Do options price predictable patterns in future stock returns? Evidence from accounting anomalies

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1 Do options price predictable patterns in future stock returns? Evidence from accounting anomalies Hyun A Hong Fogelman College of Business & Economics University of Memphis Memphis, TN hahong@memphis.edu Bryce Schonberger Marshall School of Business University of Southern California Los Angeles, CA Bryce.Schonberger.2014@marshall.usc.edu K.R. Subramanyam Marshall School of Business University of Southern California Los Angeles, CA krs@marshall.usc.edu Preliminary and Incomplete Comments Welcome Draft: March 2013

2 DO OPTIONS PRICE PREDICTABLE PATTERNS IN FUTURE STOCK RETURNS? EVIDENCE FROM ACCOUNTING ANOMALIES Abstract We examine whether option markets anticipate predictable patterns in future stock returns associated with several well-documented accounting anomalies: the post-earnings-announcement drift (PEAD), working capital accruals, net operating assets, and changes in net operating asset turnover. Results suggest that option prices do not price predictable patterns in future stock returns, rather they exactly reflect contemporaneous equity returns. Therefore, the option markets appear to be subject to similar forms of mispricing as the stock markets and are not semi-strong efficient with respect to accounting information. Further tests suggest that the high costs of trading options in terms of both time-value premiums and transaction costs preclude traders from purchasing options to exploit these opportunities. However, we find significant returns to a strategy of writing options to take advantage of these predictable return patterns.

3 DO OPTIONS PRICE PREDICTABLE PATTERNS IN FUTURE STOCK RETURNS? EVIDENCE FROM ACCOUNTING ANOMALIES 1. Introduction Options offer both leverage and downside protection. Therefore, options are a more beneficial trading vehicle than stocks for traders seeking to exploit their informational advantages (Black, 1975; Roll, Schwartz, and Subrahmanyam, 2009). Accordingly, smart money is alleged to operate in the options market, thus making them more informationally efficient than the stock markets. 1 However, trading options is costly. First, option prices include a time-value premium to compensate for the implied volatility of the underlying stock price. Second, options have relatively higher transaction costs than stocks (Phillips and Smith, 1980). For these reasons, options may not always be the ideal vehicle for traders to exploit opportunities to earn abnormal returns, especially over longer horizons. Extant research documents that option prices anticipate future stock returns, especially prior to specific news events such as earnings announcements (Amin and Lee, 1997; Roll, Schwartz, and Subrahmanyam, 2010). However, this literature is silent on the nature of these future stock returns and attributes the predictive ability of option prices to private-information based trading, i.e., strong-form efficiency. 2 There has, however, been no research to-date that examines whether option prices anticipate predictable patterns in future stock returns related to publicly available 1 For example, existing research provides some support for the greater informational efficiency of option markets relative to stock markets by documenting that price discovery seems to partially occur in the option market before the stock market (Chakravarty, Gulen, and Mayhew, 2004). 2 Amin and Lee (1997) find that trading interest in the options markets seems to anticipate the direction of news released during earnings announcement windows (see Mendenhall and Fehrs 1999 for a closely related follow-on study).similar work is conducted by Driessen, Lin, and Lu (2012) who find that option volatility spreads and volatility skews significantly predict returns earned around earnings and analyst information events. Research by Chen et al. (2011), Roll, Schwartz, and Subrahmanyam (2010), Jayaraman, Frye, and Sabherwal (2001), De Launois and Van Oppens (2003) and Chesney, Crameri, and Mancini (2010) also provides evidence on informed trading in option markets around specific information events, such as earnings announcements, Mad Money reports, and M&A announcements. 1

4 information or whether they reflect similar patterns of mispricing exhibited by stock prices. 3 Put differently, whether option markets are semi-strong efficient has not hitherto been examined. In this study, we examine whether option prices anticipate predictable patterns in future stock returns related to publicly available information. To this end, we study whether options traders exploit arbitrage opportunities presented by accounting-based trading anomalies in a timely manner. Accounting anomalies are particularly appropriate for understanding how quickly options price predictable patterns in future returns because the exact date when the accounting signal becomes available to the markets can be determined. However, many of the existing anomalies are not present in large stocks with actively traded options, which limits our examination to just a few such anomalies. In our study, we examine the following four welldocumented accounting anomalies: (1) the post-earnings announcement drift (PEAD) anomaly (e.g. Rendleman, Jones, Latane, 1982; Bernard and Thomas, 1989); (2) the accrual anomaly (Sloan, 1996); (3) the net operating asset (NOA) anomaly (Hirshleifer, Hou, Teoh, and Zhang, 2004); and (4) the change in NOA turnover anomaly (Soliman, 2008). We conduct our analysis on a sample of 50,245 firm-quarters over the period comprising 3,604 distinct firms with actively traded exchange-listed options and available data in the OptionMetrics database. We use quarterly accounting information from 10-Q filings (or 10-K for the 4 th quarter) to construct the accounting signals for each anomaly (see Appendix B for how the signals are constructed). We categorize firms into deciles based on the current quarter s signal realization relative to its distribution over the prior quarter and construct zero net investment hedge portfolios by going long or short in the extreme deciles (i.e., the BUY and 3 Goodman, Neamtiu, and Zhang (2011) examine whether option markets efficiently use accounting signals that predict stock return volatility. 2

