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The Idiosyncratic Volatility Puzzle: TimeTrend or Speculative Episodes?

Michael W. BrandtDuke University and NBER

Alon BravDuke University and NBER

John R. GrahamDuke University and NBER

Alok KumarUniversity of Texas at Austin

Campbell, Lettau, Malkiel, and Xu (2001) document a positive trend in idiosyncratic volatil-ity during the 1962–1997 period. We show that by 2003 volatility falls back to pre-1990slevels. Furthermore, we show that the increase and subsequent reversal is concentratedamong firms with low stock prices and high retail ownership. This evidence suggests thatthe increase in idiosyncratic volatility through the 1990s was not a time trend but, rather,an episodic phenomenon, at least partially associated with retail investors. Results fromcross-sectional regressions, conditional trend estimation, stock-split events, and “attention-grabbing” events are consistent with a retail trading effect. (JEL G11, G12, G14)

Studying returns of U.S. equities from July 1962 through December 1997,Campbell, Lettau, Malkiel, and Xu (2001, hereafter CLMX) document a steadyincrease in the idiosyncratic volatility of individual firms, while the aggregatemarket volatility and industry volatilities remained roughly constant throughtime. This apparent rise in idiosyncratic volatility has become one of the mostactively researched asset pricing puzzles, with several recent articles trying toexplain the phenomenon. The proposed explanations include increased institu-tional ownership (Bennett, Sias, and Starks 2003; Xu and Malkiel 2003); firmfundamentals having become more volatile (Wei and Zhang 2006) or opaque(Rajgopal and Venkatachalam 2006); newly listed firms becoming increasingly

We thank two anonymous referees, John Griffin, Cam Harvey, George Korniotis, Terrance Odean (the editor),Ludovic Phalippou, Laura Starks, and seminar participants at Duke University for comments, Wadia Haddaji andNataliya Khmilevska for research assistance, and Brad Barber, Terrance Odean, Michael Roberts, and ItamarSimonson for providing some of the data used in the article. All remaining errors and omissions are ours. Sendcorrespondence to Michael Brandt, Fuqua School of Business, Duke University, One Towerview Drive, Durham,NC 27708-0120; telephone: (919) 660-1948; fax: (919) 882-9157. E-mail: [email protected].

C© The Author 2009. Published by Oxford University Press on behalf of The Society for Financial Studies.All rights reserved. For Permissions, please e-mail: [email protected]:10.1093/rfs/hhp087 Advance Access ublication December 5, 2009p

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younger (Fink et al. 2009) and riskier (Brown and Kapadia 2007); and productmarkets becoming more competitive (Irvine and Pontiff 2009).

In this article, we show that during recent years, idiosyncratic volatility hasfallen substantially, reversing any time trend evident during the 1962–1997sample period studied by CLMX. We also find that the late 1990s surge and2000s reversal in idiosyncratic volatility is most evident in firms with low stockprices and limited institutional ownership. We conclude from this evidence thatthe time-series behavior of idiosyncratic volatility is more likely to reflect anepisodic phenomenon than a time trend. This raises the question of whether wecan tie this episode of high idiosyncratic volatility to some sensible economicphenomenon.

We show that the episodic idiosyncratic volatility phenomenon manifestsitself more strongly among low-priced stocks, which are stocks that are heldproportionally more by retail investors than institutions. Not only do manyinstitutions shy away from holding low-priced stocks for prudence reasons butfixed per-share trading costs also increase the transaction costs associated withactively trading large positions in low-priced stocks. We therefore hypothesizethat the observed idiosyncratic volatility pattern is at least partially inducedby trading on the part of retail investors. The bulk of our analysis providesevidence consistent with this hypothesis. Using retail trading data from a largeU.S. brokerage house and small-trades data from the Trade and Quote (TAQ) aswell as from the Institute for the Study of Security Markets (ISSM) databases,we provide several pieces of evidence that confirm an association between retailtrading behavior and idiosyncratic volatility.

First, we show that idiosyncratic volatility levels are higher and volatilitytrends are more evident among low-priced stocks that are held primarily by retailinvestors. Among low-priced stocks, strong idiosyncratic volatility patternsare evident only if those low-priced stocks have high levels of retail trading.Next, we show that when stock splits mechanically reduce the stock price,idiosyncratic volatility rises. Importantly, we demonstrate that price changesinfluence idiosyncratic volatility through the trading activities of retail investorsin ways that are consistent with our conjecture. When we consider other salient“attention-grabbing” events (large positive or negative returns or high turnover)that are likely to attract the attention of retail investors (Barber and Odean 2008),volatility changes around those events are also consistent with the retail tradingexplanation.

On the face of it, the interpretation of our new evidence appears to contradictthe explanation of the idiosyncratic volatility puzzle put forward by Xu andMalkiel (2003, hereafter XM) and Bennett, Sias, and Starks (2003, hereafterBSS). These two articles argue that the apparent rise in idiosyncratic volatilityin their samples is linked to increasing institutional involvement in equity mar-kets. XM support their argument by demonstrating that in a pooled time-seriesand cross-sectional regression of idiosyncratic volatility on the fraction of insti-tutional ownership and firm size, institutional ownership enters the regression

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The Review of Financial Studies / v 23 n 2 2010


The Idiosyncratic Volatility Puzzle

with a significant positive coefficient, suggesting that higher institutional own-ership is associated with higher idiosyncratic volatility. Similarly, BSS arguethat changes in institutional ownership are positively associated with changesin idiosyncratic volatility. We argue, in contrast, that low-priced stocks arevolatile precisely because they are not held widely by institutions.

To reconcile these two conflicting hypotheses, we reestimate the BSS andXM regressions for different subsamples. When we estimate the regressionsfor the entire sample, our results are very similar to the evidence in BSS andXM. However, when we estimate the regressions separately for the universeof low- and high-priced stocks, we find that among the low-priced stocks, ahigher level of institutional ownership or an increase in institutional ownershippredicts lower idiosyncratic volatility. Among the high-priced stocks, whichwe show are less relevant for the idiosyncratic volatility puzzle, the positiverelations found in the previous two articles prevail. The subsample estimatesare consistent with our conjecture that retail trading in low-priced stocks ispositively associated with the idiosyncratic volatility surge and reversal.

With respect to other recent explanations of the idiosyncratic volatility puz-zle, we do not view them as necessarily being inconsistent with our evidenceand interpretation. Instead, we emphasize that any credible explanation of thepuzzle cannot be based on a unidirectional trend but has to predict episodes thatcome and go. These other explanations could be consistent with our episodichypothesis if they can also successfully explain the recent reversal in the id-iosyncratic volatility trend.

Our overall conclusion is that low-priced stocks dominated by retail tradersplayed an important role in the rise and the fall in the idiosyncratic volatilitylevels over the past two decades. The balance of the article proceeds as follows.Section 1 describes the data and summarizes the CLMX volatility decompo-sition methodology used to obtain the time-series patterns. Section 2 presentsour new results about idiosyncratic volatility. We discuss our interpretationsof the results in Section 3, where we specifically examine the relative roles ofretail and institutional investors. In Section 4, we examine how our resultsrelate to existing explanations of the idiosyncratic volatility puzzle. Section 5concludes.

1. Data and Methodology

1.1 Data sourcesWe obtain the daily as well as monthly split-adjusted stock returns, stockprices, shares outstanding, exchange listing, Standard Industry Classification(SIC) codes, and stock split event markers for the universe of all traded NewYork Stock Exchange (NYSE), American Stock Exchange (AMEX), and Na-tional Association of Securities Dealers Automated Quotations (NASDAQ)firms from the Center for Research on Security Prices (CRSP). We restrict the

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sample to firms with share codes 10 and 11. In addition, we obtain monthlyFama-French factor returns, forty-eight SIC industry classifications, NYSEmarket capitalization decile breakpoints, and monthly risk-free rates from Ken-neth French’s data library.1 Both the daily and the monthly data range fromDecember 1925 to September 2008.

For each listed U.S. firm, we compute leverage and book-to-market ratiosusing data from Compustat. Book-to-market is the ratio of fiscal year-end bookequity plus balance sheet deferred taxes in year t − 1 to market equity inDecember of year t − 1. Firm size is computed as the market capitalizationas of June in year t − 1 and is then used during July of year t − 1 throughJune of year t . Book leverage is the ratio of book debt to book assets. Marketleverage is the ratio of book debt to the sum of book debt and market equity.The annual Compustat data are available for the 1950–2007 period, while thequarterly data are available from 1962 to 2007. Of the 27,877 CRSP stocks,the accounting data are available for 27,109 firms.

In addition to the stock data, we obtain a six-year (1991–1996) panel ofall trades and positions of a group of retail investors at a large U.S. discountbrokerage house.2 For the 1983–2000 time period, we also obtain retail tradingdata from the TAQ and the ISSM databases, where small-sized trades areused to proxy for retail trades.3 Following the recent literature (e.g., Battalioand Mendenhall 2005; Malmendier and Shanthikumar 2007; Hvidkjaer 2008;Barber, Odean, and Zhu 2009), we use the $5,000 trade size cutoff to identifysmall trades.4 Like Barber, Odean, and Zhu (2009), we use the ISSM/TAQ dataonly until 2000 because the assumption that small trades proxy retail trading isless likely to be valid after 2000. In particular, the introduction of decimalizedtrading in January 2001 and extensive order-splitting by institutions due toreduced trading costs make small trade size a less reliable proxy for retailtrading after 2000.

Last, we construct an aggregate measure of institutional ownership for eachfirm using the 13(f) institutional holdings data from Thomson Reuters. For eachfirm, over the period from 1980 through 2008Q3, we calculate the percentageof outstanding shares held by institutions.

1.2 Idiosyncratic volatility measurementWe follow the volatility decomposition framework developed in CLMX and usedaily stock returns to construct the aggregate monthly idiosyncratic volatilitytime series. First, for each stock j that belongs to industry i , we compute the

1 The data library is available at http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/.

2 See Barber and Odean (2000) for additional details about the retail investor dataset.

3 We thank Brad Barber and Terrance Odean for providing the ISSM/TAQ small-trades data. Additional detailsabout the dataset are available in Barber, Odean, and Zhu (2009).

4 Using the TORQ data, Lee and Radhakrishna (2000) show that the $5,000 trade size cutoff can effectivelyidentify trades initiated by individual investors.

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daily firm-specific residual by subtracting the daily industry-i return:

εijst = Rijst − Rist. (1)

Rijst is the return on day s in month t of stock j that belongs to industry iand Rist is the value-weighted return of industry i on day s in month t . Next,we obtain the month-t idiosyncratic volatility (IV) of stock j that belongs toindustry i as

IVijt =∑s∈t

ε2ijst. (2)

Using the monthly idiosyncratic volatility estimates for all stocks, we com-pute the value-weighted average of idiosyncratic volatility for each industry,where market capitalizations at the end of the previous month are used to obtainthe weights within the industry. Specifically,

IVit =∑j∈i

wi j t−1IVijt, (3)

where wijt is the month-t weight of stock j that belongs to industry i . Last,we compute the value-weighted average of the monthly industry idiosyncraticvolatilities to obtain the average idiosyncratic volatility across all firms in agiven month. We sum across the forty-eight Fama and French (1997) industriesand stocks that are not assigned to any industry are grouped in category 49.Specifically,

IVt =49∑

i=1

wi t−1IVit , (4)

where wi t is the month-t weight of industry i . For easier interpretation, themonthly average idiosyncratic volatility measures are presented in annualizedform.5

2. Idiosyncratic Volatility Patterns: New Evidence

In this section, we document new results about cross-sectional and time-seriesvariation in idiosyncratic volatility. We initially focus on the new empiricalfindings and then present our interpretation of the results, as well as how theyrelate to the existing explanations of the idiosyncratic volatility puzzle, in thenext two sections.

