Earnings Shocks and the Idiosyncratic Volatility Anomaly in the CrossSection of Stock Returns

Peter Wong* The Ohio State University August 2011

Abstract Ang, Hodrick, Xing, and Zhang (2006, 2009) document a puzzling negative relation between idiosyncratic volatility and cross-section of stock returns. This paper examines whether this idiosyncratic volatility discount is related to earnings shocks, and finds that a substantial portion of the idiosyncratic volatility discount can be explained by earnings momentum and post-formation earnings shocks. When these two effects are accounted for, idiosyncratic volatility has little, if any, return predictability. In addition, earnings momentum alone can explain at least 42% of the idiosyncratic volatility discount.

* I am grateful for comments from René Stulz and seminar participants at The Ohio State University. I would like to thank my advisor, Kewei Hou, for the considerable amount of time he has spent discussing this topic with me. Author’s email address: [email protected].

I. Introduction In a recent paper, Ang, Hodrick, Xing, and Zhang (2006) find that high idiosyncratic volatility (IVOL) stocks underperform low IVOL stocks by approximately 1% per month. They refer to this underperformance as the IVOL discount. This finding is robust and has since been confirmed in numerous papers. 1 The empirical fact that high IVOL stocks have lower expected returns is inconsistent with traditional asset pricing theories based on a complete market in which investors are well diversified, and do not demand a premium or a discount for holding high IVOL stocks. If, in actuality, investors demand compensation for being unable to diversify risk, 2 then they will demand a premium for holding high IVOL stocks. In particular, Merton (1987) suggests that in an information-segmented market, investors require higher returns for firms with larger firm-specific variances to compensate them for holding imperfectly diversified portfolios. Some behavioral models, like Barberis and Huang (2001), also predict that higher IVOL stocks should earn higher expected returns. Thus, it is difficult to reconcile Ang et al.’s (2006) result with existing theories on IVOL and expected returns. Even though the magnitude and statistical significance of the return spread between high and low IVOL stocks seem beyond doubt, an important question has yet to be addressed: What differences in the economic fundamentals of these stocks drive this return spread? After all, IVOL is an arbitrary indicator variable that, for unexplained economic reasons, is negatively related to future returns. Therefore, the goal of this paper is to fill this knowledge gap. Specifically, I study whether the behavior of stock returns in relation to IVOL is consistent with the behavior of earnings. As earnings serve as perhaps the most important economic signal for investors in terms of valuing shares, an exploration of the difference in earnings performance is a natural starting point for an attempt to address this issue. In addition, previous literature3 studies whether the behavior of stock prices in relation to such firm characteristics as size,

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For example, see Ang, Hodrick, Xing, and Zhang (2009), Fu (2009), and Bali, Cakici, and Whitelaw (2009). See Malkiel and Xu (2002) and Jones and Rhodes-Kropf (2003). 3 See Fama and French (1995), La porta, Lakonishok, Shleifer, and Vishny (1997), and Chan, Jegadeesh, and Lakonishok (1996). 2

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book-to-market-equity, and past return can be explained by differences in earnings performance. Therefore, my approach of investigating the relation between IVOL and earnings performance is not uncommon. My study is further motivated by Ang et al.’s (2006) finding that firms with high IVOL stocks tend to be value firms and that they are typically small, young, and past return losers. Moreover, previous research shows that firms with these characteristics typically have poor earnings performance. For example, Fama and French (1995) document that small-value firms tend to have the worst earnings performance of all stocks. In addition, Fama and French (2004) report that, starting in 1980s, newly listed firms (especially those that are small) perform badly. Consistent with this evidence, Hou and Van Dijk (2010) find that small firms experience large negative profitability shocks (post-formation earnings shocks) after the 1980s. Lastly, Chan, Jegadeesh, and Lakonishok (1996) and Chordia and Shivakumar (2006) demonstrate that price momentum losers tend to have negative earnings shocks prior to portfolio formation, and that these negative earnings shocks continue for up to four quarters after portfolio formation. Therefore, it is possible that the large IVOL discount is a result of the difference in earnings performance between the high and low IVOL stocks. I find that high IVOL stocks suffer negative earnings shocks both before and after portfolio formation. To gauge the magnitude of the difference in earnings shocks between the high and low IVOL firms, I compute average standardized unexpected earnings (SUE) for each quintile of stocks sorted by IVOL (value weighted). The difference in the SUE between the highest and the lowest IVOL quintile portfolios directly prior to portfolio formation is -1.16 with a Newey-West (1973) t-statistic of -20.90. This difference in earnings surprises persists for at least two quarters after portfolio formation. The SUE spreads between the highest and the lowest IVOL quintiles around the first and second earnings announcements after portfolio formation are -1.33 (t = -24.08) and -1.08 (t = -21.35), respectively. As an extensive amount of literature shows that firms reporting unexpectedly high earnings outperform firms

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reporting unexpectedly poor earnings even after the earnings announcement4 (the “earnings momentum effect”), this article relates the evidence on the IVOL discount to the evidence on the earnings momentum effect. In addition to the relation between the IVOL discount and the earnings momentum effect, Hou and Van Dijk (2010) and Vuolteenaho (2002) demonstrate the importance of post-formation earnings shocks in explaining realized stock returns. As high IVOL stocks tend to experience large negative earnings shocks after portfolio formation, this paper also investigates the possibility that post-formation earnings shocks may play an important role in explaining the IVOL discount. To assess the impact of the earnings momentum effect on the IVOL discount, I double sort stocks into 5x5 portfolios based on their most recent SUEs and IVOLs, and study the effect of SUEs on the IVOL discount. The results of this double-sorting exercise show that controlling for the earnings momentum effect reduces the IVOL discount from -1.11% to -0.62% per month. In addition, I follow Chordia and Shivakumar (2006) in forming the earnings momentum factor (PMN) and use this factor along with the Fama and French (1993) three-factor (FF3F) model to compute the Jensen’s alpha. The results derived from using the PMN factor to control for the earnings momentum effect is largely consistent with that obtained in the double-sorting exercise. Specifically, the PMN method reduces the IVOL discount from -1.11% to -0.65%. Lastly, to ensure that the earnings momentum effect has been properly accounted for, I double sort stocks into 25 portfolios based on their most recent SUEs and IVOLs, and compute the Jensen’s alpha, instead of returns for each of these 25 portfolios using a four-factor model in which the PMN factor is added to the FF3F model. This procedure essentially combines the first and second approaches to control for the earnings momentum effect, and it reduces the IVOL discount from -1.11% to -0.26%. Therefore, the evidence is consistent with the argument that the earnings momentum effect is important in explaining the IVOL discount. The results from the cross-section Fama-MacBeth (1973) test allow for a similar conclusion.

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For example, see Latane and Jones (1979), Bernard and Thomas (1989), and Bernard, Thomas, and Jones (1995).

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Furthermore, as high IVOL firms continue to experience negative earnings shocks even after portfolio formation, I also investigate the possibility that the large negative return spread between the high and low IVOL firms is partly due to differences in post-formation earnings shocks. To account for the effect of post-formation earnings shocks on the IVOL discount, I adjust monthly stock returns by removing the daily returns surrounding earnings announcements. Consistent with the conjecture, I find that postformation earnings shocks also explain part of the IVOL discount. Specifically, the removal of three daily returns surrounding earnings announcements reduces the IVOL discount from -1.11% to -0.83%. This is a sizable reduction considering that there are 22 trading days per month and only one-third of the firms in the sample announce earnings in a given month. In addition, I show that post-formation earnings shocks still capture approximately 20% of the IVOL discount after controlling for the earnings momentum effect. Lastly, the combined effect of earnings shocks (both pre-formation and post-formation) can explain up to 93% of the IVOL discount. This paper contributes to the ongoing debate on the sources of the IVOL discount. Several studies suggest that the IVOL discount can be captured using a more carefully constructed volatility factor (e.g., Chen and Petkova (2010) and Barinov (2010)). In contrast, Jiang, Xu, and Yao (2009), Sonmez (2008), and George and Hwang (2010) suggest that the IVOL discount is related to important corporate events, such as earnings news. This paper focuses on the latter suggestion and shows that the IVOL discount arises because high IVOL stocks experience negative earnings shocks prior to portfolio formation, and that the earnings momentum effect induces the low returns observed in these stocks. In addition, high IVOL stocks continue to surprise investors with poor earnings performance even after portfolio formation. These post-formation negative earnings shocks further adversely affect high IVOL stocks’ returns. The remainder of the paper is organized as follows. Section II introduces the data, the measurement of IVOL, earnings surprises, and the adjustment of stock returns to reflect post-formation earnings shocks. Section III introduces the summary statistics for the sample, and demonstrates that high IVOL stocks experience negative earnings shocks before and after portfolio formation. Sections IV and V present the 4

time-series tests of how the IVOL discount is affected by earnings momentum and post-formation earnings shocks, respectively. Section VI quantifies the combined effect of earnings momentum and postformation earnings shocks on the IVOL discount. Section VII examines the results using a FamaMacBeth regression and section VIII concludes. II. Data and measurements I obtain stock price data for all publicly traded firms on NYSE/AMEX/Nasdaq with sharecodes 10 or 11 (e.g., excluding ADRs, closed-end funds, and REITs) from the Center for Research in Security Prices’ (CRSP) monthly file for the period beginning January 1972 and ending December 2009. I also obtain accounting data on these firms from COMPUSTAT. Book equity (BE) is the stockholders’ equity plus the deferred tax and investment credit on the balance sheet minus the book value of preferred stock. The book-to-market ratio is calculated by dividing book equity by December t-1 market equity. To ensure that the book equity information was known before the return series against which it is measured, I match CRSP monthly returns between July of year t and June of year t+1 with book equity for the fiscal year ending in year t-1, as in Fama and French (1992). I do not include negative-BE firms, which are rare in COMPUSTAT prior to 1980. Firm age is defined as the number of years a firm has return data available in CRSP. I follow Ang et al. (2006) in computing IVOL for each firm using daily returns from the prior month, and I regress them on the Fama and French (1993) three-factor model (FF3F). IVOL is the standard deviation of the model’s residuals. Firms with less than 15 observations in fitting the FF3F model are removed from my final sample. I compute three measures of earnings surprises: SUE, SUE1, and CAR. SUE is defined as earnings in the current quarter less earnings four quarters ago and is standardized by the standard deviation of the earnings changes over the prior eight quarters. SUE1 is defined in manner similar to SUE except it is standardized by the share price four quarters ago. CAR is the three-day, cumulative, market5

