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Dissecting the Idiosyncratic Volatility Anomaly

by

Linda H. Chen1, George J. Jiang2, Danielle D. Xu3 and Tong Yao4

November, 2009

1 Linda H. Chen, Department of Accounting & Finance, College of Management, University of Massachusetts Boston, Boston, MA 02125. Email: linda.chen@umb.edu. 2 George J. Jiang, Department of Finance, Eller College of Management, University of Arizona, Tucson, Arizona 85721-0108. Phone: 520.621.3373. Fax: 520.621.1261. E-mail: gjiang@eller.arizona.edu. 3 Danielle D. Xu, School of Business Administration, Gonzaga University, Spokane, WA 99258. Email: xu@jepson.gonzaga.edu. 4 Tong Yao, Department of Finance, Henry B. Tippie College of Business, University of Iowa. Email: tong-yao@uiowa.edu.

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Dissecting the Idiosyncratic Volatility Anomaly

Abstract

The finding that stocks with high idiosyncratic volatility tend to have low future returns, as first

documented in Ang, Hodrick, Xing, and Zhang (2006), has been dubbed as the idiosyncratic

volatility anomaly in the finance literature. Several studies have since explored various potential

explanations of the anomalous relation between idiosyncratic volatility and stock returns. Some

studies even provided evidence that the relation may not be robust in certain stock samples. The

purpose of this study is to examine the robustness of the idiosyncratic volatility anomaly with

respect to two sample selection criteria: (a) penny stocks vs. non-penny stocks, and (b) common

stocks vs. non-common stocks. The findings of our analysis not only provide further evidence for

the robustness of the anomaly but more importantly highlight potential driving forces of the

anomaly.

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I. Introduction

In a recent study, Ang, Hodrick, Xing, and Zhang (2006, hereafter AHXZ) document an

empirical anomaly that stocks with higher idiosyncratic return volatility (IVOL), on average,

have lower future returns. In particular, they find that stocks in the bottom quintile of

idiosyncratic volatility outperform stocks in the top quintile by 1.06% per month, and the results

are robust to the effects of size, value, momentum, liquidity, volume, and dispersion of analyst

forecasts. Further evidence in Ang, Hodrick, Xing, and Zhang (2008) shows that this anomaly is

also present in international stock markets and it cannot be explained by trading frictions, higher

moments of returns such as skewness, or asymmetric information among investors.

The idiosyncratic volatility anomaly has since attracted considerable attention among finance

researchers. Several studies have explored potential explanations of this anomaly from different

angles. For example, according to Kapadia (2006) and Boyer, Mitton, Vorkink (2009), the IVOL

anomaly is consistent with investor preference for skewness. Huang et al. (2009) further show

that in the cross-sectional regression setting, idiosyncratic volatility no longer significantly

predicts future stock returns once past stock return is controlled for. That is, the IVOL anomaly

may be merely a manifest of short-term stock return reversal. Barinov (2008) uses a real-option

model to explain why high idiosyncratic volatility stocks have low expected returns. Avramov,

Cederburg, and Hore (2009) provide a rational asset pricing model in which high idiosyncratic

volatility is associated with low expected returns because such stocks have low exposure to the

long-run growth risk factor. Jiang et al. (2009) link the anomaly to corporate selective disclosure,

where management tends to disclose good news but withhold bad news. They provide evidence

that IVOL also negatively predicts future earnings. As such, stocks with high IVOL also tend to

have lower future returns. Boehme et al. (2009) argue that the negative volatility-return relation

is due to the combined effects of short-sale constraints and difference of opinion among investors.

They argue that in an information-segmented economy as of Merton (1987), the effect of short-

sale constraint on stock prices as predicted by Miller (1977) can lead to an inverse relation

between IVOL and future stock returns.

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A few studies have also questioned the robustness of the IVOL anomaly. For instance, Bali and

Cakici (2008) examine the relation between IVOL and stock return under various data

frequencies, portfolio weighting schemes, breakpoints and stock exchange samples. They report

that the IVOL anomaly is nonexistent in most cases they examine. Doran, Jiang, and Peterson

(2008) document an interesting pattern that the IVOL-return relation is significant positive

during Januarys while being significantly negative during non-January months.

In this study, we show that sample selection criteria largely contribute to different findings on the

IVOL anomaly -- first, whether to include penny stocks, defined as stocks with price below $5 at

the time of portfolio formation, and second, whether to include non-common–stock securities

reported in CRSP. We note that Ang et al. (2006; 2008) and Jiang et al, (2009) consider only

common stocks with price no less than $5 in their samples. On the other hand, Bali and Cakici

(2008) consider a $10 minimum price restriction but does not limit their sample to common

stocks. Huang et al. (2009) consider a sample of common stocks in part of their analysis but does

not impose any minimum price restriction. Different results obtained in those papers can be

reproduced by choosing different stock samples based on these two criteria.

The fact that two seemingly innocuous sample selection criteria make such a big difference is

perhaps surprising but certainly intriguing. We would like to first point out that the purpose of

this study is not to judge which side of the stock selection criteria is more appropriate. Rather,

the value of analyzing the sample selection issues lies in its potential to reveal what is behind the

IVOL anomaly.

We argue that the two sample selection criteria capture important characteristics of stocks. First

of all, stock return volatility may be due to investors’ information uncertainty as well as market

microstructure-induced noises such as price discreteness and bid-ask bounce. At any given time,

information uncertainty is in turn affected by both the variability of cash flows and conditional

information available to investors about future cash flows. An important difference in the return

volatility between penny stocks and non-penny stocks is the effect of market microstructure

noise, and if the IVOL anomaly is primarily a market microstructure effect, it would be stronger

after including penny stocks. Secondly, an interesting difference between common stocks and

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non-common stocks is the time variation of conditional information – firms issuing common

stocks may actively select the amount and the timing of information disclosed to investors (Jiang,

et al., 2009). Close-end funds, REITs, and issuers of many other forms of non-common stocks

are not known to actively control the amount of conditional information. Therefore, if the IVOL

anomaly is driven by conditional information, it would be strong among common stocks and

may be weak or non-existent among non-common stocks.

Our analysis shows that the idiosyncratic volatility anomaly is mainly a non-penny common

stock phenomenon. Specifically, among non-penny common stocks, the top decile portfolio

(with the highest IVOL over the past month) has an average monthly return of -0.05% while the

bottom decile (with the lowest IVOL over the past month) has an average return of 1.05%. The

top-bottom difference is -1.10%, significantly negative (t=-4.23). However, among all common

stocks including penny stocks, the return to the top decile is 0.58% while that of the bottom

decile is 1.08%. The difference becomes statistically insignificant, at -0.50% (t=-1.39). In

addition, among non-common stocks, the return to the top IVOL decile is 1.07% while that of

the bottom decile is 0.80%. The top-bottom return difference is positive, at 0.27% (t=0.58).

Therefore, there is no IVOL anomaly among non-common stocks. Not surprisingly, when non-

common stocks are combined with common stocks -- i.e., in the entire CRSP stock sample – the

return to the top decile (7% of which are non-common stocks) is 0.63% while that of the bottom

decile (26% of which are non-common stocks) is 0.96%. The top-bottom return difference of -

0.33% (t=-0.96) is further weaker in magnitude relative to that for the all common stock sample.