5 We follow the notation in CLMX to describe our volatility calculations, but we account for an unequal numberof observations within a month. If N is the number of days for which stock returns are available within a month,the idiosyncratic volatility estimate for the month is IVijt = 21

N−1

∑Ns=1 ε2

ijst. To reduce noise, we exclude stockswith fewer than twelve daily observations in a given month but our results are not sensitive to the choice of thisarbitrary cutoff. To minimize the effects of outliers, we winsorize the volatility estimates at the 0.5 and 99.5percentile levels. However, our results are qualitatively similar if we do not winsorize.

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Calendar Time (January 1926 to September 2008)

Figure 1Idiosyncratic volatility from January 1926 to September 2008This figure shows the annualized mean standard deviation (light line) and the 12-month backward moving averageof this measure (dark line) for each month between January 1926 and September 2008. Idiosyncratic volatilityis measured using daily returns following the CLMX volatility decomposition methodology.

Table 1Summary statistics: Annualized average idiosyncratic volatility

Time period VW EW

1926–1930 7.94 15.531931–1940 10.22 23.351941–1950 5.76 10.401951–1960 5.22 7.621961–1970 6.57 11.811971–1980 7.63 13.791981–1990 8.15 16.271991–2000 10.10 23.272001–2005 8.79 18.602006–2008 6.55 12.772008 only 9.02 19.89

This table reports the levels of idiosyncratic volatility of all CRSP firms, roughly by decade. It reports boththe equal-weighted (EW) and the value-weighted (VW) means of idiosyncratic volatility (annualized standarddeviation), measured using daily returns following the CLMX procedure. All entries are monthly averages overa given time period. The 2008 estimates use data only until the end of the third quarter (September).

2.1 Aggregate idiosyncratic volatility levelsFigure 1 presents time-series plots of aggregate idiosyncratic volatility. Thefigure shows both the raw (light line) and the 12-month moving average(dark line) of the annualized mean idiosyncratic volatility from January 1926through September 2008, updating the results of CLMX with the most recentdecade of data. The results are also tabulated in Table 1. We report both the

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Figure 2Market volatility from January 1926 to September 2008This figure shows the annualized standard deviation (light line) of market returns and the 12-month backwardmoving average of this measure (dark line) for each month between January 1926 and September 2008. Marketvolatility is measured using daily market returns following the CLMX volatility decomposition methodology.

value-weighted and equal-weighted annualized means of the monthly idiosyn-cratic volatility, grouped roughly by decade. For comparison, in Figure 2, weshow the market volatility time-series computed using the CLMX method.

The results in Figures 1 and 2 and Table 1 confirm that the level of id-iosyncratic volatility was high and increasing throughout the 1990s, while themarket volatility time series did not exhibit such a trend. Over the first partof the CLMX sample (the 1960s and the 1970s), the annualized VW meanidiosyncratic volatility exhibited cyclical variation around an average of about6%–7% with a few spikes above 10%. Beyond the 1970s, the annualized VWmean idiosyncratic volatility was on average 9%, with a few spikes above 20%.Looking at the 1962–1997 period alone, the latter part of the sample exhibitsan increase in the idiosyncratic volatility—the idiosyncratic volatility puzzlefirst identified in the CLMX study.

Perhaps more surprisingly, the evidence in Figures 1 and 2 and Table 1 indi-cates that the level of idiosyncratic volatility declined sharply in the past fewyears. We find that by 2003, the annualized VW mean idiosyncratic volatil-ity declined to a level of 6.59%, which is remarkably close to the averagelevel of idiosyncratic volatility over the first half of the CLMX sample. Wetherefore conclude that the idiosyncratic volatility appears to have returned tonormal levels. The increase in idiosyncratic volatility and then its return toa normal level suggests that the late 1990s’ increase in volatility was not a

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time trend but was caused by an episode of some type of activity that reverseditself.6

2.2 Evidence from the 1930sWhen we examine a longer historic perspective, we find that a large increase inidiosyncratic volatility followed by a decline back to the historical levels is not aunique event in the U.S. capital market history. A similar volatility episode wasobserved in the 1930s, where the volatility increased in the late 1920s and thendeclined, with a local peak in idiosyncratic volatility occurring in 1932. Similarto the recent episode, idiosyncratic volatility peaked shortly after the collapseof the market, and then returned to predepression levels within a few years.Specifically, the VW (EW) average idiosyncratic volatility climbed to morethan 26% (54%) shortly after the collapse of the market. But by the mid-1930s,it fell to 6.62% (13.99%), which is very close to the pre-1929 value-weightedand equal-weighted volatility levels of 6.11% and 12.32%, respectively.

This historic evidence is consistent with high idiosyncratic volatility beingan episodic phenomenon. This is not to say that both volatility episodes weredriven by the same mechanism. Our main point is that the data appear to exhibitvolatility episodes more so than a trend.

2.3 Aggregate idiosyncratic volatility trend estimatesTo directly test for the presence of a time trend in the aggregate idiosyncraticvolatility time series, and to facilitate comparisons with the previous results,we follow CLMX and use the Vogelsang (1998) trend estimation method.Specifically, we use ordinary least squares (OLS) to estimate the followingtime-series model of aggregate volatility on its first lag and a time trend:

IVt = b0 + b1t + b2IVt−1 + εt . (5)

IVt is the aggregate month-t idiosyncratic volatility, b1 is a linear trend coef-ficient that is the focus of our analysis, and εt is the error term. To determinewhether this trend estimate is significantly positive, we also follow CLMX anduse Vogelsang’s P S1 statistic to obtain the 90% confidence interval for thetrend estimate.

The trend estimates are presented in panel A of Table 2. The estimation iscarried out separately for the 1962–1997 time period used in the CLMX studyand for the extended period covering 1962–2008Q3. To facilitate comparison tothe results reported in CLMX, we obtain the trend estimates for the aggregateannualized variance rather than the aggregate annualized standard deviationseries.

The trend estimates in CLMX indicate that the aggregate idiosyn-cratic volatility time series has a statistically significant positive trend

6 The estimates from the most recent time period indicate that both the idiosyncratic volatility and the marketvolatility levels have started to rise. It is difficult to predict whether this is the beginning of another volatilityepisode or just a temporary aberration.

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Table 2Price- and size-conditional idiosyncratic volatility trend estimates

Panel A: Subperiod trend estimates

July 1962 to Dec 1997 July 1962 to Sept 2008

Firm size Firm size

Price All Small Medium Large All Small Medium Large

All 0.963 1.739 0.791 0.433 0.211 0.452 0.218 0.120Low 1.688 3.439 2.502 1.771 0.406 0.472 0.425 0.322Medium 0.854 0.977 0.876 0.170 0.367 0.352 0.296 0.188High 0.256 0.125 0.269 0.225 0.150 0.208 0.152 0.111

Panel B: Pre-break and post-break trend estimates

July 1962 to April 2000 May 2001 to Sept 2008

Firm size Firm size

Price All Small Medium Large All Small Medium Large

All 1.304 2.085 0.958 0.572 −26.629 −33.142 −14.831 −9.059Low 1.786 3.548 2.530 1.429 −33.092 −38.195 −26.394 −15.366Medium 1.153 1.201 0.974 0.284 −22.712 −30.989 −14.735 −13.491High 0.319 0.306 0.390 0.250 −10.322 −15.023 −10.990 −7.660

This table reports the idiosyncratic volatility trend estimates (multiplied by 105) using the Vogelsang (1998)methodology. We use monthly time series for all our estimates. Both panels A and B report estimates for twosubperiods. In panel B, we use April 2000 as the breakpoint in the idiosyncratic volatility time series andthe trends are estimated for the pre-break and post-break periods. The trend lines are fitted after computingthe logarithm of idiosyncratic volatility. The annualized idiosyncratic volatility measure is constructed usingthe CLMX methodology. To facilitate comparison with the CLMX trend estimates, the estimates are computedusing annualized variance series. The small-cap, mid-cap, and large-cap firm size categories are defined usingNYSE size deciles 1–3, 4–7, and 8–10, respectively. The three price categories are defined in a similar mannerusing NYSE price breakpoints. Trend coefficients that are significantly positive (at the 10% level) are indicatedin bold.

(= 0.965 × 10−5) during the 1962–1997 sample period. Our trend estimatefor this same period is very similar (= 0.963 × 10−5). However, when we ex-tend the sample to 2008Q3, the trend estimate drops to 0.211 × 10−5 and is nolonger significantly positive.

Because the trend estimates depend on the estimation time period, we ex-amine the sensitivity of the trend estimate to the chosen estimation periods.We fix the end period of the estimation window to 1997 or 2008Q3 and varythe starting period between 1926 and 1962 at roughly five-year intervals. Theresults are reported in Figure A.1 of the Internet Appendix (see the supple-mentary data online). We find that initially the trend estimate increases as thesample starts earlier. It reaches a peak when the starting point is 1950, and itdecreases for earlier starting periods. This pattern is observed for both the 1997and the 2008 ending periods, though notably, the trends ending in 2008 aremuch lower and statistically insignificant for all starting points back to 1935.When we start before 1935, the trend becomes statistically insignificant foreither ending point. These sensitivity results indicate that irrespective of thestarting period, the idiosyncratic volatility trend is considerably weaker andstatistically insignificant when we extend the time period to 2008Q3.

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2.4 Structural breakpoints in the idiosyncratic volatility seriesThe evidence of a weakening trend suggests that the aggregate idiosyncraticvolatility series was an episode that reversed itself, rather than a uniform positivetrend. The graphical evidence in Figure 1 shows that the aggregate idiosyncraticvolatility peaks in the early 2000s and declines thereafter. In this section, weconduct formal breakpoint tests to identify the locations of structural breaks inthe aggregate time series.

We use the Bai and Perron (1998, 2003) multiple breakpoints identificationmethod and estimate the following set of m + 1 time-series models of aggregatevolatility:

log(IVt ) = b j0 + b j1t + b j2 log(IVt−1) + εt ,

t = t j−1 + 1, . . . , t j ; j = 1, . . . , m + 1; t0 = 1, tm+1 = T . (6)

Here, m is the number of breakpoints and t1, t2, . . . , tm represents the locationof those m breakpoints. The form of this time-series model is identical tothe model presented in Equation (5). The only difference is that we estimatem + 1 regressions, one for each of the m + 1 segments defined by the mbreakpoints. The breakpoint estimation method identifies the location of thebreakpoints by minimizing the total residual sum of squares from the m + 1linear regression models. The key estimate of interest is b j1, which capturesthe trend in idiosyncratic volatility.

When we allow for only one breakpoint, the breakpoint in the idiosyncraticvolatility time series occurs in April 2000 (see Figure 3), with a 95% confidenceinterval spanning January 2000 to September 2000. The trend lines are shown,where the trend lines are fitted after computing the logarithm of idiosyncraticvolatility. We use the log transformation to ensure that model-predicted idiosyn-cratic volatility levels do not become negative. The plot indicates that the trendreverses sign and decreases during the 2001–2008 time period. The positivetrend estimate is 1.304 × 10−5, the negative trend estimate is −26.629 × 10−5,and both estimates are strongly statistically significant.

These breakpoint estimates show formally that the trend in volatility duringthe 1990s was consistent with an episode that reversed itself. When we allow formultiple breakpoints, the identification method also detects other breakpoints(e.g., August 1975, March 1994). We do not pursue the multiple breakpointanalysis further because there is no clear economic rationale for the number ofbreakpoints and their locations.

2.5 Idiosyncratic volatility levels in the cross-sectionWe now present intriguing new evidence that the idiosyncratic volatility patternof the 1990s is most evident among small and, more importantly, low-priced

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Figure 3Trend lines with one structural breakpointThis figure shows the two trend lines when the aggregate idiosyncratic volatility time series has a singlebreakpoint. The breakpoint is located in April 2000. The trend lines are fitted after computing the logarithm ofidiosyncratic volatility. We also plot the annualized mean standard deviation (light line) for each month betweenJanuary 1962 and September 2008. Idiosyncratic volatility is measured using daily returns following the CLMXvolatility decomposition methodology.

stocks. Specifically, we show that, for this subset of stocks, the levels of id-iosyncratic volatility are higher and the trend estimates are stronger.7

Figure 4 shows the idiosyncratic volatility time series for low-priced (bot-tom three deciles), medium-priced (middle four deciles), and high-priced (topthree deciles) stock categories. We follow standard convention and use NYSEbreakpoints to sort stocks into price categories. Examining first the high-pricedstocks, we notice that during the 1961–2008Q3 period, the rise in idiosyn-cratic volatility is less pronounced than in the aggregate results. For low-pricedstocks, in contrast, the rise and subsequent fall in idiosyncratic volatility ismore pronounced. The volatility levels of low-priced stocks are about two tothree times higher than the idiosyncratic volatility levels of high-priced stocks.

