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Ying L. Becker Assistant Professor Department of Finance Suffolk University 120 Tremont Street Boston, MA 02198 617-973-5365 [email protected]

Ki C. Han Professor Department of Finance Suffolk University 120 Tremont Street Boston, MA 02198 617-573-8561 [email protected]

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Georges Tsafack Assistant Professor Department of Finance University of Rhode Island 45 Upper College Road Kingston, RI 02881 401-874-5489 [email protected]

Earnings Announcement Premium and Idiosyncratic Risk: Is It Consistent with Risk-Return Trade-Off?

Abstract Earlier studies document that both stock returns and volatilities rise around the earnings announcement. This study focuses on the relationship between the earnings announcement returns and the return volatilities. Our findings can be summarized as follows. First, we find that the earnings announcement premium still exists, highly significant. However, the premium substantially fell recently, while volatilities rose over the sample period. Second, we find that the earnings announcement premium is inversely related to the realized volatility, but positively related to the expected volatility. The inverse relationship is stronger. Third, we find that the earnings announcement premium is greater for value stocks than for growth stocks. Given the empirical findings, it would be safe to say that the earnings announcement premium is more related to mispricing than to risk compensation.

JEL Classification: G14. Keywords: Earnings Announcement Premium, Return Volatility, Value Premium.

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Earnings Announcement Premium and Idiosyncratic Risk: Is It Consistent with Risk-Return Trade-Off?

1. Introduction Analysts spend a lot of money and time on forecasting firms’ next earnings results, and investors anticipate the earnings results with excitement and anxiety. Earnings announcement is like a quarterly ritual for many in the stock market. Not surprisingly, earnings report has been focal points of numerous studies in the literature. Ball and Brown (1968), Chari, Jagannathan, and Ofer (1988), Easton and Zmijewski (1989), Gennotte and Truemann (1996), and Kross and Schroeder (1984), among others, find that stock prices respond positively to announcements of earnings greater than expected and negatively to announcements of earnings less than expected for the firms. In addition, many studies document large, rapid equity price reactions to earnings announcements, and suggest that equity volatility increases in response to earnings news (Ball and Brown 1968; Beaver 1968; Patell and Wolfson 1984). Interestingly, it has been documented that stocks, on average, earn higher returns during months when earnings are announced than during non-announcement months. Firms on average experience stock price increases during periods when they are scheduled to report earnings. This earnings announcement premium was first discovered by Beaver (1968) and has subsequently been documented by Chari, Jagannathan, and Ofer (1988), Ball and Kothari (1991), Cohen et al. (2007), Frazzini and Lamont (2007), Berkman and Truong (2009), and Barth and So (2014). Barber et al. (2013) report that the positive earnings announcement premium is not isolated to just a few countries. Thus, the above studies report that stock returns, on average, are positive around earnings announcements. This is intriguing because an earnings announcement can be a positive surprise 3

or a negative surprise depending on the investors’ earnings estimate. When all the announcements are combined, however, the average market response is positive according to the studies. Besides, stock return volatilities rise around the announcements, the studies report. The goal of this study is to investigate this interesting phenomenon, focusing on the relationship between the earnings announcement returns and the return volatilities. First, we examine if the earnings announcement premium still exists. A lot of developments, such as regulation changes and management’s voluntary earnings guidance, have been made in the market with regard to earnings announcement, indicating that the uncertainty about earnings announcement could have been alleviated. We investigate whether the earnings announcement premium, if any, has changed, using the 1983 – 2016 data, which includes the post-financial-crisis period. We then examine whether the earnings announcement premium is related to the increased stock return volatility. Barber et al. (2013) suggest that uncertainty over the information to be released through earnings cause investors to demand the observed earnings announcement premium. They argue that the earnings announcement premium is a compensation for investors’ taking risk through the uncertain time period. Therefore, the premium should be positively related to the stock return volatility. This is a particularly interesting issue given the heated debate over the relationship between volatilities and stock returns in the literature. On the one hand, Easley et al. (2002), Ang et al. (2006, 2009), and Chen and Petkova (2012) report that stock returns are inversely related to idiosyncratic volatilities. On the other hand, Merton (1987), and Lehmann (1990), Barberis and Huang (2001), and Ammann, Verhoffen, and Suss (2009) argue that stock returns are positively related to firm-specific volatility. If the earnings announcement premium is positively related to the firm-specific volatility, the premium can be interpreted as a compensation

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for taking risk. If they are inversely related, however, the premium is more like mispricing related to investors’ behavioral bias or transaction costs. We include expected volatility as well as realized volatility in our analysis to investigate potentially different roles of both volatility dimensions in relation with stock returns. Our measure of realized volatility is the ratio of the standard deviation of daily returns for the announcement window over the standard deviation of daily returns for the reference window. As a proxy for the expected volatility, we use the average of the past sixteen recent realized volatilities. The expected volatility represents a simple mean average forecast of the realized volatility. Our findings can be summarized as follows. First, based on the 1983 – 2016 data including the post-financial-crisis period, we find that the earnings announcement premium still exists, positive and significant. However, the premium substantially fell recently, while firm-specific volatilities rose over the sample period. In fact, the earnings announcement premium substantially fell to the lowest in the most recent period, 2006 – 2016, while volatilities were the highest in the same period. We would expect that the earnings announcement premium and the volatility would move in the same direction if the premium is related to risk compensation. Second, we find that, the earnings announcement premium is inversely related to the realized volatility. The result is highly significant even when we measure the stock returns using pre- or post-announcement period. When we include the expected volatility as another explanatory variable, the announcement premium is significantly positively related to the expected volatility. This positive relationship can be interpreted as a compensation for taking the heightened risk during the earnings announcement. In other words, investors are likely to hold on to the stocks during the earnings announcement period expecting to earn positive returns. When we perform a robustness check, however, the positive relationship weakens.

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But the inverse relationship

between the premium and the realized volatility remains strong even with the robustness check, and, in fact, the inverse relationship seems to be dominant. Therefore, it would be fair to say that our results show that, controlled for Fama-French five factors (2015), higher volatility stocks earn lower returns, Third, based on the Fama-French five factor model (2015) to control for risk factors, we find that the earnings announcement premium is greater for value stocks than for growth stocks. The value premium is significant throughout the analyses. Lakonishok, Shleifer, and Vishny (1994), LaPorta (1996), LaPorta et al. (1997), Piotroski (2000), and Piotroski and So (2012) argue that the value premium is a result of some sort of expectation bias. The value premium we find in this study suggests that some sort of behavioral bias is involved with investors’ response to earnings reports. Given the empirical findings, it appears that the earnings announcement premium is more of mispricing than of risk compensation. Our study contributes to three strands of the literature. First, it contributes to the literature in the study of corporate earnings report. It shows that firms on average experience stock price increases during periods when they report earnings, although the magnitude of the average return becomes smaller recently. Interestingly, the earnings report premium is inversely related to the realized volatility, but somewhat positively related to the expected volatility.

The inverse

relationship is stronger, indicating that the earnings report premium does not seem to represent a compensation for taking risk.

It is more representative of mispricing related to investors’

behavioral bias or transaction costs. Second, our study has an implication for the heated debate in the literature over the relationship between idiosyncratic volatilities and stock returns. Our study can be taken as a study of the relationship in the context of earnings announcement. Our findings are more in line with a

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negative relationship between idiosyncratic volatilities and stock returns, reported by Easley et al. (2002), Ang et al. (2006, 2009), and Chen and Petkova (2012). Our findings do not seem to be explained by the typical risk-return relationship. It is more consistent with the argument that stocks with higher volatilities are more likely to be mispriced due to investors’ irrational preference or transaction costs. Third, the value premium we find in this study indicates that the traditional finance theory is limited in explaining what happens in the market. It is likely that investors are not nearly as rational as traditional finance theory suggests. Lakonishok, Shleifer, and Vishny (1994) attribute the high returns of value stocks to biased extrapolation of firms’ past growth. LaPorta (1996) and LaPorta et al. (1997) provide further evidence of systematic expectation errors for value and growth firms based on analyst forecasts and earnings announcement returns. Piotroski (2000) and Piotroski and So (2012) identify ex-ante expectation errors. The rest of the paper is structured as follows. Section 2 describes the methodology. Section 3 describes the data. Section 4 reports the empirical results. Section 5 summarizes and concludes the paper.