Moreover, extending the analysis in Doran, Jiang, and Peterson (2008), we show that the positive

IVOL-return relation in January exists for both non-penny common stocks and penny common

stocks, as well as for non-common stocks. However, this pattern is weaker for non-penny

common stocks relative to penny common stocks and non-common stocks. Further, after

excluding Januarys, the IVOL-return relation is significantly negative for the all common stock

sample.

The implications of our findings are that first of all, the idiosyncratic volatility anomaly is not

driven by market mircostructure noise but by conditional information related to stock return

volatility. In other words, the systematic pattern in stock returns is likely due caused by investors’

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reaction to information. Secondly, it is likely that asymmetric information between investors and

management plays an important role in the idiosyncratic volatility anomaly. That is why the

anomaly is rather stronger in common stocks but totally absent in non-common stocks. Finally,

the results based on January vs. non-January months suggest that the dampening effect of market

microstructure noise on the IVOL anomaly is concentrated in January.

The rest of the paper is structured as follows. Section II describes sample selection criteria and

presents empirical results under different sample selection criteria. Section III analyzes the

IVOL-return relation using value-weighted portfolios, controlling for past returns, and during

Januarys versus non-January periods. Section IV concludes.

II. Sample Selection and the IVOL Anomaly

II.1. Sample Selection Criteria and IVOL Estimation

Stocks with data in CRSP form the stock universe in our study. In each quarter, we select stocks

with the following two criteria: (a) common stock vs. non-common stock, and (b) penny stock vs.

non-penny stock.

Similar to Ang et al. (2006), we estimate a stock’s IVOL in each quarter from daily CRSP data

using the Fama and French (1993) three-factor model. To control for the effect of

nonsynchronous trading, we also include three lags of market returns as regressors. To be

specific, IVOL is the standard deviation of the residuals (εt) from the following regression:

α ,

where rt is the daily stock return, rm, t is the daily CRSP value-weighted index return (the market

return). The daily and monthly Fama and French factors used in our analysis are obtained from

Ken French’s Web site. As robustness checks, we also consider the above model with no lead or

lag for all variables, and one and three leads and lags for each variable, and confirm that the

empirical results are consistent. In all cases, only information before the end of the quarter is

used in the model estimation. To ensure an accurate measure of IVOL, a stock must have at least

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15 daily return observations in CRSP during a month, which is equivalent to a three-week

trading period. The sample period in our study is from January 1963 through December 2008.

Table 1 reports summary statistics of IVOL during various subperiods in our sample period,

including the cross-sectional mean (Mean) as well as the 10th (P10) and the 90th (P90)

percentiles, of idiosyncratic volatility (IVOL) during sample years. IVOL is the standard

deviation of estimated residuals from regressing daily individual stock returns onto

contemporaneous and three lags of daily market returns. The regression is performed for each

stock in each month. For each five-year period we first compute the cross-sectional mean and the

10th and 90th percentiles across stocks in each month, and then average over the period. Panel A,

B, and C report summary statistics for non-penny common stocks, penny common stocks, and

Non-common stocks, respectively. Penny (non-penny) common stocks are common stocks with

stock price below (no less than) $5 at the end of the month when IVOL is measured. N is the

average number of stocks.

As expected, penny stocks have much higher return volatility as they are mostly subject to

market microstructure noise. It is generally 2 to 3 times of that of non-penny stocks. The return

volatility of non-common stocks is comparable to that of non-penny common stocks. Overall,

there seems a upward trend in individual stock return volatility, consistent with ….

II.2. The IVOL Anomaly and Sample Selection: Equal-Weighted Portfolios

II.2.1 The Effect of Penny Stocks

Table 2 reports average IVOL, average monthly returns (RET), and average monthly Carhart

(1997) four-factor alphas (Alpha) for equal-weighed decile portfolios sorted on IVOL. In each

month we sort stocks into deciles based on the idiosyncratic volatility (IVOL) and form equal-

weighted portfolios. IVOL is the monthly standard deviation of estimated residuals from

regressing daily individual stock returns onto contemporaneous and three lags of daily market

returns. The portfolios are held for one month. They are formed within the entire common stock

sample (Panel A), within non-penny common stocks and within penny common stocks (Panel B)

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respectively. In Panel C, we also breakdown the common stocks in each IVOL decile as in Panel

A into two subgroups: non-penny common stocks and penny common stocks, and then calculate

the equal-weighted average returns of each subgroup. The purpose is to evaluate which subgroup

of stocks contributrs more to the inverse relation, if there is any, between IVOL and future

returns. N is the average number of stocks in each portfolio. Returns and alphas are in percentage

points, and t-statistics are reported in parenthesis.

As shown in Table 2, the market microstructure effect is highlighted by the difference of the

IVOL anomaly in three stock samples: 1) non-penny common stocks (i.e., common stocks with

price no less than $5 at time of portfolio formation), 2) penny common stocks (i.e., those with

price below $5 at portfolio formation), and 3) all common stocks without price restriction. From

1962 to 2006, in each month we form equal-weighted IVOL decile portfolios within each stock

sample. Among non-penny common stocks, the top decile portfolio (with the highest IVOL) has

an average monthly return of -0.05% while the bottom decile (with the lowest IVOL) has an

average return of 1.05%. The top-bottom difference is -1.10%, significantly negative (t=-4.23).

Among penny common stocks, the return to the top decile is 0.59% while that of the bottom

decile is 1.51%. The difference is -1.01%, also significantly negative (t=-2.18). However, among

all common stocks, the return to the top decile is 0.58% while that of the bottom decile is 1.08%.

The difference becomes statistically insignificant, at -0.50% (t=-1.39).

Why is the IVOL anomaly significant in both the non-penny and penny common stock samples

but insignificant when the two samples are combined? Due to market microstructure noises,

penny stocks tend to have substantially higher IVOL on average, and in each IVOL decile rank

relative to the same decile ranked among non-penny stocks. Penny stocks also tend to have

higher returns on average, and in each IVOL decile relative to non-penny stocks.5 As a result, in

the all common stock sample, the top IVOL decile is dominated by relatively high-return penny

stocks (70% are penny stocks), while the bottom IVOL decile is dominated by relatively low-

5 Several hypotheses have been proposed in the literature to explain the high return to penny stocks. The first is a bias in computing short-term returns due to market microstructure effects (xxx). The second is a bias in measuring average simple returns for highly volatile stocks (Blume and Stambaugh, 1983). The third is the liquidity premium (xxx). The fourth is the neglected stock effect (xxx).

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return non-penny stocks (only 11% are penny stocks). Therefore, market microstructure noises

weaken, rather than strengthen, the IVOL anomaly.