Since low-priced stocks tend to be small, it is possible that low stock pricejust proxies for firm size. The level and change in idiosyncratic volatility couldsomehow even depend mechanically on the level of stock prices. To examinethe conditional relation between firm-level idiosyncratic volatility, stock price,and firm size, we estimate a series of Fama-MacBeth monthly and quarterlycross-sectional regressions. The dependent variable in these regressions is the

7 Even during the 1930s volatility episode, the idiosyncratic volatility patterns are strongest among the lowest-priced CRSP stocks. This finding is notable because while the late 1920s are notorious for speculative tradingin penny stocks, CRSP does not cover these firms, which results in a sample biased toward high-priced firms.Nonetheless, the idiosyncratic volatility pattern is strongest among the low-priced CRSP stocks.

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Figure 4Stock price and idiosyncratic volatility time seriesThis figure shows the 12-month backward-moving average of the stock price conditional annualized meanstandard deviation time series for January 1926 and September 2008. The stock price (low or deciles 1–3,medium or deciles 4–7, and high or deciles 8–10) is used as the conditioning variable. The price categories areredefined each month, where NYSE price breakpoints are used to form the three price categories. Idiosyncraticvolatility is measured using daily returns following the CLMX volatility decomposition methodology.

firm-level idiosyncratic volatility in month t (computed using daily returnsduring the month) and the explanatory variables are several firm characteristics,including stock price and firm size, measured at the end of the previous month.The estimation results are presented in Table 3.

Following Bennett, Sias, and Starks (2003), we standardize both the de-pendent and the independent variables so that the coefficient estimates canbe directly compared within and across specifications. We report the averageregression coefficients along with t-statistics computed from the standard de-viation of the coefficients through time. The standard errors are corrected forpotential higher-order serial correlation using the Pontiff (1996) method.8

In the first monthly specification, where we use the full CRSP sample (1926–2008Q3), we find that the coefficient estimate for stock price is strongly negative(coefficient estimate = −0.277, t-statistic = −20.38), documenting a link be-tween idiosyncratic volatility and stock price. The coefficient on size is alsonegative and significant, suggesting that smaller firms are more volatile thanlarger firms, holding the price constant. However, the magnitude of the co-efficient on firm size is significantly lower (coefficient estimate = −0.059,

8 Specifically, we estimate an autoregressive time-series model for each coefficient estimate, where the order ofthe model is chosen by examining the Durbin-Watson statistic. In most instances, we find that three lags aresufficient to eliminate the serial correlation in the coefficient estimates.

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Table 3Determinants of idiosyncratic volatility: Fama-MacBeth cross-sectional regression estimates

Dependent variable: Log(Idiosyncratic Volatility) for stock i in period t

(1) (2) (3) (4) (5) (6)Independent variable 26-08 26-61 62-08 83-00 83-00 83-00

Intercept 0.007 0.004 0.011 0.002 −0.019 −0.013(13.44) (10.46) (10.76) (5.62) (−4.10) (−2.93)

Log(Price) −0.277 −0.266 −0.258 −0.368 −0.265 −0.262(−20.38) (−18.17) (−21.65) (−8.25) (−11.26) (−12.27)

Log(Size) −0.059 −0.154 0.014 −0.024 −0.016 −0.031(−14.89) (−9.02) (3.02) (−3.99) (−2.07) (−2.86)

Log(Lagged Idiosyncratic Volatility) 0.489 0.428 0.542 0.675 0.658 0.621(37.72) (19.13) (23.96) (9.78) (8.48) (8.56)

Retail and institutional investorsLog(1+Institutional Ownership) 0.016 0.010

(4.11) (3.52)�Institutional Ownership 0.017 0.017

(5.53) (5.95)Retail Trading Proportion 0.052 0.034

(4.75) (3.76)Low Price × High RTP 0.037 0.019

(3.34) (6.50)Low Price × Low RTP −0.010 −0.011

(−0.60) (−0.76)Other firm characteristicsBook-To-Market Ratio −0.045 −0.043

(−6.64) (−5.43)Leverage −0.032 −0.029

(−6.05) (−5.17)Past 12-Month Return −0.012 −0.019

(−1.50) (−2.39)Idiosyncratic Skewness 0.016

(2.06)Firm Age 0.002

(1.51)Volume Turnover 0.056

(6.61)Frequency Mon Mon Mon Mon Qtr QtrAverage Adjusted R2 0.541 0.565 0.510 0.604 0.717 0.728Average Number of Stocks 2,941 842 4,542 5,317 4,857 4,857

This table reports estimates from Fama-MacBeth cross-sectional regressions, where the dependent variable isthe logarithm of annualized idiosyncratic volatility constructed using the CLMX methodology. The independentvariables, measured at the end of the previous time period, include: stock price, firm size, lagged idiosyncraticvolatility, book-to-market ratio, leverage (the ratio of debt value and total assets or market value), past 12-monthstock returns, the level of institutional ownership for the most recent quarter, quarterly change in institutionalownership for the most recent quarter, retail trading proportion (total retail trading volume divided by the marketvolume), idiosyncratic skewness measured using daily returns, firm age (the number of years since the firmfirst appears in the CRSP database), and volume turnover. Low Price × High RTP is an interaction dummythat is set to one for stocks with high retail trading proportion (top third) and low prices (bottom third). LowPrice × Low RTP is defined in an analogous manner. We use the NYSE price breakpoints to form the high andlow price categories. The Pontiff (1996) methodology is used to correct the Fama-MacBeth standard errors forpotential serial correlation. The t-values, obtained using corrected standard errors, are reported in parenthesesbelow the estimates. To ensure that extreme values are not affecting the results, we winsorize all variables attheir 0.5 and 99.5 percentile levels. To allow for direct comparisons among the coefficient estimates withinand across specifications, all variables have been standardized so that each variable has a mean of zero and astandard deviation of one. The average number of observations and the average adjusted R2 are also reported.The sample period varies across the columns and is reported below the column label. The retail trading data arefrom ISSM/TAQ for the 1983–2000 period, where small-sized trades are used as proxy for retail trades. The13(f) institutional holdings data are from Thomson Reuters.

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t-statistic = −14.89). The estimated price coefficient is about five times thesize coefficient.

To facilitate comparisons with previous articles that employ the CRSP samplestarting in 1962, we split the sample and estimate the cross-sectional regressionsseparately for the 1926–1961 (column 2) and 1962–2008Q3 (column 3) timeperiods. We find that the coefficient estimates on stock price are similar in eachof the two periods. But the size coefficient flips sign and becomes mildly positiveduring the latter time period. These cross-sectional regression estimates indicatethat the negative relation between stock price and idiosyncratic volatility isstronger and more robust than the size–volatility relation. We therefore concludethat the relation between idiosyncratic volatility and stock price does not proxyfor a link between idiosyncratic volatility and firm size.9

2.6 Conditional idiosyncratic volatility trend estimatesTo further understand the stock price–idiosyncratic volatility relation, we ex-amine whether the idiosyncratic volatility trend is concentrated among smaller,low-priced stocks. For this analysis, as before, we follow the Vogelsang (1998)trend estimation methodology. We estimate the time-series trend for differentportfolios formed by sorting along stock-price and firm-size dimensions. Weuse the NYSE size breakpoints to define small-cap, mid-cap, and large-capstocks. The three price categories are defined in an analogous manner usingNYSE price breakpoints. As before, to facilitate direct comparisons with theCLMX study, we calculate the trend estimates using the annualized variancetime series.

The conditional volatility trend estimates are reported in Table 2, panel A,where the estimation is carried out separately for the 1962–1997 and 1962–2008Q3 periods. We find that trends are stronger for small and low-pricedfirms and insignificant for the high-priced and large-firm-size categories.10

For instance, during the 1962–1997 period, the trend estimate for high-pricedand large-cap firms are 0.256 and 0.433, respectively, and both estimates areinsignificant. In comparison, the trend estimates for low-priced and small-capfirms are 1.688 and 1.739, and both estimates are significant. Importantly,we find that, in comparison to firm size, the stock price level has a strongerinfluence on the volatility trend. Even among the large-cap firms, the trend issignificantly positive (1.771) when the stock price is low.

When we extend the time period to 2008, the trend estimates become sig-nificantly weaker. The only significant remaining trend is among small andlow-priced stocks. Again, consistent with our cross-sectional results, the trend

9 For robustness, we estimate a regression specification that contains shares outstanding rather than firm size asone of the independent variables. The results reported in Table A.1 of the Internet Appendix (see columns 1 and2) (see the supplementary data online) indicate that the results are qualitatively similar.

10 CLMX also report that the volatility trend is stronger among smaller firms but they do not examine the relativeroles of stock price and firm size.

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26 30 35 40 45 50 55 60 65 70 75 80 85 90 95 00 05 080

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estimates indicate that stock price is more important than firm size as a deter-minant of the idiosyncratic volatility patterns.

These subperiod and subsample trend estimates indicate that the idiosyn-cratic volatility time series contains distinct rising and falling segments. Toexamine whether the rising and falling patterns are stronger among certaintypes of stocks, we obtain the trend estimates for price- and size-sorted port-folios separately for the pre- and post-break periods. Given our evidence inSection 2.4, we use April 2000 as the series breakpoint. The subperiod esti-mates are reported in Table 2, panel B. The trend lines for price- and size-sortedportfolios are also plotted in Figure 6. As expected, the volatility trends are sig-nificantly positive during the pre-break period and strongly negative during thepost-break period. More importantly, we find that the magnitudes of the trendestimates during both pre- and post-break periods are stronger for lower-pricedfirms and smaller firms.

For additional robustness, we examine the idiosyncratic volatility patternsseparately for NASDAQ and NYSE/AMEX stocks. We expect the idiosyn-cratic volatility patterns to be weaker among relatively larger and higher-pricedNYSE/AMEX stocks. Consistent with our evidence for low-priced stocks, wefind that the idiosyncratic volatility level is lower for NYSE/AMEX stocks (seeFigure 5). Furthermore, for both the 1962–1997 and 1962–2008Q3 periods,the trend estimates are small (0.032 and −0.024, respectively) and statisticallyindistinguishable from zero for NYSE/AMEX stocks.

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Figure 6Trend lines for price- and size-sorted portfolios with one structural breakpointThis figure shows the two trend lines for price- and size-sorted portfolios. The small-cap, mid-cap, and large-capfirm size categories are defined using NYSE size deciles 1–3, 4–7, and 8–10, respectively. The three pricecategories are defined in a similar manner using NYSE price breakpoints. Other details of the plot are the sameas in Figure 3. Rows and columns are defined as in Table 2.

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Overall, our new results on idiosyncratic volatility patterns indicate that thehigh levels of idiosyncratic volatility in the 1990s are not evidence of a trend,but rather are an episodic phenomenon.11 One of the main features of highidiosyncratic volatility episodes is that the phenomenon is concentrated in low-priced stocks. The obvious question is: What is special about low-priced stocks,and how does this observation help us learn about the mechanisms that mightgenerate idiosyncratic volatility episodes? In the next section, we attempt toanswer these questions and interpret the empirical evidence presented so far.