2. Methodology There are three main variables we construct around the earning announcement. The earnings announcement premium, the realized volatility and the expected volatility. Before defining these variables, let us define the windows and timings for those variables. a. Windows and Timings We use an earnings announcement window (e.g. 20 trading days) centered inside a reference window of one quarter (or about 62 trading days). We consider three different timings: before the announcement day (pre-announcement); around the announcement day (over7

announcement); and after the announcement day (post-announcement). We base our major empirical analysis on the over-announcement window. Below is an illustration of the windows and timings. Reference Window I

Pre-Announcement Window

Reference Window II

Over-Announcement Window Reference Window III

Post-Announcement Window Announcement Day

We start with the announcement window and cover the reference window by adding the same number of days before and after. For instance if the earnings announcement is on February 28, the pre-announcement window (of 20 trading days) will cover about the month of February. The reference window will cover the months of January-February-March.

The over-

announcement window will cover the second half of February (10 trading days) and the first half of March. The post-announcement window will cover the initial 20 trading days in March. We

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also use a 10-day window, as a robustness check, for the announcement window, but the reference window is kept to 62 days. b. Premium For a given company, we define the earnings announcement premium as the difference of the geometric average daily return over the announcement window and geometric average daily return over reference period. 1 Basically if there is a higher return during the announcement window than over the course of the reference period (one quarter), this can be seen as the impact of the earning announcement. 2 It is worth noticing that here we focus on the non-risk-adjusted premium as our goal is to relate it later to idiosyncratic risk and other risk factors. c. Realized Volatility It is a ratio of two standard deviations. The numerator is the standard deviation of daily returns computed using the announcement window, while the denominator is the standard deviation of daily returns computed using the reference window. The realized volatility therefore provides the level of increase (decrease) of the risk during the announcement period. A realized volatility of less than one (more than one) means that the earnings announcement does not affect (increases) the risk. d. Expected Volatility It is the average of the past sixteen recent realized volatilities. The expected volatility represent a simple mean average forecast of the realized volatility. To analyze the dynamics of the earnings announcements premium and its relation with idiosyncratic risk, we also divide the data into three different sub-samples: 1983 – 1993, 1994 –

Our measure of the earnings announcement premium is similar to Cohen et al. (2007). The benefit of these definition is its simplicity and the fact that there is no need of selecting matching firms or using a subjective model

1 2

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2005, and 2006 – 2016. To capture the change after the financial crisis, we further split the last sub-period into two: 2006 – 2010 and 2011 – 2016. Our main analysis is focused on a 20-days period for the earnings announcement window, and the over-announcement period in particular. However, we also perform a robustness check using a shorter window of 10-days period, while still keeping 62 days for reference window.

3. Data Our analysis focuses on the U.S. publicly traded firms that have been included in the S&P 500 stock index. Not only is it one of the most regularly analyzed stock universes but it includes most actively traded large stocks defined by the market capitalization. It is also widely used as a benchmark by asset managers against which they measure their portfolio performance. a. Sample We collect quarterly earnings announcement dates of all the firms that have been listed in S&P 500 index from the Compustat quarterly file for the period January 1980 to January 2016. According to Compustat, the reported earnings announcement dates correspond to “the date in which quarterly earnings and earnings per share figures are first publicly reported in the various news media (such as the Wall Street Journal or newswire services)”. 3 Because pre-1983 data were sparse, we began the sample period from January 1983 and ended it in January 2016 to assure a better cross-section earnings dates coverage for each quarters in our analysis. This resulted in a sample of 1363 firms and 102646 firm-quarter observations, which has an average of 75 firmquarter observations for each of the firms. 4 We then formed the research sample by merging the

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Ball and Bartov (1995) state that Compustat relies on data sources such as, the Wall Street Journal, for earnings dates and they suggest that the errors are likely to be “small in number”. 4 Cohen et.al. (2007) used the firms with at least 10 firm-quarter observations, and has an average about 33 firmquarter observations for each of the firms in the studied universe.

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earnings announcement data with a stock daily price data obtained from Compustat daily file for the period of 1983 to 2016, the last month for which data were available at the start of the study. b. Dependent and Explanatory Variables The dependent variable in our analysis is the earnings announcement premium, as described above. The key explanatory variables are the realized volatility and the expected volatility of firms’ stock returns, as described above. We have defined and computed several binary dummy variables for our analysis to take consideration of factor interaction effect: 1) RGE, which is a variable taking value one when realized volatility is greater than expected volatility and zero otherwise; 2) EGR, which is a variable taking value one when expected volatility is greater than realized volatility and zero otherwise 5; 3) Crisis, which is a variable taking value one during 2008-2009 global financial crisis period and zero otherwise; 4) AftCrisis, which is a variable taking value one after crisis and zero otherwise. We also use Fama and French (2015) five factors as controls for our premium analysis. They include the market excess return (MKT), size (SML), value (HML), plus RMW (the difference in returns between portfolios with robust versus weak operating profitability) and CMA (the differences in returns between portfolios with conservative and aggressive investment, where investment is measured by the change in total assets).

The dummy RGE means that realized volatility is greater than expected volatility. The rational to include that dummy is to capture a potential change in the relation between the premium and the realized volatility, when the latter exceeds the expected volatility. Not only it introduces more flexibility in the model, but it also provides a better idea about the shape of the relation. 5

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4. Empirical Results a. Descriptive Statistics Table 1 reports the descriptive statistics for earnings announcement premium, realized volatility, and expected volatility for the whole sample period. Panel A summarizes statistics for the 20-day window, and Panel B, for the 10-day window. As can be seen in Panel A, the average premiums for the pre-, over-, and post-announcement periods are 0.0058%, 0.0284%, and 0.0232%, respectively, with the highest premium for the over-announcement period. 6 During the sample period, the average earnings risk premium is positive, particularly for the overannouncement period, consistent with earlier studies. The statistics also show that the overannouncement period does have higher average realized volatility and expected volatility. The 10day period window in Panel B presents similar statistics trends as in Panel A. Once again, the average premium is significantly positive, and it is the highest for the over-announcement period. [Table 1 here] The statistics for the over-announcement periods are presented in Table 2 for the three subperiods, 1983 – 1993, 1994 – 2005, and 2006 – 2016, separately. 7 The earnings announcement premiums are all positive and highly significant. Table 2 shows that the average earnings announcement premium rose from the first to the second sub-period, but dramatically fell in the most recent sub-period. This could be the result of many changes in the market, such as

We computed the t- statistic of the estimated mean premia, and the lowest one is 2.81. In other words, all earnings announcement premia are strongly significant (even at 1% level). 7 Although we report the sub-period results only for the over-announcement period, all the results for pre- and post-announcement periods are available. We report only the over-announcement periods’ results since these time periods are of particular concern to us. 6

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management’s voluntary release of guidance, Sarbanes Oxley act, more information production in the market, and/or change in the investors’ behavior with the financial crisis. [Table 2 here] On the other hand, volatilities increased over the sample period. Both realized volatilities and expected volatilities steadily increased over time, and they are the highest in the most recent sub-period, which is in contrast with the earnings risk premium. These results are in line with Cohen et al. (2007), who report that the volatility of stock returns rose over time, but that the earnings announcement premium fell. This is an interesting finding because we would expect both to move in the same direction if the earnings report premium is a compensation for risk. It may suggest that the earnings announcement premium may not be what we could think of as a compensation for risk. b. Earnings Announcement Premium and Realized Volatility Table 3 presents the relationships between the earnings report premium and the volatility in the presence of other control variables. The first column demonstrates that the earnings announcement premium is inversely related to the realized volatility, significant at the 1% level. This result differs from the finding by Cohen et al. (2007) and Barber et al. (2013) that the earnings report premium is positively related to idiosyncratic volatility. Barber et al. (2013) went on to argue that “uncertainty over the information to be released through earnings, and the accompanying abnormally high idiosyncratic volatility, cause investors to demand higher preannouncement returns and lead to the observed earnings announcement premium.” [Table 3 here] The negative cross-sectional relationship between the earnings announcement premium and the realized volatility is interesting given the conflicting results reported in the literature.

