Earnings Shocks and the Idiosyncratic Volatility Anomaly in the Cross- Section of Stock Returns

Transcription

1 Earnings Shocks and the Idiosyncratic Volatility Anomaly in the Cross- Section of Stock Returns Peter Wong 1 The Ohio State University July 2011 Abstract Ang, Hodrick, Xing and Zhang (2006, 2009) document a puzzling negative relation between idiosyncratic volatility and cross-sectional stock returns. This paper examines whether this idiosyncratic volatility discount is related to earnings shocks. I find that a substantial portion of the idiosyncratic volatility discount can be explained by earnings momentum and post-formation earnings shocks. Once 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. 1 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 address: wong_337@fisher.osu.edu.

2 I. Introduction In a recent paper, Ang, Hodrick, Xing and Zhang (2006) (AHXZ) finds that high idiosyncratic volatility (IVOL) stocks underperform low IVOL stocks by approximately 1% per month (i.e. the IVOL discount). This finding is robust and has been confirmed by many papers published after AHXZ 2. The empirical fact that high IVOL stocks have lower expected returns is inconsistent with the traditional asset pricing theories based on complete market, in which investors are well diversified and they do not demand a premium or a discount for holding high IVOL stocks. On the other hand, if investors demand compensation for not being able to diversify risk 3, then agents will demand a premium for holding stocks with high IVOL. In particular, Merton (1987) suggests that in an information-segmented market, firms with larger firm-specific variances require higher average returns to compensate investors 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 AHXZ s result with existing theories on IVOL and expected returns. Even though the magnitude and statistical significance of the returns spread between high and low IVOL stocks seem beyond doubt, an important question yet to be addressed is: what are the differences in their economic fundamentals that could drive this returns 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 economic void. Specifically, I study whether the behavior of stock returns, in relation to IVOL, is consistent with the behavior of earnings. Since earnings is perhaps the most important economic signal investors use to value their shares, exploring the difference in earnings performance is a natural starting point to address the above question. In addition, previous literatures 4 also study whether the behavior of stock prices, in relation to firm characteristics such as size, book-to-market- 2 For example, see Ang, Hodrick, Xing and Zhang (2009), Fu (2009), and Bali, Cakici, and Whitelaw (2009). 3 see Malkiel and Xu (2002) and Jones and Rhodes-Kropf (2003). 4 See Fama and French (1995), La porta, Lakonishok, Shleifer, and Vishny (1997), and Chan, Jegadeesh, and Lakonishok (1996). 1

3 equity, and past return, can be explained by the difference in earnings performance. Therefore, my approach of investigating the relation between IVOL and earnings performance is not uncommon in practice. My study is further motivated by AHXZ s finding. They find that high IVOL stocks tend to be small, value, young, and past return losers. Moreover, previous researches document that firms that possess these characteristics tend to have poor earnings performance. For example, Fama and French (1995) documents that small value firms tend to have the worst earnings performance among all stocks. In addition, Fama and French (2004) reports that the new listing firms (especially those that are small) after 1980s perform badly, and consistent with this evidence, Hou and Van Dijk (2010) finds that small firms experience large negative profitability shocks (post-formation earnings shocks) after 1980s. Lastly, Chan, Jegadessh, and Lakonishok (1996) and Chordia and Shivakumar (2006) both demonstrate that price momentum losers tend to have negative earnings surprises prior to portfolio formation, and these negative earnings surprises continue for up to four quarters after portfolio formation. Therefore, it is possible that the observed large IVOL discount is due to the difference in earnings performance between the high and the low IVOL stocks. In this study, I find that high IVOL stocks suffer negative earnings surprises both before and after portfolio formation. To gauge the magnitude of this difference in earnings surprises 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 most recent SUE prior to portfolio formation between the highest and the lowest IVOL quintile portfolios is with a t-statistic of This difference in earnings surprises persists for at least two more 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 (t = ) and (t = ), respectively. Since there is an extensive literature documents that firms reporting unexpectedly high earnings continue to 2