3. Explaining Episodic Idiosyncratic Volatility Patterns

3.1 Main hypothesisLow-priced stocks are special for a number of reasons. First, low-priced stocksare usually not eligible to be bought on margin (Han 1995). Second, manyinstitutions shy away from holding low-priced stocks for prudence reasons(Lakonishok, Shleifer, and Vishny 1992; Del Guercio 1996; Brav and Heaton1997). They may also simply avoid trading low-priced stocks due to illiquidityand high transaction costs. In contrast, retail investors might find lower-pricedstocks attractive for several reasons. For example, retail speculators mightbe attracted by the gambling-like skewness inherent in the returns of low-priced stocks.12 Furthermore, the scarcity of institutional investors in low-priced stocks, viewed as having access to superior information, can lead to amore level playing field for retail investors.

Whatever the reasons, if retail investors find low-priced stocks attractiveand dominate the trading in those stocks, retail investors could influence thereturns and volatility patterns of low-priced stocks. Therefore, we conjecturea link between low stock prices, trading by retail investors, and episodes ofidiosyncratic volatility.13 Analogous to previous attempts to explain the ap-parent time trend in idiosyncratic volatility with other trending variables, suchas institutional ownership, firm age, or accounting data quality, it is diffi-cult, if not impossible, to directly prove or disprove our conjecture based on

11 Idiosyncratic volatility increased appreciably toward the end of 2008 and into 2009, after our sample periodended. This behavior is consistent with idiosyncratic volatility trending for a time before eventually reversing, aswe model empirically in Table 2. We look forward to future research that extends this modeling effort to accountfor the recent increase in volatility.

12 Kumar (2009) finds that retail investors significantly overweight low-priced stocks in their portfolios, relativeto expected stock holdings if investors were to randomly choose portfolios according to market capitalizationweights. The overweighting by retail investors in low-priced stocks is particularly evident among stocks withhigh idiosyncratic volatility and high idiosyncratic skewness. This preference could reflect overweighting of thelow probabilities of extreme returns (Barberis and Huang 2008) or reflect that low-priced, high-volatility stocksoffer better opportunities for experiencing higher levels of utility realizations (Barberis and Xiong 2009).

13 CLMX also conjecture (but do not test) that day trading might influence idiosyncratic volatility. Our conjectureapplies to the entire population of retail investors and we try to identify the channels through which retail tradingmight influence idiosyncratic volatility. To the extent that our retail trading measure proxies for day trading, ourevidence is consistent with the CLMX conjecture.

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essentially one episode.14 Nonetheless, we present several pieces of evidencefrom cross-sectional tests that are consistent with retail trading being an im-portant determinant of idiosyncratic volatility patterns.

3.2 Retail trading and idiosyncratic volatilityIn the first set of tests, we directly examine whether retail trading is an importantdeterminant of the observed idiosyncratic volatility patterns. Using small-tradesdata from ISSM and TAQ, for each month we compute the proportion of totaltrading volume that can be attributed to retail investors. Specifically, the retailinvestors’ trading intensity or retail trading proportion (RTP) for a given stockin a certain month is defined as the total retail trading volume (sum of buy- andsell-initiated small trades) divided by the total trading volume in the market.We define low, medium, and high retail trading stocks as those that are inthe bottom three, middle four, and top three deciles of monthly retail tradingproportion, respectively.

In Table 3, column 5, we report the estimates from Fama-MacBeth cross-sectional regressions with retail trading measures as additional explanatoryvariables. The dependent variable is the month-t idiosyncratic volatility of acertain stock. The results indicate that the coefficient estimate of stock pricebecomes weaker (compare columns 4 and 5) when we introduce additionalvariables in the regression specification, including RTP. We also find that RTPhas a significantly positive coefficient estimate (coefficient estimate = 0.052,t-statistic = 4.75), which indicates that the degree of retail trading has anincremental effect on the level of idiosyncratic volatility. The relation betweenRTP and idiosyncratic volatility is stronger than that between institutionalownership level and change in institutional ownership, but weaker than therelation between stock price and idiosyncratic volatility.

To better understand the relation between high retail trading levels and lowstock price levels and their effect on idiosyncratic volatility patterns amonglow-priced stocks, we introduce two interaction terms in the regression spec-ification. We find that when the stock price and RTP are low, there is noincremental influence of stock price level on idiosyncratic volatility levels.The Low Stock Price × Low RTP interaction term has an insignificant co-efficient estimate (coefficient estimate = −0.001, t-statistic = −0.60). Onlywhen the retail trading levels are high do stocks with low prices have higherlevels of idiosyncratic volatility. The Low Stock Price × High RTP interac-tion term has a significant coefficient estimate (coefficient estimate = 0.037,t-statistic = 3.34). In untabulated results, we find that even for high-pricedstocks, stocks with high RTP have moderately higher levels of idiosyncraticvolatility (coefficient estimate = 0.016, t-statistic = 3.25).

14 We do not have retail-trading data for the 1920s, and even for the recent episode, the retail-trading proxy fromISSM/TAQ is available only from 1983 to 2000. The ISSM/TAQ data are available beyond 2000, but, as discussedin Section 1.1, it is problematic to use small trades to proxy for retail trading beyond 2000. See Hvidkjaer (2008)and Barber, Odean, and Zhu (2009) for additional details.

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Overall, the estimates from extended regression specifications indicate thatthe idiosyncratic volatility patterns are significantly stronger for stocks withhigh retail trading. In particular, the RTP–price interaction coefficient estimatesindicate that RTP influences idiosyncratic volatility levels in the extremes.15

Even after controlling for RTP, price remains a strong predictor of idiosyncraticvolatility, perhaps because RTP is an imperfect measure of retail trading.

3.3 Retail trading and low-priced stocksIn our next set of tests, we attempt to establish a more direct link between lowstock prices and speculative trading by retail investors. We start by examiningthe holdings and trades of both retail and institutional investors. We analyze datafrom three different sources. We consider the quarterly institutional holdingsdata from 1980 to 2007, the discount brokerage data from 1991 to 1996, andthe small-trades data from ISSM/TAQ from 1983 to 2000.

We perform one-dimensional price sorts and examine whether average in-stitutional holdings are lower among low-priced stocks. In panel A of Table 4,we summarize by decade the average level of institutional ownership for firmswith different price levels. The table reports the mean fraction of shares ownedby institutions, as identified by 13(f) filings. For each price category, we alsoreport the fraction of firms with less than 10% institutional ownership (“Low”institutional ownership column).

Two patterns emerge. First, over time, consistent with the evidence in Gom-pers and Metrick (2001) and Bennett, Sias, and Starks (2003), there is a strongtrend toward greater institutional ownership. More interesting from our per-spective, we find that in each of the three decades, the level of institutionalownership is considerably lower for low-priced stocks (price deciles 1–3) thanfor high-priced stocks (price deciles 8–10). Toward the beginning of the institu-tional sample, about 83% of low-priced firms have less than 10% institutionalownership (as shown in the “Low” column) and the average ownership levelis only 5.25%. Even during more recent years, about 44% of low-priced firmshave less than 10% institutional ownership and the average ownership level is21.44%. In contrast, the average level of institutional ownership of high-pricedstocks is 56.44% and only about 8% of those stocks have institutional own-ership below 10%. These results indicate that the ownership of low- (high-)priced stocks is relatively dominated by retail (institutional) investors.

We next examine retail trades using the small-trades data from ISSM/TAQ.We find that the RTP is stronger among stocks that have low market capitaliza-tions, low prices, low institutional ownerships, and high idiosyncratic volatility(see panel B of Table 4). Specifically, stocks with retail trading proportion in thetop three deciles typically have stock price below $10, institutional ownership

15 We also estimated a “change” regression, where change in idiosyncratic volatility is the dependent variable andchange in RTP and stock price level are the main independent variables. We find a strong positive relation betweenchange in idiosyncratic volatility and change in RTP (estimate = 0.140, t-statistic = 11.85). In addition, we find astrong negative relation between idiosyncratic volatility and stock price (estimate = −0.341, t-statistic = −8.32).

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Table 4Retail ownership, institutional ownership, and stock characteristics

Panel A: Institutional ownership

All stocks Low price Medium price High price

Time period Avg Low Avg Low Avg Low Avg Low

1981–1990 18.07 45.57 5.25 83.05 14.16 49.48 29.15 20.611991–2000 26.40 34.44 11.05 62.23 23.33 33.71 42.78 11.372001–2008 38.45 26.55 21.44 44.39 35.43 30.55 56.44 8.13

Panel B: Retail trading and stock characteristics (TAQ Sample)

RTP decile IVOL (%) Size Price Insti Own Turnover B/M

Low (D1) 11.66 $3145.18 m $46.19 50.78% 132.28% 0.592D2 12.03 $1564.64 m $27.16 44.56% 107.90% 0.639D3 13.07 $956.30 m $23.20 38.65% 100.28% 0.675D4 13.89 $545.84 m $19.67 32.79% 91.22% 0.719D5 15.12 $298.95 m $16.83 27.74% 83.78% 0.739D6 16.47 $173.64 m $13.98 23.15% 74.85% 0.765D7 18.54 $103.01 m $11.20 18.93% 67.05% 0.785D8 22.20 $57.76 m $8.28 14.83% 60.73% 0.783D9 28.50 $32.34 m $5.44 10.92% 54.34% 0.729High (D10) 41.50 $13.59 m $2.97 3.01% 42.24% 0.871

Panel C: Size, price, and retail ownership (brokerage sample)

Firm size

Price All Small Q2 Q3 Q4 Large

All 9.62 8.82 6.19 5.58 −30.21Low 14.20 8.20 4.59 1.32 0.17 −0.08Q2 5.13 0.85 2.39 1.56 0.53 −0.20Q3 2.67 0.48 0.98 1.49 0.58 −0.86Q4 0.24 0.10 0.67 1.24 1.09 −2.85High −22.24 −0.00 0.19 0.57 3.22 −26.22

This table reports several stock preference measures for both institutional investors and retail investors. For eachdecade (approximately), panel A shows the mean fraction of shares held by institutions (the “Avg” column) andthe fraction of firms with less than 10% institutional ownership (the “Low” column). The stock price (low ordeciles 1–3, medium or deciles 4–7, and high or deciles 8–10) is used as the conditioning variable. In panel B, wereport the mean characteristics (idiosyncratic volatility measured using the CLMX methodology, firm size, stockprice, institutional ownership, market volume turnover, and the book-to-market ratio) of stocks, conditional onthe degree of retail trading. The retail trading proportion (RTP) is defined as the ratio of the total volume of buy-and sell-initiated small trades to total market trading volume. In panel C, we report the mean percentage over(under) weight in retail ownership for firms sorted on firm size and price. To construct this panel, we compute a“benchmark” percentage ownership based on the total market capitalization of stocks that fall into each quintileportfolio at the end of each month. We then compute an “actual” percentage retail ownership based on the totalmarket capitalization of stocks actually owned by the retail investors in our sample. Panel values represent thedifference between these two percentages, averaged across all months in our sample period. In panel A, the 13(f)institutional holdings data for the January 1980 to September 2008 period are from Thomson Reuters. In panelB, we use the ISSM/TAQ small trades data for the 1983–2000 time period, where small-sized trades are used asproxy for retail trades. The retail investor data used in panel C are from a large U.S. discount brokerage housefor the period 1991–1996.

below 10%, and market capitalization under $100 million. The ISSM/TAQ ev-idence indicates that retail investors dominate the trading in low-priced stocks.

A similar profile of retail investors emerges when we directly examine thestock holdings and trading patterns of retail investors. Specifically, we considerthe aggregate portfolio holdings of retail investors at a large U.S. discountbrokerage house and examine the under- and overweighting of stocks (relative

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to their weights in the aggregate market portfolio) with certain characteristics.The results indicate that retail investors overweight low-priced stocks by morethan 14% and underweight high-priced stocks by more than 22% (see Table 4,panel C). They also overweight smaller stocks (by 9.62%), but the degree ofoverweighting is less than their excess weight in lower-priced stocks.16

To examine retail investors’ trading behavior in a multivariate setting, we esti-mate monthly Fama-MacBeth-type cross-sectional regressions, where a stock’sRTP in a given month is the dependent variable. A variety of stock character-istics, including stock price, volatility, skewness, institutional ownership, andchange in institutional ownership, are included as independent variables. Allindependent variables are measured at the end of the previous month. Theresults are reported in Table 5 (columns 1–3).17

We find that retail investors are more dominant (RTP is higher) amonglower-priced stocks, and higher idiosyncratic volatility stocks, even when wecontrol for other known determinants of retail trading, including firm size.Furthermore, RTP is higher among stocks with higher skewness and the lowprice–high skewness interaction dummy has a positive coefficient estimate. Asexpected, we also find that retail trading is lower among stocks with higherinstitutional ownership.