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Miller (1977), Easley et al. (2002), Ang et al. (2006, 2009), and Chen and Petkova (2012) report that stock returns are inversely related to idiosyncratic volatility. According to Miller (1977), stocks with higher return volatility are likely to be overpriced, and therefore their future returns are relatively lower. Ang et al. (2006) document that stocks with higher idiosyncratic return volatility, on average, have lower subsequent returns. Chen and Petkova (2012) argue that high volatility stocks have low expected returns since they provide hedging opportunities relative to increases in market volatility. Investors are willing to pay an insurance premium for high idiosyncratic volatility stocks. In contrast, Levy (1978), Merton (1987), and Lehmann (1990) argue that stocks returns are positively related to firm-specific volatility. According to Merton’s (1987) investor recognition hypothesis, if investors invest only in securities with familiar risk-return characteristics and, consequently, hold under-diversified portfolios, idiosyncratic risk should be priced in equilibrium. He shows that in the presence of market frictions where investors have limited access to information, stocks with high idiosyncratic volatility have high expected returns because investors cannot fully diversify away firm-specific risk. Similarly, Ammann, Verhoffen, and Suss (2009) ﬁnd a highly signiﬁcant, positive relationship between returns and lagged implied volatilities. Barberis and Huang (2001) predict that higher idiosyncratic volatility stocks should earn higher expected returns. Also, Fu (2009) reports a positive contemporaneous relationship between idiosyncratic volatility and stock return. On the other hand, Bali and Cakici (2008) conclude that no robust relation exists between idiosyncratic volatility and returns. Longstaff (1989) also finds that a cross-sectional relationship between volatility and return is insignificant.

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Our paper can be taken as a study on the relationship between stock return and volatility in the context of earnings announcement. As shown in Table 3, our finding is more in line with Miller (1977), Easley et al. (2002), Ang et al. (2006, 2009), and Chen and Petkova (2012). Clearly, the negative relationship documented in Table 3 does not seem to be consistent with the investor recognition hypothesis. It is not supportive of the argument that the earnings announcement premium is a compensation for taking risk. It seems that investors bid up the price of volatile stocks so high before the earnings report, and, as a result, the realized returns are relatively low. c. Earnings Announcement Premium and Expected Volatility Realized volatilities contain some portion of expected volatilities. In other words, a portion of realized volatilities can be expected. When we include the measure of expected volatility in the regression, the earnings announcement premium is positively related to the expected volatility as reported in Table 3. In all the empirical models, which include the measure of expected volatility as another independent variable, the earnings report premium is positively related to expected volatility, significant at the 1% level. This result can be interpreted as evidence that investors are somewhat compensated for taking risk during the earnings announcement period. More importantly, however, in all the empirical models in Table 3, the coefficient of the realized volatility remains negative and highly significant. As the first column (M1) reveals, the realized volatility subsumes the role of the expected volatility and gets inversely related to the earnings announcement premium. It is clear that the stocks of higher idiosyncratic volatility earn less returns than those of lower idiosyncratic volatility. Thus our findings are not quite supportive of the risk-based argument, and they are more in line with the argument for mispricing, whether the mispricing is related to investor behavior or transaction cost. For example, Kumar (2009) posits that certain groups of individual investors appear to exhibit a preference for stocks with high

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idiosyncratic volatility and high idiosyncratic skewness. Similarly, Cao et al. (2008), Pastor and Veronesi (2003) and Wei and Zhang (2006) show that high idiosyncratic volatility stocks tend to yield lower returns on equity. Another possible explanation for the negative relationship between idiosyncratic volatility and future stock returns is based on limits of arbitrage – idiosyncratic volatility is a proxy for the divergence of opinion (e.g., Shalen (1993)), which leads a stock to be over-valued initially and to suffer capital losses eventually when short-sales constraints are binding (Miller, 1977). d. Volatilities with Pre-announcement Premium and with Post-announcement Premium To check if the above relationship is also found right before the earnings announcement and right after, we repeat our investigation using the 20-day pre-announcement period and postannouncement period. Table 4 reports the results for the pre-announcement period. Interestingly, the results are even stronger for the pre-announcement period than for the over-announcement period.

Now the expected volatility is more strongly positively related to the earnings

announcement premium, the realized volatility is more strongly inversely related to the earnings announcement premium. All the magnitude of the coefficients are bigger, and their t-statistics are larger, with no exception. Once again, however, when the expected volatility is not included as an explanatory variable, the realized volatility subsumes the role of the expected volatility and gets inversely related to the premium. [Table 4 here] Table 5 reports similar results for the post-announcement period.

Again, the post-

announcement returns are negatively related to the realized volatility, and positively related to the expected volatility, all strongly significant (at 1% level). This indicates that the dynamics working in Table 3 are also present for both the pre-announcement period and the post-announcement

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period. Given these results, it would be fair to say that, although the evidence of risk-compensation is observed for the earnings announcement, a more powerful force works, resulting in a negative relationship between volatilities and stock returns. [Table 5 here] e. Value Premium Another interesting finding is that the earnings announcement premium is higher for socalled value stocks. Tables 3, 4, and 5 all report that the coefficient for HML is significantly positive, suggesting that value stocks earn higher returns than growth stocks. 8 This can be interpreted as follows. Value stocks are in general less exciting stocks than growth stocks, and they hardly ride on a momentum. Although there are other explanations for the value premium, Lakonishok, Shleifer, and Vishny (1994) attribute the high returns of value stocks to biased extrapolation of firms’ past growth. LaPorta (1996) and LaPorta et al. (1997) provide further evidence of systematic expectation errors for value and growth firms based on analyst forecasts and earnings announcement returns. Similarly, Piotroski (2000) and Piotroski and So (2012) identify ex-ante expectation errors by comparing firms' price multiples and their accounting-based fundamentals and find that the value premium and ex-post expectation errors and revisions are concentrated in firms with biased ex-ante expectations. Thus, it seems that the value premium evidenced in Tables 3, 4, and 5 are a result of mispricing around earnings announcements, and not a result of compensation for risk taking. f. Sub-Period Results To see the dynamics between the earnings report premium and the volatility over time, we

Value premium refers to the greater risk-adjusted return of value stocks over growth stocks. Fama and French (1992) first identified the premium, using a measure they called HML (high book-to-market ratio minus low bookto-market ratio) to measure equity returns based on valuation. 8

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implemented our analysis for the aforementioned sub-periods as well. Table 6 presents the results for the over-announcement period. 9 For the first two sub-periods, the results are virtually the same as those in Table 3. The earnings report premium is inversely related to the realized volatility, and positively related to the expected volatility. However, the results for the 2006 – 2016 period are very different. The earnings report premium is positively related to the realized volatility, and not significantly related to the expected volatility. We further divided the subsample into two: 2006 – 2010 period and 2011 – 2016 period. The results for the 2006 – 2010 period show that the report premium is somewhat positively related to the realized volatility, but negatively related to the expected volatility, although not significant. The results for the 2011 – 2016 period show that the report premium is somewhat negatively related to the realized volatility and somewhat positively related to the expected volatility, although neither is significant. It appears that the financial crisis disrupted the dynamics of earnings report premium and volatilities. [Table 6 here] The sub-period results for the pre- and post-announcement periods are reported in Tables 7 and 8, respectively. Basically Tables 7 and 8 echo the findings in Table 6. For the first two subperiods, the premium is inversely related to the realized volatility, and positively related to the expected volatility. However, we do not find such relationships for the 2006 – 2016 period. [Table 7 here] [Table 8 here] g. Robustness Check In the above empirical analyses, we used 20-day windows to measure the earnings announcement premium and the volatilities, thus well covering potential information leaks and We only report the results of estimating model 4 (see M4 in Tables 3, 4, and 5). But all the results of estimating of other models are also available.