4 outperform firms reporting unexpectedly poor earnings after the earnings announcement 5 (this is also known as the earnings momentum effect), this article relates the evidence on the IVOL discount to the evidence on the earnings momentum effect. If the IVOL discount is indeed related to the earnings momentum effect, then we should expect the returns of high/low IVOL firms correlate more with the returns of firms with negative/positive past surprises. Consistent with this conjecture, I find that high/low IVOL stocks tend to co-move strongly with negative/positive earnings surprises firms in returns. In addition to the relation between IVOL discount and earnings momentum effect, Hou and Van Dijk (2010) and Vuolteenaho (2002) both demonstrate the importance of post-formation earnings shocks in explaining realized stock returns. Since high IVOL stocks tend to experience negative earnings shocks after portfolio formation, this article also investigates the possibility that post-formation shocks may play an important role in explaining the IVOL discount. To assess the impact of earnings momentum effect on the IVOL discount, I double sort stocks into 5x5 portfolios based on their most recent SUE and IVOL and study the effect of SUE on the IVOL discount. The result from this double-sorting exercise shows that controlling for the earnings momentum effect reduces the IVOL discount from -1.11% to -0.62% per month. In addition, since high/low IVOL stocks tend to co-move strongly with negative/positive earnings surprises firms in returns, I follow Chordia and Shivakumar (2006) to form 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 result from using the PMN factor to control for the earnings momentum effect is largely consistent with that from using the double-sorting exercise. Specifically, this 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 SUE and IVOL, and compute the Jensen s alpha, instead of returns, for each of these 25 portfolios using a four-factor model which adds the PMN factor to the FF3F model. This procedure essentially combines the first and the second approaches to control for 5 For example, see Latane and Jones (1979), Bernard and Thomas (1989) and Bernard, Thomas, and Jones (1995) 3

5 the earnings momentum effect, and it reduces the IVOL discount from -1.11% to -0.26%. As a result, the evidence is consistent with the argument that earnings momentum effect is important in explaining the IVOL discount. Results from the cross-section Fama-MacBeth (1973) test provide a similar conclusion. Furthermore, since high IVOL firms continue to have negative earnings surprises even after portfolio formation, I also investigate the possibility that the large negative returns spread between the high and low IVOL firms is partly due to the 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 daily returns surrounding earnings announcement. Consistent with the conjecture, I find that, besides earnings momentum effect, post-formation earnings shocks also help explain the IVOL discount. Specifically, removing only three daily returns surrounding earnings announcement 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 1/3 of the firms in my sample announce earnings in a given month. In addition, I show that post-formation earnings shocks can still capture approximately 20% of the IVOL discount after controlling for the earnings momentum effect. Lastly, the combined effect of earnings shocks (both preformation and post-formation earnings shocks) 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 by a more carefully constructed volatility factor [e.g. Chen and Petkova (2010) and Barinov (2010)]. In contrast, Jiang, Xu, and Yao (2009), Saryal (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 explanation of the second group and shows that the IVOL discount arises because high IVOL stocks experience negative earnings shocks prior to portfolio formation, and the earnings momentum effect induces the low returns observed in these stocks. In addition, high IVOL stocks continue to surprise their investors with poor earnings performance even after portfolio formation, and these post-formation negative earnings shocks further affect high IVOL stocks returns adversely. 4

6 The rest of the paper is organized as follows. Section II introduces the data, measurement of IVOL, earnings surprises and adjustment of stocks returns to post-formation earnings shocks. Section III introduces the summary statistics of the sample, and demonstrates that high IVOL stocks experience poor earnings surprises before and after portfolio formation. Section IV and V present the time-series test on how earnings momentum and post-formation earnings shocks could affect IVOL discount, respectively. Section VI quantifies the combined effect of earnings momentum and post-formation earnings shocks on the IVOL discount. Section VII examines the results using Fama-MacBeth regression. 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 ADR s, closed-end funds, and REIT s) from the Center for Research in Security Prices (CRSP) monthly file for the period beginning in January 1972 and ending in December I also obtain accounting data on these firms from COMPUSTAT. Book equity (BE) is stockholder s equity plus balanced sheet deferred tax and investment credit minus the book value of preferred stock. Book-tomarket ratio is calculated by dividing book equity by December t-1 market equity. To ensure that book equity information is known before the returns series it measured against, I match CRSP monthly returns between July of year t and June of year t+1 with book equity for fiscal year ending in year t-1, as in Fama and French (1992). I do not use negative BE firms, which are rare on COMPUSTAT prior to Firm age is defined as the number of years a firm has return data available on CRSP. I follow AHXZ to compute IVOL for each firm using daily returns from prior month and regress them on the Fama and French (1993) three-factor (FF3F). IVOL is the standard deviation of the residuals of the model. Firms with less than 15 observations in fitting the FF3F model are removed from my final sample. 5