Taken together, the RTP cross-sectional regression results indicate that retailinvestors hold a greater proportion of low-priced stocks and trade these stocksactively. If retail (institutional) investors have a strong preference (aversion)for low-priced stocks, it seems plausible that the strong idiosyncratic volatilitypatterns in low-priced stocks could be attributed to the trading activities ofretail investors.

3.4 Shifts in ownership, trading, and idiosyncratic volatilityIn our third set of empirical tests, we directly examine the link between the retailtrading intensity, institutional ownership changes, and idiosyncratic volatilitylevels.

Measuring institutional ownership as the fraction of shares held by institu-tions, Xu and Malkiel (2003) show that in regressions of firm-level idiosyncraticvolatility on the level of institutional ownership and firm size, institutional own-ership enters with a statistically significant positive sign. Similarly, Bennett,Sias, and Starks (2003) show that change in percentage institutional holdingsduring a given quarter is positively related to the level of idiosyncratic volatilityin the following quarter, even after controlling for the effects of other stockcharacteristics, including the level of idiosyncratic volatility in the current

16 These univariate sorting results are also reported in Kumar and Lee (2006). We report these results to provide abenchmark and to motivate our subsequent analysis.

17 Like before, we standardize both the dependent and the independent variables so that the coefficient estimatescan be directly compared within specifications and across specifications. The standard errors are corrected forpotential higher-order serial correlation using the Pontiff (1996) method.

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Table 5Determinants of retail trading: Cross-sectional regression estimates

Dependent variable: RTP of stock i in month t .

(1) (2) (3) (4)Independent variable 83-00 83-00 83-00 91-96

Intercept 0.047 0.037 0.058 0.040(4.26) (2.75) (3.49) (3.22)

Log(Stock Price) −0.209 −0.196 −0.255(−6.59) (−6.70) (−6.40)

Log(Firm Size) −0.084 −0.067 −0.101(−4.60) (−3.49) (−4.91)

Log(Idiosyncratic Volatility) 0.092 0.072 0.202(4.81) (4.75) (3.55)

Idiosyncratic Skewness 0.073 0.062 0.051(2.91) (3.57) (3.11)

Low Price × High Skew 0.037 0.031 0.022(3.48) (2.75) (1.88)

Past 12-Month Stock Return −0.025 0.019 0.012(−1.23) (2.24) (1.44)

Log(Volume Turnover) −0.037 −0.017 −0.044(−4.16) (−2.79) (−3.38)

Market Beta 0.008 −0.001 0.009(2.23) (−0.30) (1.09)

Firm Age −0.066 −0.028 −0.057(−3.33) (−1.52) (−2.44)

Book-To-Market Ratio 0.032 0.028 0.033(1.68) (1.52) (2.02)

Log(1 + Institutional Ownership) −0.161 −0.056 −0.059(−5.86) (−4.87) (−3.77)

�Institutional Ownership 0.002 −0.001 −0.004(1.36) (−0.10) (−0.22)

Lagged RTP 0.651(6.60)

Overconfidence Proxy 0.082(5.43)

(Average) Adjusted R2 0.103 0.063 0.332 0.214(Average) Number of Stocks 3,464 2,655 2,655 4,760

This table reports the Fama-MacBeth-type cross-sectional regression estimates to explain the proportion of retailtrading in a stock in a given time period. The dependent variable in all specifications is the retail trading proportion(RTP) for a given stock i in month t . The independent variables include the following stock characteristics: stockprice, firm size, idiosyncratic volatility measured using the CLMX methodology, idiosyncratic skewness (theskewness of the residual from a time-series regression with excess market returns and squared excess marketreturns as the explanatory variables), past 12-month stock return, volume turnover (the ratio of the number ofshares traded and the number of shares outstanding), market beta, book-to-market ratio, level of institutionalownership, quarterly change in institutional ownership, and an overconfidence proxy, which is defined as the252-day post-trade sell-buy return differential (PTSBD). All independent variables are measured at the end ofmonth t − 1. The institutional ownership data are quarterly and, thus, ownership data from the most recent quarterare used in month t . Stocks with fewer than five buy and sell trades are not included in the analysis. The Pontiff(1996) method is used to correct the Fama-MacBeth standard errors for potential higher-order serial correlation.The t-values, obtained using corrected standard errors, are reported in parentheses below the estimates. To ensurethat extreme values are not affecting the results, we winsorize all variables at their 0.5 and 99.5 percentile levels.To allow for direct comparison among the coefficient estimates within and across specifications, all variables havebeen standardized so that each variable has a mean of zero and a standard deviation of one. The sample periodvaries across the columns and is reported below the column label. The retail trading data for the 1983–2000period are from ISSM/TAQ, where small-sized trades are used as a proxy for retail trades. The 13(f) institutionalholdings data are from Thomson Reuters.

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quarter. Taken together, these two pieces of evidence seem to suggest thathigher institutional ownership is associated with higher idiosyncratic volatility.

At first glance, the evidence from Bennett, Sias, and Starks (2003) and Xuand Malkiel (2003) seems to contradict our claim that low-priced stocks, whichare generally not held by institutions, are associated with episodic increases inidiosyncratic volatility. To better understand how our results relate to these twoarticles, we follow the estimation methodology and the regression specificationsin Bennett, Sias, and Starks (2003) and Xu and Malkiel (2003), and estimateFama-MacBeth cross-sectional regressions. The dependent variable in theseregressions is the logarithm of idiosyncratic volatility in quarter t , and theset of independent variables are those defined in Table 3. The estimation iscarried out for the full sample and also separately for firms with high (top threedeciles) and low (bottom three deciles) share prices. As before, we use NYSEbreakpoints to define low- and high-priced stock categories. All variables arestandardized and the standard errors are corrected for potential higher-orderserial correlation using the Pontiff (1996) method.

The results are presented in Table 6, where, for brevity, we present theestimates for only the main variables. In column 1, where we consider allfirms, the institutional ownership variable has a positive estimate. This estimatebecomes stronger when we reestimate the model for only the high-priced stocks(see column 2). These estimates are consistent with Xu and Malkiel’s (2003)findings, and confirm that, for high-priced stocks, a higher level of institutionalownership is associated with higher idiosyncratic volatility.

Similarly, for the full sample (column 4) and for the high-priced stocks sam-ple (column 5), the results from quarterly Fama-MacBeth regressions indicatethat change in institutional ownership during a certain quarter is positively as-sociated with the level of idiosyncratic volatility in the following quarter.18 Forthe full sample and high-priced stocks subsample, the coefficient estimates forthe “change in institutional ownership” variable are 0.022 (t-statistic = 4.86)and 0.042 (t-statistic = 4.28), respectively. This evidence is consistent with thefindings in Bennett, Sias, and Starks (2003) and confirms that, for high-pricedstocks, an increase in institutional ownership is associated with higher futureidiosyncratic volatility.

When we focus on the subsample of low-priced stocks (columns 3 and 6),the results are strikingly different in one key dimension. The sign of the slopecoefficients on institutional ownership and change in institutional ownershipare flipped. The negative and statistically significant coefficient estimates in-dicate that for the universe of low-priced stocks, a lower level of institutionalownership and a smaller change in institutional ownership are associated withhigher idiosyncratic volatility.

18 To benchmark against the evidence in Bennett, Sias, and Starks (2003), we also perform an analysis using anestimation period (June 1983 to December 1997) identical to the one they used in their study. Our coefficientestimate on “change in percentage institutional ownership” is 0.0107 (t-statistic = 4.27), which is similar to theestimate of 0.0102 with a t-statistic of 5.27 in BSS (see Table 7, p. 1227).

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Table 6Determinants of idiosyncratic volatility in price-based subsamples: Fama-MacBeth cross-sectional regression estimates

Dependent variable: Log(Idiosyncratic Volatility) for stock i in quarter t

XM model BSS model Combined model

(1) (2) (3) (4) (5) (6) (7) (8) (9)Independent variable All High Low All High Low All High Low

Log(1+InstiOwn) 0.004 0.015 −0.014 0.008 0.024 −0.018(1.82) (3.66) (−3.58) (2.07) (0.86) (−4.74)

�InstiOwn 0.022 0.042 −0.017 0.009 0.021 −0.023(4.86) (4.28) (−2.58) (3.49) (4.07) (−3.97)

Retail Trading Prop 0.039 0.042 0.051(4.07) (3.53) (4.55)

Log(Stock Price) −0.191 −0.067 −0.186 −0.176 −0.066 −0.172 −0.197 −0.056 −0.269(−7.59) (−5.59) (−7.14) (−6.74) (−7.23) (−6.09) (−9.31) (−5.10) (−9.88)

Log(Firm Size) −0.052 −0.083 −0.019 −0.051 −0.094 −0.021 −0.057 −0.083 −0.034(−6.32) (−7.07) (−3.20) (−6.32) (−6.21) (−3.58) (−5.28) (−5.04) (−3.74)

(Other Estimates Suppressed)Frequency Qtr Qtr Qtr Qtr Qtr Qtr Qtr Qtr QtrAverage Adjusted R2 0.734 0.553 0.581 0.739 0.572 0.594 0.768 0.607 0.645Average Number of Stocks 4,857 2,671 2,186 4,857 2,671 2,186 4,857 2,671 2,186

The table provides Fama-MacBeth-type point estimates and t-statistics from cross-sectional regressions for price-based subsamples. The sample period is from 1983 to 2000. Thedependent variable is the logarithm of annualized idiosyncratic volatility constructed using the CLMX methodology. The independent variables, measured at the end of the previous timeperiod, include: stock price, firm size, lagged idiosyncratic volatility, market beta, standard deviation of returns, past 12-month stock returns, the level of institutional ownership for themost recent quarter, quarterly change in institutional ownership for the most recent quarter, retail trading proportion (total retail trading volume divided by the market volume), firm age(the number of years since the firm first appears in the CRSP database), volume turnover, and dividend yield. The sample period is from January 1983 to December 2000. The full sampleis used in columns 1, 4, and 7; the high-priced subsample is used in columns 2, 5, and 8; low-priced subsample is used in columns 3, 6, and 9. We use the NYSE price breakpoints to formthe high and low price categories. The Pontiff (1996) method is used to correct the Fama-MacBeth standard errors for potential serial correlation in the coefficient estimates. The t-values,obtained using corrected standard errors, are reported in parentheses below the estimates. To ensure that extreme values are not affecting the results, we winsorize all variables at their 0.5and 99.5 percentile levels. To allow for direct comparisons among the coefficient estimates, the independent variables have been standardized so that each variable has a mean of zero anda standard deviation of one. The average number of observations and the average adjusted R2 are also reported. The retail trading data for the 1983–2000 period are from ISSM/TAQ,where small-sized trades are used as a proxy for retail trades. The 13(f) institutional holdings data are from Thomson Reuters.

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inancial Studies / v 23 n 2 2010



Last, to examine the relative roles of retail and institutional investors ingenerating the idiosyncratic volatility patterns, we estimate the Fama-MacBethcross-sectional regressions with a retail trading measure (i.e., RTP) and the twoinstitutional measures. These estimates for the full sample, high-priced stockssubsample and low-priced stocks subsample are reported in Table 6, columns7–9, respectively. We find that RTP has a strong positive coefficient estimate inthe low-priced stocks sample (column 9). In contrast, the two institutional own-ership measures continue to have significantly negative coefficient estimates.We also find that the coefficient estimates for institutional ownership and retailtrading are very similar when we consider a slightly different specificationshown in column 6 of Table 3.

