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The Changing Relation Between Stock Market Turnover and Volatility

Paul Schultz*

October, 2006

*Mendoza College of Business, University of Notre Dame

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Extensive research shows that for both individual stocks, and for market indices,volatility is positively correlated with trading volume or turnover. This correlation could arisefrom private information being impounded in prices through trading. It could also occur ifinvestors re-weighted their portfolios in response to price changes. Finally, the correlationbetween volatility and trading could in part be mechanical. A price movement could triggerstanding limit orders or stop-loss orders that would otherwise go unexecuted.

The relation between volatility and trading volume has been changing over time. It isobvious to even casual observers that trading volume has increased dramatically. This is not justa result of more stocks and more outstanding shares though. I estimate that turnover, that istrading volume divided by outstanding shares, increased 700% between 1963 and 2004. I showfurther that the increase in turnover is not due to changes in the types of stocks that trade on theexchanges as turnover increases are similar for those stocks that trade over the entire period. Ialso show that the increase in turnover is also not attributable to an increase in the size of firmson the NYSE and Amex.

But, while recent turnover is eight times as great as turnover forty years ago, volatilityhas hardly changed. Using the methodology of Campbell, Lettau, Malkiel, and Xu (2001), Iestimate market-wide, industry, and firm-specific volatility. All three volatilities fluctuatesignificantly over the period, but none of them increases significantly between 1962 and 2004.This contrasts with Campbell et. al.’s finding that firm-specific volatility has increased. Thedifference appears to be that I restrict my sample to NYSE and Amex stocks, while the Nasdaqstocks they include assume a greater and greater significance over their sample period.

In this paper, I explore three ways in which turnover can increase while volatility remainsunchanged. It is possible that investors now trade more frequently for liquidity reasons that areunrelated to stock returns. A second explanation for increasing turnover with constant volatilityis that deeper equity markets may allow investors to trade more shares when they haveinformation. Finally, it is possible that a larger proportion of information is being incorporatedthrough trading on private information rather than through public disclosure. Of course, theseexplanations are not mutually exclusive. For example, an increase in liquidity trading wouldmake it easier for informed investors to conceal their orders, and thus trade more shares inresponse to a piece of information.

To examine the relation between turnover and volatility, I first estimate unexpectedmarket turnover and volatilities by subtracting their mean values over the previous 100 days. Ithen regress unexpected turnover on the unexpected volatilities and other variables using theCochrane-Orcott methodology to adjust for remaining autocorrelation. A key finding is thatwhen all three volatilities are included, almost all of the explanatory power is due to firm-specific volatilities and very little to market-wide volatility or industry volatility. This has twoimplications. First, the relation between market turnover and market volatility documented inearly studies is primarily due to the correlation between market and firm-specific volatilities.Second, trading on private information is likely to be an important component of the relationbetween turnover and volatility. Investors’ are much more likely to have private informationabout individual companies than about an industry or the market. On the other hand, ifrebalancing of portfolios was behind the turnover-volatility relation, we would expect marketand industry volatilities to have a big impact on turnover.

The regressions are then rerun with time-trend variables and separately for subperiods.

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This leads to several conclusions. First, turnover that is unrelated to volatility increasessignificantly over 1962 - 2004. This indicates that the amount of liquidity trading has grown overthe sample period. suggests that more trading for liquidity reasons is occurring recently. Second,turnover is much more sensitive to firm specific volatility in recent years than during the 1960's.This suggests that informed traders are able to exploit deeper markets toward the end of thesample period. Finally, when firm-specific volatility is included in the regressions, a significantpositive relation between market turnover and market-wide variance only appears in the latterpart of the sample period.

I also test whether the proportion of firm specific information that is incorporated intostock prices through trading increases over 1962 - 2004. To do this, I regress the firm specificvolatility measures on turnover for six subperiods. The R2's from the regressions increase overtime, indicating that an increasingly large proportion of information is incorporated into pricesthrough trading. At the same time though, the coefficients on the market turnover variablesdeclines over time, indicating that the market has become increasingly liquid.