7 I also follow Fama and French (1995) to construct earnings to book equity ratio, EI(t)/BE(t-1), for each IVOL quintile. Specifically, EI(t) is earnings before extraordinary items but after depreciation, taxes, interest, and preferred dividends for year t or quarter t 6. EI(t)/BE(t-1) is the sum of EI i (t) for all firms i in an IVOL quintile, divided by the sum of BE i (t). I compute three measures of earnings surprises. SUE is defined as earnings current quarter less earnings four quarters ago and standardized by the standard deviation of the earnings changes over the prior eight quarters. SUE1 is defined similar to SUE except it is standardized by share price four quarters ago. CAR is the three-day cumulative (value-weighted) market-adjusted returns from one day before to one day after an earnings announcement. 7. I also follow Chordia and Shivakumar (2006) to form an earnings momentum factor to capture the post-earnings announcement drift phenomenon. Specifically, for each month t, I sort all NYSE-AMEX 8 firms on the CRSP files with data on COMPUSTAT into deciles based on their SUE from the most recent earnings announcement. I equal weight firms in each decile. The positions are held for six months, t+1 through t+6 9. The difference in returns between the highest and the 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 on the five IVOL quintile portfolios. I form five quintile portfolios each month based on IVOL, and for each portfolio I report the time-series averages of the value-weighted characteristics. The Return column shows the well-documented IVOL discount, i.e., the 6 Figure 1A shows quarterly EI/BE. Figure 1B shows annual EI/BE. 7 My results are robust to replacing value weighted market return with equally weighted market return in calculating abnormal return. 8 Data on earnings announcements are available for most Nasdaq stocks as of Including Nasdaq stocks in forming 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. 9 I follow Jagedeesh and Titman (1993) to account for overlapping returns. 6

8 average returns difference between the high and the low IVOL quintiles, is -1.11% per month with a t- statistic of 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, while low IVOL stocks have an average age of 40 years. High IVOL stocks are also small value firms with poor prior 12-month return (skipping most recent month). These characteristics of high IVOL stocks are all associated with poor earnings performances that have been documented in size, value, and momentum literatures. Therefore, it is possible that the observed large IVOL discount is due to the difference in earnings performance between the high and the low IVOL stocks. Accordingly, a natural question then is: Do high IVOL stocks have inferior earnings performance than low IVOL stocks? Figure 1 addresses this question directly. Figure 1A shows mean values of EI(t+i)/BE(t+i-1) for 17 quarters around portfolio formation. For each portfolio formation month in quarter t, the ratios are calculated for quarter t+i, i= -8,..,+8, using firms with accounting data for quarter t and t+i, but not necessarily for other quarters. The ratio for quarter t+i is then averaged across portfolio formation months. The plots capture average profitability, as a function of IVOL, for a long period around portfolio formation periods. The question answered is: how do earnings behave before and after firms are classified as high or low IVOL? Figure 1A shows that IVOL is associated with persistent differences in profitability, measured by EI/BE. High IVOL stocks are on average less profitable than low IVOL stocks for 8 quarters before and 8 quarters after portfolio formation. This evidence is consistent with Jiang, Xu and Yao s (2009) result, which shows that IVOL is a negative predictor for future earnings. This result is robust even if I use annual earnings numbers to plot the graph. Specifically, Figure 1B plots the EI/BE ratio for 11 years around portfolio formation, and the pattern remains largely the same. Figure 1A and 1B raise two 7

9 questions about the IVOL discount. First, since high IVOL stocks tend to have inferior earnings performance than low IVOL stocks prior to portfolio formation, can the well-known earnings momentum effect help explain the IVOL discount? That is, are the low returns of high IVOL stocks due to delayed price reaction to their poor earnings news prior to portfolio formation? Second, high IVOL stocks continue to do poorly in earnings even after portfolio formation; are investors surprised by this persistency in poor earnings performance? If they are, could these post-formation earnings shocks also contribute to the poor returns of high IVOL stocks? To explore the possibility that earnings momentum may help explain the IVOL discount, panel A of Table 2 reports the value-weighted average earnings surprises, as measured by SUE, SUE1, and CAR, of portfolios sorted into quintiles based on their IVOL. Furthermore, panel B of Table 2 reports the excess correlation between the returns of each IVOL quintile and the returns of each SUE quintile 10. Excess correlation between IVOL quintile i and SUE quintile j is defined as the correlation between IVOL quintile i and SUE quintile j subtracts the average correlations between IVOL quintile i and all SUE quintiles not equal to j. 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 that is 0.95 for the stocks in the lowest IVOL quintile. The SUE spread between the extreme IVOL quintiles is therefore (t = ). Looking at SUE1 and CAR provides a similar picture. The spreads in SUE1 and CAR between the highest and the lowest IVOL quintiles are -1.83% (t = -9.82) and -1.53% (t = -9.54), respectively. Consistent with figure 1, this evidence suggests that high IVOL stocks experience poor earnings performance prior to portfolio formation, and importantly, investors are surprised by these poor earnings performance. Since there is a comprehensive literature documents that firms tend to have lower stocks returns after negative earnings surprises, it is natural to 10 I equal weight each firm when computing returns for each SUE quintile. Using value-weighting scheme provides similar results. 8