Given that the low-priced and high-priced samples yield opposite results, theremaining question is, which results matter more for explaining the episodicspikes in idiosyncratic volatility. We believe that the low-priced stocks sub-sample, where we demonstrated a positive (negative) relation between retail(institutional) ownership and idiosyncratic volatility, is more relevant for under-standing idiosyncratic volatility. This regression is more relevant in our opinionbecause we have already shown that episodic increases in idiosyncratic volatil-ity are concentrated in low-priced stocks (see, for example, Table 2). The factthat high levels of institutional ownership and a greater increase in institutionalownership are associated with higher idiosyncratic volatility in high-pricedstocks is certainly interesting. However, we believe that this evidence is notdirectly relevant to the episodic idiosyncratic volatility pattern in hand.

3.5 Granger causality testsOur evidence thus far demonstrates that retail trading and idiosyncratic volatil-ity levels are positively related, but the direction of causality is unclear. We nowexamine the lead–lag relation between retail trading and idiosyncratic volatilityusing a bivariate vector autoregression (VAR) framework.

Table 7 presents the VAR estimates (panels A and B) and Granger causalityprobabilities (panel C). We consider both value-weighted and equal-weightedtime series of average idiosyncratic volatility and retail trading. We find thatboth RTP and idiosyncratic volatility (IVOL) series are very persistent. Forexample, when we examine the value-weighted series, the lagged RTP andlagged IVOL have coefficient estimates of 0.741 (t-statistic = 13.54) and 0.555(t-statistic = 10.47), respectively. More importantly, we find that lagged RTPcan predict the current levels of IVOL, while lagged IVOL is a weak (andstatistically insignificant) predictor of current RTP. The results obtained usingequal-weighted and value-weighted series are qualitatively similar. Overall, wedo not find evidence that idiosyncratic volatility “causes” retail trading.

3.6 Stock splits and attention-grabbing eventsOur next piece of evidence linking retail trading and idiosyncratic volatil-ity comes from analyzing changes in retail trading behavior, changes in

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Table 7Vector autoregression estimation and Granger causality tests

Panel A: Vector autoregressive model estimates (value-weighted)

Dependent variable Constant RTPt−1 IVOLt−1 Adj. R2

RTPt 0.245 0.741 0.096(0.39) (13.54) (1.14) 0.606

IVOLt 2.832 0.230 0.555(7.26) (6.68) (10.47) 0.646

Panel B: Vector autoregressive model estimates (equal-weighted)

RTPt 0.291 0.768 0.032(0.34) (16.65) (0.73) 0.605

IVOLt 2.023 0.093 0.887(3.02) (2.59) (16.02) 0.797

Panel C: Granger causality probabilities

Value-weighted Equal-weighted

Variable RTP IVOL RTP IVOL

RTP 0.000 0.255 0.000 0.465IVOL 0.000 0.000 0.010 0.000

This table reports the vector autoregression estimates and Granger causality test probabilities for thefollowing vector autoregressive model of order 1 (VAR(1)):

(RTPt

IVOLt

)=

(b10

b20

)+

(b11 b12

b21 b22

) (RTPt−1

IVOLt−1

)+

(ε1t

ε2t

),

where RTPt is the average retail trading proportion in month t and I V O Lt is the aggregate idiosyncraticvolatility in month t . The retail trading proportion is defined as the ratio of the total retail trading volume(measured in dollar terms) and the total market trading volume. Idiosyncratic volatility is measured usingdaily returns following the CLMX volatility decomposition methodology. In panels A and B, the VARestimates for value-weighted and equal-weighted series, respectively, are reported and the t-statisticsfor the coefficient estimates are shown in parentheses below the estimates. In panel C, the probabilitymatrices from Granger causality tests are shown, where a matrix element represents the impact of columnvariable on the row variable. The retail trading data for the 1983–2000 period are from ISSM/TAQ, wheresmall-sized trades are used as a proxy for retail trades.

institutional holdings, and changes in idiosyncratic volatility around certainsalient events. This investigation is motivated by the belief that event studiesallow us to better capture the relation between retail trading and idiosyn-cratic volatility. We consider two types of events: (i) regular stock splits; and(ii) attention-grabbing extreme return and turnover events. We analyze theevents in two ways that are related to our conjecture. First, we determinewhether a firm’s idiosyncratic volatility changes around salient events are re-lated to changes in retail trading activities. Second, we investigate whethertrading activities around these events change in a way that indicates a retailpreference for low-priced stocks.

To examine the relation between price changes and volatility changes aroundstock splits, we estimate a regression model. For each split event, we calculatethe difference between average annualized idiosyncratic volatility in the sixmonths subsequent to the month of the split (post-event window) and averageannualized idiosyncratic volatility over the six months prior to the month of

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the split (pre-event window). To control for the observed trend in the aggre-gate idiosyncratic volatility time series, we subtract the aggregate change inidiosyncratic volatility from the actual change in idiosyncratic volatility aroundthe split event. We use this aggregate-trend-adjusted change in idiosyncraticvolatility as the main dependent variable. The key explanatory variables arechange in the average stock price around the split event, the split factor, changein retail trading proportion around the event, change in institutional ownershiparound the event, and an interaction dummy that is set to one for stocks witha large (top third) change in RTP and a large (top third in absolute value)price drop. The retail trading proportion measure is computed using both theISSM/TAQ and the brokerage samples.

We also include the following control variables in the regression specifica-tion: past 12-month stock return, a dividend-paying dummy, the book-to-marketratio, volume turnover measured in the pre-event window to account for liq-uidity, and firm size in the month prior to the event to control for varioussize-related effects. The past return variable serves as a control for the knowneffects of past returns on the trading behavior of retail investors (Barber andOdean 2008). For instance, investors’ trading activities might be influenced bytheir contrarian tendencies, trend-following behavior, or because they exhibitthe disposition effect (Shefrin and Statman 1984; Odean 1998a).19 We includea dividend-paying dummy and the book-to-market ratio as additional controlvariables to ensure that the results do not simply reflect the known relation be-tween future growth opportunities and idiosyncratic volatility (Xu and Malkiel2003; Cao, Simin, and Zhao 2008).

We estimate different specifications of the model and consider differentsample periods, depending upon the availability of data. During the full sampleperiod (1926–2007), there are a total of 16,741 regular stock split events (CRSPdistribution code = 5523). During the 1983–2000 and 1991–1996 periods, thereare 9,737 and 2,925 split events, respectively.

The regression results for stock splits are presented in Table 8, panel A. In thefirst specification, we examine splits during the full sample period (1926–2007)and consider only the price change around the split event and split factor asindependent variables. We find that idiosyncratic volatility increases as stockprice falls and we observe the same pattern when we consider splits during the1983–2000 time period (see column 2). These results are consistent with ourearlier findings, which indicate that low prices are associated with higher levelsof idiosyncratic volatility. Because retail trading intensity is higher amonglow-priced stocks, this evidence also implies that higher levels of idiosyncraticvolatility are associated with higher levels of retail trading.

19 We also experiment with a direct measure of the disposition effect obtained following the Odean (1998) methodand using retail trades around the event date. When we include this direct disposition effect variable in thesplit regression specification as an additional control variable, in all instances the disposition effect has a mildlypositive but insignificant coefficient estimate.

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Table 8Idiosyncratic volatility and retail trading around stock splits and attention-grabbing events

Dependent variable is

(1):�IV (2):�IV (3):�IV (4):�IV (5):�RTP1 (6):�RTP2 (7):�IOIndependent variable 26-07 83-00 83-00 91-96 83-00 91-96 83-00

Panel A: Regular stock splitsConstant 0.002 0.003 0.041 −0.001 0.025 0.001 −0.011

(0.27) (0.27) (3.24) (−0.03) (1.87) (0.05) (−1.11)Main determinants�Price −0.110 −0.146 −0.129 −0.185 −0.403 −0.113 0.296

(−10.90) (−11.74) (−9.53) (−6.28) (−9.37) (−3.74) (11.94)Split Factor 0.043 0.061 0.055 0.106 0.073 0.035 0.018

(4.01 (4.48) (3.41) (3.62) (4.86) (1.67) (1.37)�RTP 0.049 0.047

(4.50) (2.61)Large �RTP × 0.061 0.111Large Price Drop (6.25) (5.77)�InstiOwn −0.067 −0.075 −0.022 −0.013

(−3.86) (−3.83) (−1.94) (−0.66)Other determinantsPast 12-Month Return −0.166 −0.144 0.090 0.016 0.075

(−8.42) (−7.21) (8.11) (1.87) (6.44)Volume Turnover −0.031 −0.053 0.091 0.145 −0.156

(−2.24) (−2.44) (6.61) (5.72) (−12.76)Firm Size −0.037 −0.084 −0.064 −0.051 −0.049

(−3.17) (−4.26) (−5.43) (−3.24) (−4.52)Dividend Paying Dummy −0.023 −0.061 −0.085 −0.036 −0.053

(−2.01) (−3.05) (−7.22) (−1.49) (−4.88)Book-To-Market Ratio 0.018 0.011 0.003 0.004 0.013

(1.17) (0.87) (0.19) (1.13) (0.90)Adjusted R2 0.020 0.034 0.094 0.113 0.156 0.059 0.124Number of Events 15,552 9,681 9,562 1,841 9,562 1,841 9,384

(continued overleaf )

Next, we examine the link between retail trading and idiosyncratic volatilitydirectly using an extended split regression specification. We introduce two retailtrading measures in the specification: (i) change in the RTP measure; and (ii) aninteraction term defined using RTP. We also include the change in institutionalownership and other control variables. In column 3 of Table 8, we measure RTPusing the ISSM/TAQ data, while in column 4, RTP is obtained using investors’trades in the brokerage data.

We find that the coefficient estimates of price change and split factor vari-ables in the extended specification are only slightly different from those in thefirst specification. More importantly, we find that both retail trading measuresare positively associated with the change in idiosyncratic volatility, while thechange in institutional ownership variable has a negative coefficient estimate.The coefficient estimates are very similar (and somewhat stronger) when weuse the brokerage data to measure changes in the degree of retail trading andconsider a shorter sample period from 1991 to 1996.20

20 The results are similar when we use buy-sell imbalance (BSI) measures of retail trading using dollar value oftrades or number of trades instead of the RTP measure. The dollar volume-based BSI for a given stock in aparticular month is defined as the ratio of the excess buy volume (total buy volume − total sell volume) to the

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Table 8(Continued)

Panel B: Extreme return and turnover events

Dependent variable: � (idiosyncratic volatility) around the event

Event type is

Independent variable (1):RetPos (2):RetPos (3):RetNeg (4):RetNeg (5):Turn (6):Turn

Constant −0.002 0.018 0.007 0.079 −0.010 0.027(−0.17) (1.69) (0.41) (3.33) (−0.04) (3.80)

Main determinants�Price −0.136 −0.145 −0.210 −0.192 −0.199 −0.187

(−14.40) (−9.60) (−11.82) (−8.99) (−29.26) (−22.21)Event Strength −0.020 −0.008 0.020 0.041 −0.003 −0.001

(−2.05) (−0.63) (1.08) (2.07) (−0.44) (−0.16)�RTP 0.029 0.063 −0.008

(3.19) (3.73) (−1.19)Large �RTP × −0.112 0.115 0.118Large Price Drop (−11.53) (6.03) (16.71)�InstiOwn −0.004 0.027 0.001

(−0.39) (1.69) (0.01)Other determinantsPast 12-Month Return −0.014 −0.099 −0.056

(−0.92) (−2.50) (−6.12)Volume Turnover −0.079 −0.071 −0.103

(−6.68) (−3.30) (−3.02)Firm Size 0.009 0.036 −0.015

(0.64) (1.67) (−1.80)Dividend Pay Dummy −0.089 0.011 −0.084

(−8.27) (0.51) (−9.22)Book-To-Market Ratio −0.006 −0.026 0.030

(−0.39) (−0.99) (0.21)Adjusted R2 0.019 0.057 0.047 0.082 0.040 0.084Number of Events 10,774 9,346 2,908 2,553 20,396 18,151