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delayed market responses to earnings reports. Nevertheless, we adopted 10-day windows as well to see if our results are sensitive to the choice of window span. Table 9 presents the 10-day window results for the over-announcement period. The 10-day window refers to 5 days before the announcement and 5 days after. The earnings report premium is inversely related to the realized volatility and positively related to the expected volatility. The inverse relationship between the realized volatility and the report premium is still strong, all significant at the 1% level with no exception. However, the positive relationship between the expected volatility and the report premium is weakened. In two of the four models, the coefficient of the expected volatility is not significant. This again suggests that the earnings announcement premium is more pertaining to mispricing than to risk compensation, which is supported by the highly significant coefficient for HML. [Table 9 here] Tables 10 and 11 report the 10-day window results for the pre- and post-announcement periods. The results are largely the same as those in Tables 4 and 5. One thing is noteworthy. When our analyses are based on 10-day windows, the coefficient for Year is somewhat negative, consistent with Table 2 results. It is probably because with the financial crisis, the premium got weaker. [Table 10 here] [Table 11 here]

5. Conclusion We have an extensive list of studies on earnings announcement and the market response to it. One of the most interesting findings in the literature is the positive earnings announcement

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premium. Many studies report that the average stock return around the earnings announcement is positive. Corporate earnings reports can be positive surprises or negative surprises as the actual earnings reports can be higher or lower than investors’ earnings estimates. According to the studies, however, when all the earnings reports are combined, the average market response is positive, which is intriguing. This study examines the earnings announcement premium with a focus on the relationship between the earnings announcement returns and the return volatilities. First, we examine if the earnings announcement premium still exists, and whether the earnings announcement premium, if any, has changed, using the 1983 – 2016 data, which includes the post-financial-crisis period. We then examine whether the earnings announcement premium is related to the stock return volatility. We include expected volatility as well as realized volatility in our analysis to see a potentially different role of expected volatility in relation with stock returns. The relationship between stock returns and volatilities is interesting on its own given the heated debate over the issue. Our study can be taken as a study of volatilities and stock returns in the context of earnings announcement. Our findings can be summarized as follows. First, based on the long-term data including the post financial crisis period, we find that the earnings announcement premium still exists, but that its magnitude decreased recently. The results show that the premium is lowest in the most recent sub-period while the volatility is the highest. We conjecture that the financial crisis contributed to the weakening of the premium. Second, the announcement premium is inversely related to the realized volatilities, but positively related to the expected volatilities, although the inverse relationship seems to be dominant. It appears that the relationship between the earnings report premium and the volatility is negative, although there is some evidence of positive relationship between the premium and the expected volatility. Third, we also find, based on the

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Fama-French 5 factors, that the announcement premium is more for value stocks than for growth stocks. Considering all these results, it would be fair to say that the earnings announcement premium is not consistent with risk compensation during the announcement period, but it is more consistent with mispricing related to behavioral bias or transaction costs. The future research will be fruitful in identifying the source of the mispricing. Our findings seem to be in line with the argument by Bernard and Thomas (1989) and Cohen et al. (2007) that the results are caused by some sort of mispricing in the market. In fact, many researchers raised questions concerning the level of sophistication exhibited by the market in responding to information in a timely and unbiased fashion (see, e.g., Bernard and Thomas [1990]; Ball [1992]; Bartov [1992]; Soffer and Lys [1999]).

The future research should examine whether the

mispricing is coming from investors’ irrational behavior or from transaction costs.

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Bernard, V. L., and J, K. Thomas. "Post-Earnings-Announcement Drift; Delayed Pricing Response or Risk Premium?" Journal of Accounting Research (Supplement 1989): 1-36. Bernard, V. L., and J. K. Thomas. 1990. "Evidence That Stock Prices Do Not Fully Reflect the Implications of Current Earnings for Future Earnings." Journal of Accounting and Economics 13: 305-340. Cao, C., Simin, T., Zhao, J., 2008. Can growth options explain the trend in idiosyncratic risk? Review of Financial Studies 21, 2599–2633. Chari, V., Jagannathan, R., & Ofer, A. (1988). Seasonalities in security returns: The case of earnings announcements. Journal of Financial Economics, 21, 101–121. Chen, Z., and R. Petkova. 2012. Does Idiosyncratic Volatility Proxy for Risk Exposure? The Review of Financial Studies 25: 2745-2787. Cohen, D. A., A. Dey, T. Z. Lys, and S. V. Sunder. 2007. Earnings announcement premia and limits to arbitrage. Journal of Accounting and Economics 43: 153–180. Easley, D., Hvidkjaer, S., and O’Hara, M., 2002. Is information risk a determinant of asset returns? Journal of Finance 57, 2185–2221. Easton, P., & Zmijewski, M. (1989). Cross-sectional variation in the stock market response to the announcement of accounting earnings. Journal of Accounting and Economics, 11, 117–142. Fama, Eugene F. and Kenneth R. French, 1992, “The Cross-Section of Expected Stock Returns,” Journal of Finance 47 (1992), 427-466. Fama, E. F., and K. R. French. 2015. “A Five-Factor Asset Pricing Model.” Journal of Financial Economics, Vol. 116, No. 1: pp. 1-22. Fu, F., 2009. Idiosyncratic risk and the cross-section of expected stock returns. Journal of Financial Economics 91 (2009) 24–37 Gennotte, G., & Truemann, B. (1996). The strategic timing of corporate disclosures. Review of Financial Studies, 9, 665–690. Kross, W., & Schroeder, D. (1984). An empirical investigation of the effect of quarterly earnings announcement timing on stock returns. Journal of Accounting Research, 22, 153–176. Kumar, A. 2009. Who gambles in the stock market? Journal of Finance 64, 1889-1933. Lakonishok, Josef, Andrei Shleifer, and Robert W. Vishny. 1994. “Contrarian Investment, Extrapolation, and Risk." Journal of Finance 49: 1541-1578.

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LaPorta, Rafael. 1996. “Expectations and the cross-section of stock returns." Journal of Finance 51:1715-1742. LaPorta, Rafael, Josef Lakonishok, Andrei Shleifer, and Robert W. Vishny. 1997. “Good news for value stocks: Further evidence on market efficiency." Journal of Finance 52: 859-874. Lehmann, Bruce N., 1990, Residual risk revisited, Journal of Econometrics 45, 71–97. Levy, H., 1978. Equilibrium in an imperfect market: a constraint on the number of securities in the portfolio. American Economic Review 68, 643–658. Longstaff, Francis A., 1989, Temporal aggregation and the continuous-time capital asset pricing model, Journal of Finance 44, 871–887. Merton, R. 1987. A Simple Model of Capital Market Equilibrium with Incomplete Information. Journal of Finance 42:483–510. Miller, E., 1977. Risk, uncertainty, and divergence of opinion. Journal of Finance 32, 1151–1168. Pastor, L., and Veronesi, P., 2003. Stock valuation and learning about profitability. Journal of Finance 58, 1749–1790. Patell, J., and M. Wolfson. 1984. The intraday speed of adjustment of stock prices to earnings and dividend announcements. Journal of Financial Economics 13: 223–252. Piotroski, Joseph D. 2000. “Value investing: The use of historical financial statement information to separate winners from losers." Journal of Accounting Research 38:1-40. Piotroski, Joseph D., and Eric C. So. 2012. “Identifying expectation errors in value/glamour strategies: A fundamental analysis approach." Review of Financial Studies 38: 2841-2875. Shalen, C., 1993. Volume, volatility, and the dispersion of beliefs. Review of Financial Studies 6, 405–434. Soffer, L. C, and T. Lys. 1999. "Post-Earnings Announcement Drift and the Dissemination of Predictable Information." Contemporary Accounting Research 16:305-331. Wei, S. X., and Zhang, C., 2006. Why did individual stocks become more volatile? Journal of Business 79, 259–292.

24

Table 1: Descriptive Statistics A 20-day over-announcement window covers 20 trading days centered on quarterly earnings announcement. The earnings announcement premium is the difference between the geometric average daily return over the 20-day window and the geometric average daily return over reference period. The realized volatility is a ratio of the standard deviation of daily returns computed using the 20-day window over the standard deviation of daily returns computed using the reference window. The expected volatility is the average of the recent sixteen realized volatilities. A 20-day pre-announcement (post-announcement) window covers 20 trading days prior to (after) quarterly earnings announcement. The premium, realized volatility, and expected volatility are calculated in the same way as for a 20-day over-announcement window. A 10-day window statistics are similarly defined. The sample covers the U.S. publicly traded firms that have been included in the S&P 500 stock index for the period, January 1983 to January 2016.