The rest of the paper is organized as follows. A brief survey of the literature on volumeand volatility is presented in Section I. Section II discusses the turnover and volatility data usedhere. The determinants of trading and the changing nature of the relation between turnover andvolatility is examined in Section IV. Section V offers a summary of the paper and drawsconclusions.

I. Research on the Relation Between Volume and Volatility

An excellent survey of the early literature on the relation between volume and volatilityis provided by Karpoff (1987). He cites 18 articles published between 1966 and 1987 that find apositive relation between volume and the absolute value of price changes. The studies are robustto the use of daily or intraday data, and examine futures, individual stocks, and stock marketaggregates. He also discusses several papers that find that volume is correlated with the size ofthe return as well as the size of the absolute value of the return. One reason given for this relationis that short-sale constraints may limit the volume associated with negative returns.

The most sophisticated treatment of the topic from an econometric standpoint is providedby Gallant, Rossi, and Tauchen (1992). They use daily NYSE data for 1928 through 1987 andadjust for calendar regularities like the day of the week or month of the year that are known toaffect volume or volatility. They also incorporate linear and quadratic trend terms. They thencalculate a semi-nonparametric estimate of the joint density of the price change and volume.They find that variance increases with above average volume, but is relatively stable across awide range of below average volume.

Bessembinder, Chan, and Seguin (1996) examine daily trading volume in S&P 500futures contracts and NYSE stocks over May 1982 through December 1991. Volume and openinterest figures are detrended by taking a 40-day moving average. In a regression, NYSEvolume is positively affected by the absolute value of the market return, but more strongly withthe mean deviation of individual stock returns from market returns. S&P 500 futures volume onthe other hand is strongly positively related to absolute market return, but negatively related tothe average deviation of individual stock returns from the market return. The conclusion they

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draw from this is that people with market-wide information trade the futures, while investorswith information on individual stocks trade in the spot market. These results also hold when thesample period is split into May 1982 - October 1987, and November 1987 - December 1991.When firms are divided into size quintile portfolios, volume is positively and significantlyrelated to market return for only the portfolio of largest firms.

Some recent work attempts to model the relation between volatility and trading volumeas arising endogenously as a result of optimal decisions by investors. In Wang (1994), someinvestors have more information about a stock’s value than others. In his model, informedinvestors also have private investment opportunities that prevent uninformed investors fromextracting their information by observing their trades. Wang shows that under thesecircumstances, there is a positive correlation between the absolute value of price changes andvolume. When information asymmetries are greater, uninformed investors demand a greaterprice concession to trade with the informed, and hence the correlation between volume and pricechanges is higher. In this model, investors also trade in response to new public informationbecause it changes the asymmetry of knowledge between informed and uninformed investors.The greater the asymmetry, the greater the volume in response to public information.

In Llorente, Michaely, Saar, and Wang (2002), investors trade for two reasons: torebalance portfolios and to speculate on private information. Portfolio rebalancing leads tonegative return autocorrelation while information trading results in positive autocorrelation asinformation is gradually released. Llorente, Michaely, Saar, and Wang test their model usingindividual NYSE/Amex stocks over 1993-1998. They regress daily returns on the prior day’sreturns and the product of the prior days return and log turnover. For small firms, firms withlarge bid-ask spreads, and firms with little analyst coverage, the coefficient on this product isusually positive, as would be expected when a lot of trading is based on private information.Large firms, firms with small bid-ask spreads, and firms with a lot of analyst coverage are usedas proxies for firms with few information asymmetries. In regressions for these firms, thecoefficient on the interaction between returns and volume tends to be negative. For these firms,portfolio rebalancing rather than speculating on private information seems to be the primaryreason for trading.