adjusted (value-weighted) returns from one day prior to an earnings announcement to one day after that announcement.5 I also follow Chordia and Shivakumar (2006) in forming an earnings momentum factor to capture the post-earnings announcement drift phenomenon. Specifically, for each month t, I sort all NYSE-AMEX6 firms in the CRSP files with data in COMPUSTAT into deciles based on their SUE from the most recent earnings announcement. I equally weight the firms in each decile. The positions are held for six months, t+1 through t+6.7 The difference in returns between the highest and lowest SUE deciles is the earnings momentum factor. III. Do high IVOL stocks experience negative earnings surprises before and after portfolio formation? Table 1 presents the summary statistics for the five IVOL quintile portfolios. I form five quintile portfolios each month based on IVOL and I report the time-series averages of the value-weighted characteristics for each portfolio. The Return column shows that the IVOL discount, i.e., the average return difference between the high and low IVOL quintiles, is -1.11% per month with a t- statistic of -3.13. The differences in CAPM and FF3F alpha are -1.40% (t = -4.49) and -1.45% (t = -5.84), respectively. Post-formation IVOL is measured for the month after portfolio formation and it is monotonically increasing across IVOL portfolios. Thus, stocks with high pre-formation IVOL continue to experience high IVOL after portfolio formation. In addition, high IVOL stocks are relatively younger, with an average age of 13 years, than low IVOL stocks, which have an average age of 40 years. High IVOL stocks are also small-value firms with poor returns for the preceding 12 month (excluding the most recent month). These characteristics of high IVOL stocks are all associated with poor earnings performance, as

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My results are robust to replacing value-weighted market return with equally weighted market return when calculating abnormal return. 6 Data on earnings announcements are available for most Nasdaq stocks as of 1984. The inclusion of Nasdaq stocks in the formation of the earnings momentum factor has no qualitative impact on my results. I follow Chordia and Shivakumar (2006) and use NYSE-AMEX stocks to form the earnings momentum factor. 7 I follow Jegedeesh and Titman (1993) in order to account for overlapping returns.

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documented in the size, value, and momentum literature streams8. Therefore, the observed large IVOL discount may be due to the difference in earnings performance between the high and the low IVOL stocks. Accordingly, a natural question is then whether the earnings performance of high IVOL stocks is inferior to that of low IVOL stocks. Figure 1 9 , which shows the value-weighted average earnings surprises for each of the IVOL-sorted portfolios eight quarters before and eight quarters after portfolio formation, addresses this question directly. The three measures – SUE, SUE1, and CAR – are employed to capture earnings surprises. The plots capture average earnings surprises as a function of IVOL for a long period around portfolio formation periods. The question is: How do earnings behave before and after firms are classified as high or low IVOL? Figure 1 shows that IVOL is associated with persistent differences in earnings surprises when such surprises are measured using SUE, SUE1, or CAR. Specifically, high IVOL stocks experience more negative earnings shocks than low IVOL stocks two quarters before and two quarters after portfolio formation. This evidence is consistent with Jiang, Xu, and Yao’s (2009), which shows that IVOL is a negative predictor of future earnings. Figure 1 raises two questions about the IVOL discount. First, as high IVOL stocks tend to have earnings performance that is inferior to low IVOL stocks prior to portfolio formation, can the well-known earnings momentum effect help explain the IVOL discount? This question focuses on whether the low returns of high IVOL stocks are due to delayed price reactions to their poor earnings news prior to portfolio formation. Second, as high IVOL stocks continue to perform poorly in earnings terms even after portfolio formation, could these post-formation earnings shocks also contribute to the poor returns of high IVOL stocks? To gauge the magnitudes of the earnings shocks surrounding portfolio formation, panel A of Table 2 reports the value-weighted average earnings surprises and the average cross-section standard

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See Fama and French (1995), La porta, Lakonishok, Shleifer, and Vishny (1997), and Chan, Jegadeesh, and Lakonishok (1996). 9 Figures 1A, 1B, and 1C plot SUE, SUE1, and CAR, respectively.

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deviations of the earnings surprises of IVOL-sorted quintile portfolios. As the IVOL portfolios are rebalanced monthly and earnings surprises are measured quarterly, Newey-West t-statistics with three lags are reported in Table 2. Panel A of Table 2 shows that high IVOL stocks experience large, negative earnings shocks in the quarter just prior to portfolio formation. Specifically, the average SUE of the highest IVOL quintile is -0.21, while it is 0.95 for the stocks in the lowest IVOL quintile. The SUE spread between the extreme IVOL quintiles, therefore, is -1.16 (t = -20.90). SUE1 and CAR provide a similar picture. The spreads in SUE1 and CAR between the highest and the lowest IVOL quintiles are -1.83% (t = -3.31) and -1.53% (t = -6.01), respectively. This evidence suggests that high IVOL stocks experience poor earnings performance prior to portfolio formation and, importantly, that investors are surprised by such poor performance. As an extensive amount of literature documents that firms tend to have lower stocks returns after poor earnings surprises, it is natural to examine whether the IVOL discount is related to the earnings momentum effect. Figure 1 shows that high IVOL stocks have poor earnings surprises both before and after portfolio formation. Columns 3 to 6 in panel A of Table 2 report value-weighted average earnings surprises (SUE, SUE1, and CAR) for each IVOL quintile after portfolio formation. Interestingly, the difference in earnings performance between the extreme IVOL quintiles continues in the periods following portfolio formation. For instance, the spreads in the SUE, SUE1, and CAR between the highest and the lowest IVOL quintiles directly after portfolio formation are -1.33 (t = -24.08), -3.57% (t = -4.70), and -0.80% (t = -5.35), respectively. The SUE and SUE1 spreads between the high and the low IVOL quintiles are actually wider in the quarter following portfolio formation than prior to formation. This may simply be a symptom of a misspecified model of expected earnings, so that an examination of the behavior of returns around earnings announcements would provide a more direct piece of evidence. High IVOL stocks experience -0.57% CAR around the first quarterly earnings announcement after portfolio formation, while low IVOL stocks experience 0.23% CAR.

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The average firm makes one quarterly earnings announcement within three months of portfolio formation. Therefore, one way to gauge the economic magnitude of this -0.80% CAR spread between the extreme IVOL quintiles is to compare it to the average three-month buy-and-hold abnormal returns of the long-short IVOL portfolios (long on high IVOL quintile stocks and short low IVOL quintile stocks). Panel C of Table 2 reports the average, long-horizon, characteristic-adjusted returns (adjusted for size and book-to-market) of the IVOL quintiles. The characteristic-adjusted returns procedure largely follows Daniel et al. (1997) and is further motivated by Daniel and Titman (1997). The quarterly IVOL discount is -2.88%. Therefore, the -0.80% spread in CAR after portfolio formation accounts for 27.78% of the quarterly IVOL discount. In contrast, if the IVOL discount was evenly distributed across the three-month holding period, we would expect to observe less than 5% of the IVOL discount occurring in the days around earnings announcements in the three-month holding period. 10 Moreover, high IVOL stocks continue to surprise investors with poor earnings performance even during the second earnings announcement after portfolio formation. The difference in CAR between the high and low IVOL quintiles during the second earnings announcement period is -0.29%. To put this in perspective, the spread in characteristic-adjusted returns between the extreme IVOL quintiles is -4.61% in the first six months after portfolio formation. The combined spread of -1.09% in CAR around the subsequent two announcements of quarterly earnings thus accounts for 23.64% of the six-month, buy-and-hold, characteristic-adjusted returns. After two quarters, there is little difference between the quintiles’ abnormal returns around earnings announcements. Interestingly, Table 2 shows that high IVOL stocks also tend to have larger dispersion in SUE1 and CAR 11 (reported in square brackets) both before and after portfolio formation. This result is

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An average quarter has 66 trading days and I only remove three trading days out of each quarter. Therefore, if the IVOL discount was evenly distributed across the three-month holding period, we would expect 3/66, or 4.5%, of the IVOL discount to occur in the days around the earnings announcement in the three-month holding period. 11 The difference in the standard deviation of SUE across IVOL quintiles is trivial. This is expected because SUE is defined as changes in earnings divided by the standard deviation of earnings changes.

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consistent with Vulteenaho’s (2002) finding that variations in firm-level stock returns are mainly driven by variations in earnings news. To summarize, the sorting of stocks on the basis of the previous month’s IVOL yields large differences in subsequent returns (the IVOL discount). Furthermore, high IVOL stocks tend to have large, negative earnings shocks before portfolio formation. In addition, high IVOL stocks continue to surprise investors with poor earnings performance even two quarters after portfolio formation, which raises the possibility that post-formation earnings shocks may also play an important role in explaining the IVOL discount. Therefore, the next two sections analyze the importance of the earnings momentum effect and post-formation earnings shocks to the IVOL discount, respectively. IV. Earnings momentum and the IVOL discount Section III demonstrates that high IVOL stocks tend to experience large, negative earnings shocks prior to portfolio formation. An extensive range of literature documents that firms reporting unexpectedly high earnings continue to outperform firms reporting unexpectedly poor earnings after earnings announcements. Therefore, this section investigates the importance of earnings momentum in explaining the IVOL discount. Three methods are employed to assess the impact of earnings momentum on the IVOL discount. First, I double sort stocks into 25 portfolios based on their most recent SUE and IVOL 12, and study the effect that SUE has on the IVOL discount. Second, I follow Chordia and Shivakumar (2006) in forming the earnings momentum factor (PMN), and I use this factor along with the Fama and French (1993) three-factor (FF3F) model to compute Jensen’s alpha. Lastly, to ensure that the earnings momentum effect has been properly accounted for, I double sort stocks into 25 portfolios based on their most recent SUE and IVOL, and compute the Jensen’s alpha, instead of the return, for each of these 25 portfolios using a four-factor model in which the PMN factor is added to the FF3F model. This procedure essentially combines the first and second approaches to control for the earnings momentum effect. 12

This is a sequential sort. I first sort stocks into five SUE quintiles. Within each SUE quintile, I further sort stocks into five IVOL quintiles.