Panel A: 20-day Windows Pre-Announcement Variable

Obs.

Mean

Std. Dev.

Min

Max

Premium (%)

95,108

0.0058

0.6353

-19.3087

42.3568

Realized Volatility

95,098

1.0072

0.2468

0.0000

1.7918

Expected Volatility

77,437

1.0088

0.0751

0.6002

1.3742

Obs.

Mean

Std. Dev.

Min

Max

Premium (%)

95,202

0.0284

0.6656

-16.7887

43.0339

Realized Volatility

95,191

1.0293

0.3626

0.0000

2.5135

Expected Volatility

77,519

1.0328

0.1188

0.5191

1.6598

Over-Announcement Variable

Post-Announcement Variable

Obs.

Mean

Std. Dev.

Min

Max

Premium (%)

94,823

0.0232

0.6443

-24.3823

43.3984

Realized Volatility

94,813

0.9634

0.2453

0.0000

1.7789

Expected Volatility

77,181

0.9647

0.0766

0.6881

1.3565

Obs.

Mean

Std. Dev.

Min

Max

Premium (%)

95,154

0.0312

1.1744

-26.6965

115.6924

Realized Volatility

95,144

1.0288

0.3619

0.0000

2.4988

Expected Volatility

77,482

1.0324

0.1185

0.5409

1.6469

Panel B: 10-day Windows Pre-Announcement Variable

Over-Announcement Variable

Obs.

Mean

Std. Dev.

Min

Max

Premium (%)

95,202

0.0390

1.1559

-30.5035

134.0421

Realized Volatility

95,191

1.0601

0.5228

0.0000

3.7129

Expected Volatility

77,519

1.0650

0.1889

0.4589

2.2137

Obs.

Mean

Std. Dev.

Min

Max

Premium (%)

95,037

0.0320

1.0999

-23.5095

141.6569

Realized Volatility

95,026

0.9843

0.3532

0.0000

2.5570

Expected Volatility

77,373

0.9859

0.1214

0.5123

1.7647

Post-Announcement Variable

25

Table 2: Descriptive Statistics A 20-day over-announcement window covers 20 trading days centered on quarterly earnings announcement. The earnings announcement premium is the difference between the geometric average daily return over the 20-day window and the geometric average daily return over reference period. The realized volatility is a ratio of the standard deviation of daily returns computed using the 20-day window over the standard deviation of daily returns computed using the reference window. The expected volatility is the average of the recent sixteen realized volatilities. The sample covers the U.S. publicly traded firms that have been included in the S&P 500 stock index for the period, January 1983 to January 2016.

Over-Announcement All: 1983 - 2016 Variable Premium (%) Realized Volatility Expected Volatility

Obs

Mean

Std. Dev.

Min

Max

95,202 95,191 77,519

0.0284 1.0293 1.0328

0.6656 0.3626 0.1188

-16.7887 0.0000 0.5191

43.0339 2.5135 1.6598

Obs 30,452 30,452 17,087

Mean 0.0212 1.0063 1.0143

Std. Dev. 0.5534 0.3640 0.1039

Min -10.6358 0.0000 0.5540

Max 21.5644 2.5135 1.4948

Obs 38,589 38,579 35,086

Mean 0.0481 1.0333 1.0257

Std. Dev. 0.7397 0.3582 0.1046

Min -16.7887 0.0000 0.5191

Max 43.0339 2.4926 1.5991

Obs 26,161 26,160 25,346

Mean 0.0077 1.0502 1.0551

Std. Dev. 0.6691 0.3660 0.1413

Min -12.9543 0.0000 0.5583

Max 28.7103 2.4976 1.6598

Sub Period: 1983 - 1993 Variable Premium (%) Realized Volatility Expected Volatility Sub Period: 1994 - 2005 Variable Premium (%) Realized Volatility Expected Volatility Sub Period: 2006 - 2016 Variable Premium (%) Realized Volatility Expected Volatility

26

Table 3: Over-Announcement: 20 day window. The dependent variable is the earnings announcement premium, the difference between the geometric average daily return over the 20-day window and the geometric average daily return over reference period. The realized volatility is a ratio of the standard deviation of daily returns computed using the 20-day window over the standard deviation of daily returns computed using the reference window. The expected volatility is the average of the recent sixteen realized volatilities. Several binary dummy variables are included as independent variables: 1) RGE, which is a variable taking value one when realized volatility is greater than expected volatility and zero otherwise; 2) EGR, which is a variable taking value one when expected volatility is greater than realized volatility and zero otherwise; 3) Crisis, which is a variable taking value one during 2008-2009 global financial crisis period and zero otherwise; 4) AftCrisis, which is a variable taking value one after crisis and zero otherwise. There are also Fama and French (2015) five factors: the market excess-return (MKT), size (SML), value (HML), plus RMW (the difference in returns between portfolios with robust versus weak operating profitability) and CMA (the differences in returns between portfolios with conservative and aggressive investment, where investment is measured by the change in total assets). The sample covers the U.S. publicly traded firms that have been included in the S&P 500 stock index for the period, January 1983 to January 2016.

M1

M2

M3

M4

M5

-0.0658***

-0.1497***

-0.1502***

-0.1342***

-0.1346***

[11.07]

[11.41]

[11.45]

[13.28]

[13.33]

Expected Volatility

0.1006***

0.0976***

0.1710***

0.1682***

[4.83]

[4.70]

[7.59]

[7.48]

Realized Volatility × RGE

0.0692***

0.0692***

[10.11]

[10.11] -0.0893***

-0.0894***

Realized Volatility

Expected Volatility× EGR Crisis

[12.80]

[12.80]

0.0099

0.0115

-0.0012

0.01

-0.0027

[1.01]

[1.21]

[0.13]

[1.05]

[0.29]

AftCrisis

-0.0229***

-0.0229***

[3.87] Year

[3.87]

-0.0002

-0.0011***

-0.0011***

[0.78]

[3.72]

[3.69]

MKT

-0.1854***

-0.2171***

[9.01]

[9.51]

[9.23]

[9.50]

[9.22]

SMB

-0.0412

-0.0296

-0.0405

-0.0296

-0.0405

[1.31]

[0.92]

[1.27]

[0.93]

[1.27]

HML

0.3442***

0.3642***

0.3585***

0.3645***

0.3588***

[9.69]

[9.72]

[9.55]

[9.73]

[9.56]

RMW

0.0324

0.0281

0.0294

0.0299

0.0312

[0.94]

[0.76]

[0.80]

[0.81]

[0.85]

-0.3471***

-0.3994***

-0.3899***

-0.4021***

-0.3925***

CMA

-0.2108***

-0.2167***

-0.2104***

[6.86]

[7.56]

[7.38]

[7.62]

[7.43]

0.4996

2.2493***

0.0501**

2.2373***

0.0535***

[0.98]

[3.80]

[2.48]

[3.78]

[2.65]

Observations

95191

77514

77514

77514

77514

Adjusted R-squared

0.0039

0.0051

0.0052

0.0059

0.0059

Constant

Absolute value of t statistics in brackets * significant at 10%; ** significant at 5%; *** significant at 1%

27

Table 4: Pre-Announcement. 20 day window. The dependent variable is the premium, the difference between the geometric average daily return over the 20-day window and the geometric average daily return over reference period. The realized volatility is a ratio of the standard deviation of daily returns computed using the 20-day window over the standard deviation of daily returns computed using the reference window. The expected volatility is the average of the recent sixteen realized volatilities. Several binary dummy variables are included as independent variables: 1) RGE, which is a variable taking value one when realized volatility is greater than expected volatility and zero otherwise; 2) EGR, which is a variable taking value one when expected volatility is greater than realized volatility and zero otherwise; 3) Crisis, which is a variable taking value one during 2008-2009 global financial crisis period and zero otherwise; 4) AftCrisis, which is a variable taking value one after crisis and zero otherwise. There are also Fama and French (2015) five factors: the market excess-return (MKT), size (SML), value (HML), plus RMW (the difference in returns between portfolios with robust versus weak operating profitability) and CMA (the differences in returns between portfolios with conservative and aggressive investment, where investment is measured by the change in total assets). The sample covers the U.S. publicly traded firms that have been included in the S&P 500 stock index for the period, January 1983 to January 2016.