5 SELL portfolios, respectively). 4 We then track equity and option returns to the hedge portfolio over the 90 days following the filing of the 10-Q (or 10-K) report. 5 Before embarking on our primary analyses, we examine whether the four anomalies we study generate significant abnormal stock returns over the 90-day post-filing window for our sample of firms with actively traded options during our sample period ( ). We find statistically and economically significant hedge (stock) returns over the 90-day window ranging from 3.3% to 5.5% for all anomalies except the PEAD. 6 This evidence allows us to next examine whether option prices anticipate these predictable returns in a timely manner. To examine whether option prices anticipate predictable future returns to the underlying equity security, we examine patterns of put-call parity violations (Ofek, Richardon and Whitelaw, 2004) and put-call implied volatility spreads (Cremers and Weinbaum, 2010) across extreme deciles based on a sort on the respective accounting signal realization (henceforth, the BUY and SELL portfolios). If option prices concurrently reflect predictable future returns to the underlying equity security, then call prices are predicted to be higher (lower) than put prices for firms in the BUY (SELL) portfolio. This will generate a significantly positive difference in putcall parity violations between the BUY and SELL portfolios 7 We should observe similar 4 Consider the accrual anomaly. We form hedge portfolios that take a long position in stocks in the decile of firms with the smallest working capital accruals (the BUY portfolio) and an offsetting short position in firms in the largest working capital accrual decile (the SELL portfolio). 5 All four accounting anomalies exhibit abnormal return patterns for up to a year (or more) following release of the signal. However, we limit our trading horizon to 90 days because of the paucity of options with maturities greater than 180 days. 6 The absence of the PEAD anomaly for option firms arises because such firms are typically large firms with a welldeveloped information environment, and the PEAD anomaly is significant only for smaller, less-liquid firms (Bernard and Thomas, 1989; Fama and French, 2008). 7 Ofek et al. (2004) measure put-call parity violations using the ratio 100*ln(S/S*), where S*= PV(K) + C - P (the option contract designed to replicate a long position in the underlying equity) and S is the underlying equity close price. We adjust this measure in two primary ways. First, we multiply the measure by -1 so that a positive put-call parity violation implies that, ceteris paribus, the call price is relatively higher than the put price. Similarly, we measure implied volatility spreads so that positive put-call implied volatility spreads suggest that the call price is relatively higher than the put price. Second, we examine the unlogged version of this ratio as 100*(S*-S)/S. This 3

6 differences in the put-call implied volatility spreads across the BUY and SELL portfolios. In contrast, we find little evidence of put-call parity violations (or significant put-call implied volatility spreads) in the days following the 10-Q (or 10-K) filings; differences are statistically insignificant in a majority of the cases and of economically trivial magnitudes even when they are statistically significant. These results suggest that option prices do not anticipate predictable patterns in future stock returns for the accounting anomalies we study. To confirm that option prices merely track contemporaneous stock prices over the holding period, we next examine two types of returns to the option portfolios: reverse conversion returns and delta-hedged call option returns. Reverse conversion returns are the returns to an options contract that seeks to replicate the buy-and-hold returns from a long position in the underlying equity security. We find that reverse conversion returns for the hedge portfolio (i.e., difference between the BUY and SELL portfolios) closely track the respective buy-and-hold stock returns for all four accounting anomalies over the 90-day window following the filing date. Deltahedged call option returns measure returns to a purchased call option after controlling for movements in the underlying stock price (Jones and Shemesh, 2009). We find that delta-hedged call returns for the hedge portfolio are close to zero over the 90 day holding period, which suggests that option prices do not reflect any information outside of that contained in the underlying stock price. Results of both the reverse conversion returns and the delta-hedged call returns suggest that option prices simply mirror contemporaneous movements in the stock price over the holding period for each of the four accounting anomalies examined. We next turn to why option markets do not price predictable patterns in future stock returns, with particular emphasis on whether options are too costly a vehicle for traders to exploit returns ratio may be interpreted in terms of the percentage difference between the option implied price and the underlying equity price. This allows for a direct comparison with predicted equity return magnitudes. 4

7 to the accounting anomalies. Absent all costs, hedge returns to options over the 90-day window range from 10% to 15% for the three anomalies other than the PEAD, illustrating the benefits of leverage when trading options. However, two types of costs are incurred when trading options. The first is the time-value premiums that are built into option prices to compensate for future stock return volatility and must be incurred when buying options. The second is transaction costs. To isolate the effect of the implied volatility premium, we first examine hedge portfolio returns to options in the absence of transaction costs. We find that the hedge returns for a strategy of only purchasing options are negative and significant for all four anomalies. This suggests that the time-value premiums swamps the hedge strategy returns, indicating that the magnitude of the anomaly returns is not commensurate to the cost of the downside protection provided by options. Consequently, strategies that sell (write) options are profitable, with returns ranging from 12% to 19% over the 90-day period. Finally, we examine the returns to various options strategies after considering transaction costs. These returns give an idea of the true returns that could be earned from the four accounting anomalies through trading options. We find that strategies that buy options or concurrently buy and sell options are not profitable. However, selling (writing) options are profitable for the three anomalies except the PEAD, with magnitudes ranging from 5% to 9% after factoring in the bid-ask spread over the 90-day window. Our study contributes to better understanding how markets price options. Options are derivative securities whose values are determined purely by the concept of no arbitrage, specifically the absence of arbitrage between the derivative security (option) and the underlying (stock). Our study asks whether option prices exhibit arbitrage with respect to the underlying equity securities mechanically in a contemporaneous fashion, or in a sophisticated and forwardlooking manner and by arbitraging anticipated future stock price movements. Our evidence is 5