II.2.2 The Effect of Non-Common Stocks

Table 3 reports average monthly returns (RET), and average monthly Carhart (1997) four-factor

alphas (Alpha) for equal-weighed decile portfolios sorted on IVOL, formed within the entire

CRSP stock sample, within common stocks only and within non-common stocks only. In each

month we sort stocks into deciles based on the idiosyncratic volatility (IVOL) and form equal-

weighted portfolios. The portfolios are formed within all CRSP stocks (Panel A), and formed

within all common stocks and all non-common stocks (Panel B). Further, within each decile

portfolio formed on all CRSP stocks as in Panel A, we breakdown all stocks into two subgroups:

common stocks and non-common stocks, and then calculate the equal-weighted average returns

of each subgroup. We require both sub-portfolios to have at least 10 stocks in a month;

otherwise the returns for both subportfolios in that month are excluded from the calculation.

IVOL is the monthly standard deviation of estimated residuals from regressing daily individual

stock returns onto contemporaneous and three lags of daily market returns. The portfolios are

held for one month. N is the average number of stocks in each sub-portfolio. Returns and alphas

are in percentage points. t-statistics are reported in parenthesis. The entire sample period is from

1963 to 2008.

The effect of including non-common stocks is highlighted by comparing the IVOL anomaly

among all common stocks, non-common stocks, and all stocks in the CRSP data. Among non-

common stocks, the return to the top IVOL decile is 1.07% while that of the bottom decile is

0.80%. The top-bottom return difference is positive, at 0.27% (t=0.58). Therefore, there is no

IVOL anomaly among non-common stocks. Not surprisingly, when non-common stocks are

combined with common stocks -- i.e., in the entire CRSP stock sample – the return to the top

decile (7% of which are non-common stocks) is 0.63% while that of the bottom decile (26% of

which are non-common stocks) is 0.96%. The top-bottom return difference of -0.33% (t=-0.96)

is further weaker in magnitude relative to that for the all common stock sample. As discussed

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earlier, this is consistent with the hypothesis that the IVOL anomaly is related to time-varying

conditional information.

II.3 Further Evidence on Sample Selection

To provide further evidence on the effect of sample selection, we construct portfolios based on

stratifications between penny and pon-penny stocks, and between common and non-common

stocks. Table 4 reports average monthly returns (RET), and average monthly Carhart (1997)

four-factor alphas (Alpha) for equal-weighed decile portfolios sorted on IVOL, formed within

the following stock samples: penny noncommon stocks and nonpenny noncommon stocks in

Panel A, penny all-CRSP stocks and nonpenny all-CRSP stocks in Panel B. In Panel C, we

further separate out common and non-common stocks within the penny all-CRSP portfolio to

form equal-weighted sub-portfolios respectively. In Panel D, we further separate out common

and non-common stocks within the nonpenny all-CRSP portfolio to form equal-weighted sub-

portfolios respectively. In Panel C and D, we require both sub-portfolios to have at least 10

stocks in a month; otherwise the returns for both subportfolios in that month are excluded from

the calculation. IVOL is the monthly standard deviation of estimated residuals from regressing

daily individual stock returns onto contemporaneous and three lags of daily market returns. The

portfolios are held for one month. N is the average number of stocks in each sub-portfolio.

Returns and alphas are in percentage points.

The results further show that the idiosyncratic volatility anomaly is a non-penny common stock

phenomenon.

III. Further Analysis

III.1. The Myth of Value-weighted Portfolios

When examining the relation between idiosyncratic volatility and future stock returns, several

studies also calculate value-weighted portfolio returns instead of equal-weighted portfolio returns.

For example, Ang et al. (2006) mainly report VW results. Bali and Cakici (2008) show that

IVOL anomaly only exists in VW portfolios. The differences between equal-weighted portfolio

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returns and value-weighted portfolio returns are often interpreted as size effect since equal-

weighted portfolio puts much higher weights on small cap stocks. In this section, we examine the

patterns of value-weighted portfolio returns.

Table 5 reports average monthly returns (RET), and average monthly Carhart (1997) four-factor

alphas (Alpha) for value-weighed decile portfolios sorted on IVOL, formed within the entire

CRSP stock sample, and within non-common stocks only. In each month we sort stocks into

deciles based on the idiosyncratic volatility (IVOL) and form value-weighted portfolios. The

portfolios are formed within all CRSP stocks, and formed within all non-common stocks. Further,

within each portfolio formed on all CRSP stocks, we further form two value-weighted sub-

portfolios based on common stocks and non-common stocks respectively. We require both sub-

portfolios to have at least 10 stocks in a month; otherwise the returns for both subportfolios in

that month are excluded from the calculation. IVOL is the monthly standard deviation of

estimated residuals from regressing daily individual stock returns onto contemporaneous and

three lags of daily market returns. The portfolios are held for one month. N is the average

number of stocks in each sub-portfolio. In Panel B, weight is the percentage weight of common

and non-common stocks, respectively, in the decile portfolios formed within all-CRSP stocks.

Table 6 reports average monthly returns (RET), and average monthly Carhart (1997) four-factor

alphas (Alpha) for value-weighed decile portfolios sorted on IVOL, formed within the entire

common stock sample, as well as for two sub-portfolios formed with Penny stocks and non-

penny stocks separately. In each month we sort stocks into deciles based on the idiosyncratic

volatility (IVOL) and form value-weighted portfolios. The portfolios are formed within all

common stocks but within each portfolio we further form two value-weighted sub-portfolios

among penny common stocks and non-penny common stocks. We require both sub-portfolios to

have at least 10 stocks in a month; otherwise the returns for both subportfolios in that month are

excluded from the calculation. IVOL is the monthly standard deviation of estimated residuals

from regressing daily individual stock returns onto contemporaneous and three lags of daily

market returns. The portfolios are held for one month. N is the average number of stocks in each

sub-portfolio. In Panel B, weight is the percentage weight of penny and non-penny stocks,

respectively, in the decile portfolios formed within all common stocks.

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The above results can explain some patterns documented in the existing literature about the

IVOL anomaly. For example, Bali and Cakici (2008) report that among all CRSP stocks, the

IVOL anomaly exists based on value-weighted portfolios but does not exist based on equal

weighted portfolios. This finding is intriguing as it appears to suggest mispricing is stronger

among larger firms. However, this interpretation is not necessarily correct according to our

analysis. We find is that penny stocks and non-common stocks tend to have substantially smaller

market cap than non-penny stocks. As a result, the weights of these stocks in value-weighted

portfolios are substantially smaller than their weights in equal-weighted portfolios. In other

words, returns to value-weighted portfolios are primarily determined by returns to non-penny

common stocks in the portfolios. As a result, for value-weighted portfolios, the negative IVOL-

return relation is significant among non-penny common stocks, all common stocks, and all CRSP

stocks.

III.2. The Effect of Short-term Return Reversal

In this section, we perform Fama-MacBeth regressions as further robustness checks. One

particular issue we examine is the return reversal effect. As noted earlier, Huang et al. (2009)

report that IVOL no longer significantly predicts stock return once controlling for past monthly

stock return. Their result is based on the sample of all common stocks without price restriction.

We find that for the non-penny common stocks, past stock returns cannot explain away the

return-predictive power of IVOL. Inclusion of penny stocks is key for the results of Huang et al.,

for two reasons. First, penny stocks have high IVOL due to market microstructure noises.