10 examine whether the IVOL discount is related to the earnings momentum effect. Furthermore, if the IVOL discount is indeed related to the earnings momentum effect, then we should expect the returns of high/low IVOL firms should correlate more with the returns of firms with negative/positive past surprises. Consistent with this argument, I find that high/low IVOL stocks tend to co-move strongly with negative/positive earnings surprises firms in returns. For example, the excess correlation between the high IVOL quintile and the negative/positive SUE quintile is 2.10%/-2.91%. On the other hand, the excess correlation between the low IVOL quintile and the negative/positive SUE quintile is -4.68%/5.80%. This co-movement result validates the argument that the IVOL discount is related to the earnings momentum effect. Figure 1 suggests that high IVOL stocks have poor earnings surprises not only before portfolio formation, but also after portfolio formation. To investigate whether differences in post-formation earnings shocks can help in explaining the IVOL discount, column 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 across the extreme IVOL quintiles continues over the periods following portfolio formation. For instance, the spreads in most recent SUE, SUE1, and CAR after portfolio formation between the highest and the lowest IVOL quintiles are (t = ), -3.57% (t = ), and -0.80% (t = -7.28), respectively. The SUE and SUE1 spreads between the high and the low IVOL quintiles are actually wider in the following quarter when compared to the SUE and SUE1 prior to portfolio formation. This may simply be a symptom of a mis-specified model of expected earnings, so examining the behavior of returns around earnings announcement dates provides a more direct piece of evidence. High IVOL stocks experience -0.57% CAR during the first quarterly earnings announcement after portfolio formation, while low IVOL stocks experience 0.23% CAR. An average firm makes one quarterly earnings announcement within the three months after portfolio formation and therefore, one way to gauge the economic magnitude of this -0.80% CAR spread between the extreme IVOL quintiles is to compare it with the average three-month buy-and-hold returns of the 9

11 long-short IVOL portfolios (buy high IVOL quintile stocks and short low IVOL quintile stocks). Panel C of Table 2 reports the average long horizon returns of the IVOL quintiles. The quarterly IVOL discount is -2.80%, and therefore, the -0.80% spread in CAR after portfolio formation accounts for 28.50% 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 around earnings announcement days in the three-month holding period 11. Moreover, High IVOL stocks continue to surprise investors with their 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 returns between the extreme IVOL quintiles is -4.82% 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 22.61% of the six-month buy-and-hold returns. After two quarters, there is not much difference between the quintiles abnormal returns around earnings announcements. To summarize, sorting stocks on the basis of previous month s IVOL yields large difference in subsequent returns (The IVOL discount). Furthermore, high IVOL stocks also tend to have large and negative earnings surprises before portfolio formation. To confirm the IVOL discount is indeed related to the earnings momentum effect, panel B of Table 2 shows that high/low IVOL stocks tend to co-move strongly with negative/positive earnings surprises firms in returns. This co-movement result is consistent with the argument that earnings momentum effect is important in explaining the IVOL discount. In addition, high IVOL stocks continue to surprise investors with poor earnings performance even two quarters after portfolio formation, and this raises the possibility that post-formation earnings shocks may also play an important role in explaining the IVOL discount. The next two sections analyze the 11 An average quarter has 66 trading days, and since I am only removing 3 trading days out of one 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 occurring around earnings announcement days in the three-month holding period. 10

12 importance of earnings momentum effect and post-formation earnings shocks in explaining the IVOL discount, respectively. IV. How important is earnings momentum in explaining the IVOL discount? The previous section demonstrates that high IVOL stocks tend to experience large and negative earnings surprises prior to portfolio formation. Since there is an extensive literature documents that firms reporting unexpectedly high earnings continue to outperform firms reporting unexpectedly poor earnings after the earnings announcements, this section investigates the importance of earnings momentum in explaining the IVOL discount. Three methods are employed to assess the impact of earnings momentum effect 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) to form the earnings momentum factor (PMN) and 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 returns, for each of these 25 portfolios using a four-factor model which adds the PMN factor to the FF3F model. This procedure essentially combines the first and the second approaches to control for the earnings momentum effect. 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, which is the difference in average returns between the highest and the lowest quintile 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 worst earnings surprises firms, while the IVOL discount is only -0.02% (t = -0.07) 12 This is a sequential sort. I first sort stocks into 5 SUE quintiles, and within each SUE quintile, I further sort stocks into 5 IVOL quintiles. 11