8 consistent with the former. That is, we find that option prices contemporaneously reflect the underlying stock prices, but do not price predictable patterns in future stock returns. Because of this, we find that option markets are subject to the exact forms of mispricing displayed by the stock markets, which contradicts the notion that options are any more semi-strong efficient than the stock markets. Our evidence also suggests that it may be costly for arbitrageurs to exploit returns associated with the anomalous patterns in stock returns based on publicly available information. Our study also adds to the literature on accounting anomalies. While a large number of studies have investigated the presence of several accounting anomalies, much of this literature is focused on the stock markets. There have been very few studies that examine whether other markets process accounting signals in an efficient manner. We add to this literature by studying option markets. One advantage of examining options over stocks is that option prices are not determined by stochastic discount factors or other notions of systematic risk that are inherently difficult to measure. As a result, it is relatively easier to draw inferences about the mispricing of accounting information using option markets. 2. Motivation 2.1. The informational efficiency of the option markets Black and Scholes,(1973) argue that in complete markets, equity option contracts are redundant assets since the return patterns of option contracts can be replicated by forming a synthetic portfolio including riskless bonds and shares of the underlying stock. Option trading should thus convey no new information to market participants. For example, if the equity prices reflect the accounting-based trading anomalies, the corresponding options prices are expected to do so, with prices in the options market not fully reflecting the implication of publicly available 6

9 accounting information just like their counterparts in the equity market (semi-strong form of efficiency). However, in the presence of market frictions such as information asymmetry, informed traders may prefer to trade options instead of the underlying equity for two reasons. First, options offer both leverage and downside protection and therefore are arguably more beneficial to traders who seek to exploit their informational advantages (e.g., Roll, Schwartz, and Subrahmanyam, 2009). 8 Second, investors with private information on volatility of the underlying equity price can only make their bet on volatility in the options market (Back, 1993; Cherian, 1993; Chan, Chung and Fong, 2002). These frictions are consistent with option markets being where the smart money operates and therefore being more informationally efficient than underlying equity markets. A stream of recent studies in accounting and finance find evidence that prices in the options market behave in a more informationally efficient manner relative to equity market prices. Specifically, these studies document that option volume predict future equity returns (see Easley, O Hara, and Srinivas, 1998; Pan and Poteshman, 2006; Chen et al., 2011; and Roll, Schwartz, and Subrahmanyam, 2010) and that option volume predict the direction of upcoming earnings releases (see Amin and Lee, 1997; and Mendenhall and Fehrs, 1999). Additional research in the area finds that option prices in the form of put-call parity violations also predict future equity returns, primarily for securities with greater short sale restrictions (see Ofek, Richardson, and Whitelaw, 2004; and Cremers and Weinbaum, 2010). Collectively, findings in these studies support the notion first advanced by Black (1975) that equity options provide informed investors with a more efficient trading vehicle for capitalizing on a given piece of private information 8 In the same context, Grossman (1988, 275) argues that the notion that a real security is redundant when it can be synthesized by a dynamic trading strategy ignores the informational role of real securities. 7

10 relative to the underlying equity security due to the truncated payoff structure and the leverage inherent in option contracts. As a result, options do not function as redundant securities, where option prices merely reflect the price of the underlying equity security. Instead, option markets may play a role in price discovery (e.g., the ability of options returns to foreshadow future returns of the underlying equity). However, extant studies are silent on the nature of these future stock returns and typically attribute the predictive ability of option prices to private-information based trading, i.e., strong-form efficiency. There has, however, been no research to-date that examines whether option prices reflect predictable (anomalous) patterns in stock prices because arbitrageurs use options to exploit stock mispricing. Put differently, nobody has examined whether option markets are informationally efficient in a semi-strong fashion, or whether they reflect similar patterns of mispricing that is exhibited in the stock markets. Our paper attempts to bridge this gap in the literature by examining whether option prices anticipate predictable future returns associated with accounting anomalies. Perhaps the most closely related paper to our study is Goodman, Neamtiu, and Zhang (2011). This paper examines whether fundamental accounting signals that are associated with future equity volatility are able to predict option straddle returns above and beyond the information in implied and historical equity volatility. Results indicate that option prices do not fully incorporate this fundamental information on volatility into current option prices. While the inferences in this study are broadly consistent with ours, i.e., option markets are not efficient, the two studies are very different in their objectives and design. We study whether option markets price predictable returns, while Goodman et al. examine whether option markets price 8