This table reports the regression estimates for stock splits (panel A) and other “attention-grabbing” events (panelB). Attention-grabbing events are defined as the extreme (at least three standard deviations above the mean)positive return events (RetPos), extreme negative (at least 1.5 standard deviations below the mean) return events(RetNeg), and extreme (at least three standard deviations above the mean) turnover events (Turn). In panel A, incolumns 1–4, the dependent variable is the change in idiosyncratic volatility around the split event, where boththe pre-split and post-split periods are six months long. In specifications (4) and (5), the dependent variable isthe change in retail trading proportion around the split event, measured using ISSM/TAQ and brokerage data,respectively. In specification (6), the dependent variable is the change in institutional ownership around the splitevent. The sample period varies across the columns and is reported below the column label. In panel B, thedependent variable is the change in idiosyncratic volatility around attention-grabbing events in all specifications.The sample period is from 1983 to 2000. In columns 1 and 2, we consider extreme positive return events; incolumns 3 and 4, we consider extreme negative return events; and in columns 5 and 6, we consider extremeturnover events. The independent variables are: (i) change in average stock price between pre-split and post-splitperiods; (ii) split factor, which measures the split intensity; and (iii) change in average retail trading proportion(RTP) between pre-split and post-split periods, measured using either small trades data from ISSM/TAQ or actualretail trades from a large U.S. brokerage house. The retail trading proportion is defined as the ratio of the totalretail trading volume (measured in dollar terms) and the total market trading volume. For the ISSM/TAQ sample,retail trades are proxied using small trades. For regular stock splits, positive return events, and high turnoverevents, the Large �RTP × Large Price Drop is the interaction dummy that is set to one for stocks with high�RTP (top third) and large price drop (bottom third). We use the past 12-month return to control for the effectsof past returns on retail trading, including the disposition effect. Other independent variables include the meanvolume turnover measured in the pre-event window, firm age, a dividend-paying dummy that is set to one if thestock pays a dividend in the past one year, and the book-to-market ratio. The ISSM/TAQ data are available forthe 1983–2000 time period and the brokerage data are available for the 1991–1996 time period. Robust standarderrors are used to compute the t-statistics. The t-values, obtained using corrected standard errors, are reported inparentheses below the estimates. The retail trading data for the 1983–2000 period are from ISSM/TAQ, wheresmall-sized trades are used as a proxy for retail trades. The 13(f) institutional holdings data are from ThomsonReuters.

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The control variables have the expected signs. For example, the change inidiosyncratic volatility is higher for stocks that have performed poorly in thepast, are smaller in size, have lower liquidity, and do not pay dividends. Thenegative coefficient estimate for the dividend-paying dummy is consistent withthe results in Xu and Malkiel (2003), who show that idiosyncratic volatility ispositively associated with future growth opportunities. Overall, the evidencefrom split regressions indicates that the split-induced price decline coupled withan increased degree of retail trading and reduction in institutional ownership isassociated with higher idiosyncratic volatility levels following stock splits.

Among the independent variables, the price change variable has the strongestcoefficient estimate. To examine whether the large coefficient estimate on pricechange variable is related to changes in RTP or changes in institutional owner-ship, we estimate three additional regressions in columns 5, 6, and 7. In theseregressions, the dependent variable is the change in RTP or change in insti-tutional ownership around the event. We find that price change has a strongnegative coefficient estimate in the change in RTP regressions (columns 5 and6), which indicates that retail trading intensity increases following split-inducedprice drops. In contrast, institutional ownership decreases following stock splits(column 7).

We next investigate whether the relation between retail trading and idiosyn-cratic volatility generalizes to corporate events other than stock splits. Thisanalysis is motivated by the findings in Lee (1992) and Barber and Odean(2008), who show that, irrespective of news content, retail trading intensityincreases around attention-grabbing events.21 Specifically, we follow Barberand Odean (2008) and identify return- and turnover-based events that are likelyto catch the attention of retail investors. We define attention-grabbing events asdays on which the return is either at least three standard deviations higher or 1.5standard deviations lower than the mean daily return of the stock.22 In addition,we identify days with daily turnover greater than three standard deviations fromthe mean turnover level. The regression estimates for these events defined overthe 1983–2000 period are presented in Table 8, panel B.

The estimates for positive and negative return- and turnover-based events areremarkably similar to the split events. In all three instances, there is an increasein idiosyncratic volatility when stock price drops, along with an increase inretail trading that is associated with an increase in idiosyncratic volatility. Asexpected, the effects are stronger for events that are associated with larger

total trading volume. Number of trade-based BSI is defined in a similar manner. For example, in specification(3) of Table 8, when we use �BSI as an independent variable instead of �RTP, it has a coefficient estimate of0.046 (t-statistic = 3.86). This evidence indicates that an increase in retail trading activities around stock splitsis associated with higher levels of buying.

21 Also, see Graham and Kumar (2006). Consistent with the attention hypothesis, they show that older and low-income investors purchase stocks that recently announced dividends.

22 We use different cutoffs for defining positive and negative return events to get a sufficient number of positive aswell as negative events. Our results are robust to different cutoffs used to define positive and negative events.

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changes in RTP and stock price. The interaction term has a large absolutecoefficient estimate in all three cases.

Collectively, the evidence from these event studies provides a link betweenretail trading and idiosyncratic volatility. The split regressions indicate thatwhen a stock splits and its price falls, its idiosyncratic volatility typicallyincreases. Furthermore, we find that an increase in retail trading is associatedwith greater volatility around split events. These results are similar to thecross-sectional regression estimates for low-priced stocks in Table 6 and areconsistent with the conjecture that retail trading is related to volatility in returns.

3.7 Investor overconfidence and idiosyncratic volatilityOur analysis so far is consistent with attention and trading by retail investorsbeing related to idiosyncratic volatility in returns. In our last test, we consideran additional channel through which retail trading could influence idiosyncraticvolatility, namely, investor overconfidence. Gervais and Odean (2001) arguethat due to biased self-attribution, investors might become more overconfi-dent when markets rise. Moreover, Odean (1998b) shows that overconfidentinvestors can induce greater idiosyncratic volatility in stock returns. Thus,the increasing idiosyncratic volatility in rising markets might reflect investoroverconfidence.

The positive relation between monthly volume turnover and idiosyncraticvolatility shown earlier (see Table 3, column 6) is consistent with the over-confidence hypothesis. To more directly examine the potential link betweenoverconfidence and idiosyncratic volatility, we use the brokerage sample todefine a proxy for investor overconfidence. The proxy we use is based on theassumption that overconfident investors make larger investment mistakes. In-vestors might be overconfident about the quality of their private information orthey could overestimate their ability to process private information. In eithercase, an overconfident investor is likely to make systematic errors when sheformulates her trading decisions. Consequently, the stocks she sells are likelyto systematically outperform the stocks she purchases by a significant margin.

With this motivation, and following Odean (1999), we use the k-day post-trade sell-buy return differential (PTSBD) as a proxy for investor overconfi-dence. We use the trades of all sample investors in stock i in month t to computethe PTBSD of the stock in month t . A large positive value of PTSBD for a stockindicates that investors holding the stock systematically make mistakes, wherethey either systematically misinterpret their private information or overestimatetheir abilities. In contrast, if an investor does not exhibit overconfidence andsimply trades in a random fashion, the stocks she sells will perform similarly tothe stocks she purchases. Consequently, the PTSBD would be close to zero.23

We estimate a regression model, in which the month-t stock-level RTP isthe dependent variable and the monthly stock-level overconfidence proxy along

23 See Odean (1999) for further details.

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with other determinants of RTP identified earlier serve as independent variables.All independent variables are measured in month t − 1. The estimation resultsare presented as column 4 in Table 5. We find that RTP is positively associatedwith the overconfidence proxy (coefficient estimate = 0.082, t-stat = 5.43),even after accounting for the known determinants of RTP. Thus, RTP levelsare higher among stocks where investors make ex post worse trading deci-sions, perhaps due to their overconfidence. This evidence is consistent withRTP possibly influencing idiosyncratic volatility at least partially through theoverconfidence channel.24

Our analysis does not fully explain what drives retail preferences and tradingactivities. We demonstrate that stock characteristics and proxies for behavioralfactors are associated with the level of retail trading. However, lacking aninstrument for retail trading, our results should be interpreted as identifying anassociation rather than causality. We leave for future research the modeling ofretail trading that would identify the causal mechanisms.25 For example, otherfactors such as innovations in macroeconomic variables could influence RTP.

4. Alternative Explanations

In the last section of the article, we entertain four alternative explanations forthe idiosyncratic volatility puzzle and examine how those explanations relateto our findings.

4.1 Firm valuation, financial distress, and idiosyncratic volatilityIn the first test, we examine whether higher idiosyncratic volatility levels areassociated with higher market valuations, which might be related to specula-tive euphoria induced by retail investors. Specifically, we examine the relationbetween firm-level idiosyncratic volatility and firm valuation, as measuredby book-to-market (B/M) ratios. Our hypothesis is that companies with highmarket valuations relative to book values, a possible sign of high growth oppor-tunities that might cause speculative exuberance about the firm or its industry,have higher levels of idiosyncratic volatility.

This hypothesis is opposite to the key implication from the Merton (1974)model, in which equity claims are interpreted as a call option on the value of thefirm, with the strike price being the point beyond which the firm cannot repayits debt. In Merton’s model, as the value of the firm falls relative to its debtobligations and the financial distress rises, stock price falls and the volatilityof equity claims increases. Thus, leverage has an explicit role in Merton’smodel and the B/M ratio is a measure of how far the firm is from default. This

24 Our results are based on k = 252, but the results are very similar when we choose other values of k, such as126 (six months) or 63 (three months). For example, when k = 126, the Overconfidence Proxy has a coefficientestimate of 0.077 (t-statistic = 2.93).

25 In a recent study, Foucault, Sraer, and Thesmar (2009) use an instrumental variable approach to examine thecausal relation between retail trading and volatility and find evidence consistent with our main hypothesis.

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model predicts that the B/M ratio would be positively related to idiosyncraticvolatility and, moreover, it should statistically diminish the significance of thestock price effect. To examine the Merton model explanation for the level ofidiosyncratic volatility, we include the leverage ratio and the book-to-marketratio as additional variables explaining firm-specific volatility. We also includethe stock return over the past year as an additional proxy for financial distress.

The regression results in Table 3, column 5, indicate that neither predictionof the Merton (1974) model is borne out in the regression results. We find thatidiosyncratic volatility decreases with the B/M ratio. After controlling for stockprice and firm size, the relation between idiosyncratic volatility and the B/Mratio is negative and statistically significant. This result is inconsistent with theMerton model implication regarding distress.

Like the B/M ratio, leverage enters the regression with a sign opposite to thatpredicted by the model (i.e., firms with higher leverage appear to have loweridiosyncratic volatility). Lagged return enters the regression with the appropri-ate sign. A negative return is associated with higher idiosyncratic volatility, butthe estimate is statistically weak. We conclude from these regression estimatesthat the negative relation between stock price and idiosyncratic volatility isunlikely to be induced by financial distress. Rather, the evidence is consistentwith trading among low-priced and low B/M stocks, perhaps on the part ofretail investors, inducing greater idiosyncratic volatility in returns.

4.2 Volatility of firm fundamentalsRecent research proposes that a link between idiosyncratic volatility and firmfundamentals could explain the late 1990s idiosyncratic volatility trend, ar-guing that fundamentals had become more volatile (Wei and Zhang 2006) ormore opaque (Rajgopal and Venkatachalam 2006). These explanations are atleast partially consistent with the new evidence we present. The fundamentalsof low-priced stocks are quite possibly more volatile because they are also lessclosely followed by analysts due to limited institutional involvement in thesestocks, thus reducing the information content of these asset prices and financialstatements. For this to be a complete explanation, however, the volatility offundamentals explanation must shed light on why the volatility of fundamen-tals for low-priced stocks suddenly increased in the 1990s, and then, just assuddenly, dropped back to normal levels by 2003.