These studies have not examined changes in the relation between volatility and volume,the subject of this paper. A recent paper by Bhattacharya and Galpin (2005) does look atchanges in the motivation for trading. They build on the insight of Lo and Wang (2000) that iftwo-fund separation holds, turnover should be identical for all stocks. They run cross-sectionalregressions each month of the log of trading volume on the log of the number of sharesoutstanding. If all investors indexed and two-fund separation held, the R2 from the regressionshould be one. So, a measure of the maximum proportion of trading that can be explained bystock picking is 1- R2. Bhattacharya and Galpin (2005) report that stock picking isdeclining all over the world. Of the 43 countries in their sample, 38 have a lower portion of stockpicking in 2000 - 2004 than in 1995 - 1999. For the United States, stock picking declined fromover 0.7 in the mid-1960's to less than 0.25 after 2000. This suggests more indexing by investorsand less trading on firm-specific information than in the past.

II. Data

1See Anderson and Dyl (2005)

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The data used in this paper comes from the CRSP daily files and includes the period fromJuly 1962 through December 2004. Only NYSE/Amex stocks are included because tradingvolume for listed and Nasdaq stocks is not directly comparable.1 SIC codes from CRSP are usedto assign stocks to 48 industries as defined in Fama and French (1997), and to two-digit SICcode industries. Volatility and trading volume measures are calculated daily.

A. Market Turnover

Turnover, the measure of trading volume used here, is intuitively meaningful. For asingle stock, it is the proportion of shares that trade on a particular day. The value-weightedmarket turnover used here is the proportion of the market’s value that will trade that day. Anadvantage of turnover over volume is that it is not affected by the number of outstanding shares,thus removing that source of non-stationarity.

There are good theoretical reasons for using turnover also. Tkac (1999) shows that animplication of the intertemporal capital asset pricing model is that turnover ratios should beequal across stocks. Thus market turnover, unlike market volume, should provide informationabout the trading of individual stocks as well. Lo and Wang (2000) consider the implications ofportfolio theory for trading volume. With k+1 fund separation, Lo and Wang show that theturnover of each stock should be approximated by a k-factor linear structure. Lo and Wang sortstocks into ten portfolios on the basis of the coefficient of the stock turnover on the marketturnover. A principle components analysis is then used to show that turnover is almostcompletely explained by a two-factor model.

For each day from July 1962 through 2004 I calculate the turnover of each stock thattraded on the NYSE or Amex on that day by dividing its share volume by its outstanding shares.I then calculate a market turnover by taking a weighted average across stocks, using each stocks’market capitalization on that date as a weight. For the market turnover series, I calculate movingaverages based on the prior 100 days. Fig. 1a depicts the 100-day moving average of marketturnover. There is a clear upward trend in turnover over the 1963 through 2004 period. During1963, about 0.05% of the value of NYSE/Amex shares traded each day. By 2004, about 0.40%of the value of the NYSE/Amex shares traded each day. In other words, a typical NYSE/Amexshare traded eight times as frequently in 2004 as in 1963 or 1964. Had Fig.1a shown tradingvolume instead, the increase would have been even more dramatic because the number ofoutstanding shares has increased steadily for NYSE/Amex stocks over this period.

It is natural to ask whether the increase in outstanding shares and capitalizations ofNYSE/Amex stocks is behind the increase in turnover. To answer this, I calculate daily turnoverfor all firms with market capitalizations of $50 million to $400 million at the beginning of eachyear. I use capitalizations fixed in nominal rather than real terms because commission schedulesand tick sizes were set in nominal terms. A firm with a capitalization of $50 million ranged fromthe 14th to the 66th size percentile over the sample period and was at the 37th percentile onaverage. A firm with a capitalization of $400 million ranged from the 38th to the 91st sizepercentile. On average it was at the 70th percentile.