11 predictable volatility. Also, while our primary examination involves put-call parity tests, Goodman et al. examine returns to options straddles. 2.2 Accounting Anomalies To address this gap in the literature, we examine whether equity options traders exploit arbitrage opportunities presented by four well-documented accounting anomalies in the equity market: the post-earnings announcement drift (PEAD) anomaly (e.g. Foster et al., 1984; Bernard and Thomas, 1989, 1990), the accruals anomaly (Sloan, 1996), the net operating assets (NOA) anomaly (Hirshleifer et al., 2004) and the change in NOA turnover (Soliman, 2008). Turning first to the PEAD anomaly, PEAD is documented as the predictability of future stock returns based on the sign and magnitude of quarterly standardized unexpected earnings at the earnings announcement (Foster et al., 1984; Bernard and Thomas, 1989, 1990). Equity prices drift in the direction of the initial market response to quarterly unexpected earnings for at least 120 trading days subsequent to the earnings announcement, with a large part of the price corrections happening in the days surrounding the subsequent two quarters earnings releases (e.g. Foster, Olsen, Shevlin, 1984; Rendleman, Jones, Latane, 1987; Bernard and Thomas, 1989, 1990; Freeman and Tse, 1989). With respect to the accrual anomaly, the original work by Sloan (1996) shows that future stock returns are predictable based on the level of standardized working capital accruals. That is, firms with low standardized accruals earn positive future abnormal returns, while firms with high standardized accruals earn negative future abnormal returns. Finally, prior studies have documented the role of particular financial statement ratios in foreshadowing future equity returns. 9 In particular, the net operating asset anomaly documented 9 For a more detailed discussion of the issue, refer to Lipe 1986; Ou 1990; Ouand Penman 1989; Lev and Thiagarajan 1993; Fairfield, Sweeney and Yohn

12 by Hirshleifer et al. (2004) shows that future stock returns are predictable using a firm s net operating assets scaled by total assets. Stocks characterized by high (low) NOA are known to earn negative (positive) future abnormal returns. Similarly, Soliman (2008) relies on DuPont analysis to provide evidence that the change in net operating asset turnover, which represent firms asset utilization and efficiency, is significantly related to future equity returns. 10 The popular explanation for the above anomalies is that stock market traders fail to fully understand the implications of publicly available accounting information. For example, the PEAD may exist because stock market traders fail to entirely comprehend the auto-correlations of unexpected earnings across ensuing quarters. With respect to the accrual anomaly, researchers argue that the accrual anomaly arises from stock market participants apparent inability to factor in the differential persistence of accruals and cash flows. With regard to the net operating asset anomaly, Hirshleifer et al. (2004) show that investors with limited attention consider only accounting profitability while neglecting information on cash profitability. Net operating assets, the accumulation of the differences between these two, engender investors excessive optimism (pessimism) when the value of net operating assets is high (low). Finally, Soliman (2008) finds that the change in NOA turnover is significantly related to future changes in return on NOA, consistent with the notion that investors fail to fully appreciate the implications of asset utilization and efficiency information contained in the change in NOA turnover. The common feature of these accounting signals is that they display the ability to predict future equity returns in a consistent manner, thus presenting an arbitrage opportunity for informed traders to earn abnormal returns. Given the role of option markets as potential vehicles for informed trading, we complement 10 The change in NOA turnover is a proxy for asset utilization and efficiency, which generally comes from the efficient use of property, plant, and equipment; efficient inventory processes; and other forms of working capital management. Soliman (2008, page 824). 10

13 previous studies on option listing effects by investigating whether options traders exploit the arbitrage opportunities presented by these four well-documented accounting-trading anomalies in equity markets. Our analysis is based on the assumption that informed traders can trade on their ability to quickly process public disclosures into tradable private information (Glosten and Milgrom, 1985, Kim and Verrecchia, 1994). In this regard, Glosten and Milgrom (1985, p. 77) state that they refer to the informed traders as insiders, even though other interpretations are possible, for example, they may merely be individuals who are particularly skillful in processing public information Costs associated with options trading Suppose that accounting-trading anomalies documented in the equity market are also present in the options market. In that case, a natural question arises: why do option traders, who are presumably more sophisticated than equity investors, fail to arbitrage away these money-making opportunities in equilibrium? Stock options are derivative financial contracts of the underlying stock. As such, the valuation model of options is based upon an arbitrage strategy hedging the option against the underlying equity and rebalancing continuously until expiration (Figlewski, 1989). This arbitrage strategy is, however, only feasible in a frictionless market and the options include two types of trading costs, e.g., a premium of implied volatility and transaction costs. First of all, option prices include a premium to account for implied volatility of the underlying stock price. These implied volatility premiums are built into option prices, and must be incurred when buying options, increasing with the expected volatility of the underlying stock price over the life of the option. This premium can be very substantial for longer maturity 11 The literature provides a supportive evidence that price and volume promptly responds to public earnings announcements (Lee 1992), that informed trading sharply rises during earnings announcements (Lee, Mucklow, and Ready 1993, Krinsky and Lee 1996), and that transient institutional investors trading strategy incorporates the anomalous equity prices based on the sign of earnings surprise (Ke and Ramalingegowda 2005). 11