13 among the most positive earnings surprises firms. The fact that the IVOL discount resides mostly among the negative earnings surprises firms is consistent with the evidence of slower information diffusion regarding 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) and this is substantially lower than the -1.11% (t = -3.13) IVOL discount produced by the univariatesorted IVOL quintiles, as reported in 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 previous analyses; the IVOL discount resides mostly among stocks with poor prior earnings performance. The average IVOL discount across the 5 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 earnings momentum factor to control for earnings momentum effect Panel C of Table 3 reports the intercepts, Jensen s alpha, from regressing excess returns of each IVOL quintile on a four-factor model which adds the PMN factor to the FF3F model. Last column of panel C shows the PMN loadings for each IVOL quintile. PMN loading is monotonically declining in IVOL. The PMN loadings spread between the extreme IVOL quintiles is This suggests that high/low IVOL firms co-move strongly with negative/positive earnings surprises firms, and this is consistent with the earlier excess correlation results. To gauge whether this 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. The PMN factor on average earns 0.89% per month, and therefore, the

14 spread in the PMN loadings accounts for x 0.89% = -0.77% of the difference in average returns between the extreme IVOL quintiles. As a result, the spread in FF3F_PMN alpha between the highest and the lowest IVOL quintiles is -0.65% with a t-statistic of (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 returns spread obtained by sorting stocks into quintiles based on IVOL (Table 1, column2). Furthermore, PMN loadings are highly significant in four out of five quintiles; thus, it is unlikely that PMN is a useless factor in the sense of Kan and Zhang (1999). As a result, controlling earnings momentum effect via this approach provides a similar conclusion as in the previous subsection. That is, earnings momentum effect plays an important role in explaining the IVOL discount. C. Combining double-sorting and earnings momentum factor In the previous two sub-sections (A and B), earnings momentum effect is controlled by either through double-sorting or using the earnings momentum factor, PMN, to compute the Jensen s alpha. To ensure that the earnings momentum effect has been properly accounted for, I combine the previous two approaches to control for the earnings momentum effect. However, it is possible that the previous two approaches act as perfect substitute for one another in controlling for the earnings momentum effect, and therefore, combining them would not further reduce the IVOL discount. To address this concern, panel A of Table 4 reports the PMN loadings of the 25 SUE/IVOL sorted portfolios. PMN loading is decreasing in IVOL across all five SUE quintiles, and the loadings spreads between the extreme IVOL quintiles are all economically and statistically significant. The average spreads in the PMN loadings across all five SUE quintiles is with a t-statistic of This suggests that high IVOL stocks are still highly negatively exposed to the earnings momentum factor regardless whether they reside in positive or negative SUE quintile. As a result, there does not seem to be too much overlap these two methods (double-sorting and the PMN factor approaches) in controlling for the earnings momentum effect. 13

15 The smallest PMN loadings spread in magnitude is (the highest SUE quintile), and since the PMN premium earns 0.89% per month, the PMN loadings spread accounts for x 0.89% = -0.27% returns spread between the extreme IVOL quintiles among the highest SUE stocks. This is a sizable amount considering 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 from combining the double-sorting and the PMN factor approach. 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 once the PMN factor is introduced into the FF3F model. The average IVOL discount, as measured by the spread in FF3F_PMN alpha between the extreme IVOL quintiles, across all five SUE portfolios is only -0.26% per month with a t-statistic of In contrast, sorting stocks into five quintiles based on IVOL alone produces FF3F_PMN alpha spread of -0.65%, with a t-statistic of (Table 3, Panel C). On the other hand, double-sorting stocks on IVOL and SUE produce 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 earnings momentum effect when explaining the IVOL discount. The evidence in this section has provided a clear picture on how prior earnings performance is related to the IVOL discount. Specifically, investors under-react to earnings news, especially to those firms with negative earnings surprises and high IVOL. This result is consistent with the evidence of slower information diffusion regarding negative news. Bali and Cakici (2008) show that high IVOL stocks are small, illiquid, and low-priced stocks and these characteristics associated high IVOL stocks can also be viewed as short-sale constraints. Thus, a significant portion of the IVOL discount reflects failure to incorporate negative earnings news appropriately in stock prices due to market frictions that are associated with these high IVOL stocks. V. How important are post-formation earnings shocks in explaining the IVOL discount? 14