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Fig. 1b shows the 100-day moving average of turnover for a value-weighted portfolio ofstocks with $50 million to $400 million in market capitalization. The large capitalization firmsthat dominated the value-weighted turnover in Fig.1a are now excluded, so this is, in effect, adifferent sample of smaller firms. Just as in Fig. 1a though, turnover increases significantly overthe sample period, rising from less than 0.10% in 1963, to over 0.50% at the end of the sampleperiod.

The stocks listed on the exchanges changed over 1962 - 2004, so it is interesting to ask ifthe changes in aggregate turnover occurred because stock turnovers increased, or becausedifferent stocks with higher turnovers came to be listed on the NYSE and Amex. There are (42 x41)/2 = 866 pairs of calendar years for the 1963 - 2004 sample period. For each of these pairs, Ifind all stocks that traded on the NYSE or Amex for at least 200 days in both years. For example,there are 938 stocks that traded at least 200 days during both 1975 and 1994, and 290 that traded200 days in both 1963 and 2004. I calculate the average daily turnover of each stock in bothyears of the pair. I then calculate average daily turnovers for the stocks each year by takingequal-weighted averages of the stock turnovers, and value-weighted averages where the weightof the stock for each year is the proportion of the market value of that portfolio at the beginningof the year. Finally, I calculate the ratio of the turnover in the latter year to the ratio of theturnover in the earlier year.

Table I reports the ratios of turnovers in stocks in later years to turnover in earlier years.Because of the large number of observations, I only report every other year in the early years andevery sixth year among the later years. Panel A reports the ratios for value-weighted portfolios.For example, the portfolio of stocks that traded in both 1975 (seventh row) and 1994 (fourthcolumn) turned over 3.359 times as frequently in 1994 as in 1975. The portfolio of stocks thattraded in both 1963 and 2004 (first row and seventh column) turned over 12.543 times asfrequently at the end of the sample period as at the beginning. For almost all combinations ofyears, the ratios exceed one. Turnover has been steadily increasing. When the years are a decadeor more apart, the ratios far exceed one. The increase in aggregate turnover has occurred becauseindividual stock turnovers are increasing, not because the market now contains more stocks thatturn over rapidly.

Panel B reports the ratios for equal-weighted portfolios. The main results of Panel A alsohold here. The great majority of the ratios are above one. Turnover has increased steadily whenequal-weighted portfolios are used. When a long time separates the years, the ratio is typicallytwo or higher. Stocks that traded both in 1963 and 2004 turned over an average of 6.246 times asfrequently in the latter year. A comparison on Panels A and B indicates though that ratios areusually much larger when value-weighted portfolios are used. The growth in turnover has beengreater for large stocks than small ones.

There are a number of potential exogenous changes in the markets that could be behindthe increase in turnover. One is the dramatic decline in commissions. For most of the NYSE’shistory, commissions were based solely on the price of the traded stock, and were the sameamount per share regardless of the number of shares traded. In 1968, in response to pressuresfrom the SEC and institutional investors, volume discounts were built into the commission scalefor orders of more than 1,000 shares. Fixed trade commissions, which had been industry practicesince 1792, were ended entirely by the Securities Acts Amendments of 1975 . Negotiated tradecommissions became legal on May 1, 1975, and many institutional investors immediately began

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paying lower trading costs, particularly on large trades. Ofer and Melnick (1978) examine tradesof ten banks’ trust departments in the first year following deregulation and find that they paid, onaverage, 36% less in commissions than under the old fixed-price schedule. Commissions did notdecline as quickly for retail investors. Nevertheless, trades that would have cost a retail investorhundreds of dollars to execute in 1975, cost less than $10 to execute online today.

A second important change is the emergence of equity derivatives. In the 1960's, tradingvolume in equity derivatives was small, and confined almost entirely to over-the-counter options.In 1973, exchange-traded options made their debut on the Chicago Board Options Exchange. In1982, the Kansas City Board of Trade launched the first stock index future, a contract on theValue-line index. The success of that contract led the Chicago Board of Trade to introduceoptions on the S&P 500 contract. Options on indices followed in 1983 when the CBOEintroduced options on the CBOE 100 index, which later became the S&P 100 index. All of thesecontracts can create additional demand to trade stocks. All of them can be used to hedge risks inthe market, or can be used in conjunction with stocks to create alternative payoffs. Arbitragebetween futures and stock markets also leads to increased trading.