14 options. For these reasons, options may be an inefficient trading vehicle for capitalizing on returns earned over more than a few days. 12 Second, prior studies find that transaction costs are another source of market frictions, and may drive the primary difference in the valuation of option contracts and shares of the underlying stock (Leland, 1985, Merton, 1989, Shen, 1990, and Boyle and Vorst, 1991). Figlewski (1989, p. 301) suggests,...transactions costs make a substantial difference in the outcome of an options arbitrage, even when done by a market maker. Transaction costs on most security exchanges consist of two components: (1) commissions and other explicit fees and (2) the bid-ask spread. Although commissions and other explicit fees (e.g., the costs of floor trading and clearing fees) are widely studied, the bid-ask spread has been largely ignored even though it is potentially the largest among the transaction costs (e.g., Phillips and Smith, 1980). Phillips and Smith (1980) show that quoted spreads on options are 6 to 10 percent of the contract price, whereas quoted spreads on stocks are typically less than 1 percent of the stock price. In their study on the S&P 100 index options market, George and Longstaff (1993) suggest that since market-making is highly competitive in S&P 100 index options, bid-ask spreads should be equal to the expected marginal cost of supplying liquidity services. Theoretically, market makers price protect themselves by increasing spreads in the face of higher information asymmetry risk. If market makers set sufficiently wide spreads in options in response to informed trading in the options market, option traders will not on average earn abnormal trading profits. While earlier studies contend that investors do earn abnormal profits by trading options based on the Black- Scholes model (e.g., Galai 1977, 1978), later studies counter that after transaction costs it is 12 There are two components comprising an option's price, e.g., intrinsic value and time value. An option's intrinsic value is the amount that the option is in-the-money. The time value (extrinsic value) of an option is the premium a rational investor would pay over its current exercise value (intrinsic value), based on the likelihood that its value will increase before expiry. Specifically, the option becomes more profitable to exercise before expiry because it will gain in the implied volatility over time. Time value decays exponentially to zero at expiration. 12

15 difficult for traders in the options market to earn abnormal returns. Collectively, due to a relatively higher bid-ask spread and the time value of the option, it may be costly for traders to use options for exploiting opportunities to earn abnormal returns. We, however, note that there are countervailing arguments provided by several studies showing that informed traders prefer to trade in the options market for certain transactions. For example, Black, 1975, Cox and Rubinstein, 1985, Manaster and Rendleman, 1982, and Skinner, 1990 have argued that privately informed traders in the options market may find lower implicit borrowing rates, more favorable margin requirements, and fewer constraints on short-selling relative to trading in the underlying equity (both in terms of the Uptick Rule in equity markets and the interest paid on the proceeds of short-selling). Taken together, it is an empirical question whether in the presence of transaction costs, option markets are used by informed traders to exploit informational advantages and are therefore more informationally efficient than the underlying equity markets. We therefore explore the roles of each of these transaction costs in determining returns to various trading strategies in the options market. 3. Sample and data As discussed above, this paper studies optioned and non-optioned equity returns, and the option market characteristics (e.g., put-call parity, put-call implied volatility spread, option returns and delta-hedged option returns) to examine whether the option market participants incorporate into their trading strategies the predictable patterns in future equity returns, which arise from the accounting anomalies. Our empirical tests employ data from three sources OptionMetrics, Compustat Quarterly, and Center for Research in Security Prices (CRSP). First, option data are collected from OptionMetrics, a database providing end-of-day bid and ask 13

16 quotes, implied volatilities, open interests, trading volumes, option Greeks (e.g., delta, gamma, theta) and other relevant information for all options listed in the U.S. option market. The accounting data and equity prices and returns are then obtained from the Compustat Quarterly files and the CRSP daily stock returns files, respectively. Our sample covers all firm-quarters with available data on these three databases for firms with a fiscal period ending between 12/31/1995 and 12/31/2006. We follow the option literature and impose a set of sample selection criteria. These criteria are discussed in detail in Appendix C, but the primary requirements are that call (put) options have a corresponding put (call) option with the same maturity and exercise price and that both the call and put have non-missing values of open interest and implied volatility. Additionally, we focus our attention on a sample of actively traded options and eliminate option pairs if they do not have prices available for all 13 weeks following the 10-Q/K filing date. This requirement allows each firm-quarter observation to have some missing trading days during each week following the filing date, but requires that information is available on at least one day each week. We further require the availability of variables to measure the four accounting anomalies examined in our study for each firm-quarter observation. This means that each firm-quarter must have non-missing data to calculate: (1) standardized unexpected earnings (SUE) calculated following the seasonal random walk model (Livnat et al., 2006), (2) working capital accruals (Hribar and Collins, 2002; Richardson, Sloan, Soliman, and Tuna, 2005), (3) net operating assets (Hirshleifer et al., 2004), and (4) change in net operating asset turnover (Soliman, 2008). After imposing these criteria, we obtain a final sample size with 50,245 firm-quarter observations representing 3,604 unique firms. 14