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A. Double-sorting on SUE and IVOL Panel A of Table 3 shows the average returns and t-statistics of the 25 portfolios resulting from the double-sorting procedure. This panel also reports the IVOL discount – the difference in average returns between the highest and lowest quintiles of IVOL firms – within each SUE quintile. First, the IVOL discount is monotonically declining in SUE. Specifically, the IVOL discount is -1.36% (t = -2.77) among the firms with the worst earnings surprises, while the IVOL discount is only -0.02% (t = -0.07) among the firms with the most positive earnings surprises. The fact that the IVOL discount resides mostly among the firms with worst earnings surprises is consistent with the evidence of slower diffusion of negative news found in Hong, Lim, and Stein (2000), Hou (2005), Hou and Moskowitz (2005), and Diether, Malloy, and Scherbina (2002). Second, to control for the earnings momentum effect, I average the returns of each IVOL quintile over the five SUE portfolios. Therefore, these IVOL quintile portfolios control for the differences in earnings shocks. The average IVOL discount is -0.62% (t = -1.92), which is substantially lower than the -1.11% (t = -3.13) IVOL discount produced by the univariate-sorted IVOL quintiles (Table 1). Panel B of Table 3 reports the FF3F alpha and t-statistics of the 25 SUE- and IVOL-sorted portfolios. The evidence in this panel largely agrees with the previous analyses; the IVOL discount resides mostly among stocks with poor prior earnings performance. The average IVOL discount across the five SUE quintiles is -0.97% (t = -4.48) per month. Although the -0.97% FF3F alpha is still economically and statistically significant, the univariate-sorted 5-1 IVOL portfolio produces an even larger FF3F alpha spread (-1.45% with t = -5.84; see Table 1). Therefore, controlling for the most recent earnings performance reduces the IVOL discount substantially. B. Using the earnings momentum factor to control for the earnings momentum effect Panel C of Table 3 reports the intercepts (Jensen’s alpha) from regressing the excess returns of each IVOL quintile on a four-factor model in which the PMN factor is added to the FF3F model. The last 11

column of panel C shows the PMN loadings for each IVOL quintile. PMN loading is monotonically declining in IVOL. The spread of the PMN loadings between the extreme IVOL quintiles is -0.86. This suggests that high (low) IVOL firms co-move closely with negative (positive) earnings surprises firms, which is consistent with earlier results that show that high (low) IVOL firms tend to experience more negative (positive) earnings shocks prior to portfolio formation. To gauge whether this -0.86 spread in PMN loadings is economically significant, I report the average premium on the PMN factor during my sample period in the bottom row of panel C. On average, the PMN factor earns 0.89% per month and, therefore, the -0.86 spread in the PMN loadings accounts for -0.86 x 0.89% = -0.77% of the difference in average returns between the extreme IVOL quintiles. As a result, the spread in the FF3F_PMN alpha between the highest and the lowest IVOL quintiles is -0.65% with a t-statistic of -2.53 (Table 3, panel C, column 2), compared to the -1.45% (t = -5.84) alpha spread obtained from the FF3F model (Table 1, column 4) and the -1.11% (t = -3.13) raw return spread obtained by sorting stocks into quintiles based on IVOL (Table 1, column2). Furthermore, PMN loadings are highly significant in four of the five quintiles. Thus, PMN is not likely to be a useless factor in the sense of Kan and Zhang (1999). As a result, controlling for the earnings momentum effect in this manner provides a conclusion similar to that made in the previous subsection. That is, the earnings momentum effect plays an important role in explaining the IVOL discount. C. Combining double-sorting and the earnings momentum factor Thus far, the earnings momentum effect has been controlled for using either double-sorting (subsection A) or the earnings momentum factor, PMN, to compute the Jensen’s alpha (sub-section B). To ensure that the earnings momentum effect has been properly accounted for, I combine these two approaches. However, it is possible that these two approaches act as perfect substitutes for one another in controlling for the earnings momentum effect. In such a situation, combining them would not further reduce the IVOL discount. To address this concern, panel A of Table 4 reports the PMN loadings of the 12

25 SUE/IVOL sorted portfolios. PMN loading is decreasing in IVOL across all five SUE quintiles, and the spreads of the loadings between the extreme IVOL quintiles are all economically and statistically significant. The average spread in the PMN loadings across all five SUE quintiles is -0.69 with a tstatistic of -7.46. This suggests that high IVOL stocks are still highly negatively exposed to the earnings momentum factor regardless of whether they reside in a positive- or negative-SUE quintile. As a result, there does not seem to be much overlap between the double-sorting and PMN factor approaches to controlling for the earnings momentum effect. The smallest PMN loadings spread in magnitude is -0.30 (the highest SUE quintile). As the PMN premium earns 0.89% per month, the -0.30 PMN loadings spread accounts for -0.30 x 0.89% = -0.27% of the returns spread between the extreme IVOL quintiles among the highest SUE stocks. This is a sizable amount given that the IVOL discount, as measured by FF3F alpha, is only -0.35% among the highest SUE stocks (Table 3, panel B). Panel B of Table 4 presents the results obtained when the double-sorting and the PMN factor approaches are combined. Specifically, it reports the FF3F_PMN alpha of the 25 SUE/IVOL-sorted portfolios. Consistent with the prior results, the IVOL discount is substantially weaker when the PMN factor is introduced into the FF3F model. The average IVOL discount across all five SUE portfolios, as measured by the spread in FF3F_PMN alpha between the extreme IVOL quintiles, is only -0.26% per month with a t-statistic of -1.17. In contrast, sorting stocks into five quintiles based on IVOL alone produces a FF3F_PMN alpha spread of -0.65% with a t-statistic of -2.53 (Table 3, panel C). On the other hand, double-sorting stocks on IVOL and SUE produces an average IVOL discount, as measured by the FF3F alpha, of -0.97% (t = -4.48) (Table 3, panel B). Thus, this combined approach seems to provide a more adequate control of the earnings momentum effect in terms of explaining the IVOL discount. The evidence in this section presents a clear picture of how prior earnings performance is related to the IVOL discount. Specifically, investors under-react to earnings news, especially for those firms with 13

worst earnings surprises and high IVOLs. This result is consistent with the evidence that negative news diffuses more slowly. Bali and Cakici (2008) show that high IVOL stocks are typically small, illiquid, and low-priced stocks, and that these characteristics can also be viewed as short-sale constraints. Thus, a significant portion of the IVOL discount reflects a failure to appropriately incorporate negative earnings news in stock prices due to the market frictions that are associated with these high IVOL stocks. V. The importance of post-formation earnings shocks in explaining the IVOL discount Earlier results (see Table 2 and Figure 1) suggest that high IVOL stocks experience earnings disappointments both before and after portfolio formation. This section investigates how post-formation earnings shocks may play a role in explaining the IVOL discount. To examine this issue, I adjust monthly stock returns to reflect earnings shocks using the following procedures: 1) If there is an earnings announcement within a given month, I replace the daily returns in [-1,0,+1] with 0, with time 0 being the earnings announcement date.13 2) I compound the daily returns over that month using these “adjusted” daily returns. This new monthly return is called adjusted monthly return or adjusted return. 3) If no earnings announcement takes place during that month, the adjusted return equals the CRSP monthly return for that month. 4) Alpha is obtained by using the adjusted returns in excess of the risk-free rate with respect to one of the asset pricing models, such as CAPM, the FF3F model, or the FF3F_PMN model. The alpha obtained using this adjusted returns series is called the adjusted alpha. The goal here is to explore the effect of post-formation earnings shocks on the IVOL discount. If post-formation earnings shocks are not important in explaining the IVOL discount, the removal of three days per month when calculating monthly returns should not substantially affect the IVOL discount.

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The replacement of returns with risk-free rate, value, or equally weighted market returns does not qualitatively change the results.

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Panel A of Table 5 reports the average monthly statistics for the firms that announce earnings. In addition, panel B of Table 5 reports the adjusted monthly returns and adjusted alphas obtained using different asset pricing models. On average, the lowest IVOL quintile has 256 firms reporting quarterly earnings results per month, while the highest IVOL quintile has 204 firms. The overall average number of firms in each quintile (with or without earnings announcements during the month) is 750. Therefore, the adjusted return procedure affects only (256 + 204)/1500 = 30.67% of the total sample of quintiles one and five. In addition, the adjusted return procedure only involves removing three daily returns, or 13.64%, of the twenty-two trading days in an average month. Therefore, if the IVOL discount is randomly distributed across trading days and if post-formation earnings shocks are not important in explaining the IVOL discount, then the adjusted return procedure should only remove 30.67% x 13.64% = 4.13% of the IVOL discount. Column two of panel B of Table 5 shows that the spread of the adjusted returns between the extreme IVOL quintiles is -0.83%, while the unadjusted return spread is -1.11% (Table 1). Thus, the adjustment to reflect post-formation earnings shocks reduces the IVOL spread by [1.11-0.83]/1.11 = 25.23%, which is substantially higher than the 4.13% benchmark. This result is consistent with Xu, Yao, and Jiang (2009), who find that one-quarter-ahead SUE is useful in explaining the IVOL discount. The result presented above is univariate in the sense that returns are adjusted for post-formation earnings shocks but the relevant asset pricing factors are not taken into account. To address this issue, columns 3 and 4 of panel B of Table 5 report the CAPM and the FF3F adjusted alpha, respectively. The CAPM and the FF3F adjusted alpha spreads are -1.10% (t = -3.76) and -1.16% (t = -4.91), respectively, while the corresponding CAPM and the FF3F alpha obtained using unadjusted returns are -1.40% (t = -4.49) and -1.45% (t = -5.84) (Table 1). Therefore, the respective reductions in the CAPM and the FF3F alpha are 27% and 20%. This suggests that the differences in loadings on MKTRF, SMB, and HML cannot subsume the importance of post-formation earnings shocks in explaining the IVOL discount.