Another change is the growing importance of institutional investors. According to the2001 NYSE fact book, institutional investors held only 7.2% of U.S. equities at the end of 1950.At the end of 1970, institutional holdings made up 28.2% of U.S. equities. Holdings reached45.8% at the end of 2000, and continues to grow. This affects turnover because institutions trademore frequently than individuals. One reason they trade more frequently is that trading costs forinstitutions tend to be lower than for retail investors. In addition, many do not pay taxes and areunconcerned about triggering capital gains through trading.

A fourth change in the equity markets has been the move to finer price increments. Theminimum price increment, or tick, for NYSE stocks had been $0.125 since 1792. In June of1997, the tick was halved to $0.0625. In January 2001, decimalization began and the tick wasreduced to $0.01. A smaller tick size is synonymous with a narrower minimum bid-ask spread,so the decline in tick size meant lower trading costs for many investors.

Finally, trading technology has improved dramatically over the last 40 years. In thebeginning of the sample period, much of the brokerage business took place over the telephone.Online submission of orders became common for individual in the 1990's. The ease andconvenience of online trading usually encourages people to trade more (Barber and Odean(2002)). For institutions, program trading involving dozens or even hundreds of stocks, iscommonplace now but was impossible in the 1960's.

B. Volatility

I calculate separate measures of market, industry, and firm-specific volatility. Themethodology I use to calculate these measures is similar to that of Campbell et. al. For themarket, I calculate two measures of volatility. The market variance for day t is the square of thedifference between the return of the value-weighted index on day t, and the average return of thevalue-weighted index over the entire period. That is,

σ Mkt t Mkt t MktR R, ,( ) ( )2 2 1= −

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σ ϖ

ϖ

ϖ

Stk t J J t i J tJ

N

Stk t J J t i J ti

N

J

R R

R R R

Where the percentage of industry i s capitalization in firm J

, , ( ),

, , ( ),

( ) ( )

| | | | ( )

'

2 2

1

1

5

6

= −∑

= −∑

=

=

=

The absolute value of the market return deviation on day t is the absolute value of the differencebetween the value-weighted index on day t and the average return of the value-weighted indexover the entire period. The value-weighted index in each case is composed of NYSE and Amexstocks only.

| | | | ( ), ,R R RMkt t Mkt t Mkt= − 2

I next calculate analogous measures of industry volatility for each of the forty-eight Famaand French (1997) industries. The industry variance for industry i on day t is the squareddifference between the industry return on that day and the market return. The absolute value ofthe return deviation for industry i on day t is the absolute value of the difference between theindustry return on day t and the market return on day t. I then take weighted averages of theindustry variances and absolute values of industry return deviations using industrycapitalizations as weights to produce aggregate industry measures. That is,

σ ω

ω

ω

Ind t i i t Mkt ti

Ind t i i t Mkt ti

i

R R

R R R

Where the percentage of market capitalization in industry i

, , ,

, , ,

( ) ( )

| | | | ( )

2 2

1

48

1

48

3

4

= −∑

= −∑

=

=

=

Finally, analogous measures of idiosyncratic stock volatility are calculated for each day. I firstcalculate the squared difference between each stock j’s return and its industry return for day tand the absolute value of the difference between stock j’s return and its industry return that day. Ithen compute aggregate measures of idiosyncratic stock volatility for each day by takingweighted averages of individual stocks’ squared differences between return and industry returnand the absolute value of the differences between individual stocks’ returns and the returns oftheir industries. Weights are the capitalizations of each individual stock. The measures ofindividual stock volatility can be written as

This procedureis used inChristie andHuang (1995)to decomposevolatilities. It isalso used inCampbell et. al. (2001). They observe that individual industry and individual stock measures ofvolatility may be off if the industry beta with respect to the market differs from one, or if the

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stock beta with respect to the industry differs from one. Campbell et al. note that thesedeviations, however, will cancel out when aggregate measures of industry or return volatilitiesare calculated.