Realized Volatility

M1

M2

M3

M4

M5

-0.3190***

-0.4545***

-0.4539***

-0.4575***

-0.4569***

[38.51]

[28.84]

[28.81]

[33.38]

[33.34]

0.1898***

0.2063***

0.2989***

0.3150***

[6.21]

[6.73]

[9.34]

[9.81]

0.0920***

0.0919***

[14.46]

[14.44] -0.1213***

-0.1211***

[18.31]

[18.28]

-0.0164*

-0.0321***

-0.0174**

[1.86]

[3.57]

Expected Volatility Realized Volatility × RGE Expected Volatility× EGR Crisis

-0.0333***

-0.0310***

[3.60]

[3.44]

Aft_Crisis Year

[1.98]

0.0390***

0.0390***

[6.96]

[6.95]

0.0017***

0.0009***

0.0009***

[7.00]

[3.33]

[3.38]

MKT

-0.0486**

-0.0247

[2.49]

[1.13]

[1.54]

[1.15]

[1.56]

SMB

-0.1419***

-0.1367***

-0.1254***

-0.1360***

-0.1245***

[4.76]

[4.50]

[4.14]

[4.48]

[4.11]

0.1885***

0.0644*

0.0795**

0.0648*

0.0798**

[5.60]

[1.81]

[2.24]

[1.83]

[2.25]

-0.0217

0.0198

0.0198

0.0219

0.0219

[0.67]

[0.57]

[0.57]

[0.63]

[0.63]

-0.4134***

-0.3362***

-0.3511***

-0.3385***

-0.3534***

[8.61]

[6.71]

[7.01]

[6.76]

[7.06]

-3.0383***

-1.6399***

0.2018***

-1.6600***

0.2112***

[6.30]

[2.91]

[6.77]

[2.95]

[7.09]

HML RMW CMA Constant

-0.0336

-0.0251

-0.034

Observations

95098

77432

77432

77432

77432

Adjusted R-squared

0.0168

0.0156

0.016

0.0172

0.0176

Absolute value of t statistics in brackets * significant at 10%; ** significant at 5%; *** significant at 1%

28

Table 5: Post-Announcement. 20 day window. The dependent variable is the premium, the difference between the geometric average daily return over the 20-day window and the geometric average daily return over reference period. The realized volatility is a ratio of the standard deviation of daily returns computed using the 20-day window over the standard deviation of daily returns computed using the reference window. The expected volatility is the average of the recent sixteen realized volatilities. Several binary dummy variables are included as independent variables: 1) RGE, which is a variable taking value one when realized volatility is greater than expected volatility and zero otherwise; 2) EGR, which is a variable taking value one when expected volatility is greater than realized volatility and zero otherwise; 3) Crisis, which is a variable taking value one during 2008-2009 global financial crisis period and zero otherwise; 4) AftCrisis, which is a variable taking value one after crisis and zero otherwise. There are also Fama and French (2015) five factors: the market excess-return (MKT), size (SML), value (HML), plus RMW (the difference in returns between portfolios with robust versus weak operating profitability) and CMA (the differences in returns between portfolios with conservative and aggressive investment, where investment is measured by the change in total assets). The sample covers the U.S. publicly traded firms that have been included in the S&P 500 stock index for the period, January 1983 to January 2016.

Realized Volatility

M1

M2

M3

M4

M5

-0.2474***

-0.4432***

-0.4409***

-0.4004***

-0.3984***

[29.12]

[26.08]

[25.97]

[27.40]

[27.29]

0.1140***

0.1834***

0.1890***

0.2587***

[3.50]

[5.57]

[5.52]

[7.48]

0.1142***

0.1138***

[16.16]

[16.11] -0.1224***

-0.1220***

[16.65]

[16.61]

Expected Volatility Realized Volatility × RGE Expected Volatility× EGR Crisis

-0.0454***

-0.0405***

-0.0644***

-0.0416***

-0.0654***

[4.81]

[4.24]

[6.85]

[4.35]

[6.94]

AftCrisis Year

-0.0723***

-0.0723***

[11.79]

[11.80]

-0.0017***

-0.0010***

-0.0010***

[6.90]

[3.44]

[3.39]

-0.0993***

-0.1166***

-0.1019***

-0.1162***

-0.1015***

[5.00]

[5.05]

[4.41]

[5.03]

[4.39]

0.1535***

0.1264***

0.1145***

0.1285***

0.1168***

[5.06]

[3.91]

[3.56]

[3.98]

[3.63]

0.0544

0.1963***

0.1623***

0.1978***

0.1637***

[1.59]

[5.22]

[4.31]

[5.26]

[4.35]

0.2541***

0.1768***

0.1773***

0.1797***

0.1801***

[7.68]

[4.78]

[4.80]

[4.86]

[4.87]

0.1316***

0.0373

0.0692

0.0335

0.0655

[2.69]

[0.70]

[1.30]

[0.63]

[1.23]

3.6536***

2.3613***

0.2137***

2.3395***

0.2246***

[7.43]

[3.92]

[7.08]

[3.88]

[7.45]

Observations

94813

77176

77176

77176

77176

Adjusted R-squared

0.013

0.0145

0.0162

0.0147

0.0164

MKT SMB HML RMW CMA Constant

Absolute value of t statistics in brackets * significant at 10%; ** significant at 5%; *** significant at 1%

29

Table 6: Over-Announcement. 20 day window. The dependent variable is the earnings announcement premium, the difference between the geometric average daily return over the 20-day window and the geometric average daily return over reference period. The realized volatility is a ratio of the standard deviation of daily returns computed using the 20-day window over the standard deviation of daily returns computed using the reference window. The expected volatility is the average of the recent sixteen realized volatilities. Several binary dummy variables are included as independent variables: 1) RGE, which is a variable taking value one when realized volatility is greater than expected volatility and zero otherwise; 2) EGR, which is a variable taking value one when expected volatility is greater than realized volatility and zero otherwise; 3) Crisis, which is a variable taking value one during 2008-2009 global financial crisis period and zero otherwise; 4) AftCrisis, which is a variable taking value one after crisis and zero otherwise. There are also Fama and French (2015) five factors: the market excess-return (MKT), size (SML), value (HML), plus RMW (the difference in returns between portfolios with robust versus weak operating profitability) and CMA (the differences in returns between portfolios with conservative and aggressive investment, where investment is measured by the change in total assets). The sample covers the U.S. publicly traded firms that have been included in the S&P 500 stock index for the period, January 1983 to January 2016.

[1983 - 1993]

[1994 - 2005]

[2006 - 2016]

[2006 - 2010]

[2011 - 2016]

-0.1950***

-0.2369***

0.0453**

0.0887***

-0.028

[10.27]

[15.85]

[2.39]

[2.93]

[1.31]

0.1479***

0.2972***

0.0094

-0.0107

0.038

[3.20]

[8.13]

[0.25]

[0.18]

[0.90]

-0.0989***

-0.1274***

-0.0287**

-0.0196

-0.0295**

[7.50]

[12.22]

[2.24]

[0.99]

[1.98]

0.0065***

-0.0043***

0.0013

-0.0117**

0.0316***

[3.19]

[4.04]

[0.83]

[2.13]

[7.25]

-0.1794***

-0.5518***

-0.0929**

0.0486

-0.2155***

[3.03]

[15.37]

[2.18]

[0.80]

[3.37]

-0.053

-0.1949***

0.4679***

1.2708***

-1.1089***

[0.79]

[4.45]

[5.75]

[9.29]

[8.49]

HML

0.8329***

0.1971***

0.1956***

0.2055*

-2.1683***

[9.73]

[3.15]

[2.73]

[1.88]

[11.48]

RMW

0.7976***

-0.2274***

-0.2624**

0.2745

-1.9169***

[5.36]

[3.96]

[2.15]

[1.51]

[8.92]