Therefore, they have a strong influence on the cross-sectional regression result where IVOL is an

explanatory variable. Second, penny stocks exhibit stronger monthly return reversal, also due to

market microstructure reasons. These two effects combined explain why once penny stocks are

included in cross-sectional regressions the return-predictive power of IVOL is driven away by

past returns. To attenuate the influence of penny stocks, we further perform alternative analysis

using absolute deviation regression and using weighted OLS where weights are market caps. We

find that for the all common stock sample and for all CRSP stock sample, IVOL continue to have

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significant power in predicting stock returns even when past return is included as a control

variable.

Table 7 reports the results of the following Fama-MacBeth regressions. The dependent variable

is the monthly individual stock returns during the month after month t, the month when

idiosyncratic volatility is measured. The explanatory variables include idiosyncratic volatility

(IVOL), log of market capitalization (SIZE), log of book-to-market ratio (BM), stock returns

during the 11 months prior to month t. RET0 is the stock return during month t. SIZE and BM

are measured using available information at the end of month t. The cross-sectional regressions

are performed in each month. We report the time-series averages of regression coefficients, their

corresponding t-statistics, as well as the adjusted Rsquares. RET0 is included as an explanatory

variable in Panel A but is not used as an explanatory variable in Panel B. Returns are in

percentage points. The t-statistics, reported in parenthesis, are computed using the Newey-West

procedure with 12 lags. The regressions are performed separately for Nonpenny common stocks,

penny common stocks, all common stocks, non-common stocks, as well as for all CRSP stocks.

Table 8 reports the results of the following Fama-MacBeth regressions. The dependent variable

is the monthly individual stock returns during the month after month t, the month when

idiosyncratic volatility is measured. The explanatory variables include idiosyncratic volatility

(IVOL), log of market capitalization (SIZE), log of book-to-market ratio (BM), stock returns

during the 11 months prior to month t. RET0 is the stock return during month t. SIZE and BM

are measured using available information at the end of month t. In each month, we perform

weighted least squared (WLS) cross-sectional regressions, and the weights are the market

capitalization of each stock. RET0 is included as an explanatory variable in Panel A but is not

used as an explanatory variable in Panel B. We report the time-series averages of regression

coefficients, their corresponding t-statistics, as well as the adjusted Rsquares. Returns are in

percentage points. The t-statistics, reported in parenthesis, are computed using the Newey-West

procedure with 12 lags. The regressions are performed separately for Nonpenny common stocks,

penny common stocks, all common stocks, non-common stocks, as well as for all CRSP stocks.

III.3 Januarys vs. Non-Januarys

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Finally, we examine the effect of the two sample selection issues on the different IVOL-return

relations between Januarys and Non-January sample periods. Doran, Jiang, and Peterson (2008)

document an interesting pattern that the IVOL-return relation is significant positive during

Januarys while being significantly negative during non-January months. Their sample includes

all common stocks (excluding financials and utilities).

Table 9 reports average monthly returns (RET), and average monthly Carhart (1997) four-factor

alphas (Alpha) for equal-weighed decile portfolios sorted on IVOL, separately for Januarys and

non-January months. In each month we sort stocks into deciles based on the idiosyncratic

volatility (IVOL) and form equal-weighted portfolios. IVOL is the monthly standard deviation of

estimated residuals from regressing daily individual stock returns onto contemporaneous and

three lags of daily market returns. The portfolios are held for one month. We report average

returns and Carhart four-factor alphas for Januarys and non-January months. The portfolios are

formed within non-penny common stocks (Panel A), penny common stocks (Panel B), all

common stocks (Panel C), non-common stocks (Panel D), and all CRSP stocks (Panel E). N is

the average number of stocks in each portfolio. Returns and alphas are in percentage points. t-

statistics are reported in parenthesis.

The results show that the positive IVOL-return relation in January exists for both non-penny

common stocks and penny common stocks, as well as for non-common stocks. However, this

pattern is weaker for non-penny common stocks relative to penny common stocks and non-

common stocks. Further, after excluding January, the IVOL-return relation is significantly

negative for the all common stock sample. Therefore, the dampening effect of market

microstructure noise on the IVOL anomaly is concentrated in January.

IV. Conclusions

The finding that stocks with high idiosyncratic volatility tend to have low future returns, as first

documented in Ang, Hodrick, Xing, and Zhang (2006), has been dubbed as the idiosyncratic

volatility anomaly in the finance literature. Several studies have since explored various potential

15

explanations of the anomalous relation between idiosyncratic volatility and stock returns. Some

studies even provided evidence that the relation may not be robust in certain stock samples. The

purpose of this study is to examine the robustness of the idiosyncratic volatility anomaly with

respect to two sample selection criteria: (a) penny stocks vs. non-penny stocks, and (b) common

stocks vs. non-common stocks. The findings of our analysis not only provide further evidence for

the robustness of the anomaly but more importantly highlight potential driving forces of the

anomaly.

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24

Table 1

Summary Statistics of Idiosyncratic Volatility This table reports the summary statistics, including the cross-sectional mean (Mean) as well as the 10th (P10) and the 90th (P90) percentiles, of idiosyncratic volatility (IVOL) during sample years. IVOL is the standard deviation of estimated residuals from regressing daily individual stock returns onto contemporaneous and three lags of daily market returns. The regression is performed for each stock in each month. For each five-year period we first compute the cross-sectional mean and the 10th and 90th percentiles across stocks in each month, and then average over the period. Panel A, B, and C report summary statistics for penny common stocks, non-penny common stocks, and Non-common stocks, respectively. Penny (non-penny) common stocks are common stocks with stock price below (no less than) $5 at the end of the month when IVOL is measured. N is the average number of stocks. The entire sample period is from 1963 to 2008.

Year N Mean P10 P90

Panel A Penny Common Stocks 1963-1969 186 4.096 2.117 6.579 1970-1974 400 3.729 2.128 5.728 1975-1979 1441 3.429 0.968 6.255 1980-1984 1191 3.404 0.729 6.422 1985-1989 1882 4.032 0.948 7.563 1990-1994 2069 5.698 1.599 10.535 1995-1999 1718 6.532 2.830 11.186 2000-2004 1735 6.054 2.581 10.342 2005-2008 929 4.118 1.876 6.921 Panel B NonPenny common Stocks 1963-1969 1787 1.710 0.786 2.899 1970-1974 2480 2.026 0.905 3.412 1975-1979 3220 1.800 0.715 3.114 1980-1984 3651 1.830 0.671 3.227 1985-1989 4054 1.987 0.782 3.482 1990-1994 3804 2.342 0.894 4.132 1995-1999 5330 2.513 1.001 4.394 2000-2004 4201 2.731 1.078 4.877 2005-2008 3791 1.972 0.840 3.363 Panel C NonCommon Stocks 1963-1969 75 1.718 0.676 3.273 1970-1974 133 1.840 0.875 3.103 1975-1979 266 2.198 0.802 4.199 1980-1984 322 1.951 0.713 3.617 1985-1989 612 2.267 0.730 4.458 1990-1994 947 2.478 0.715 5.107 1995-1999 1501 2.210 0.683 4.567 2000-2004 1716 2.360 0.549 4.970 2005-2008 2051 1.504 0.436 2.984