17 4. Results 4.1 Predictable equity returns to accounting signals In this subsection, we begin by replicating the equity returns for the four accounting anomalies using the Compustat/CRSP universe of firms with data available to calculate all anomalies for the period Specifically, after the release of quarterly reports, we compute the following accounting signals: standardized earnings surprise (SUE), working capital accruals (WC Accruals), non-current operating accruals (NCO Accruals), financing accruals (FIN Accruals), net operating assets (NOA), and change in net operating asset turnover (dnoa_to). 13 Appendix B discusses the detailed construction of the accounting signals. We then assign firms to decile portfolios based on the distribution of these accounting signals in the prior quarter. This avoids look-ahead bias based on differing filing dates for firms during the calendar quarter (Foster, Olsen, and Shevlin, 1984). Decile portfolios are constructed such that the hedge portfolio (short DECILE 1 and long DECILE 10) is expected to yield abnormally positive equity returns during our measurement window (e.g., in the 90 days subsequent to the release of the quarterly report). We calculate a range of option metrics starting from the 10-Q (10-K for the fourth quarter) because accounting data necessary for constructing the accounting anomaly hedge portfolio in our study becomes available on the filing date. Specifically, we form zero net investment hedge portfolios that take a long position in firms in the smallest working capital accrual decile (e.g., DECILE 10) and an offsetting short position in firms in the largest working capital accrual decile (e.g., DECILE 1) (Sloan, 1996; Collins and Hribar, 2002; Richardson, Sloan, Soliman, and Tuna, 2005).Thus, DECILE 10 (DECILE 1) corresponds to the BUY (SELL) portfolio. 13 We thank Jeff McMullin for extracting a list of 10-K/Q filing dates for firms on the SEC Edgar database by using PERL code. We matched this list to Compustat Quarterly data via the CIK code. 15

18 Table 1, Panel A presents ex-dividend equity returns and Sharpe Ratios during the period following the release of quarterly reports across extreme deciles (DECILE 10 - DECILE 1) for each accounting signal. Equity Returns are buy-and-hold returns calculated using CRSP daily returns, ignoring dividends in order to more closely reflect the price changes in the option market. Ex-dividend returns are calculated during a holding period that begins at the close of trading one day following the 10-K/Q filing to allow for filings that occur after hours on day 0. In Table 1, Panel A, the magnitudes of the hedge portfolio returns based on the Compustat/CRSP universe firms are broadly consistent with those reported by prior studies (see Collins and Hribar, 2002; Richardson, Sloan, Soliman, and Tuna, 2005; Hirshleifer, Hou, Teoh, and Zhang, 2004; Soliman, 2008). For example, the PEAD (WC Accruals) hedge portfolios using extreme deciles generates 90-day equal-weighted buy-and-hold returns of 6.03% (3.68%), while Collins and Hribar (2002) report 4.24% (2.76%) cumulative size and risk adjusted returns accruing to the PEAD (WC Accruals) hedge portfolios over the years After confirming that returns exist for the full Compustat/CRSP sample over the period, we then compare equity returns between optioned firms and the Compustat/CRSP universe firms. Our test is motivated by two influential studies on the options market by Mayhew, Sarin, and Shastri (1995) and Kumar, Sarin, and Shastri (1998) who find evidence that stocks with options traded on them generally have greater price efficiency. The column for the options sample in Table 1, Panel A illustrates that the magnitudes of equity returns are similar between the Compustat/CRSP universe firms and the optioned firms, with the exception of the PEAD portfolio sort. The absence of the abnormal hedge returns for PEAD among the sample of firms with actively traded options may be explained by prior findings that optioned firms are typically large and the PEAD phenomenon is more significant for smaller, less-liquid firms with a lower 16

19 number of analyst following (e.g., Latané and Jones, 1979; Bernard and Thomas, 1989; Bhushan, 1994; Bartov et al, 2000; Ng, Rusticus, and Verdi, 2008; Chordia et al, 2009). 14 Overall, Table 1, Panel A indicates that returns to several accounting signals are present not only for the Compustat/CRSP universe firms, but also for firms with exchange-listed options. To select a set of unique accounting-based trading anomalies in the equity market in our analysis, we include all of the accounting signals in a multivariate regression framework. The multivariate analyses are motivated by prior studies that find evidence that some of the accounting anomalies overlap (Fama and French, 1996, Kraft, 2000, Raedy, 2000,and Desai, Rajgopal and Venkatachalam, 2002). Table 1, Panel B presents results of regressing the 90-day buy and hold ex-dividend equity returns onto an indicator for each anomaly. Each anomaly indicator takes on a value of -0.5 if the firm-quarter observation is in decile 1 for the anomaly, 0 for deciles 2-8, and +0.5 for decile 10. Thus, coefficients on these indicators are interpreted as the percent return in moving from DECILE 1 to DECILE 10 (hedge portfolio return). In this regression, we also include controls for standard asset pricing characteristics. The liquidity and momentum controls are based on lagged 6-month returns prior to the 10-K/Q filing month. Market capitalization is measured as of the end of the fiscal period using Compustat end of quarter price and shares outstanding. Thus, the control variables are all measured prior to the 90- day return window, consistent with the accounting signals of interest that are measured on the 10-K/Q filing date. The regression is run using the Fama-MacBeth (1973) methodology, which controls for cross-sectional correlation in the t-statistics by running separate regressions for each calendar quarter. Results show that the coefficients on the anomaly indicators are significant except NCO Accruals and FIN Accruals, indicating that the equity returns of NCO Accruals and 14 PEAD returns do not substantially differ if we use day +1 following the earnings announcement in place of the 10-K/Q filing date. Several alternative measures of standardized unexpected earnings also do not yield significant returns for firms with actively traded options. 17