-0.7394***

-0.1930***

-0.9471***

-1.9383***

2.6544***

[4.40]

[2.87]

[7.17]

[9.27]

[13.20]

-12.7430***

8.6305***

-2.6566

23.4918**

-63.5260***

[3.16]

[4.07]

[0.83]

[2.12]

[7.25]

Observations

17087

35082

25345

13446

11899

Adjusted R-squared

0.0157

0.0178

0.0052

0.018

0.0251

Realized Volatility Expected Volatility Expected Volatility× EGR Year MKT SMB

CMA Constant

Absolute value of t statistics in brackets * significant at 10%; ** significant at 5%; *** significant at 1%

30

Table 7: Pre-Announcement. 20 day window. The dependent variable is the premium, the difference between the geometric average daily return over the 20-day window and the geometric average daily return over reference period. The realized volatility is a ratio of the standard deviation of daily returns computed using the 20-day window over the standard deviation of daily returns computed using the reference window. The expected volatility is the average of the recent sixteen realized volatilities. Several binary dummy variables are included as independent variables: 1) RGE, which is a variable taking value one when realized volatility is greater than expected volatility and zero otherwise; 2) EGR, which is a variable taking value one when expected volatility is greater than realized volatility and zero otherwise; 3) Crisis, which is a variable taking value one during 2008-2009 global financial crisis period and zero otherwise; 4) AftCrisis, which is a variable taking value one after crisis and zero otherwise. There are also Fama and French (2015) five factors: the market excess-return (MKT), size (SML), value (HML), plus RMW (the difference in returns between portfolios with robust versus weak operating profitability) and CMA (the differences in returns between portfolios with conservative and aggressive investment, where investment is measured by the change in total assets). The sample covers the U.S. publicly traded firms that have been included in the S&P 500 stock index for the period, January 1983 to January 2016.

[1983 - 1993]

[1994 - 2005]

[2006 - 2016]

[2006 - 2010]

[2011 - 2016]

-0.5811***

-0.6830***

-0.0464*

0.1095***

-0.1732***

[23.17]

[33.14]

[1.82]

[2.84]

[5.33]

0.4150***

0.3674***

0.0271

-0.0332

0.1062

[6.65]

[6.92]

[0.52]

[0.42]

[1.59]

-0.1909***

-0.1810***

0.0158

0.0438**

-0.0109

[15.82]

[18.13]

[1.28]

[2.41]

[0.69]

Year

0.0063***

-0.0002

0

0.006

-0.0288***

[3.30]

[0.22]

[0.03]

[1.23]

[6.42]

MKT

0.1858***

-0.1178***

-0.0595

-0.0051

-0.4650***

[3.16]

[3.38]

[1.50]

[0.09]

[7.05]

-0.0239

-0.2681***

-0.1005

0.2341*

-0.2887**

[0.38]

[6.31]

[1.33]

[1.93]

[2.13]

HML

0.1979**

0.1022*

-0.1423**

-0.3081***

-0.1765

[2.49]

[1.69]

[2.14]

[3.17]

[0.91]

RMW

0.0084

-0.0863

-0.6331***

-1.2897***

-0.3743*

[0.06]

[1.55]

[5.59]

[7.97]

[1.69]

-0.3138*

-0.2232***

-0.6767***

-0.6712***

-0.4539**

[1.96]

[3.43]

[5.52]

[3.63]

[2.18]

-12.2685***

0.8759

0.1261

-12.1274

58.1085***

[3.23]

[0.43]

[0.04]

[1.24]

[6.44]

Observations

16975

35079

25378

13448

11930

Adjusted R-squared

0.0341

0.035

0.0055

0.0134

0.0204

Realized Volatility Expected Volatility Expected Volatility× EGR

SMB

CMA Constant

Absolute value of t statistics in brackets * significant at 10%; ** significant at 5%; *** significant at 1%

31

Table 8: Post-Announcement. 20 day window The dependent variable is the premium, the difference between the geometric average daily return over the 20-day window and the geometric average daily return over reference period. The realized volatility is a ratio of the standard deviation of daily returns computed using the 20-day window over the standard deviation of daily returns computed using the reference window. The expected volatility is the average of the recent sixteen realized volatilities. Several binary dummy variables are included as independent variables: 1) RGE, which is a variable taking value one when realized volatility is greater than expected volatility and zero otherwise; 2) EGR, which is a variable taking value one when expected volatility is greater than realized volatility and zero otherwise; 3) Crisis, which is a variable taking value one during 2008-2009 global financial crisis period and zero otherwise; 4) AftCrisis, which is a variable taking value one after crisis and zero otherwise. There are also Fama and French (2015) five factors: the market excess-return (MKT), size (SML), value (HML), plus RMW (the difference in returns between portfolios with robust versus weak operating profitability) and CMA (the differences in returns between portfolios with conservative and aggressive investment, where investment is measured by the change in total assets). The sample covers the U.S. publicly traded firms that have been included in the S&P 500 stock index for the period, January 1983 to January 2016.

[1983 - 1993]

[1994 - 2005]

[2006 - 2016]

[2006 - 2010]

[2011 - 2016]

-0.5863***

-0.5724***

-0.0196

0.0716

-0.0404

[23.25]

[27.35]

[0.67]

[1.55]

[1.18]

0.4286***

0.3609***

-0.0129

0.0114

-0.0177

[6.43]

[6.62]

[0.21]

[0.12]

[0.25]

-0.1961***

-0.1875***

0.015

0.0092

0.0149

[15.56]

[17.24]

[1.06]

[0.41]

[0.89]

Year

0.0083***

-0.0014

0.0021

-0.0279***

0.0660***

[4.37]

[1.37]

[1.22]

[4.82]

[13.68]

MKT

-0.2413***

-0.4312***

0.2909***

0.3962***

0.2866***

[4.13]

[12.26]

[6.41]

[6.21]

[4.08]

-0.1930***

0.3364***

-0.2020**

-0.072

-0.0499

[3.08]

[7.81]

[2.33]

[0.50]

[0.34]

HML

0.0834

0.0046

0.4699***

0.5668***

-0.5141**

[1.05]

[0.08]

[6.16]

[4.94]

[2.46]

RMW

0.5636***

0.0546

0.5291***

1.3260***

0.4282*

[4.10]

[0.97]

[4.08]

[6.94]

[1.80]

0.1202

0.0225

-0.4812***

-1.1048***

1.9862***

[0.75]

[0.34]

[3.43]

[5.04]

[8.93]

-16.2425***

3.2221

-4.175

55.9012***

-132.7615***

[4.31]

[1.55]

[1.23]

[4.81]

[13.67]

Observations

16961

35004

25211

13426

11785

Adjusted R-squared

0.0375

0.0319

0.0036

0.0105

0.0224

Realized Volatility Expected Volatility Expected Volatility× EGR

SMB

CMA Constant

Absolute value of t statistics in brackets * significant at 10%; ** significant at 5%; *** significant at 1%

32

Table 9: Over-Announcement. 10 day window. The dependent variable is the earnings announcement premium, the difference between the geometric average daily return over the 10-day window and the geometric average daily return over reference period. The realized volatility is a ratio of the standard deviation of daily returns computed using the 10-day window over the standard deviation of daily returns computed using the reference window. The expected volatility is the average of the recent sixteen realized volatilities. Several binary dummy variables are included as independent variables: 1) RGE, which is a variable taking value one when realized volatility is greater than expected volatility and zero otherwise; 2) EGR, which is a variable taking value one when expected volatility is greater than realized volatility and zero otherwise; 3) Crisis, which is a variable taking value one during 2008-2009 global financial crisis period and zero otherwise; 4) AftCrisis, which is a variable taking value one after crisis and zero otherwise. There are also Fama and French (2015) five factors: the market excess-return (MKT), size (SML), value (HML), plus RMW (the difference in returns between portfolios with robust versus weak operating profitability) and CMA (the differences in returns between portfolios with conservative and aggressive investment, where investment is measured by the change in total assets). The sample covers the U.S. publicly traded firms that have been included in the S&P 500 stock index for the period, January 1983 to January 2016.