25

Table 2 Returns and Alphas to Equal-Weighted Common Stock Portfolios Sorted by IVOL: Penny vs. Non-

Penny Stocks This table reports average monthly returns (RET), and average monthly Carhart (1997) four-factor alphas (Alpha) for equal-weighed decile portfolios sorted on IVOL, formed within the entire common stock sample, as well as for two sub-portfolios formed with Penny stocks and non-penny stocks separately. In each month we sort stocks into deciles based on the idiosyncratic volatility (IVOL) and form equal-weighted portfolios. The portfolios are formed within all common stocks but within each portfolio we further form two equal-weighted sub-portfolios among penny common stocks and non-penny common stocks. We require both sub-portfolios to have at least 10 stocks in a month; otherwise the returns for both subportfolios in that month are excluded from the calculation. IVOL is the monthly standard deviation of estimated residuals from regressing daily individual stock returns onto contemporaneous and three lags of daily market returns. The portfolios are held for one month. N is the average number of stocks in each sub-portfolio. Returns and alphas are in percentage points. t-statistics are reported in parenthesis. The entire sample period is from 1963 to 2008.

Panel A Common

IVOL RET Alpha N 1-Low 0.616 1.073 0.164 475 2 1.061 1.151 0.163 475 3 1.353 1.249 0.233 475 4 1.642 1.282 0.240 475 5 1.956 1.293 0.242 475 6 2.315 1.209 0.138 475 7 2.752 1.166 0.079 475 8 3.342 0.970 -0.119 475 9 4.288 0.803 -0.347 475 10-High 7.532 0.573 -0.632 475 H-L 6.916 -0.499 -1.254 tstat 63.161 -1.383 -4.016

26

Panel B Common NonPenny Common Penny

IVOL RET Alpha N IVOL RET Alpha N 1-Low 0.621 1.047 0.158 351 1.212 1.510 0.567 125 2 0.984 1.165 0.191 351 2.118 1.453 0.405 124 3 1.221 1.229 0.223 351 2.674 1.850 0.772 124 4 1.446 1.301 0.274 351 3.157 2.063 0.967 125 5 1.682 1.287 0.235 351 3.636 1.582 0.408 125 6 1.944 1.283 0.214 352 4.157 1.783 0.721 124 7 2.251 1.190 0.098 352 4.786 1.485 0.310 125 8 2.639 1.075 0.014 351 5.610 1.555 0.272 124 9 3.210 0.740 -0.325 352 6.926 1.242 0.111 124 10-High 4.850 -0.052 -1.065 351 11.284 0.576 -0.810 125 H-L 4.229 -1.098 -1.681 10.094 -1.030 -1.913 tstat 92.117 -4.228 -9.189 64.909 -2.215 -4.075

Panel C Penny Common Shocks NonPenny Common Shocks

IVOL RET Alpha IVOL RET Alpha 1-Low 1.130 0.294 60 1.064 0.165 412 2 0.972 -0.012 24 1.183 0.197 450 3 1.215 0.107 32 1.283 0.267 443 4 1.231 0.207 44 1.324 0.285 431 5 1.592 0.532 64 1.310 0.261 411 6 1.836 0.686 90 1.181 0.131 385 7 1.923 0.821 127 1.048 -0.014 347 8 1.836 0.680 180 0.720 -0.304 294 9 1.912 0.786 255 0.130 -0.875 219 10-High 1.158 -0.079 355 -0.713 -1.629 117 H-L -0.250 -1.168 -1.777 -2.252 tstat -0.435 -2.077 -6.396 -10.013

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Table 3

Returns and Alphas to Equal-weighted All-CRSP Stock Portfolios Sorted by Idiosyncratic Volatility: Common vs. Non-common Stocks

This table reports average monthly returns (RET), and average monthly Carhart (1997) four-factor alphas (Alpha) for equal-weighed decile portfolios sorted on IVOL, formed within the entire CRSP stock sample, and within non-common stocks only. In each month we sort stocks into deciles based on the idiosyncratic volatility (IVOL) and form equal-weighted portfolios. The portfolios are formed within all CRSP stocks, and formed within all non-common stocks. Further, within each portfolio formed on all CRSP stocks, we further form two equal-weighted sub-portfolios based on common stocks and non-common stocks respectively. We require both sub-portfolios to have at least 10 stocks in a month; otherwise the returns for both subportfolios in that month are excluded from the calculation. IVOL is the monthly standard deviation of estimated residuals from regressing daily individual stock returns onto contemporaneous and three lags of daily market returns. The portfolios are held for one month. N is the average number of stocks in each sub-portfolio. Returns and alphas are in percentage points. t-statistics are reported in parenthesis. The entire sample period is from 1963 to 2008

Panel A All CRSP Stocks

IVOL Ret Alpha N 1-Low 0.550 0.953 0.083 556 2 0.974 1.091 0.133 556 3 1.256 1.213 0.210 556 4 1.537 1.270 0.234 556 5 1.844 1.263 0.218 556 6 2.201 1.229 0.145 557 7 2.635 1.138 0.047 556 8 3.221 1.037 -0.056 556 9 4.160 0.796 -0.363 556 10-High 7.374 0.624 -0.575 556 H-L 6.824 -0.330 -1.115 tstat 63.826 -0.928 -3.727

28

Panel B Common Stocks NonCommon Stocks

IVOL Ret Alpha N Ivol Ret Alpha N 1-Low 0.616 1.073 0.164 475 0.483 0.790 -0.017 81 2 1.061 1.151 0.163 475 0.788 0.866 0.048 81 3 1.353 1.249 0.233 475 0.975 0.865 -0.021 81 4 1.642 1.282 0.240 475 1.161 0.932 -0.033 81 5 1.956 1.293 0.242 475 1.369 0.975 0.052 81 6 2.315 1.209 0.138 475 1.625 1.043 0.087 81 7 2.752 1.166 0.079 475 1.965 0.958 -0.024 81 8 3.342 0.970 -0.119 475 2.463 1.022 -0.063 81 9 4.288 0.803 -0.347 475 3.327 0.888 -0.290 81 10-High 7.532 0.573 -0.632 475 6.316 1.038 -0.088 81 H-L 6.916 -0.499 -1.254 5.833 0.248 -0.529 tstat 63.161 -1.383 -4.016 63.176 0.533 -1.174

Panel C Breakdowns of All CRSP Data Common NonCommon

Ret Alpha N Ret Alpha N 1-Low 1.076 0.178 371 0.860 0.054 183 2 1.147 0.166 421 0.937 0.078 134 3 1.254 0.235 455 0.938 0.032 101 4 1.304 0.260 475 0.951 -0.010 81 5 1.289 0.234 489 1.019 0.086 66 6 1.250 0.157 500 0.973 0.022 56 7 1.154 0.051 505 0.863 -0.142 50 8 1.046 -0.049 509 0.836 -0.214 47 9 0.796 -0.355 510 0.760 -0.491 46 10-High 0.586 -0.628 507 1.207 0.251 46 H-L -0.490 -1.263 0.347 -0.260 tstat -1.371 -4.162 0.543 -0.404