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VI. Combining the earnings momentum effect and post-formation earnings shocks. The previous two sections show that the earnings momentum effect and post-formation earnings shocks both play a role in explaining the IVOL discount. In this section, I combine these two effects, and quantify the impact of pre-formation and post-formation earnings shocks on the IVOL discount. Table 6 presents the results. Panel A of Table 6 reports the average adjusted returns and the t-statistics of the 25 SUE/IVOLsorted portfolios. The average IVOL discount across all five SUE quintiles is -0.46% (t = -1.50) per month when computed with adjusted returns, while the average IVOL discount is -0.62% (t = -1.92) when computed using unadjusted returns (Table 3, panel A). Notice that the IVOL discount is further reduced when returns are adjusted for post-formation earnings shocks. As mentioned in Section V, if postformation earnings shocks are not important in explaining the IVOL discount, the use of adjusted returns should reduce the IVOL discount by less than 5%. However, the adjusted returns reduce the IVOL discount by (0.62-0.46)/0.62 = 26% even after controlling for the earnings momentum effect. 14 This confirms that the earnings momentum effect and post-formation earnings shocks are both important in explaining the IVOL discount. The inclusion of the adjusted alpha from the FF3F model does not substantially change the result. Panel B of Table 6 reports the FF3F adjusted alpha of the 25 portfolios. The average FF3F adjusted alpha across all five SUE quintiles is -0.77% (t = -3.74), while the average FF3F alpha is -0.97% (t = -4.48) (Table 3, panel B) when computed using unadjusted returns. The reduction in FF3F alpha is (0.97-0.79)/0.97 = 19%. To ensure that the earnings momentum effect is properly accounted for, I also control for the earnings momentum factor when computing the alpha for each of the 25 SUE/IVOL-sorted portfolios. Panel C of Table 6 reports the FF3F_PMN adjusted alpha of these 25 portfolios. The average adjusted

14

I also use the earnings momentum factor along with adjusted returns to study the combined effect of earnings shocks on the IVOL discount. The result is presented in column four of Panel B of Table 6. The use of adjusted returns reduces the FF3F_PMN alpha by 24 basis points.

16

FF3F_PMN alpha across all five SUE quintiles is -0.08% (t = -0.38), while it is -0.26% (t = -1.17) (Table 4, panel B) when computed using unadjusted returns. The 19 basis-point reduction in the IVOL discount is similar in magnitude to the reduction in FF3F alpha or raw returns, as reported in panels A and B, respectively. Thus far, the evidence is consistent with the arguments that high IVOL stocks experience large, negative earnings shocks before portfolio formation, and that the earnings momentum effect contributes substantially to the IVOL discount. This section also shows that differences in post-formation earnings shocks are important in explaining the IVOL discount. That is, high IVOL stocks tend to experience negative earnings shocks after portfolio formation, while low IVOL stocks do not, and the differences in these post-formation earnings shocks are important in explaining the IVOL discount. The combined effect of earnings shocks can explain a substantial portion of the IVOL discount. VII. Fama-MacBeth cross-sectional regressions Table 7 examines the relations among earnings momentum, post-formation earnings shocks, and the cross-section of average returns using Fama and MacBeth (1973) regressions. The regressions adds further robustness to the results, as they include all securities without imposing quintile breakpoints; they allow for the inclusion of more controls in returns, including liquidity measures; and they provide an alternative weight scheme for portfolios.15 The cross-section of stock returns in excess of the one-month T-bill rate each month is regressed on the firm characteristics. I implement several controls for the earnings momentum effect and post-formation earnings shocks. To control for post-formation earnings shocks, excess adjusted returns, instead of excess returns, are used in the regressions. In order to allow for comparison with the results from time-series section, I use three approaches to control for the earnings momentum effect. First, I include the most recent SUE as 15

Each coefficient in a Fama-MacBeth regression is the return to the minimum variance portfolio with weights that sum to zero, weighted characteristic on its corresponding regressor that sums to one, and weighted characteristics on all other regressors that sum to one. The weights are tilted toward stocks with the most extreme (volatile) returns.

17

a control variable in the regressions. The results are essentially unchanged when the most recent CAR, as defined in section II, is used. Second, in the Fama-MacBeth regressions, I follow Brennan et al.’s (1998) methodology to control for exposure to the earnings momentum factor. Third, to ensure that the earnings momentum effect is properly accounted for, I not only control for the most recent SUE but I also filter returns using Brennan et al.’s (1998) methodology to control for exposure to the earnings momentum factor. This final approach essentially combines the first and second methods. Brennan et al.’s (1998) method utilizes individual security returns after adjusting for their exposure to known factors. This approach not only avoids the data-snooping biases that are inherent in the portfolio-based approaches (see Lo and MacKinlay, 1990) but also circumvents the error-in-variables bias created by errors in estimating factor loadings. Two factor models, the FF3F model and a four-factor model in which the PMN factor is added to the FF3F model, are employed to adjust returns for their exposure to risk factors. I begin by estimating the factor loadings for each year from 1972 to 2009 for all of the securities that had at least 24 return observations over the preceding 60 months. As the PMN data begins in January 1972, the factor loadings in the first month of the regression period (January 1974) are estimated using 24 observations per factor, the factor loadings in the second month of the regression period are estimated using 25 observations, and so on, until the 60-month level is reached, at which point the observation interval is kept constant at 60 months. The factor-model filtered return is: (realized excess return - realized factor return x estimated factor loading). These filtered returns are then used as the left-hand-side variable and are regressed on a set of firm characteristics. The standard Fama and MacBeth (1973) estimators are the time-series averages of these coefficients. While the factor loadings are estimated with errors, these errors affect only the dependent variable, filtered returns. Although the factor loadings will be correlated with the security’s characteristics, there are no priori reasons to believe that the errors in the estimated loadings will be correlated with the security’s characteristics. This implies that the estimated coefficient from the crosssection regression should be unbiased. 18

However, if the errors in the estimated factor loadings are correlated with the security’s characteristics, the monthly estimates of the coefficients will be correlated with the factor realizations and the Fama-MacBeth estimators will be biased by an amount that depends upon the mean factor realizations. Therefore, the purged estimator is obtained for each of the characteristics as the constant term from the regression of the monthly coefficient estimates on the time-series of the factor realizations. This estimator, which was first developed by Black et al. (1972), purges the monthly estimates of the factor-dependent component. It is also used by Chordia and Shivakumar (2006) and Hou and Van Dijk (2010). The standard errors of the estimators are taken from the time series of monthly estimates in the case of the Fama-MacBeth estimator and from the standard error of the constant from the OLS regression in the case of the purged estimator. The cross-section of stock returns in excess of the one-month T-bill rate for each month is regressed on the firm characteristics of: log of size (Size); log of BE/ME (B/M); the cumulative return over the two months ending at the beginning of the previous month, i.e., from month t-3 to t-2 (RET2-3); the cumulative return over the three months ending three months previously, i.e., from month t-6 to t-4 (RET4-6); the cumulative return over the six months ending six months previously, i.e., from month t-12 to t-7 (RET7-12); and the measure of IVOL (IVOL). Amihud’s (2002) measure is included as a proxy for liquidity. I also include the previous month’s return (Reversal) as an additional control for Jegadeesh’s (1990) one-month reversal effect. If this effect is largely driven by bid-ask bounce and illiquidity, then this regressor can be viewed as another liquidity control. It is well known that the IVOL effect is stronger among high-price stocks and, therefore, I include the log of the reciprocal of the share price from the prior month (Price) to control for this phenomenon. The values for the size, book-to-market, and Amihud variables are for the previous year. The results are presented in Table 7. The second column of panel A of Table 7 confirms the standard results found in the literature – average returns are negatively related to IVOL. The estimated coefficient on IVOL is -12.59%. The economic significance of IVOL is also in line with my previous 19

result. The coefficient on IVOL in column 1 of panel A implies a difference in monthly returns between the lowest quintile, which has an average IVOL of 0.94%, to the highest quintile, which has a measure of 5.46% (Table 1), of -57 basis points. The difference in returns is lower than the results reported in Table 1. This is not surprising because Fama-MacBeth regressions minimize least squares, which tends to put more weight on smaller stocks. Furthermore, it is well known that IVOL effect is stronger in the valueweighted setting.16 Nevertheless, IVOL is highly significant with a t-statistic of -3.20. Columns 3 and 4 present results with risk-adjusted returns, with the risk adjustment made using the FF3F. Consistent with the prior results, IVOL becomes even stronger in explaining stock returns when the FF3F model is used to adjust for returns. One way of controlling for the earnings momentum effect is to include the most recent SUE in the regressions. Columns 7 to 9 of panel A report the same set of regressions as those reported in columns 2 to 4 except columns 7 to 9 include the most recent prior SUE to control for the earnings momentum effect. The Fama-MacBeth and purged estimators on the IVOL are uniformly reduced in each of the specifications when SUE is included in the regressions. For example, column 7 shows that the inclusion of SUE in the regression reduces the Fama-MacBeth estimator on IVOL to -10.77% (t = -2.76) from -12.59% (t = -3.20). Another way to account for the earnings momentum effect is to control for exposure to the earnings momentum factor. The fifth and sixth columns use the FF3F_PMN model to filter returns. Consistent with the time-series results, the IVOL effect is considerably weakened. The purged estimator shows that the coefficient on IVOL is -7.91% with a t-statistic of -2.24. This magnitude on the IVOL coefficient is considerably smaller than that estimated using either excess returns (-12.59%) or FF3Ffiltered returns (-20.15%). Lastly, to ensure that the earnings momentum effect is properly accounted for, I not only filter returns with the FF3F_PMN model but I also include SUE in the regression. Columns 10 and 11 present the results. The purged estimator on IVOL is -6.81% with a t-statistic of -1.91. Consistent 16

See Bali and Cakici (2008).