Christie and Huang (1994) examine monthly idiosyncratic volatilities over 1926 - 1988.They find that idiosyncratic volatilities vary over time, and are greater during economicdownturns. They also demonstrate that idiosyncratic volatilities are much larger for small firmsthan for large firms.

Campbell et. al. examine volatilities of U.S. stocks over 1962-1997. Most of the volatilityis firm-specific volatility rather than market or industry volatility. They find that firm-specific volatility increases over the sample period while market wide and industry volatility do not. Putanother way, the correlation of returns of individual stocks with each other is declining overtime. Campbell et. al. also look more closely at the ten largest industries. For each industry, firmspecific volatility increases over their sample period.

Campbell et. al. propose several possible reasons for increasing volatility over time. Oneis a trend toward breaking up conglomerates. Another is the tendency of firms to go publicearlier. A third is that granting stock options to executives provides an incentive for more risktaking. Finally, Campbell et. al. suggest that the growth of derivative markets could also bebehind the increase in firm-specific volatility, but note that most earlier work finds thatintroducing derivatives decreases volatility.

For the market, industry, and firm volatility series, like the market turnover series, Icalculate 100-day moving averages. The 100 day moving average of the value-weighted marketvariance is shown in Fig. 2a. In contrast to turnover, there is no trend in the moving average of market variance. Variance is particularly high in the mid-1970's and from 1998 through 2002. Itruncate the volatility from the 1987 market crash because, at 0.008, it is very large relative tothe volatility for the rest of the sample period. The 100-day moving average of the Fama-Frenchindustry variance is shown in Fig 2b. Like the moving average of the market variance, it has notrend. Industry variances are correlated with market variances, but are generally lower and do notfluctuate as much. Industry variance is particularly high in 1999 and 2000 when the technologyand telecommunications sectors were variable relative to the market as a whole. Movingaverages of individual stock variances are shown in Fig. 2c. With the exception of the 1987crash, the weighted-average stock variance is larger and more variable than the market variance.Individual stock variances are particularly high during the mid-1970's and during 1999 - 2000.

In most ways, my findings on the intertemporal behavior of volatilities are similar tothose of Campbell et. al.. Like them, I find firm-specific variances to be larger than the marketvariance, which is, in turn larger than the average industry variance. Also, like Campbell et. al., Ifind that all three volatilities are positively correlated. A major difference between this paperand theirs’ is that I find no evidence of a trend in the firm-specific variance series. This may bebecause my sample period ends in 2004 while Campbell et. al.’s. ends several years earlier in1997. A more significant difference though is that my sample is restricted to NYSE/Amex stockswhile Campbell et. al. also include Nasdaq stocks. Nasdaq stocks appear in CRSP at the end of1972, almost ten years into the sample period. Nasdaq stocks make up increasing proportions ofboth the number and capitalization of stocks over the sample period. It seems likely that much ofthe increase in firm-specific volatility that Campbell et. al. document arises from the inclusion ofmore volatile stocks in the universe of publicly traded firms. Unfortunately, trading volume and

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hence turnover are not directly comparable across NYSE/Amex and Nasdaq stocks. Hence Iconfine my sample to NYSE/Amex stocks only.

III. The Changing Relation Between Turnover and Volatility

A. The Determinants of TurnoverSo, while turnover in 2004 is approximately eight times as large as in 1963 and 1964,

volatility is similar. There are at least three possible reasons for the divergence of turnover andvolatility. One is that there is now much more trading for liquidity purposes. It would not besurprising if investors were more likely to sell stock for consumption purposes since the costs oftrading have declined significantly over the past forty years. Increased liquidity trading couldshow up in the data in increases in turnover that is unrelated to volatility.