29

Table 4 Returns and Alphas to Equal-weighted All-CRSP Stock Portfolios Sorted by Idiosyncratic Volatility:

Further Stratifications between Penny and Non-penny Sctosk, and between Common and Non-common Stocks

This table reports average monthly returns (RET), and average monthly Carhart (1997) four-factor alphas (Alpha) for equal-weighed decile portfolios sorted on IVOL, formed within the following stock samples: penny noncommon stocks and nonpenny noncommon stocks in Panel A, penny all-CRSP stocks and nonpenny all-CRSP stocks in Panel B. In Panel C, we further separate out common and non-common stocks within the penny all-CRSP portfolio to form equal-weighted sub-portfolios respectively. In Panel D, we further separate out common and non-common stocks within the nonpenny all-CRSP portfolio to form equal-weighted sub-portfolios respectively. In Panel C and D, we require both sub-portfolios to have at least 10 stocks in a month; otherwise the returns for both subportfolios in that month are excluded from the calculation. IVOL is the monthly standard deviation of estimated residuals from regressing daily individual stock returns onto contemporaneous and three lags of daily market returns. The portfolios are held for one month. N is the average number of stocks in each sub-portfolio. Returns and alphas are in percentage points. t-statistics are reported in parenthesis. The entire sample period is from 1963 to 2008.

Panel A Penny Noncommon NonPenny NonCommon

IVOL RETM1 Alpha Nob IVOL RETM1 Alpha Nob 1-Low 0.823 0.800 -0.123 15 0.500 0.803 -0.002 67 2 1.671 0.987 -0.049 14 0.750 0.852 0.067 67 3 2.216 1.128 0.127 15 0.908 0.872 0.023 67 4 2.669 1.071 -0.007 14 1.059 0.962 0.046 67 5 3.146 1.446 0.354 15 1.220 0.961 0.050 67 6 3.642 0.856 -0.264 14 1.402 0.964 0.014 67 7 4.277 1.052 -0.184 15 1.630 1.027 0.079 67 8 5.098 0.725 -0.720 14 1.940 0.914 -0.060 67 9 6.381 1.743 0.998 15 2.432 1.069 0.111 67 10-High 10.809 1.483 0.170 15 3.860 0.353 -0.619 67 H-L 10.160 0.567 -0.331 3.360 -0.450 -1.074 tstat 46.672 0.842 -0.472 89.086 -1.523 -4.018

30

Panel B Penny All CRSP NonPenny All CRSP

IVOL RETM1 Alpha Nob IVOL RETM1 Alpha Nob 1-Low 1.147 1.571 0.655 138 0.560 0.915 0.071 418 2 2.064 1.404 0.405 138 0.904 1.078 0.138 418 3 2.621 1.541 0.464 138 1.135 1.195 0.217 419 4 3.104 1.976 0.885 138 1.355 1.258 0.241 418 5 3.582 1.568 0.462 138 1.586 1.271 0.231 418 6 4.106 1.792 0.716 138 1.845 1.260 0.190 419 7 4.729 1.471 0.260 138 2.151 1.212 0.134 419 8 5.551 1.408 0.102 138 2.538 1.081 0.017 418 9 6.849 1.235 0.168 138 3.108 0.778 -0.296 419 10-High 11.224 0.783 -0.539 138 4.732 -0.015 -1.022 418 H-L 10.077 -0.788 -1.652 4.172 -0.930 -1.550 tstat 63.925 -1.720 -3.579 92.877 -3.574 -8.693

Panel C Breakdown of Penny CRSP Stocks Common NonCommon

rivol RETM1 Alpha Nob RETM1 Alpha Nob 0 1.481 0.512 116 1.469 0.641 22 1 1.582 0.558 121 0.645 -0.309 16 2 1.660 0.528 122 0.885 -0.217 16 3 2.035 0.900 124 1.304 0.227 14 4 1.594 0.411 124 1.272 0.243 13 5 1.832 0.763 125 1.030 -0.355 13 6 1.484 0.271 125 0.926 -0.608 12 7 1.454 0.121 126 0.494 -0.972 12 8 1.219 0.088 126 1.499 1.009 12 9 0.758 -0.577 125 1.532 0.216 12 10 -0.763 -1.614 0.092 -0.729 11 -1.676 -3.509 0.120 -0.904

31

Panel D Breakdown of NonPenny CRSP Stocks Common NonCommon

rivol RETM1 Alpha Nob RETM1 Alpha Nob 0 1.046 0.176 268 0.815 0.020 148 1 1.153 0.193 305 0.920 0.078 113 2 1.243 0.243 330 0.995 0.122 88 3 1.296 0.265 347 0.929 0.003 71 4 1.305 0.259 359 0.933 -0.037 59 5 1.295 0.212 368 1.022 0.092 50 6 1.233 0.143 376 1.003 0.077 42 7 1.103 0.026 381 0.861 -0.073 37 8 0.782 -0.298 386 0.750 -0.267 32 9 -0.008 -1.022 388 0.063 -0.847 29 10 -1.054 -1.656 -0.771 -1.335 11 -4.016 -9.188 -2.294 -4.256

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Table 5 Returns and Alphas to Value-weighted All-CRSP Stock Portfolios Sorted

by Idiosyncratic Volatility: Common vs. Non-common Stocks This table reports average monthly returns (RET), and average monthly Carhart (1997) four-factor alphas (Alpha) for value-weighed decile portfolios sorted on IVOL, formed within the entire CRSP stock sample, and within non-common stocks only. In each month we sort stocks into deciles based on the idiosyncratic volatility (IVOL) and form value-weighted portfolios. The portfolios are formed within all CRSP stocks, and formed within all non-common stocks. Further, within each portfolio formed on all CRSP stocks, we further form two value-weighted sub-portfolios based on common stocks and non-common stocks respectively. We require both sub-portfolios to have at least 10 stocks in a month; otherwise the returns for both subportfolios in that month are excluded from the calculation. IVOL is the monthly standard deviation of estimated residuals from regressing daily individual stock returns onto contemporaneous and three lags of daily market returns. The portfolios are held for one month. N is the average number of stocks in each sub-portfolio. In Panel B, weight is the percentage weight of common and non-common stocks, respectively, in the decile portfolios formed within all-CRSP stocks. Returns and alphas are in percentage points. t-statistics are reported in parenthesis. The entire sample period is from 1963 to 2008.