20

with the results in the time-series section, filtering returns with the FF3F_PMN model and including the most recent SUE in the regression seems to allow for more adequate control of the earnings momentum effect. The time-series evidence shows that post-formation earnings shocks are also important in explaining the IVOL discount. Panel B of Table 7 employs the adjusted returns to account for postformation earnings shocks. Consistent with the results presented in Section V, post-formation earnings shocks are also important in explaining the IVOL discount in the Fama-MacBeth regression. For example, the use of adjusted returns in the regression reduces the Fama-MacBeth estimator on IVOL from -12.59% (t = -3.20; panel A, column 2) to -8.07% (t = -2.18; panel B, column 2). Similar reductions in the estimators and t-statistics are observed in columns 3 and 4, which show the results of adjusted returns filtered by the FF3F model. Lastly, I quantify the impact of pre-formation and post-formation earnings shocks on the IVOL discount in the Fama-MacBeth regression framework. To accomplish this, I filter adjusted excess returns using the FF3F_PMN model and include the most recent SUE in the regressions. The last two columns of Panel B report the results. The purged estimator on IVOL is -2.95% with a t-statistic of -0.94. The IVOL spread between the extreme IVOL quintiles is 4.52% (reported in Table 1). When combined with the estimated IVOL discount of -2.95%, this suggests that the average return spread between the extreme IVOL quintiles is only -13.34 basis points per month. Consistent with the time-series evidence, the results presented in panels A and B of Table 7 suggest that the earnings momentum effect and the post-formation earnings shocks are essential in explaining the IVOL discount. Panels C and D of Table 7 present a similar analysis except that they include additional control variables: lag monthly return (Reversal), momentum measures (RET2-3, RET4-6, and RET7-12), last month’s share price (Price), and a liquidity measure (Amihud). The second columns of panels C and D confirm that IVOL remains highly significant even when all of the control variables are included in the 21

regressions. The point estimate of the IVOL coefficient declines slightly from panel A and B, which is not surprising given the high correlations between IVOL and most of the control variables, but it remains economically and statistically significant. The size effect is no longer significant, as it was in panels A and B. This is consistent with prior research showing that size is not important in explaining stock returns after the 1980s. The positive coefficient on Amihud is consistent with Amihud (2002), and the strong reversal effect, as demonstrated by the coefficient on Reversal, is consistent with Jegadeesh (1990). Columns 3 and 4 of panel C demonstrate that IVOL becomes more significant, with a purged estimator of -10.60% and a t-statistic of -4.27, when the FF3F model is used, which is consistent with the results in panel A. More importantly, IVOL is significantly weakened in explaining stock returns when the PMN factor is incorporated into the FF3F model. The purged estimator on IVOL is only -6.03% with a tstatistic of -1.91, as reported in column 5 of panel C. In addition to the other firm characteristics, columns 7 to 11 of panel C include the most recent prior SUE to further control for the earnings momentum effect. The results are largely in line with those in panel A of Table 7. The explanatory power of IVOL is further weakened when controlling for SUE. However, this reduction is not as impressive as that from filtering returns with exposures to the earnings momentum factor. For example, filtering returns with the FF3F_PMN model (without including SUE) produces a purged estimator on IVOL of -6.03% (t = -1.91), which can be compared to the -8.09% (t = 2.91) obtained when SUE is included in the regression (without using the FF3F_PMN model to filter returns). Nevertheless, the last two columns of panel C show that the combined approach (including SUE and filtering returns with the FF3F_PMN model) provides a more adequate control for the earnings momentum effect. Lastly, panel D of Table 7 reports the results obtained after adjusting for post-formation earnings shocks. The point estimate on IVOL is further weakened by this adjustment to reflect post-formation earnings shocks. Specifically, using the FF3F_PMN model to filter returns and controlling for SUE produces a purged estimator on IVOL of -3.23% with a t-statistic of -1.21. The corresponding figures 22

when using unadjusted returns are -5.35% and -1.71, respectively. Similar reductions in the IVOL point estimates and the t-statistics can also be observed in other specifications across the panel.

VIII. Conclusion A robust, negative cross-section relation between idiosyncratic volatility and future stock returns has been documented in the finance literature. However, little is known about the relation between earnings performance and IVOL, or, more importantly, how the correlation between earnings surprises and IVOL may affect the relation between the returns of high and low IVOL stocks. This paper addresses these questions. In this study, I find that high IVOL stocks suffer negative earnings surprises before and after portfolio formation. The well-known earnings momentum effect and the post-formation earnings shocks are responsible for the IVOL discount. When these two effects are accounted for, idiosyncratic volatility has little, if any, return predictability. Moreover, the earnings momentum effect alone captures approximately 42% of the IVOL discount. The results from a series of Fama-MacBeth (1973) crosssection regressions provide a similar conclusion.

23

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Chordia, Tarun, and Lakshmanan Shivakumar. "Earnings and price momentum." Journal of Financial Economics, 80, 2006: 627-656. Daniel, Kent, and Sheridan Titman. "Evidence on the Characteristics of Cross Sectional Variation in Stock Returns." Journal of Finance, 52, 1997: 1-33. Daniel, Kent, Mark Grinblatt, Sheridan Titman, Mark Grinblatt, and Russ Wermers. "Measuring Mutual Fund Performance with Characteristic-Based Benchmarks." Journal of Finance, 52, 1997: 10351058. Diether, Karl B, Christopher J Malloy, and Anna Scherbina. "Differences of opinion and the cross-section of stock returns." Journal of Finance, 57, 2002: 2113-2141. Fama, Eugene F, and James D MacBeth. "Risk return, and equilibrium: Empirical tests." Journal of Political Economy, 71, 1973: 607-636. Fama, Eugene F, and Kenneth R French. "New lists: Fundamentals and survival rates." Journal of Financial Economics, 2, 2004: 229-269. Fama, Eugene F, and Kenneth R French. "Size and book-to-market factors in earnings and returns." Journal of Finance, 1, 1995: 131-155. Foster, George, Chris Olsen, and Terry Shevlin. "Earnings releases, anomalies, and the behavior of security returns." The Accounting Review, 59, 1984: 574-603. French, Kenneth R, and Eugene F Fama. "Common risk factors in the returns on stocks and bonds." Journal of Financial Economics, 53, 1993: 427-465. Fu, Fangjian . "Idiosyncratic risk and the cross-section of expected stock returns." Journal of Financial Economics, 91, 2009: 24-37. George, J Thomas, and Chuan-Yang Hwang. "Why do firms with high idiosyncratic volatility and high trading volume volatility have low returns?" Working paper, University of Houston and Hong Kong University of Science & Technology, 2010. Hong , Harrison , Terence Lim , and Jeremy C Stein . "Bad news travel slowly: Size, Analyst coverage and the profitability of momentum strategies." Journal of Finance, 55, 2000: 265-296. Hou, Kewei. "Industry information diffusion and the lead-lag effect in stock returns." Review of Financial Studies, 20, 2007: 1113-1138. Hou, Kewei, and Mathijs A Van Dijk. "Profitability shocks and the size effect in the cross-section of expected stock returns." Working paper, The Ohio State University and Erasmus University, 2010. Hou, Kewei, and Tobias J Moskowitz. "Market frictions, price delay, and the cross-section of expected returns." Review of Financial Studies, 18, 2005: 981-1020. Jegadeesh, Narasimhan. "Evidence of predictable behavior of security returns." Journal of Finance, 45, 1990: 881-898. 25

Jegadeesh, Narasimhan, and Daniel Titman. "Returns to buying winners and selling losers; implications for stock market efficiency." Journal of Finance, 48, 1993: 65-91. Jones, Charles M, and Matthew Rhodes-Kropf. "The price of diversifiable risk in venture capital and private equity." Working paper, Columbia University, 2003. Jones, Charles P, and Henry A Latané. "Standardized unexpected earnings." Journal of Finance, 34, 1979: 717-724. Joy, O.Maurice , Robert H Litzenberger, and Richard W McNally. "The adjustment of stock prices to announcements of unanticipated changes in quarterly earnings." Journal of Accounting Research, 15, 1977: 207-225. Kan, Raymond M, and Chu Zhang. "Two-pass tests of asset pricing models with useless factors." Journal of Finance, 54, 1999: 203-235. Lo, Andrew W, and Craig A MacKinlay. "Data-snooping biases in tests of financial asset pricing models." Review of Financial Studies, 3, 1990: 431-468. Malkiel, Burton G, and Yexiao Xu. "Idiosyncratic risk and security returns." Working paper, University of Texas at Dallas, 2002. Merton, Robert C. "Presidential address: A simple model of capital market equilibrium with incomplete information." Journal of Finance, 42, 1987: 483-510. Pastor, Lubos, and Robert F Stambaugh. "Liquidity risk and expected stock returns." Journal of Political Economy, 111, 2003: 642-685. Petkov, Ralitsa, and Zhanhui Chen. "Does idiosyncratic volatility proxy for risk exposure?" Working paper, Texas A&M University, 2011. Rafael, La Porta, Josef Lakonishok, Andrei Shleifer, and Robert Vishny. "Good news for value stocks: Further evidence on market efficiency." Journal of Finance, 2, 1997: 859-874. Rendleman, Richard J, Charles P Jones, and Henry A Latané. "Empirical anomalies based on unexpected earnings and the importance of risk adjustments." Journal of Financial Economics, 10, 1982: 269-287. Sonmez, Fatma. "Rethinking idiosyncratic volatility: Is it really a puzzle?" Working paper, University of Toronto, 2008. Vuolteenaho, Tuomo. "What drives firm-level stock returns." Journal of Finance, 2002: 233-264. Watts, Ross L. "Systematic 'abnormal' returns after quarterly earnings announcements." Journal of Financial Economics, 6, 1978: 127-150. Xu, Danielle , Tong Yao, and George J Jiang. "The information content of idiosyncratic volatility." Journal of Financial and Quantitative Analysis, 44, 2009: 1-28. 26

Figure1B

Figure1A

Figure1C Figure 1: 16-quarter SUE, SUE1, and CAR for idiosyncratic volatility sorted portfolios in each month of quarter i (quarter 1 on the horizontal axis). For each portfolio formation month from 1972 to 2009, stocks are sorted into five portfolios based on based on idiosyncratic volatility relative to the Fama-French (1993) three-factor model (using daily data from the prior month). Figures 1A, 1B, and 1C report the value-weighted average SUE, SUE1, and CAR, respectively, for each portfolio eight quarters before and eight quarters after portfolio formation. SUE is defined as current quarter earnings less earnings four quarters ago, and this change is standardized by the standard deviation of the earnings changes over the prior eight quarters. SUE1 is defined similar to SUE except SUE1 is standardized by the quarter-end share price. CAR is the average buy-and-hold abnormal returns for three days around the earnings announcement date [-1, 0, +1]. Abnormal return is defined as: (daily return - value-weighted market return).

