods. 5. Additional Analysis There are a variety of reasons why volatility skew would predict crashes in earnings periods, but not in non-earnings periods. One reason, that crashes do not occur outside of earnings periods, can be immediately dismissed 22% of observations experience at least a 15% stock price drop in the non-earnings period (11% for drops of 20%). I examine other possible explanations in the following subsections Lack of Earnings News in Non-Earnings Announcement Periods Although option investors seem to have information about future earnings (Xing et al. 2010), it is possible that many firms do not disclose information about future earnings outside of the quarterly earnings announcement periods. If true, option investors superior information would be much less valuable outside of those periods. To evaluate this possibility, I restrict the sample to include only those firms for which the First Call CIG database records a management forecast between three days after the current earnings period and three days before the next earnings period, and perform a similar regression to that shown in Table 6. This sample is appealing for two reasons. First, there is no doubt that the firm disclosed material earnings information in the non-earnings period. Second, based on the results documented by Kothari et al. (2009), management forecasts often represent the revelation of previously stockpiled bad news, making a crash quite likely. 22

25 This forecasting sample consists of 5,868 observations (about 27% of the sample used in the non-earnings regression documented in Table 6). The sample experiences crashes at a higher frequency than the corresponding non-forecasting sample: 29% of forecast observations experience a 15% stock price drop compared with 20% of non-forecast observations, while 17% of forecast observations experience a 20% stock price drop compared with 9% of non-forecast observations. 11 If volatility skew predicts crashes only when significant earnings news is disclosed, this sample should demonstrate that predictability. Table 7 shows the result of a probit regression identical to that shown in Table 6, except for the sample used. For brevity, I show the full regressions for all three extreme return cutoffs. In none of the regressions is the coefficient on Skew significantly positive. Nor is the Skew variable significantly positive in any of the reduced regressions (columns 1-3 in prior tables) or in the sample of observations for which the firm did not issue a forecast in the nonearnings period. Based on these results, the failure of volatility skew to predict crashes in nonearnings periods is not due to a lack of earnings news in those periods Lack of Transparency Bradshaw et al. (2010) report that volatility skew is highly correlated with financial reporting opacity. Although the results in Table 5 showed that skew contains information beyond that in measured opacity, perhaps option investors are best at predicting crashes for those firms with opaque financial reporting. On the other hand, perhaps those firms that are more 11 The increased frequency of crashes is consistent with these forecasts being largely unexpected (Rogers et al. 2009) and firms often using management forecasts to disclose bad news on a timely basis (Skinner 1994). 12 In the forecast sample, Skew is measured three days after the current earnings announcement, while the forecast may take place at any point between this earnings announcement and the next quarter s earnings announcement. To assess whether staleness in measured skew is affecting the forecast sample results, I perform an alternative regression similar to the earnings announcement regression shown in Table 5. In this (untabulated) regression, I measure Skew three trading days prior to the forecast and identify crashes based on 3-day returns surrounding the forecast date. In this alternative specification, Skew is not associated with the likelihood of a forecast-related crash. 23

26 transparent in their disclosure practices are more likely to disclose their bad news outside of earnings announcement periods. I evaluate whether financial reporting transparency/opacity affects the predictive ability of volatility skew by segmenting my sample into terciles based on Opacity. I repeat the Table 6 regression separately for the most transparent (lowest Opacity) and most opaque (highest Opacity) observations. Consistent with the results shown by Hutton et al. (2009), crashes are more likely for opaque firms than transparent firms: 32% of opaque observations experience a 15% decline, while only 14% of transparent observations experience such a decline. (Using a 20% decline cutoff, the frequency is 16% for opaque firms compared to 6% for transparent firms.) Table 8 shows the results of this split, with the Transparent sample in Panel A and the Opaque sample in Panel B. As in Table 7, I report the full regressions for both samples. For both the Opaque sample and the Transparent sample, Skew fails to predict crashes at the 10% statistical level, regardless of the cutoff used to identify crashes. (The t-statistics are less than 1 for all cutoffs for the transparent firms in Panel A and less than 1.3 for all cutoffs for the opaque firms in Panel B.) The lack of predictive power holds for financial reporting opacity, as well. Opacity is not a significant predictor of crashes in non-earnings period for either sample at any cutoff. In contrast, at-the-money implied volatility and the future earnings surprise represent the dominant predictors of crash risk in the non-earnings announcement period. The results in Table 8 provide no evidence that differences in opacity are behind volatility skew s inability to predict crashes in non-earnings periods Lack of Information in Options Prices 24

27 The tests described in Tables 6 through 8 are all based on a definition of crash that focuses on 3-day periods. Using relatively short periods to define crashes is natural, as the prior option literature generally focuses on the sharp discontinuities that disrupt financial markets and impede dynamic hedging. Nevertheless, option investors may view the entire non-earnings announcement period as a single event and, conditional on the stock price at the option s maturity, be unconcerned with the stock price path until that date. In other words, put option investors may expect significant negative news to arrive during the non-earnings period, but not know (or even care) if that news will be disclosed suddenly or gradually, as long as the ending stock price is unaffected. In recognition of this possibility, I again perform a non-earnings regression similar to Table 6, this time using a different definition for the crash dependent variable. Rather than using 3-day returns to identify crashes, I now identify crashes based on the cumulative firm return from 3 days following the earnings announcement to 3 days prior to the next earnings announcement. Although this definition will include many gradual price declines that might not be viewed as traditional crashes, all observations represent the aggregate revelation of bad news that option investors may be anticipating. Using this alternative definition of a crash, 22% of observations experience a cumulative crash of 15% or worse, while 16% of observations experience a cumulative crash of 20% or worse. Table 9 shows the results, with Panel A reporting the outcomes from increasingly comprehensive sets of independent variables and Panel B reporting the full regression based on the 3 different thresholds for identifying crashes. Unlike the results in Table 6 through 8, volatility skew does have some ability to predict crashes, albeit weakly. Panel A shows that, even after controlling for next quarter s earnings surprise and the remaining independent 25