Realized Volatility

M1

M2

M3

M4

M5

-0.0585***

-0.1205***

-0.1205***

-0.1149***

-0.1151***

[8.14]

[6.59]

[6.59]

[9.43]

[9.45]

0.0269

0.0292

0.1270***

0.1293***

[1.15]

[1.26]

[4.76]

[4.87]

0.0693***

0.0691***

[5.90]

[5.89] -0.1139***

-0.1138***

[9.71]

[9.70]

Expected Volatility Realized Volatility × RGE Expected Volatility× EGR Crisis

0.0354**

0.0350**

0.0222

0.0329**

0.02

[2.08]

[2.13]

[1.38]

[2.00]

[1.24]

Aft_Crisis

-0.0311***

-0.0313***

[3.03]

[3.05]

0.0007

-0.0009*

-0.0009*

[1.62]

[1.67]

[1.69]

-0.3031***

-0.3807***

-0.3733***

-0.3790***

-0.3715***

[8.48]

[9.68]

[9.48]

[9.64]

[9.44]

-0.049

0.0008

-0.0093

0.0025

-0.0077

[0.90]

[0.01]

[0.17]

[0.04]

[0.14]

0.4822***

0.5292***

0.5175***

0.5290***

0.5173***

[7.81]

[8.19]

[7.99]

[8.20]

[7.99]

0.0124

-0.0065

-0.0061

-0.0042

-0.0038

[0.21]

[0.10]

[0.10]

[0.07]

[0.06]

-0.6532***

-0.7764***

-0.7638***

-0.7765***

-0.7638***

[7.42]

[8.53]

[8.38]

[8.53]

[8.39]

-1.3239

1.8457*

0.1117***

1.8615*

0.1133***

[1.50]

[1.78]

[4.88]

[1.80]

[4.95]

Observations

95191

77514

77514

77514

77514

Adjusted R-squared

0.0025

0.0032

0.0032

0.0039

0.004

Year MKT SMB HML RMW CMA Constant

Absolute value of t statistics in brackets * significant at 10%; ** significant at 5%; *** significant at 1%

33

Table 10: Pre-Announcement. 10 day window The dependent variable is the premium, the difference between the geometric average daily return over the 10-day window and the geometric average daily return over reference period. The realized volatility is a ratio of the standard deviation of daily returns computed using the 10-day window over the standard deviation of daily returns computed using the reference window. The expected volatility is the average of the recent sixteen realized volatilities. Several binary dummy variables are included as independent variables: 1) RGE, which is a variable taking value one when realized volatility is greater than expected volatility and zero otherwise; 2) EGR, which is a variable taking value one when expected volatility is greater than realized volatility and zero otherwise; 3) Crisis, which is a variable taking value one during 2008-2009 global financial crisis period and zero otherwise; 4) AftCrisis, which is a variable taking value one after crisis and zero otherwise. There are also Fama and French (2015) five factors: the market excess-return (MKT), size (SML), value (HML), plus RMW (the difference in returns between portfolios with robust versus weak operating profitability) and CMA (the differences in returns between portfolios with conservative and aggressive investment, where investment is measured by the change in total assets).

Realized Volatility

M1

M2

M3

M4

M5

-0.2368***

-0.3761***

-0.3772***

-0.3763***

-0.3772***

[22.54]

[17.08]

[17.13]

[22.22]

[22.28]

0.2131***

0.2066***

0.3777***

0.3714***

[6.10]

[5.94]

[10.00]

[9.86]

0.1215***

0.1218***

[10.60]

[10.63] -0.1814***

-0.1817***

[15.55]

[15.57]

Expected Volatility Realized Volatility × RGE Expected Volatility× EGR Crisis

0.0654***

0.0715***

0.0737***

0.0687***

0.0711***

[3.80]

[4.50]

[4.73]

[4.32]

[4.56]

Aft_Crisis Year MKT

0.0256***

0.0258***

[2.60]

[2.62]

0.0019***

-0.0004

-0.0004

[4.14]

[0.76]

[0.73]

-0.2202***

-0.2335***

-0.2375***

-0.2326***

-0.2367***

[6.08]

[6.10]

[6.20]

[6.08]

[6.18]

-0.0841

-0.0937*

-0.0933*

-0.0913*

-0.0907*

[1.52]

[1.75]

[1.75]

[1.71]

[1.70]

0.5367***

0.4503***

0.4665***

0.4471***

0.4633***

[8.58]

[7.20]

[7.44]

[7.15]

[7.39]

-0.1420**

-0.1194*

-0.1169*

-0.1128*

-0.1103*

[2.35]

[1.94]

[1.90]

[1.83]

[1.80]

-0.9280***

-0.8978***

-0.9067***

-0.9001***

-0.9091***

[10.41]

[10.17]

[10.26]

[10.20]

[10.30]

-3.4205***

0.899

0.1425***

0.8696

0.1481***

[3.82]

[0.91]

[4.21]

[0.88]

[4.38]

Observations

95144

77477

77477

77477

77477

Adjusted R-squared

0.0069

0.0065

0.0066

0.0082

0.0083

SMB HML RMW CMA Constant

Absolute value of t statistics in brackets * significant at 10%; ** significant at 5%; *** significant at 1%

34

Table 11: Post-Announcement. 10 day window. The dependent variable is the premium, the difference between the geometric average daily return over the 10-day window and the geometric average daily return over reference period. The realized volatility is a ratio of the standard deviation of daily returns computed using the 10-day window over the standard deviation of daily returns computed using the reference window. The expected volatility is the average of the recent sixteen realized volatilities. Several binary dummy variables are included as independent variables: 1) RGE, which is a variable taking value one when realized volatility is greater than expected volatility and zero otherwise; 2) EGR, which is a variable taking value one when expected volatility is greater than realized volatility and zero otherwise; 3) Crisis, which is a variable taking value one during 2008-2009 global financial crisis period and zero otherwise; 4) AftCrisis, which is a variable taking value one after crisis and zero otherwise. There are also Fama and French (2015) five factors: the market excess-return (MKT), size (SML), value (HML), plus RMW (the difference in returns between portfolios with robust versus weak operating profitability) and CMA (the differences in returns between portfolios with conservative and aggressive investment, where investment is measured by the change in total assets).

Realized Volatility

M1

M2

M3

M4

M5

-0.1364***

-0.3414***

-0.3407***

-0.3050***

-0.3045***

[13.45]

[15.45]

[15.43]

[18.23]

[18.22]

0.1902***

0.2234***

0.3246***

0.3578***

[5.51]

[6.50]

[8.64]

[9.57]

0.1339***

0.1336***

[11.49]

[11.47] -0.1697***

-0.1695***

[14.41]

[14.40]

Expected Volatility Realized Volatility × RGE Expected Volatility× EGR Crisis

-0.0348**

-0.0361**

-0.0638***

-0.0380**

-0.0658***

[2.15]

[2.34]

[4.20]

[2.47]

[4.33]

Aft_Crisis Year MKT SMB HML RMW CMA Constant

-0.0736***

-0.0738***

[7.45]

[7.47]

-0.0016***

-0.0015***

-0.0015***

[3.74]

[3.07]

[3.08]

-0.1661***

-0.2385***

-0.2217***

-0.2377***

-0.2209***

[4.88]

[6.44]

[5.98]

[6.42]

[5.96]

0.0203

0.0627

0.0435

0.0678

0.0485

[0.39]

[1.21]

[0.84]

[1.31]

[0.94]

0.1414**

0.2865***

0.2560***

0.2877***

0.2572***

[2.41]

[4.73]

[4.22]

[4.75]

[4.24]

0.1447**

0.1010*

0.1019*

0.1045*

0.1053*

[2.55]

[1.70]

[1.71]

[1.76]

[1.77]

0.1836**

0.0254

0.0557

0.0225

0.0529

[2.19]

[0.30]

[0.65]

[0.26]

[0.62]

3.3224***

3.1645***

0.0812***

3.1741***

0.0819***

[3.94]

[3.20]

[2.59]

[3.21]

[2.62]

Observations

95026

77368

77368

77368

77368

Adjusted R-squared

0.0039

0.0061

0.0067

0.007

0.0076

Absolute value of t statistics in brackets * significant at 10%; ** significant at 5%; *** significant at 1%

35