27

Table 1: Characteristics of IVOL-sorted portfolios Value-weighted quintile portfolios are formed every month by sorting stocks based on idiosyncratic volatility relative to the Fama-French (1993) three-factor model (using daily data from the prior month). Portfolio 1 (5) is the portfolio of stocks with the lowest (highest) idiosyncratic volatilities. The value-weighted average characteristics of these quintile portfolios are computed monthly. The column labeled Return is measured in monthly percentage terms and applies to total, not excess, simple returns. Columns 3 and 4 report Jensen's alphas with respect to the CAPM or the Fama-French (1993) three-factor model, respectively. Column 5 reports the average idiosyncratic volatility relative to the Fama-French (1993) three-factor model using daily data from the previous month. Column 6 reports the average idiosyncratic volatility relative to the Fama-French (1993) three-factor model using daily data from the return month. The Age statistic is the average number of years that a firm has data available on CRSP. B/M reports the average book-to-market ratio, and Size reports the average market capitalization. Momentum is the cumulative average return over the past year (skipping the most recent month). The row "5-1" refers to the difference in statistics between portfolios 5 and 1. The sample period is January 1972 to December 2009. The t-statistics are in parentheses.

IVOL quintile

Return

CAPM alpha

FF3F alpha

IVOL

Post-formation IVOL

Age

B/M

1

0.94

0.16

0.10

0.94

1.10

40.31

0.63

Size (% of aggregate market) 50.29

2

0.95

0.07

0.03

1.54

1.53

30.51

0.63

25.68

14.86

0.89

-0.08

-0.08

2.20

2.01

22.83

0.64

13.30

16.05

4

0.51

-0.53

-0.50

3.14

2.64

17.15

0.69

7.44

14.56

5

-0.17

-1.24

-1.35

5.46

3.85

13.38

0.95

3.29

4.82

5-1

-1.11

-1.40

-1.45

4.52

2.76

-26.93

0.32

-47.00

-9.85

(-3.13)

(-4.49)

(-5.84)

(67.27)

(51.05)

(-112.52)

(11.01)

(-20.99)

(-6.24)

3

t-test on 5-1

Momentum 14.68

Table 2: Earnings surprises of IVOL-sorted portfolios

Value-weighted quintile portfolios are formed every month by sorting stocks based on idiosyncratic volatility relative to the Fama-French (1993) threefactor model. Daily data from the previous month are used to compute idiosyncratic volatility and rebalance the portfolio monthly. Panel A reports the means and average cross-section standard deviations (reported in square brackets) of earnings surprises (SUE, SUE1, and CAR), one quarter before and four quarters after portfolio formation. Three measures are employed to capture earnings surprises. SUE is defined as current quarter earnings less earnings four quarters ago, and this change is standardized by the standard deviation of the earnings changes over the prior eight quarters. SUE1 is defined similar to SUE except SUE1 is standardized by quarter-end share price. CAR is the average buy-and-hold abnormal returns for three days around the earnings announcement date [-1, 0, +1]. Abnormal return is defined as: (daily return - value-weighted market return). Panel B reports the long-term buy-and-hold characteristic-adjusted returns (adjusted for size and B/M) of the (high IVOL - low IVOL) portfolio. The benchmark portfolio is based on an extension and variation of the matching procedure used in Daniel et al. (1997). The sample period is January 1972 to December 2009. Newey-West (1987) t-statistics with three lags are reported in parentheses. Panel A: Earnings shocks of IVOL-sorted portfolios

IVOL quintile

Most recent SUE prior to portfolio formation

First-quarter SUE after portfolio formation

Second-quarter SUE after portfolio formation

Third-quarter SUE after portfolio formation

Fourth-quarter SUE after portfolio formation

1

0.95 [1.97]

0.88 [2.13]

0.82 [2.13]

0.77 [2.16]

0.73 [2.15]

2

0.74 [1.99]

0.66 [2.17]

0.63 [2.15]

0.59 [2.18]

0.56 [2.16]

3

0.55 [1.96]

0.44 [2.14]

0.39 [2.10]

0.35 [2.12]

0.36 [2.08]

4

0.22 [1.89]

0.05 [2.11]

0.08 [1.99]

0.06 [1.98]

0.15 [1.94]

5

-0.21 [1.83]

-0.45 [2.10]

-0.26 [1.82]

-0.14 [1.98]

-0.03 [1.71]

5-1

-1.16

-1.33

-1.08

-0.91

-0.75

t-test on 5-1

(-20.90)

(-24.08)

(-21.35)

(-18.17)

(-14.76)

29

IVOL quintile

Most recent SUE1 prior to portfolio formation (%)

First-quarter SUE1 after portfolio formation (%)

Second-quarter SUE1 after portfolio formation (%)

Third-quarter SUE1 after portfolio formation (%)

Fourth-quarter SUE1 after portfolio formation (%)

1

0.14 [3.15]

0.10 [3.74]

0.03 [3.92]

-0.01 [4.23]

-0.08 [4.54]

2

0.09 [4.26]

0.01 [5.33]

-0.07 [5.54]

-0.25 [6.36]

-0.48 [6.84]

3

-0.06 [5.99]

-0.18 [7.74]

-0.35 [8.28]

-0.61 [9.31]

-0.42 [9.74]

4

-0.44 [9.04]

-1.05 [12.25]

-1.23 [12.49]

-1.35 [13.52]

-1.01 [13.69]

5

-1.68 [16.67]

-3.47 [24.15]

-2.64 [22.16]

-1.45 [22.28]

0.23 [21.63]

5-1

-1.83

-3.57

-2.68

-1.44

0.30

t-test on 5-1

(-3.31)

(-4.70)

(-2.36)

(-0.63)

(1.23)

30

IVOL quintile

Most recent CAR prior to portfolio formation (%)

First-quarter CAR after portfolio formation (%)

Second-quarter CAR after portfolio formation (%)

Third-quarter CAR after portfolio formation (%)

Fourth-quarter CAR after portfolio formation (%)

1

0.33 [4.63]

0.23 [5.31]

0.15 [5.44]

0.14 [5.55]

0.15 [5.65]

2

0.24 [6.17]

0.23 [6.85]

0.21 [6.98]

0.20 [7.09]

0.16 [7.15]

3

0.02 [7.79]

0.19 [8.41]

0.17 [8.50]

0.14 [8.60]

0.10 [8.71]

4

-0.43 [9.74]

-0.19 [10.08]

-0.01 [10.11]

0.11 [10.12]

0.03 [10.19]

5

-1.20 [13.34]

-0.57 [12.80]

-0.14 [12.62]

-0.01 [12.45]

0.21 [12.35]

5-1

-1.53

-0.80

-0.29

-0.15

0.06

t-test on 5-1

(-6.01)

(-5.35)

(-3.11)

(-1.91)

(0.31)

31

Panel B: Long-term buy and hold characteristic-adjusted returns in % (adjusted for BM and Size) IVOL quintile

First-quarter return

Semi-annual return

Annual return

1

0.13

0.16

0.12

2

0.13

0.18

0.26

3

0.00

-0.02

0.19

4

-0.95

-1.46

-1.17

5

-2.75

-4.44

-5.18

5-1

-2.88

-4.61

-5.30

t-test on 5-1

(-4.20)

(-3.95)

(-3.12)

32

Table 3: Interaction between earnings momentum and the IVOL discount Value-weighted quintile portfolios are formed every month by first sorting stocks based on the most recent SUE. Within each SUE quintile, stocks are further sorted into five quintiles based on idiosyncratic volatility relative to the Fama-French (1993) three-factor model. Daily data from the previous month are used to compute idiosyncratic volatility and rebalance the portfolio monthly. This double-sorting procedure produces 25 portfolios. Panels A and B report the average returns and alphas obtained from Fama-French (1993) three-factor model, respectively. The entry “Average” denotes the average returns of each IVOL quintile across the five SUE portfolios. The entry “Average (5-1)” denotes the differences in average returns between the highest and lowest IVOL portfolios. Panel C reports the time-series results of regressing excess returns on the Fama-French three-factor model and the earnings momentum factor (PMN). The column labeled "FF3F_PMN alpha" reports the time-series intercept (alpha) of the regression (in percentage). The last four columns of Panel B report the estimated loadings on the market factor (MKTRF), the size factor (SMB), the value factor (HML), and the earnings momentum factor (PMN). “Average return on PMN (%)” reports the average monthly returns, in percentage, of the earnings momentum factor (PMN). *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively (applies only to panel C column labeled “Loadings on PMN”). The sample period is January 1972 to December 2009. Panel A: Returns on each of the 25 double-sorted portfolios (SUE and IVOL)

IVOL

SUE

1

1 0.75

2 0.77

3 0.61

4 -0.21

5 -0.61

-1.36

t-test on 5-1 (-2.77)

2

0.72

0.79

0.87

0.51

-0.18

-0.90

(-2.34)

3

0.87

0.91

0.83

0.83

0.40

-0.47

(-1.40)

4

1.06

1.00

0.99

0.98

0.72

-0.34

(-0.90)

5 Average

1.12

1.17

1.15

1.09

1.10

-0.02

(-0.07)

0.90 (4.83)

0.93 (3.93)

0.89 (3.15)

0.64 (1.86)

0.29 (0.69)

Average (5-1)

t(5-1) (-1.92)

t(Average)

33

5-1

-0.62

Panel B: Fama-French three-factor alpha on each of the 25 double-sorted portfolios (SUE and IVOL)

IVOL

SUE

1

1 -0.22

2 -0.28

3 -0.46

4 -1.32

5 -1.92

5-1 -1.70

t-test on 5-1 (-4.08)

2

-0.27

-0.25

-0.28

-0.61

-1.53

-1.26

(-4.29)

3

-0.05

-0.08

-0.24

-0.26

-0.92

-0.87

(-3.34)

4

0.23

0.09

0.06

-0.03

-0.42

-0.65

(-2.25)

5 Average

0.38

0.40

0.33

0.25

0.03

-0.35

(-1.36)

0.01 (0.25)