A second explanation for why volatility and turnover have diverged is that increasedliquidity in recent years allows investors to better exploit private information by trading moreshares. We would see this in the data as increases in the turnover generated by a given level ofvolatility. This could occur in conjunction with increased liquidity trading, as liquidity tradingmakes it easier for informed investors to hide their trades quickly (see Admati and Pfleiderer(1988)).

Finally, the increased turnover for a given level of volatility could imply that moreinformation is being incorporated into prices through trading, rather than as result of publicannouncements. It has been long-established that much information is incorporated in stockprices through the trading process rather than through disclosure. French and Roll (1986)demonstrate that stock return variances are much higher during periods when the market is openthan when it is closed - even when the period of market closure includes a regular business day.Roll (1988) shows that only a small portion of individual stock returns can be explained bymarket or industry returns, or by public news announcements. Both articles point to trading onprivate information as the primary source of stock returns. Numerous microstructure papers (e.g.Hasbrouck (1991a) and Hasbrouck (1991b)) demonstrate this more directly. Buy orders arefollowed by permanent price increases while sell orders are accompanied by permanent pricedeclines. If the proportion of information that is incorporated through trading increases over thesample period, we would expect higher regression R2's in later years when volatility is regressedon turnover.

Table II reports correlations between the daily market turnover and daily measures ofmarket, industry, and individual stock volatilities. Market turnover is correlated with all of thevolatility measures, but the correlation is higher with measures of industry volatility than withmeasures of individual stock or particularly market volatility. The correlation between turnoverand the variance of market returns is lowest at 0.1629. In general, measures of volatility based onabsolute values of return deviations have slightly higher correlations with market turnover thando variances. For example, the correlation between the market turnover and the variance ofFama-French industry returns is 0.4212, while the correlation between market turnover and theaverage absolute value of the difference between the market and the Fama-French industry returnis 0.5104. Volatility measures based on Fama-French and two-digit SIC codes are very highlycorrelated. For example, the correlation between the mean absolute value of the two-digit SIC

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Turn Turn R R R R R R

Days Days Jan Jan WkDay WkDay

t t Mkt t Mkt t Ind t Ind t Stk t Stk t

t t t t n tn

n tn

t

& & ( ) (| & | | & | ) (| & | | & | ) (| & | | & | )

( ) ( ) ( ) ( )

, , , , , ,− = − + − + − + −

+ − + − + ∑ − +

− − − −

− − = −

ρ α ρ α ρ α ρ α ρ

α ρ α ρ δ ρ ε

1 0 1 1 2 1 3 1

4 1 4 1 1

4

1

1

8

code industry return and the mean absolute value of the Fama-French industry return is 0.9934.Because they are so highly correlated, in the rest of the paper I focus exclusively on industry andfirm-specific volatilities as defined by Fama-French industries.

Table III provides autocorrelations and partial autocorrelations of daily market turnoverand daily measures of market, industry, and firm variance. All of these series exhibit positiveautocorrelation. The first order autocorrelation of market turnover is 0.9437, and all of the firstfive autocorrelations are above 0.9. Individual stock volatility is also highly autocorrelated.When volatility is measured as the average absolute value of the deviation between stock returnsand industry returns, the first order autocorrelation is 0.8423. Autocorrelations remain high formany lags, and remain above 0.68 after seven days. Industry volatilities are also highlyautocorrelated with first order autocorrelations of 0.6863 when industry volatility is measured asthe average absolute value of the difference between industry and market returns. Marketvolatility is also significantly autocorrelated, although the autocorrelations are smaller thaneither industry or individual firm volatility.