Panel A All CRSP

VWRETM1 Alpha weights 1-Low 0.839 0.047 0.002 2 0.922 0.083 0.002 3 0.941 0.099 0.002 4 0.901 0.020 0.002 5 0.960 0.063 0.002 6 0.979 0.106 0.002 7 0.710 -0.192 0.002 8 0.622 -0.275 0.002 9 0.094 -0.884 0.002 10-High -0.501 -1.495 0.002 H-L -1.340 -1.999 tstat -4.007 -7.406

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Panel B NonCommon

VWRETM1 Alpha weights 1-Low 0.772 0.048 0.046 2 1.052 0.313 0.043 3 0.820 -0.044 0.042 4 0.760 -0.137 0.043 5 0.883 0.070 0.044 6 0.903 0.089 0.042 7 0.992 0.168 0.043 8 1.069 0.294 0.043 9 1.011 0.201 0.043 10-High 0.244 -0.847 0.045 H-L -0.528 -1.352 tstat -1.217 -3.217

Panel C Breakdowns of All CRSP Data Common NonCommon

VWRETM1 Alpha weights VWRETM1 Alpha weights 1-Low 0.852 0.039 0.892 0.908 0.201 0.114 2 0.911 0.065 0.924 1.043 0.293 0.079 3 0.966 0.120 0.918 0.750 -0.075 0.085 4 0.908 0.031 0.910 0.894 -0.044 0.093 5 0.974 0.061 0.904 0.836 0.015 0.099 6 0.970 0.075 0.906 1.012 0.315 0.098 7 0.698 -0.223 0.899 0.627 -0.113 0.106 8 0.546 -0.359 0.902 0.855 -0.039 0.102 9 0.018 -0.967 0.907 0.694 -0.217 0.096 10-High -0.553 -1.591 0.913 -0.253 -1.071 0.091 H-L -1.404 -2.087 -1.160 -1.730 tstat -4.081 -7.557 -2.381 -3.600

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Table 6 Returns and Alphas to Value-weighted Common Stock Portfolios Sorted by Idiosyncratic Volatility:

Penny vs. Non-Penny Stocks This table reports average monthly returns (RET), and average monthly Carhart (1997) four-factor alphas (Alpha) for value-weighed decile portfolios sorted on IVOL, formed within the entire common stock sample, as well as for two sub-portfolios formed with Penny stocks and non-penny stocks separately. In each month we sort stocks into deciles based on the idiosyncratic volatility (IVOL) and form value-weighted portfolios. The portfolios are formed within all common stocks but within each portfolio we further form two value-weighted sub-portfolios among penny common stocks and non-penny common stocks. We require both sub-portfolios to have at least 10 stocks in a month; otherwise the returns for both subportfolios in that month are excluded from the calculation. IVOL is the monthly standard deviation of estimated residuals from regressing daily individual stock returns onto contemporaneous and three lags of daily market returns. The portfolios are held for one month. N is the average number of stocks in each sub-portfolio. In Panel B, weight is the percentage weight of penny and non-penny stocks, respectively, in the decile portfolios formed within all common stocks. Returns and alphas are in percentage points. t-statistics are reported in parenthesis. The entire sample period is from 1963 to 2008.

Panel A All Commons

VWRETM1 Alpha weights Nob 0.878 0.046 0.003 472 0.918 0.096 0.003 474 0.844 -0.010 0.003 475 0.961 0.106 0.003 475 1.004 0.116 0.003 474 0.822 -0.070 0.003 475 0.764 -0.100 0.003 475 0.465 -0.475 0.003 474 -0.022 -0.952 0.003 474 -0.643 -1.673 0.003 472 -1.521 -2.176 -4.480 -8.058

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Panel B PennyCommon NonPenny Common

VWRETM1 Alpha weights Nob VWRETM1 Alpha weights Nob 1-Low 1.038 0.041 0.041 125 0.831 0.016 0.003 349 2 1.325 0.182 0.042 124 0.923 0.066 0.003 351 3 1.751 0.720 0.046 124 0.902 0.075 0.003 351 4 1.722 0.573 0.041 124 0.863 -0.008 0.003 351 5 1.103 -0.171 0.046 124 0.927 0.060 0.003 351 6 1.013 0.021 0.043 124 1.003 0.089 0.003 351 7 0.680 -0.582 0.043 124 0.886 -0.010 0.003 351 8 0.403 -0.834 0.044 124 0.700 -0.162 0.003 351 9 -0.196 -1.350 0.043 124 0.388 -0.503 0.003 351 10-High -1.796 -3.204 0.045 123 -0.226 -1.063 0.003 351 H-L -2.939 -3.794 -1.057 -1.537 tstat -6.281 -7.934 -3.466 -6.922

Panel C Breakdown of All Common Stocks Penny NonPenny

RETM1 Alpha weights RETM1 Alpha weights 1-Low 0.862 0.226 0.002 0.878 0.046 0.998 2 1.208 0.097 0.001 0.917 0.096 0.999 3 1.459 0.237 0.002 0.844 -0.010 0.998 4 1.002 -0.182 0.004 0.961 0.108 0.996 5 1.723 0.556 0.011 1.002 0.120 0.989 6 1.697 0.504 0.024 0.815 -0.068 0.976 7 1.601 0.460 0.054 0.741 -0.100 0.946 8 1.400 0.173 0.108 0.408 -0.482 0.892 9 1.104 0.011 0.213 -0.165 -0.999 0.787 10-High -0.445 -1.689 0.386 -0.875 -1.674 0.614 H-L -1.731 -2.906 -1.754 -2.177 tstat -2.882 -5.016 -5.421 -8.045

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Table 7 Idiosyncratic Volatility and Stock Returns: Fama-MacBeth Regressions

This table reports the results of the following Fama-MacBeth regressions. The dependent variable is the monthly individual stock returns during the month after month t, the month when idiosyncratic volatility is measured. The explanatory variables include idiosyncratic volatility (IVOL), log of market capitalization (SIZE), log of book-to-market ratio (BM), stock returns during the 11 months prior to month t. RET0 is the stock return during month t. SIZE and BM are measured using available information at the end of month t. The cross-sectional regressions are performed in each month. We report the time-series averages of regression coefficients, their corresponding t-statistics, as well as the adjusted Rsquares. RET0 is included as an explanatory variable in Panel A but is not used as an explanatory variable in Panel B. Returns are in percentage points. The t-statistics, reported in parenthesis, are computed using the Newey-West procedure with 12 lags. The regressions are performed separately for Nonpenny common stocks, penny common stocks, all common stocks, non-common stocks, as well as for all CRSP stocks. The sample period is from 1963 to 2008.

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Model NonPenny Common Penny Common All Commons NonCommons All CRSP

Panel A Intercept 0.032 0.095 0.027 0.025 0.031 5.405 8.379 4.185 3.187 5.248 IVOL -0.339 0.058 -0.125 -0.092 -0.166 -7.290 1.114 -2.336 -1.098 -2.821 Ln(SIZE) -0.001 -0.009 -0.001 -0.001 -0.002 -2.709 -7.999 -1.960 -2.338 -3.584 Ln(BM) 0.002 0.006 0.005 2.693 4.662 5.048 PRRET 0.007 -0.003 0.003 0.005 0.003 5.773 -1.970 2.489 2.844 2.521 RET0 -0.028 -0.088 -0.056 -0.030 -0.054 -6.065 -8.915 -9.316 -4.280 -8.008 Adj. Rsquare 0.047 0.029 0.044 0.052 0.038