16 Earlier results (See Table 2 and Figure 1) suggest that high IVOL stocks have poor earnings surprises not only before portfolio formation, but also after portfolio formation. To investigate the possibility that post-formation earnings shocks may help in explaining the IVOL discount, this section presents evidence of how post-formation earnings shocks may play a role in explaining the IVOL discount. To examine the importance of post-formation earnings shocks in explaining the IVOL discount, I adjust monthly stock returns with earnings shocks. Specifically, monthly stock returns are adjusted by the following procedures. 1) If there is an earnings announcement within a given month, I replace the daily returns in [-1,0,+1] by 0, with time 0 being the earnings announcement date. 13 2) I compound the daily returns over that month by 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 to the CRSP monthly return for that month. 4) Alpha is obtained by using the adjusted returns, in excess of 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 adjusted alpha. The goal here is to explore the effect that post-formation earnings shocks have on the IVOL discount. If post-formation earnings shocks are not important in explaining the IVOL discount, removing three days out of one month in calculating monthly returns should not affect the IVOL discount substantially. Panel A of Table 5 reports the average monthly statistics on the number of firms that announce earnings. In addition, panel B of Table 5 reports the adjusted monthly returns and adjusted alpha using different asset pricing models. 13 Replacing returns with risk free rate, value or equally weighted market returns do not change the results qualitatively. 15

17 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 announcement made during the month) is 750. Therefore, under the adjusted return procedure, quintile one and five populate ( )/1500 = 30.67% of the overall sample of these two quintiles. In addition, the adjusted return procedure only involves removing three daily returns out of twenty-two trading days (13.64%) for an average month. Therefore, if the IVOL discount was randomly distributed across trading days, and if 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 adjusted returns spread between the extreme IVOL quintiles is -0.83% while the unadjusted returns spread is -1.11%, as reported in Table 1. Thus, my adjustment to post-formation earnings shocks reduces the IVOL spread by [ ]/1.11 = 25.23%, and this is substantially higher than the 4.13% benchmark. This result is consistent with Xu, Yao, and Jiang (2009) and they find that one quarter ahead SUE is useful in explaining the IVOL discount. The previous result is univariate in the sense that returns are adjusted for post-formation earnings shocks but none of the relevant asset pricing factors is accounted for. To address this issue, column three and four of panel B of Table 5 report the CAPM and the FF3F adjusted alpha. The CAPM and the FF3F adjusted alpha spread are -1.10% (t = -3.76) and -1.16% (t = -4.91), respectively. On the other hand, the CAPM and the FF3F alpha obtained using unadjusted returns series are -1.40% (t = -4.49) and -1.45% (t = -5.84), respectively (Table 1). The reductions in the CAPM and the FF3F alpha are therefore, 27% and 20%, respectively. 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. VI. Combining earnings momentum effect and post-formation earnings shocks. The previous two sections show that earnings momentum effect and post-formation earnings shocks are both important in explaining the IVOL discount by themselves. In this section, I combine these 16

18 two effects and quantify the impact of both pre-formation and post-formation earnings shocks on the IVOL discount. Table 6 reports the results. Panel A of Table 6 reports the average adjusted returns and the t-statistics of the 25 SUE/IVOL sorted portfolios. The average IVOL discount, computed with adjusted returns, across all five SUE quintiles is -0.46% (t = -1.50) per month, while the average IVOL discount is -0.62% (t = -1.92) when computed using un-adjusted 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 earlier sections, if postformation earnings shocks are not important in explaining the IVOL discount, using adjusted-returns should only reduce the IVOL discount by less than 5%. However, the adjusted returns reduce the IVOL discount by ( )/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. Using adjusted alpha from the FF3F model does not change the result substantially. Panel B of Table 6 reports the FF3F adjusted alpha of the 25 portfolios. The average adjusted alpha across all five SUE quintiles is -0.77% (t = -3.74), while the average alpha is -0.97% (t = -4.48) (Table 3, panel B) when computed using un-adjusted returns. The reduction in FF3F alpha is ( )/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 FF3F_PMN alpha across all five SUE quintiles is -0.08% (t = -0.38), while that is -0.26% (t = -1.17) (Table 4, panel B) when computed using un-adjusted returns. The 19 basis points reduction in the IVOL discount is similar to the reduction in FF3F alpha or raw returns in magnitude, as reported in panel A and B. 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. Using adjusted returns reduce the FF3F_PMN alpha by 24 basis points. 17

19 The evidence so far is consistent with the argument that high IVOL stocks experience large and negative earnings shocks before portfolio formation, and the well-documented 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 turn out to be important in explaining the IVOL discount. The combined effect of earnings shocks can explain a substantial portion of the IVOL discount. Section VII. Fama-MacBeth cross-sectional regressions Table 7 examines the relation between earnings momentum, post-formation earnings shocks, and the cross-section of average returns using Fama and MacBeth (1973) regressions. The regressions provide further robustness of my results since they employ all securities without imposing quintile breakpoints, allow for more controls in returns, including liquidity measure, and 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 do the followings to control for the earnings momentum effect and the post-formation earnings shocks. To control for the post-formation earnings shocks, excess adjusted returns are used, instead of excess returns, in the regressions. To align with the time-series section, I use three approaches to control for the earnings momentum effect. First, I include the most recent SUE as a control variable in the regressions. The results are essentially unchanged if the most recent CAR, as defined in section II, is used instead. Second, I follow Brennan et al. (1998) methodology in the Fama-MacBeth regressions to control for the exposure to the earnings momentum factor. Lastly, to ensure the earnings momentum effect is properly accounted for, not only I control for the recent SUE, but I also filter returns using Brennan et al. 15 Each coefficient from a Fama-MacBeth regression is the return to the minimum variance portfolio with weights that sum to zero, weighted characteristic on its corresponding regerssor that sums to one, and weighted characteristics on all other regressors that sum on one. The weights are tilted toward stocks with the most extreme (volatile) returns. 18