20 FIN Accruals may be subsumed by those of other accounting signals. Our subsequent analysis will be focused on PEAD, WC Accruals, Net Oper Assets and ΔNOA Turnover. 4.2 Put-call parity violations In this subsection, we test whether option market traders incorporate the accounting anomalies into their trading strategies by examining whether put-call parity is violated in the direction of the accounting signals. This test is motivated by asset pricing theory when the capital market is complete, identical securities with identical state-contingent payoffs have identical prices (e.g., Lamont and Thaler 2003). Put-call parity is a well-known no-arbitrage relation, which implies that synthetic shares constructed using options plus borrowing and lending should have the same price as actual shares (Klemkosky and Resnick 1979). Under the condition of no arbitrage, it is well known that for European options on nondividend paying stocks, put-call parity holds, e.g., ( ) where PV k,i,t is the option strike price discounted at the zero rate of interest provided by OptionMetrics on day t, C i,t is the call option price on day t, P i,t is the put option price with a strike price and expiration date matching the call option on day t, S i,t is the underlying equity security close price on day t, on options with strike price K and the same maturity (Stoll, 1969). However, for American options, Merton (1973) shows that puts will be more valuable because they can be exercised early. Specifically, ( ) Hence, Eq. (2) can be rewritten as S i,t = PV k,i,t + C i,t P i,t + EEP i,t (3) 18

21 where EEP i,t is the early exercise premium on the American put option. Ofek et al. (2004) follow this approach and measure deviations from put-call parity as the natural log of the ratio of the actual stock price to the synthetic stock price implied by equation (3). Formally, Ofek et al. measure put-call parity violations using the ratio 100*ln(S/S*), where S*= PV(K) + C P + EEP (the option contract designed to replicate a long position in the underlying equity) and S is the underlying equity close price. We make several adjustments to Ofek et al. s parity measure. First, we multiply the measure by -1 so that a positive put-call parity violation implies that, ceteris paribus, the call price is relatively higher than the put price. Second, we examine the unlogged version of this ratio as 100*(S*-S)/S. This ratio may be interpreted in terms of the percentage difference between the option implied price and the underlying equity price. This allows for a direct comparison with predicted equity return magnitudes. Finally, we exclude the Black-Scholes imputed early exercise premium for put options, because we are interested in empirically observed option prices. 15 Formally, we measure deviations from put-call parity as a percentage of closing equity price calculated as (PV k,i,t + C i,t P i,t S i,t ) / S i,t using closing mid-quote prices for options and the underlying equity as of day t and for stock i. That is, the deviation of the synthetic stock price from its actual price is expressed as the percentage of the actual stock price. As an alternative measure to put-call parity, we employ the implied volatility spread, e.g., differences in implied volatilities for at-the-money call vs. put options with matching strike price and expiration date (Amin, Coval and Seyhun, 2004; Cremers et al., 2010; Jin, Livnat, and 15 Prior studies provide guidance for estimating the additional value of American versus European calls and puts, e.g., early exercise premium (Johnson 1983; Geske and Johnson 1984; Ho et al. 1994; Unni and Yadav 1999; Ofek et al. 2004). Thus, as an additional analysis, when we follow those studies and include the premium due to early exercise feature into our put-call parity metric, we find that our results are qualitatively the same. However, we choose to exclude the early exercise premium from our primary tests for two reasons: (1) a significant loss of the sample after requiring that stocks are non-dividend paying to eliminate the early exercise premium for calls, and (2) a heavy reliance upon the Black-Scholes model to compute the early exercise premium for puts. 19

22 Zhang, 2012). High call implied volatility relative to put implied volatility suggests that calls are expensive relative to puts, and vice versa. To be directionally consistent with our measure of putcall parity, we subtract put implied volatility from call implied volatility so that positive differences should predict positive equity returns (calls are relatively more expensive than puts). In other words, for each day t and for every stock i with put and call option volume on day t, we measure the implied volatility spread as where i refers to pairs of put and call options with the same strike prices and maturity, IV i,t denotes the OptionMetrics implied volatility (adjusted for dividends, stock splits, and early exercise). 16 Thus, if option traders price expected returns following the announcement of the accounting signals, the direction of put-call parity violations and implied volatility spreads should be directionally consistent with predicted equity returns to the accounting anomaly portfolio sorts. Specifically, call price should be relatively higher (lower) than put price for DECILE 10 (DECILE 1). Similarly, the implied volatility of call options should be relatively greater (smaller) than that of put options for DECILE 10 (DECILE 1). To examine this prediction, we compute average daily put-call parity violations and implied volatility spreads by firm over the weeks just following the 10-K/Q filing date. Table 2 presents the results of the put-call parity (Put-Call Parity) and implied volatility spread (IV Diff Parity) analysis. Table 2 shows that there is no consistent pattern of put-call parity and put-call implied volatility spreads across the extreme anomaly portfolios. Further, even in the case that 16 For American options on individual stocks in OptionMetrics, implied volatilities are calculated using a binomial tree, taking into account discrete dividend payments and the possibility of early exercise, and using historical LIBOR/Eurodollar rates for interest rate inputs as well as the closing transaction price on the underlying asset (Cremers and Weinbaum, 2010). 20