Panel B Intercept 0.034 0.111 0.035 0.030 0.040 5.691 9.252 5.333 3.876 6.409 IVOL -0.394 -0.053 -0.209 -0.107 -0.245 -9.305 -1.188 -4.380 -1.318 -4.691 Ln(SIZE) -0.001 -0.010 -0.002 -0.002 -0.002 -2.916 -8.519 -3.090 -3.084 -4.856 Ln(BM) 0.003 0.008 0.006 3.027 6.243 6.059 PRRET 0.007 -0.001 0.003 0.005 0.003 6.486 -1.196 3.189 2.969 3.031 RET0 0.040 0.020 0.036 0.042 0.030

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Table 8

Idiosyncratic Volatility and Stock Returns: Weighted Least Squared Fama-MacBeth Regressions

This table reports the results of the following Fama-MacBeth regressions. The dependent variable is the monthly individual stock returns during the month after month t, the month when idiosyncratic volatility is measured. The explanatory variables include idiosyncratic volatility (IVOL), log of market capitalization (SIZE), log of book-to-market ratio (BM), stock returns during the 11 months prior to month t. RET0 is the stock return during month t. SIZE and BM are measured using available information at the end of month t. In each month, we perform weighted least squared (WLS) cross-sectional regressions, and the weights are the market capitalization of each stock. RET0 is included as an explanatory variable in Panel A but is not used as an explanatory variable in Panel B. We report the time-series averages of regression coefficients, their corresponding t-statistics, as well as the adjusted Rsquares. Returns are in percentage points. The t-statistics, reported in parenthesis, are computed using the Newey-West procedure with 12 lags. The regressions are performed separately for Nonpenny common stocks, penny common stocks, all common stocks, non-common stocks, as well as for all CRSP stocks. The sample period is from 1963 to 2008. Panel A Panel B

Model Model NonPenny Common All Commons All CRSP NonPenny Common All Commons All CRSP

Intercept 0.032 0.032 0.030 0.033 0.033 0.030 4.827 4.906 4.768 4.800 4.818 4.620 IVOL -0.289 -0.298 -0.331 -0.329 -0.336 -0.366 -3.710 -4.215 -4.570 -4.474 -5.030 -5.331 Ln(SIZE) -0.001 -0.001 -0.001 -0.001 -0.001 -0.001 -2.884 -2.882 -2.750 -2.954 -2.906 -2.730 Ln(BM) 0.002 0.002 0.002 0.002 1.864 1.979 2.151 2.330 PRRET 0.005 0.004 0.005 0.005 0.004 0.005 2.304 2.091 2.417 2.428 2.315 2.581 RET0 -0.027 -0.027 -0.024 -4.788 -4.910 -4.066 Adj. Rsquare 0.091 0.085 0.067 0.078 0.074 0.055

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Table 9

Returns and Alphas to Equal-weighted Decile Portfolios Sorted on Idiosyncratic Volatility: Januarys vs. Non-Januarys

This table reports average monthly returns (RET), and average monthly Carhart (1997) four-factor alphas (Alpha) for equal-weighed decile portfolios sorted on IVOL, separately for Januarys and non-January months. In each month we sort stocks into deciles based on the idiosyncratic volatility (IVOL) and form equal-weighted portfolios. IVOL is the monthly standard deviation of estimated residuals from regressing daily individual stock returns onto contemporaneous and three lags of daily market returns. The portfolios are held for one month. We report average returns and Carhart four-factor alphas for Januarys and non-January months. The portfolios are formed within non-penny common stocks (Panel A), penny common stocks (Panel B), all common stocks (Panel C), non-common stocks (Panel D), and all CRSP stocks (Panel E). N is the average number of stocks in each portfolio. Returns and alphas are in percentage points. t-statistics are reported in parenthesis. The entire sample period is from 1963 to 2008.

Jan NonJan

IdioRank RETM1m1 Alpha Nobs RETM1m1 Alpha Nobs

Panel A NonPenny Commons 1-Low 2.288 0.059 347 0.936 0.183 351 2 2.764 0.040 347 1.023 0.218 352 3 3.200 0.092 348 1.053 0.244 352 4 3.548 0.176 347 1.102 0.289 352 5 4.001 0.280 347 1.045 0.233 352 6 4.451 0.654 348 1.001 0.185 352 7 4.795 0.678 348 0.870 0.051 352 8 5.139 1.088 347 0.713 -0.072 352 9 5.511 1.201 348 0.316 -0.450 352 10-High 4.866 0.679 347 -0.489 -1.205 351 H-L 2.579 0.193 -1.425 -1.846 tstat 3.121 0.351 -5.305 -9.703

Panel B Penny Commons 1-Low 8.367 4.477 132 0.905 0.271 125 2 10.201 5.630 132 0.689 0.029 124 3 11.983 6.441 129 0.945 0.320 124 4 13.148 7.732 132 1.093 0.461 124 5 13.402 7.941 132 0.548 -0.152 124 6 14.854 8.768 130 0.618 0.090 124 7 14.321 8.304 132 0.364 -0.320 124 8 16.731 9.792 129 0.197 -0.524 124 9 16.260 10.735 132 -0.068 -0.682 124 10-High 22.616 13.438 132 -1.361 -1.987 124 H-L 14.249 8.537 -2.378 -2.815 tstat 4.682 2.334 -6.324 -7.392

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Panel C All Commons 1-Low 2.714 0.172 476 0.927 0.175 475 2 2.991 -0.084 477 0.987 0.189 475 3 3.735 0.230 477 1.027 0.234 475 4 4.311 0.436 477 1.013 0.219 475 5 5.054 1.023 477 0.959 0.177 475 6 5.815 1.352 477 0.799 0.030 475 7 6.746 1.953 477 0.669 -0.084 475 8 8.202 3.081 477 0.326 -0.390 475 9 9.974 4.008 477 -0.013 -0.725 475 10-High 15.122 7.894 476 -0.721 -1.360 475 H-L 12.409 7.294 -1.648 -1.993 tstat 5.932 3.692 -5.513 -7.885

Panel D Non Commons 1-Low 2.416 0.603 80 0.645 80.774 0 2 3.257 1.219 81 0.654 81.317 0 3 3.617 1.352 81 0.620 81.406 0 4 4.065 0.945 81 0.654 81.306 0 5 3.955 1.244 81 0.710 81.180 0 6 4.936 1.763 81 0.696 81.485 0 7 5.879 2.858 81 0.520 81.412 0 8 6.593 3.018 81 0.526 81.298 0 9 8.983 3.401 81 0.168 81.426 -1 10-High 11.944 6.169 80 0.067 80.878 -1 H-L 9.528 5.139 -0.578 -1 tstat 5.195 2.611 -1.250 -2

Panel E All CRSP 1-Low 2.880 0.498 557 0.782 0.061 556 2 3.141 0.328 557 0.909 0.126 556 3 3.700 0.354 557 0.992 0.201 556 4 4.160 0.401 557 1.013 0.217 556 5 4.832 0.860 557 0.945 0.162 556 6 5.616 1.200 557 0.839 0.051 556 7 6.641 1.833 557 0.648 -0.112 556 8 7.862 2.831 557 0.430 -0.300 556 9 9.846 3.888 557 -0.009 -0.731 556 10-High 14.737 7.562 557 -0.632 -1.273 556 H-L 11.857 6.637 -1.414 -1.792 tstat 5.955 3.617 -4.693 -7.202