20 (1998) methodology to control for the exposure to the earnings momentum factor. This approach essentially combines the first and the second methods. The Brennan et al. (1998) methodology examines individual security returns adjusted 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 avoids the error-in-variables bias created by errors in estimating factor loadings. Two factor models, the FF3F model and a four factor model which adds the PMN factor to the FF3F model, are employed to adjust returns with exposures to risk factors. I begin by estimating the factor loadings for each year from 1972 to 2009 for all securities that had at least 24 return observations over the prior 60 months. Since the PMN data begins in January 1972, the factor loadings in the first month of the regression period (January 1974) are estimated from 24 observations per factor, the factor loadings in the second month of the regression period are estimated from 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. Note that although the factor loadings are estimated with error, this error affects only the dependent variable, filtered returns. While the factor loadings will be correlated with the security characteristics, there are no priori reasons to believe that the errors in the estimated loadings will be correlated with the security characteristics. This implies that the estimated coefficient from the crosssection regression should be unbiased. However, if the errors in the estimated factor loadings are correlated with the security characteristics, the monthly estimates of the coefficients will be correlated with the factor realizations and the Fama and MacBeth estimators will be biased by an amount that depends upon the mean factor 19

21 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, and it was 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 Fama-MacBeth estimator, and from the standard error of the constant from the OLS regression in the case of purged estimator. The cross-section of stock returns in excess of the one-month T-bill rate 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, from month t-3 to t-2 (RET2-3), the cumulative return over the three months ending three months previously, from month t-6 to t-4 (RET4-6), the cumulative return over the six months ending six months previously, from month t-12 to t-7 (RET7-12), and the measure of IVOL (IVOL). Amihud s (2003) measure is being included as a proxy for liquidity. I further include the previous month s return (Reversal) as an additional control for the one month reversal effect of Jegadessh (1990). 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 reciprocal of share price from prior month (Price) to control for this phenomenon. The size, book-to-market, and Amihud variables are from the previous year. The results are presented in Table 7. Let me first focus on panel A. The second column of panel A of Table 7 confirms the standard results found in the literature that average returns are negatively related to IVOL. The estimated coefficient on IVOL is %. The economic significance of the IVOL is also in line with my previous result. Moving from the lowest quintile, which has an average IVOL of 0.94%, to the highest quintile, which has a measure of 5.46% (Table 1), the coefficient on IVOL in first column of panel A implies a difference in monthly returns between the two quintiles of -57 basis points. 20

22 This returns difference is lower than the results reported in Table 1, which is not surprising because Fama-MacBeth regressions minimize least squares which tends to put more weight on smaller stocks, and it is well known that IVOL effect is stronger in the value-weighted setting 16. Nevertheless, IVOL is highly significant with a t-statistic of The third and the fourth columns present results with risk-adjusted returns, with the risk adjustment being done using the FF3F. Consistent with the prior results, IVOL becomes even stronger in explaining stocks returns after using the FF3F model to adjust for returns. One way to control for the earnings momentum effect is via including most recent SUE in the regressions. Column 7 to column 9 of panel A report the same set of regressions as those reported in column 2 to column 4 except column 7 to column 9 include most recent prior SUE to control for the earnings momentum effect. The Fama-MacBeth and the purged estimators on the IVOL are uniformly reduced in each of the specifications once SUE is included in the regressions. For example, column 7 shows that, including SUE in the regression reduces the Fama-MacBeth estimator on IVOL to % (t = -2.76) from % (t = -3.20). Another way to account for the earnings momentum effect is to control for the exposures 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 This magnitude on the IVOL coefficient is considerably smaller than that estimated by using either excess returns (-12.59%) or FF3F filtered returns (-20.15%). Lastly, to ensure the earnings momentum effect is properly accounted for, not only I filter returns with the FF3F_PMN model but I also include SUE in the regression. Column 10 and column 11 report the results. The purged estimator on IVOL is -6.81% with a t-statistic of Consistent with results in the time-series section, filtering returns with the FF3F_PMN model and including the most recent SUE in the regression seem to provide a more adequate control of the earnings momentum effect. 16 See Bali and Cakici (2008). 21