-0.03 (-0.39)

-0.12 (-1.28)

-0.40 (3.27)

-0.95 (-4.88)

Average (5-1)

t(5-1) (-4.48)

t(Average)

Panel C: Returns adjusted with earnings momentum factor (PMN) FF3F_PMN alpha

Loadings on MKTRF

Loadings on SMB

Loadings on HML

Loadings on PMN

1

0.03

0.92

-0.21

0.09

0.06***

2

0.11

1.10

-0.08

0.07

-0.05*

3

0.06

1.21

0.21

-0.07

-0.14***

4

-0.10

1.28

0.50

-0.23

-0.43***

5

-0.62

1.33

0.86

-0.16

-0.80***

5-1

-0.65

0.42

1.08

-0.25

-0.86

(-2.53)

(6.56)

(12.19)

(-2.81)

(-7.46)

IVOL Quintile

t-test on 5-1

Average return on PMN factor (%)

0.89

34

-0.97

Table 4: Combination of the two approaches to control for the earnings momentum effect Value-weighted quintile portfolios are formed every month by first sorting stocks based on the most recent SUE. Within each SUE quintile, stocks are further sorted into five quintiles based on idiosyncratic volatility relative to the Fama-French (1993) three-factor model. Daily data from the previous month are used to compute idiosyncratic volatility and rebalance the portfolio monthly. This double-sorting procedure produces 25 portfolios. Panel A reports the loadings on the earnings momentum factor (PMN) of the 25 portfolios (estimated with a four-factor model encompassing the three Fama-French factors and the earnings momentum factor). Panel B reports the intercepts (alphas) from time-series regressions of the value-weighted excess returns on a four-factor model in which the earnings momentum factor (PMN) is added to the FamaFrench (1993) three-factor model. The entry “Average” denotes the average return of each IVOL quintile across the five SUE portfolios. The entry “Average (5-1)” denotes the difference in average returns between the highest and lowest IVOL portfolios. The t-statistics are in parentheses.

Panel A: Loadings on PMN factor

IVOL

SUE

1

1 -0.42

2 -0.36

3 -0.61

4 -0.87

5 -1.39

5-1 -0.97

t-test on 5-1 (-5.41)

2

-0.07

-0.40

-0.51

-0.52

-1.02

-0.94

(-7.69)

3

0.02

-0.01

-0.19

-0.42

-0.59

-0.62

(-5.52)

4

0.13

0.20

0.16

0.03

-0.50

-0.63

(-5.08)

5 Average

0.31

0.14

0.13

0.10

0.01

-0.30

(-2.36)

-0.01 (-1.07)

-0.09 (-3.07)

-0.20 (-5.12)

-0.33 (-6.53)

-0.70 (-8.73)

Average (5-1)

t(5-1) (-7.46)

t(Average)

35

-0.69

Panel B: Fama-French three-factor model and PMN model alpha on each of the 25 double-sorted portfolios (SUE and IVOL)

IVOL

SUE

1

1 0.22

2 0.11

3 0.18

4 -0.41

5 -0.47

5-1 -0.68

t-test on 5-1 (-1.54)

2

-0.19

0.17

0.25

-0.07

-0.46

-0.28

(-0.90)

3

-0.08

-0.07

-0.04

0.18

-0.30

-0.22

(-0.80)

4

0.09

-0.12

-0.11

-0.07

0.11

0.01

(0.04)

5 Average

0.16

0.25

0.19

0.14

0.02

-0.14

(-0.49)

0.04 (0.68)

0.07 (0.93)

0.09 (0.96)

-0.04 (-0.35)

-0.22 (-1.11)

Average (5-1)

t (5-1) (-1.17)

t(Average)

36

-0.26

Table 5: Returns adjusted for post-formation earnings shocks Panel A reports the average, median, maximum, and minimum numbers of firms reporting quarterly earnings per month. For reference, the bottom row of panel A reports the overall average number of firms per quintile in the sample (with and without earnings announcements). Panel B reports the value-weighted average adjusted returns of the idiosyncratic volatility sorted portfolios. To compute adjusted returns, three daily returns, [-1, 0, +1] around earnings announcement dates are replaced with zero, and the daily returns within the month are computed to derive the adjusted return. CRSP monthly return is used if no earnings announcement was made during a month. Columns 3 to 5 of Panel B report the intercepts (alphas) from time-series regressions of the valueweighted excess adjusted returns on the CAPM model, the Fama-French (1993) three-factor model, and a four-factor model in which the earnings momentum factor (PMN) is added to the Fama-French (1993) three-factor model. The last four columns in Panel B report the loadings on the market factor (MKTRF), the size factor (SMB), the value factor (HML) and the earnings momentum factor (PMN). These estimated loadings are obtained by regressing excess adjusted return on MKTRF, SMB, HML, and PMN. The sample period is from January 1972 to December 2009. The t-statistics are in parentheses.

Panel A: Number of firms reporting earnings Average number of firms reporting IVOL Quintile quarterly earnings (per month) 1 256

Median number of firms reporting quarterly earnings (per month)

Maximum number of firms reporting quarterly earnings (per month)

Minimum number of firms reporting quarterly earnings (per month)

208

899

14

2

255

223

794

13

3

245

231

716

2

4

232

220

634

1

5

204

171

572

5

Average number of firms per quintile (monthly, with or without earnings announcements)

37

750

Panel B: Returns adjusted for post-formation earnings shocks

IVOL quintile

Adjusted return

CAPM adjusted alpha

FF3F adjusted alpha

FF3F_PMN adjusted alpha

Loading on MKTRF

Loading on SMB

Loading on HML

Loading on PMN

1

0.81

0.06

0.00

-0.06

0.81

-0.21

0.15

0.06

2

0.79

-0.05

-0.09

-0.04

0.99

-0.07

0.07

-0.05

0.20

-0.07

-0.14

3

0.75

-0.17

-0.17

-0.03

1.11

4

0.54

-0.45

-0.43

-0.06

1.18

0.47

-0.23

-0.39

5

-0.02

-1.04

-1.15

-0.47

1.22

0.79

-0.14

-0.76

5-1

-0.83 (-2.51)

-1.10 (-3.76)

-1.16 (-4.91)

-0.41 (-1.66)

0.41

1.00

-0.29

-0.82

(7.81)

(13.18)

(-3.53)

(-7.22)

t-test on 5-1

38

Table 6: The combination of all adjustments (earnings momentum effect and post-formation earnings shocks) Value-weighted quintile portfolios are formed every month by first sorting stocks based on the most recent SUE. Within each SUE quintile, stocks are further sorted into five quintiles based on idiosyncratic volatility relative to the Fama-French (1993) three-factor model. Daily data from the previous month is used to compute idiosyncratic volatility and rebalance the portfolio monthly. This double-sorting procedure produces 25 portfolios. Panels A, B, and C report the average adjusted returns, adjusted Fama-French three-factor alpha, and adjusted alpha obtained from a four-factor model in which the earnings momentum factor (PMN) is added to the Fama-French (1993) three-factor model, respectively. Adjusted returns are obtained by replacing three daily returns, [-1, 0, +1], around earnings announcement date with zero and compounding the daily returns within the month to derive the adjusted return. CRSP monthly return is used if no earnings announcement was made during a month. Adjusted alpha (either from the Fama-French (1993) three-factor model or from the four-factor model mentioned above) is the time-series intercept derived from regressing excess adjusted returns on the factors. The entry “Average” denotes the average returns of each IVOL quintile across the five SUE portfolios. The entry “Average (5-1)” denotes the difference in average returns between the highest and lowest IVOL portfolios. The t-statistics are in parentheses.

Panel A: Adjusted returns on each of the 25 double-sorted portfolios (SUE and IVOL)

IVOL

SUE

1

1 0.63

2 0.61

3 0.52

4 -0.15

5 -0.59

5-1 -1.22

t-test on 5-1 (-2.64)

2

0.65

0.63

0.83

0.56

-0.04

-0.69

(-1.88)

3

0.69

0.81

0.72

0.81

0.49

-0.20

(-0.64)

4

0.93

0.87

0.86

0.92

0.71

-0.21

(-0.61)

5 Average

0.99

0.98

0.94

0.95

1.04

0.05

(0.16)

0.78 (4.56)

0.78 (3.67)

0.77 (3.00)

0.62 (1.96)

0.32 (0.85)

Average (5-1)

t(5-1) (-1.50)

t(Average)

39

-0.46

Panel B: Adjusted Fama-French three-factor alpha on each of the 25 double-sorted portfolios (SUE and IVOL)

IVOL

SUE

1

1 -0.31

2 -0.38

3 -0.50

4 -1.16

5 -1.85

5-1 -1.54

t-test on 5-1 (-3.91)

2

-0.26

-0.36

-0.24

-0.53

-1.28

-1.02

(-3.61)

3

-0.19

-0.13

-0.28

-0.22

-0.77

-0.58

(-2.28)

4

0.15

0.00

-0.04

-0.06

-0.37

-0.53

(-1.94)

5 Average

0.28

0.25

0.14

0.13

0.08

-0.20

(-0.88)

-0.07 (-1.23)

-0.12 (-1.99)

-0.19 (-2.11)

-0.37 (-3.16)

-0.84 (-4.46)

Average (5-1)

t(5-1) (-3.74)

t(Average)

-0.77

Panel C: Adjusted Fama-French three-factor and PMN model alpha on each of the 25 double-sorted portfolios (SUE and IVOL)

IVOL

SUE

1

1 0.06

2 -0.02

3 0.17

4 -0.37

5 -0.47

5-1 -0.53

t-test on 5-1 (-1.26)

2

-0.20

0.03

0.33

-0.05

-0.24

-0.04

(-0.12)

3

-0.26

-0.15

-0.07

0.11

-0.09

0.18

(0.67)

4

0.06

-0.19

-0.16

-0.12

0.10

0.04

(0.13)

5 Average

0.09

0.03

-0.01

0.03

0.03

-0.06

(-0.23)

-0.05

-0.06

0.05

-0.08

-0.13

Average (5-1)

t(Average)

(-0.86)

(-0.88)

(0.52)

(-0.65)

(-0.69)

-0.08

t(5-1) (-0.38)