The same argument applies to the explanations of Fink et al. (2005) andBrown and Kapadia (2007), who argue that the trend in idiosyncratic volatilityis related to the stock market listing of increasingly less mature or more riskyfirms.26 A similar point applies to Irvine and Pontiff (2009), who argue that the

26 Fink et al. (2005) document a drop in the number of new listings beyond 2000 but do not relate this drop to adecline in the level of idiosyncratic volatility. Note that all of our main results hold on the subsample of firms thathave existed for at least five years, so our findings are distinct from a “young firm, low price effect.” For example,when we estimate specification (3) in Table 3 for a subsample of firms with a minimum age of five years, thecoefficient estimates (t-statistics) of the Price, Size, and Lagged Idiosyncratic Volatility variables are −0.263(−26.83), 0.026 (5.39), and 0.505 (25.27), respectively.

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trend in idiosyncratic volatility is related to increasingly competitive productmarkets. For any of these explanations to fully explain the evidence, the trendsin firm maturity or market competitiveness must have reversed over the pastfew years.

In summary, it is possible to correlate a trend in idiosyncratic volatility withother trends, such as that in the volatility of firm fundamentals, accountinginformation quality, firm maturity, market competitiveness, and undoubtedlyothers. But it appears, at least to us, much more difficult to find explanations forboth the ebbs and flows in idiosyncratic volatility. An episodic phenomenon,such as the level of idiosyncratic volatility, needs to be explained by anotherepisodic phenomenon.

4.3 IlliquidityTo the extent that the methods we use to measure idiosyncratic volatility aremisspecified, it is possible that an omitted common factor whose importancehas changed over time might account for the observed pattern in idiosyncraticrisk. In particular, small firms, and those with low prices, might comove morewith a factor reflecting liquidity risk. We therefore employ the liquidity factorof Pastor and Stambaugh (2003) in an attempt to determine whether the factor’sown variability and firm loadings on this additional factor might account forthe increase in idiosyncratic risk. In untabulated results, however, we find noevidence that the exposure to this extra factor captures the increased volatilitylevels. Furthermore, we use monthly market turnover to control for liquidity inour cross-sectional regressions. The link between speculative retail trading andidiosyncratic volatility is significant, even after accounting for turnover.

4.4 Microstructure biasesOne obvious issue with comparing volatility across firms with different shareprices is that microstructure effects mechanically introduce greater bias intothe volatility of low-priced stocks than high-priced stocks. This is pointed outby Ohlson and Penman (1985), as well as by Dravid (1988) in the contextof stock splits. However, just like the volatility of fundamentals explanation,microstructure biases are less able to explain an episodic spike in idiosyncraticvolatility.

To investigate whether market microstructure effects can explain the differ-ence between the idiosyncratic volatility of high- and low-priced stocks, weperform a simulation study following closely the setup of Hasbrouck (1999).We assume that the unobserved true returns of high- and low-priced stockshave the same volatility, but in the actual data, returns are contaminated byprice discreteness and bid-ask spreads. Since the relative importance of bothprice discreteness and bid-ask spreads depends on the price level, the volatil-ity of the observed returns also differs between high- and low-priced stocks.However, our stimulation study indicates that, for realistic levels of price

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contamination, the magnitude of this effect is very small relative to the ob-served difference in idiosyncratic volatility.

Related to microstructure effects, low-priced stocks might simply have more“outlier” observations resulting in higher idiosyncratic volatility. If the numberof these observations has increased over time, it could potentially explain thefinding that the increase in idiosyncratic volatility is concentrated in small, low-priced stocks. We find, however, that various filters designed to delete outlierobservations barely affect the observed trend. Upon deletion of such outliers,the level of idiosyncratic volatility of small, low-priced stocks decreases slightlybut shows the same trend that we find for the full sample.

5. Summary and Conclusion

Campbell et al. (2001) document a steady increase in the idiosyncratic volatilityof individual firms through the late 1990s, while the aggregate market volatilityand industry volatilities remained constant. This apparent rise in idiosyncraticvolatility is one of the most actively researched asset pricing puzzles. Over thepast few years, new research has lined up the 1990s time trend in idiosyncraticvolatility with other trends that are potentially related.

We present new evidence related to this idiosyncratic volatility puzzle. Weshow that idiosyncratic volatility dropped to below pre-1990s levels by 2003,reversing any evidence of a time trend in the 1962–1997 time period. We alsoshow that the high and rising idiosyncratic volatility patterns are particularlyacute in firms with low share prices. We interpret the new results as indicatingthat the rise in idiosyncratic volatility through the 1990s was an episodic phe-nomenon rather than a time trend, and at least partially induced by the trading ofretail investors. Using small-trades data from ISSM/TAQ and brokerage data,we provide several pieces of evidence that support this conjecture.

First, we show that retail investors dominate low-priced stocks. Second, weshow that idiosyncratic volatility patterns are stronger (idiosyncratic volatilitylevels are higher and trend estimates are more positive) among stocks witha greater concentration of retail investors. Third, we show that around stocksplits or other attention-grabbing events, increases (decreases) in idiosyncraticvolatility levels are associated with increases (decreases) in retail trading in-tensity. Overall, our evidence links retail trading with idiosyncratic volatility.

While other explanations for the idiosyncratic volatility puzzle have beenproposed, our new evidence raises the bar for potential explanations. It isnecessary to explain both the increase in idiosyncratic volatility throughout the1990s and also the more sudden drop in idiosyncratic volatility over the pastfew years.

Supplementary Data

Supplementary data are available online at http://rfs.oxfordjournals.org/.

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ReferencesBai, J., and P. Perron. 1998. Testing for and Estimation of Multiple Structural Changes. Econometrica 66:47–79.

———. 2003. Computation and Analysis of Multiple Structural Changes. Journal of Applied Econometrics18:1–22.

Barber, B. M., and T. Odean. 2000. Trading Is Hazardous to Your Wealth: The Common Stock InvestmentPerformance of Individual Investors. Journal of Finance 55:773–806.

———. 2008. All That Glitters: The Effect of Attention and News on the Buying Behavior of Individual andInstitutional Investors. Review of Financial Studies 21:785–818.

Barber, B. M., T. Odean, and N. Zhu. 2009. Do Retail Trades Move Markets? Review of Financial Studies22:151–86.

Barberis, N., and M. Huang. 2008. Stocks as Lotteries: The Implications of Probability Weighting for SecurityPrices. American Economic Review 98:2066–2100.

Barberis, N., and W. Xiong. 2009. Realization Utility. http://ssrn.com/abstract=1289674.

Battalio, R. H., and R. R. Mendenhall. 2005. Earnings Expectations, Investor Trade Size, and Anomalous Returnsaround Earnings Announcements. Journal of Financial Economics 77:289–319.

Bennett, J. A., R. W. Sias, and L. T. Starks. 2003. Greener Pastures and the Impact of Dynamic InstitutionalPreferences. Review of Financial Studies 16:1203–38.

Brav, A., and J. B. Heaton. 1997. The Economic Effects of Prudent Man Laws: Empirical Evidence from StockOwnership Dynamics. Working Paper, Fuqua School of Business, Duke University.

Brown, G., and N. Kapadia. 2007. Firm-Specific Risk and Equity Market Development. Journal of FinancialEconomics 84:358–88.

Campbell, J. Y., M. Lettau, B. G. Malkiel, and Y. Xu. 2001. Have Individual Stocks Become More Volatile? AnEmpirical Exploration of Idiosyncratic Risk. Journal of Finance 56:1–43.

Cao, C., T. Simin, and J. Zhao. 2008. Can Growth Options Explain the Trend in Idiosyncratic Risk? Review ofFinancial Studies 21:2599–633.

Del Guercio, D. 1996. The Distorting Effect of the Prudent Man Law on Institutional Equity Investments. Journalof Financial Economics 40:31–62.

Dravid, A. R., 1988. A Note on the Behavior of Stock Returns around Ex-Dates of Stock Distributions. Journalof Finance 42:163–68.

Fama, E. F., and K. R. French. 1997. Industry Costs of Equity. Journal of Financial Economics 43:153–93.

Fink, J., K. W. Fink, G. Grullon, and J. P. Weston. Forthcoming. What Drove the Increase in IdiosyncraticVolatility during the Internet Boom? Journal of Financial and Quantitative Analysis.

Foucault, T., D. Sraer, and D. Thesmar. 2009. Individual Investors and Volatility. http://ssrn.com/abstract=1105470.

Gervais, S., and T. Odean. 2001. Learning to Be Overconfident. Review of Financial Studies 14:1–27.

Gompers, P. A., and A. Metrick. 2001. Institutional Investors and Equity Prices. Quarterly Journal of Economics116:229–59.

Graham, J. R., and A. Kumar. 2006. Do Dividend Clienteles Exist? Evidence on Dividend Preferences of RetailInvestors. Journal of Finance 61:1305–36.

Han, K. C. 1995. The Effects of Reverse Splits on the Liquidity of the Stock. Journal of Financial and QuantitativeAnalysis 30:159–69.

Hasbrouck, J. 1999. Security Bid/Ask Dynamics with Discreteness and Clustering. Journal of Financial Markets2:1–28.

898




Hvidkjaer, S. 2008. Small Trades and the Cross-Section of Stock Returns. Review of Financial Studies 21:1123–51.

Irvine, P. J., and J. Pontiff. 2009. Idiosyncratic Return Volatility, Cash Flows, and Product Market Competition.Review of Financial Studies 22:1149–77.

Kumar, A. 2009. Who Gambles in the Stock Market? Journal of Finance 64:1889–933.

Kumar, A., and C. M. Lee. 2006. Retail Investor Sentiment and Return Comovements. Journal of Finance61:2451–86.

Lakonishok, J., A. Shleifer, and R. Vishny. 1992. The Impact of Institutional Trading on Stock Prices. Journalof Financial Economics 32:23–43.

Lee, C. M. 1992. Earnings News and Small Traders: An Intraday Analysis. Journal of Accounting and Economics15:265–302.

Lee, C. M., and B. Radhakrishna. 2000. Inferring Investor Behavior: Evidence from TORQ Data. Journal ofFinancial Markets 3:83–111.

Malmendier, U., and D. M. Shanthikumar. 2007. Are Small Investors Naive about Incentives? Journal of FinancialEconomics 85:457–89.

Merton, R. C. 1974. On the Pricing of Corporate Debt: The Risk Structure of Interest Rates. Journal of Finance29:449–70.

Odean, T. 1998a. Are Investors Reluctant to Realize Their Losses? Journal of Finance 53:1775–98.

———. 1998b. Volume, Volatility, Price, and Profit When All Traders Are above Average. Journal of Finance53:1887–934.

———. 1999. Do Investors Trade Too Much? American Economic Review 89:1279–98.

Ohlson, J. A., and S. H. Penman. 1985. Volatility Increases Subsequent to a Stock Split: An Empirical Aberration.Journal of Financial Economics 14:251–66.

Pastor, L., and R. F. Stambaugh. 2003. Liquidity Risk and Expected Stock Returns. Journal of Political Economy111:642–85.

Pontiff, J. 1996. Costly Arbitrage: Evidence from Closed-End Funds. Quarterly Journal of Economics 111:1135–51.

Rajgopal, S., and M. Venkatachalam. 2006. Financial Reporting Quality and Idiosyncratic Volatility over theLast Four Decades. http://ssrn.com/abstract=650081.

Shefrin, H. M., and M. Statman. 1984. Explaining Investor Preference for Cash Dividends. Journal of FinancialEconomics 13:253–82.

Vogelsang, T. 1998. Trend Function Hypothesis Testing in the Presence of Serial Correlation. Econometrica66:123–48.

Wei, S. X., and C. Zhang. 2006. Why Did Individual Stocks Become More Volatile? Journal of Business79:259–92.

Xu, Y., and B. G. Malkiel. 2003. Investigating the Behavior of Idiosyncratic Volatility. Journal of Business76:613–44.

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