23 The time-series evidence from the time-series section 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 the post-formation earnings shocks. Consistent with the result from previous sections, postformation earnings shocks are also important in explaining the IVOL discount. For example, using adjusted returns in the regression reduces the Fama-MacBeth estimator on IVOL to -8.07% (t = -2.18) (panel B, column 2) from % (t = -3.20) (panel A, column 2). Similar reductions in the estimators and t-statistics are also observed in column 3 to column 4, which show the results of adjusted returns filtered by the FF3F model. Lastly, I quantify the impact of both 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 by FF3F_PMN model and include the most recent SUE in the regressions. Last two columns of Panel B report the results. The purged estimator on IVOL is -2.95% with a t-statistic of The IVOL spread between the extreme IVOL quintiles is 4.52% (reported in Table 1); combining with this estimated IVOL discount of -2.95%, this suggests the average returns spread between the extreme IVOL quintiles is only basis points per month. Consistent with the time-series evidence, the results presented in panel 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. Panel C and panel D of Table 7 conduct similar analysis as in panel A and panel B of Table 7 except that panel C and D include more control variables. The additional control variables are: lag monthly return (Reversal), momentum measures (RET2-3, RET4-6 and RET7-12), last month s share price (Price), and a liquidity measure (Amihud). Column 2 of both panel C and panel D confirm that IVOL remains highly significant even with all the control variables in the regressions. The point estimate of the IVOL coefficient declines slightly when compared to panel A and panel B, which is not surprising given the high correlations between IVOL and most of the control variables, but remains economically and statistically significant. The size effect is no longer significant as it was in panel A and panel B. This 22

24 is consistent with many papers which document size is no longer important in explaining stock returns after 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). Consistent with the results from panel A, the third and fourth columns of panel C demonstrate that IVOL becomes more significant, with a purged estimator of % and a t-statistic of -4.27, when the FF3F model is used. More importantly, IVOL is significantly weakened in explaining stocks returns once the PMN factor is being incorporated into the FF3F model; the purged estimator on IVOL is only -6.03% with a t-statistic of -1.91, as reported in the fifth column of panel C. In addition to the other firm characteristics, columns seventh to eleventh of panel C includes most recent prior SUE to further control for the earnings momentum effect. The results are largely in line with those from panel A of Table 7. Controlling for SUE further weakened the explanatory power of IVOL. However, this reduction is not as impressive as that from filtering returns with exposures to the earnings momentum factor. For example, filtering returns with FF3F_PMN model (without including SUE) produces a purged estimator on IVOL of -6.03% (t = -1.91), while that is -8.09% (t = -2.91) when SUE is included in the regression (without using FF3F_PMN model to filter returns). Nevertheless, the last two columns of panel C show that the combined approach (including SUE and filter returns with the FF3F_PMN model) is a more adequate control for the earnings momentum effect. Lastly, panel D of Table 7 reports the results with adjustment to post-formation earnings shocks. The point estimate on IVOL is further weakened by this adjustment to 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, while these are -5.35% and -1.71, respectively, if un-adjusted returns are used instead. Similar reductions on the IVOL point estimates and the t-statistics can also be observed in other specifications across the panel. 23

25 Section 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, and more importantly, how correlation between earnings surprises and IVOL may affect the returns relation between high and low IVOL stocks. This paper addresses these questions directly. In this study, I find that high IVOL stocks suffer negative earnings surprises before and after portfolio formation. The well-known earnings momentum effect combined with post-formation earnings shocks are responsible for the IVOL discount. Once these two effects are accounted for, idiosyncratic volatility has little, if any, return predictability. Moreover, earnings momentum effect alone can capture approximately 42% of the IVOL discount. Results from Fama-MacBeth (1973) cross-section regressions provide a similar conclusion. 24

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29 Figure 1A Figure 1B Figure quarter and 11-year evolution of earnings on book equity, earnings (t+i)/book equity (t+i-1), for idiosyncratic volatility sorted portfolios in each month of quarter t or year t (quarter 0 and year 0 on the horizontal axis). For each portfolio formation month in year t = 1972 to 2009, the Earnings (t+i)/book equity (t+i-1) ratio for each idiosyncratic volatility sorted quintile portfolio is defined as the sum (across firms) of Earnings (t+i) across firms divided by the sum (across firms) of Book equity (t+i-1). Earnings (t+i) is earnings before extraordinary items but after interest, depreciation, taxes, and preferred dividends for the fiscal quarter (Figure 1A) or fiscal year (Figure 1B). Book equity (t+i-1) is book common equity for t+i-1. 28