23 differences are significant, they are very small as a percentage of equity price (e.g., the maximum hedge portfolio put-call parity violation is around 16 basis points). Therefore, we conclude that option prices tend to just track equity prices and do not seem to pick up predictable returns to these anomalies before the equity prices Option returns vs. contemporaneous equity returns To confirm that option prices are merely tracking equity prices over the holding period as demonstrated in the previous section, we next examine two types of option returns, e.g., reverse conversion returns and delta-hedged call option returns. Reverse conversion returns are buy-andhold returns to a contract that seeks to replicate the payoff to a long position in the underlying equity security. The reverse conversion contract is calculated as (PV k,t+n + C t+n P t+n ), where PV k is the option strike price discounted at the zero rate of interest provided by OptionMetrics at time t+n, C is the call option mid-quote price on day t+n, and P is the put option mid-quote price on day t+n with a strike price and expiration date matching the call option. If option prices mechanically observe put-call parity over the entire 90-day holding period, changes in the value of the reverse conversion contract will closely track returns to the underlying equity security. To formally test this prediction, we compare buy-and-hold equity returns to the percentage change in the reverse conversion contract over the 90-day holding period. In addition, we examine delta-hedged call option returns as an alternative means to determine how closely option returns track equity returns over the 90-day holding period. Intuitively, delta-hedged option returns are the returns earned after removing the effects of changes in the underlying equity prices. Jones and Shemesh (2011) define option returns as 17 For the put-call parity, implied volatility, and option return tests, we require that options have positive open interest. We remove this requirement when examining open interest differences in Table 5 to ensure that option holdings are completely reflected for this test. As a result, Table 5 will have more observations relative to Tables 1-4. Equity returns are unchanged for this larger sample with zero open interest observations included. 21

24 where C t is the option bid-ask midpoint. Delta hedging adjusts this return for the change in the underlying equity security in order to remove the effect of equity price changes from the option return. Formally, the change in value of a delta-hedged portfolio is ( ) Formally, we define the delta-hedged return 18 as This corresponds to the return on a portfolio consisting of one option contract with a zerocost position in shares worth of single-stock futures (Jones and Shemesh 2011).As such, this delta-hedged call option returns represent returns to a purchased call option after controlling for movements in the underlying stock price (Jones and Shemesh, 2009).Table 3 presents buy-andhold equity returns, reverse conversion returns, and delta-hedged call option returns over the 90- day window following the filing date for each accounting signal. Results show that equity returns and reverse conversion returns are very close to each other over the full 90-day window following the filing date. Furthermore, the Diff column indicates only marginal differences between the equity and reverse conversion contract returns, indicating that option returns closely track returns to the underlying equity securities over the full trading window. 18 In a Black-Scholes world, the option price C t of an option is defined as: ( ) Here, the delta (e.g., the sensitivity of option price to the underlying stock price) is expressed ( ( ) ) For calls, the delta is as 22

25 This inference is confirmed by the delta-hedged call option returns across these portfolios. Delta hedging, while not perfect, can be expected to eliminate the sensitivity of the option price to the underlying stock price to a significant extent. 19 We document that delta-hedged call returns are also close to zero over the subsequent 90 days. This trivial delta-hedged option return indicates that option prices are not moving significantly apart from movements of the underlying equity prices. These results are illustrated graphically in Figure 1. The graphs of the equity returns and reverse conversion returns are nearly identical for DECILE 1, DECILE 10, and for the hedge return. Taken together, these results are consistent with no price corrections occurring for options; option prices just track the equity prices in a mechanical fashion Returns to option trading strategies Having documented that option returns closely mirror equity returns over the 90-day holding window, we next examine whether transaction costs in the options market preclude option traders from arbitraging away the predictable patterns in future equity returns based on the accounting signals. To isolate the effect of time value premiums relative to bid-ask spreads on option returns, Table 4 considers three option trading strategies designed to take advantage of returns over the subsequent 90-day window. To compute returns for each trading strategy, we calculate option returns both with and without the effect of bid-ask spread. Returns without spread use option prices at the average of the bid and ask (mid-quote prices) at the close of the trading day: Call_ret=100*(Call_mid t+n /Call_mid t - 1); and Put_ret=100*(Put_mid t+n /Put_mid t - 1) 19 Jones and Shemesh (2011) argue that the use of the Black-Scholes model is relatively marginal when computing delta-hedged returns. Even if the delta used to calculate hedged returns is note accurate, those hedged returns nevertheless correspond to the returns on a feasible investment strategy (abstracting from transactions costs). In the same vein, Hull and Suo (2002) contend that Black-Scholes is as effective as any other model in this respect. 23