40

Table 7: Fama-MacBeth regressions This table presents the Fama-Macbeth estimates of monthly cross-sectional regressions. The dependent variable in the column 2 is the excess return, while the dependent variable in columns 3 and 4 is the factor-filtered return using the Fama-French factors (FF3F). In columns 5 and 6, the dependent variable is the filtered return using the FF3F along with the earnings momentum factor (PMN). Size represents the logarithm of market capitalization. B/M is the logarithm of the book-to-market ratio. Price is the logarithm of the reciprocal of the share price. SUE represents the most recent standardized unexpected earnings. Amihud is defined as average daily absolute return divided by dollar trading volume over the past year. RET2-3, RET4-6, and RET7-12 are the cumulative returns over the second through third, fourth through sixth, and seventh through twelfth months prior to the current month, respectively. Reversal is the previous month’s return. IVOL is the standard deviation of the error terms obtained by regressing the prior month’s daily returns on the FF3F. Columns 6 to 10 are similar to columns 1 to 5 except columns 6 to 10 include the most recent SUE in the regressions. The figures in the column labeled “Raw” are the standard Fama-MacBeth coefficients, while the coefficients labeled “Purged” are the intercept term obtained by regressing the time series of coefficients on the factors. Panels B and D apply adjusted returns in the regressions to account for ex-post earnings shocks. The sample period is from January 1972 to December 2009. All coefficients are multiplied by 100. The t-statistics are in parentheses. Panel A: Base-case regression (without adjusting for post-formation earnings shocks)

Excess return

Size IVOL B/M

Excess return filtered by FF3F

Excess return filtered by FF3F and PMN

Excess return

Excess return filtered by FF3F

Excess return filtered by FF3F and PMN

Raw

Purged

Raw

Purged

Raw

Raw

Purged

Raw

Purged

Raw

-0.13

-0.11

-0.10

-0.12

-0.19

-0.14

-0.11

-0.17

-0.09

-0.15

(-3.59)

(-4.31)

(-3.75)

(-1.95)

(-3.42)

(-3.94)

(-4.76)

(-4.18)

(-2.14)

(-3.65)

-12.59

-20.15

-18.46

-7.91

-9.18

-10.77

-18.40

-16.84

-6.81

-7.54

(-3.20)

(-6.40)

(-6.00)

(-2.24)

(-2.91)

(-2.76)

(-5.93)

(-5.56)

(-1.91)

(-2.37)

0.30

0.11

0.17

0.27

0.12

0.40

0.21

0.26

0.34

0.21

(3.74)

(2.06)

(3.17)

(1.62)

(0.79)

(5.16)

(3.95)

(4.88)

(2.02)

(1.40)

0.26

0.25

0.23

0.18

0.24

(18.23)

(17.37)

(15.67)

(9.19)

(12.58)

SUE

41

Panel B: Base-case regression (adjusting for post-formation earnings shocks)

Adjusted excess return

Size IVOL B/M

Adjusted excess return filtered by FF3F

Adjusted excess return filtered by FF3F and PMN

Adjusted excess return

Adjusted excess return filtered by FF3F

Adjusted excess return filtered by FF3F and PMN

Raw

Purged

Raw

Purged

Raw

Raw

Purged

Raw

Purged

Raw

-0.13

-0.11

-0.10

-0.13

-0.19

-0.14

-0.13

-0.11

-0.14

-0.19

(-3.89)

(-4.84)

(-4.17)

(-2.38)

(-3.90)

(-4.23)

(-5.31)

(-4.60)

(-2.59)

(-4.13)

-8.07

-15.28

-13.59

-3.96

-5.33

-6.40

-13.66

-12.10

-2.95

-3.85

(-2.18)

(-5.16)

(-4.69)

(-1.26)

(-1.90)

(-1.74)

(-4.68)

(-4.23)

(-0.94)

(-1.37)

0.22

0.04

0.10

0.19

0.07

0.31

0.13

0.19

0.25

0.15

(2.94)

(0.87)

(2.00)

(1.41)

(0.54)

(4.33)

(2.75)

(3.68)

(1.85)

(1.22)

SUE

42

0.24

0.23

0.22

0.16

0.22

(18.27)

(17.63)

(15.69)

(10.91)

(14.04)

Panel C: Full specification (without adjusting for post-formation earnings shocks)

Excess return

Size IVOL B/M Price Amihud Reversal RET2-3 RET4-6 RET7-12

Excess return filtered by FF3F

Excess return filtered by FF3F and PMN

Excess return

Excess return filtered by FF3F

Excess return filtered by FF3F and PMN

Raw

Purged

Raw

Purged

Raw

Raw

Purged

Raw

Purged

Raw

-0.05

-0.11

-0.08

-0.01

0.02

-0.05

-0.11

-0.08

-0.02

0.02

(-1.41)

(-3.99)

(-2.89)

(-0.15)

(0.33)

(-1.60)

(-4.21)

(-3.11)

(-0.23)

(0.24)

-9.04

-10.60

-9.77

-6.03

-7.04

-8.09

-9.71

-8.87

-5.35

-6.13

(-3.22)

(-4.27)

(-3.96)

(-1.91)

(-2.45)

(-2.91)

(-3.97)

(-3.64)

(-1.71)

(-2.16)

0.25

0.09

0.15

0.18

0.07

0.35

0.19

0.25

0.26

0.16

(3.97)

(2.13)

(3.44)

(1.03)

(0.42)

(5.57)

(4.24)

(5.51)

(1.50)

(1.04)

0.11

-0.14

-0.11

0.20

0.41

0.16

-0.11

-0.07

0.24

0.46

(1.19)

(-1.65)

(-1.28)

(0.67)

(1.55)

(1.65)

(-1.16)

(-0.79)

(0.79)

(1.70)

0.18

0.18

0.19

0.19

0.16

0.16

0.17

0.18

0.18

0.15

(5.30)

(6.05)

(6.53)

(2.63)

(2.52)

(4.93)

(5.67)

(6.15)

(2.49)

(2.32)

-5.16

-5.70

-5.64

-5.71

-5.81

-5.10

-5.63

-5.57

-5.67

-5.74

(-13.90)

(-12.17)

(-12.39)

(-8.86)

(-10.22)

(-13.84)

(-12.06)

(-12.30)

(-8.82)

(-10.14)

-1.00

-1.56

-1.91

-2.25

-1.55

-1.47

-2.03

-2.37

-2.63

-2.01

(-3.39)

(-4.53)

(-5.53)

(-5.02)

(-3.77)

(-4.93)

(-5.89)

(-6.85)

(-5.84)

(-4.88)

0.75

0.52

0.34

0.14

1.42

0.28

0.06

-0.11

-0.25

0.97

(3.65)

(2.38)

(1.50)

(0.12)

(1.34)

(1.37)

(0.28)

(-0.50)

(-0.21)

(0.91)

0.95

0.68

0.54

0.23

0.48

0.64

0.36

0.23

-0.04

0.17

(6.75)

(4.36)

(3.35)

(0.76)

(1.73)

(4.53)

(2.36)

(1.45)

(-0.12)

(0.61)

0.29

0.28

0.28

0.24

0.28

(23.88)

(23.01)

(22.87)

(17.39)

(21.34)

SUE

43

Panel D: Full specification (adjusting for post-formation earnings shocks)

Adjusted excess return

Size IVOL B/M Price Amihud Reversal RET2-3 RET4-6 RET7-12

Adjusted excess return filtered by FF3F

Adjusted excess return filtered by FF3F and PMN

Adjusted excess return

Adjusted excess return filtered by FF3F

Adjusted excess return filtered by FF3F and PMN

Raw

Purged

Raw

Purged

Raw

Raw

Purged

Raw

Purged

Raw

-0.02

-0.08

-0.05

0.01

0.03

-0.03

-0.09

-0.06

0.00

0.03

(-0.81)

(-3.15)

(-2.12)

(0.14)

(0.60)

(-1.00)

(-3.39)

(-2.35)

(0.05)

(0.49)

-5.89

-7.46

-6.46

-3.87

-4.66

-5.02

-6.64

-5.63

-3.23

-3.82

(-2.19)

(-3.12)

(-2.71)

(-1.44)

(-1.89)

(-1.87)

(-2.81)

(-2.38)

(-1.21)

(-1.56)

0.18

0.04

0.09

0.11

0.01

0.27

0.12

0.17

0.18

0.10

(3.02)

(0.86)

(2.09)

(0.73)

(0.10)

(4.60)

(2.91)

(4.09)

(1.23)

(0.77)

0.20

-0.04

-0.01

0.29

0.47

0.24

0.00

0.02

0.33

0.50

(2.19)

(-0.47)

(-0.17)

(1.14)

(2.04)

(2.62)

(-0.01)

(0.28)

(1.26)

(2.19)

0.13

0.13

0.14

0.14

0.12

0.12

0.12

0.13

0.13

0.11

(4.36)

(4.74)

(5.20)

(2.55)

(2.34)

(3.99)

(4.36)

(4.82)

(2.39)

(2.12)

-4.72

-5.17

-5.14

-5.16

-5.22

-4.66

-5.10

-5.08

-5.11

-5.15

(-13.29)

(-12.13)

(-12.45)

(-9.10)

(-10.43)

(-13.22)

(-12.01)

(-12.35)

(-9.04)

(-10.33)

-0.81

-1.30

-1.61

-1.99

-1.33

-1.23

-1.72

-2.02

-2.33

-1.74

(-2.88)

(-4.19)

(-5.15)

(-5.42)

(-3.87)

(-4.37)

(-5.55)

(-6.47)

(-6.31)

(-5.07)

0.85

0.61

0.45

0.20

1.38

0.43

0.20

0.04

-0.14

0.98

(4.55)

(3.06)

(2.18)

(0.21)

(1.57)

(2.29)

(0.98)

(0.20)

(-0.15)

(1.11)

0.94

0.72

0.59

0.32

0.56

0.65

0.44

0.31

0.08

0.28

(7.29)

(5.13)

(4.07)

(1.32)

(2.48)

(5.09)

(3.11)

(2.16)

(0.34)

(1.25)

SUE

44

0.26

0.26

0.25

0.22

0.26

(23.54)

(22.76)

(22.33)

(18.37)

(21.98)