The autocorrelations in Table III underscore the difficulty in measuring the relationbetween turnover and volatility. Lo and Wang (2000) show that weekly turnover is highlyautocorrelated for at least ten lags for both value-weighted and equal-weighted portfolios.Further tests suggest that turnover is non-stationary. Lo and Wang try linear and quadraticdetrending as well as first differences, but none seem completely successful in producing astationary series. Hence, they employ the raw turnover data in most of their tests. I follow theexample of Bessembinder, Chan, and Seguin (1996) who subtract the average turnover from theprevious forty days to calculate a daily abnormal turnover. I subtract the mean market turnoverfrom the previous 100 days from turnover and the mean volatility from the past 100 days fromeach volatility measure to calculate abnormal turnovers and volatilities. To examine the relationbetween turnover and volatility abnormal market turnover is then regressed on abnormal market,industry, and stock volatilities, on the number of calendar days since the last trading day, on dayof the week dummies, and a dummy variable that takes a value of one if the day is in the firsthalf of January. Even when abnormal turnover and volatilities are used, regression residualsremain highly autocorrelated. Hence, Cochrane-Orcott regressions, which assume the residualsfollow an AR(1) process are estimated as: Turn Turn

Days Days Jan Jan WkDay WkDay

t t M t M t Ind t Ind t J t J t

t t t t n tn

tn

n t

& & ( ) ( & & ) ( & & ) ( & & )

( ) ( ) ( ) ( )

, , , , , ,− = − + − + − + −

+ − + − + − +∑

− − − −

− − −=

ρ α ρ α σ ρσ α σ ρσ α σ ρσ

α ρ α ρ δ ρ ε

1 0 12

12

22

12

32

12

4 1 4 1 11

4

1

7

Where Turnt is the market turnover on day t, D is the coefficient from the AR(1) process, FM,t isthe standard deviation of the market on day t, FInd,,t is the weighted average of the industrystandard deviations for day t, FJ,,t is the weighted average of each stock J’s standard deviation onday t, Days is the number of calendar days since the last trading day, Jan is a dummy variable

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that takes a value of one for days in the first half of January, and WkDay is a serious of fordummy variables that take values of one on Monday, Tuesday, Thursday, and Friday. Incalculating weighted averages, weights are the proportion of market capitalization represented bythe stock or industry on that day t. In (7) and (8), a dot over a variable signifies the differencebetween the variable and its average value over the previous 100 days. WkDayn is a dummyvariable that takes a value of one if the day of the week is day n, where the 1 - 4 representMonday, Tuesday, Thursday, and Friday.

Panel A of Table IV reports regression results when volatilities are measured as theaverage absolute value of the return deviation. The first row reports the regression when all daysare included, but the average absolute value of the deviation between the market return and itsaverage return is the only volatility measure. In the regression, the coefficient on the number oftrading days is -0.0601 and is highly significant. All else equal, there is less turnover onMondays and following holidays than on other days. The coefficient on the January dummy ispositive and significant, indicating higher turnover during the first few trading days of the year.The coefficient on the absolute value of the market return deviation is 0.0152, with a t-statistic of26.61. Greater market volatility is associated with greater market turnover.

The next two rows report regressions that include, respectively, the average absolutevalue of industry return deviations only, and the average absolute value of stock returndeviations only. The adjusted R2 goes from 0.1294 when only market volatility is used to 0.1907when only industry volatility is used, to 0.3741 when only firm-specific volatility is used.

The regression reported in the fourth row of the table includes all volatility measures andobservations from the entire sample period. The adjusted R2 is 0.3753, not much different fromthe value of 0.3741 obtained when only firm-specific volatility is included. In other words, firm-specific volatility is the principle determinant of market turnover. Neither market-wide volatilitynor industry volatility has much impact on share turnover. This can also be seen by comparingthe coefficients on the three volatility types. At 0.1577, the coefficient on the firm-specificvolatility is 54 times as large as the coefficient on the market volatility. The coefficient on theabnormal industry return is actually negative, albeit an insignificant -0.0022. So, if the marketreturn deviates from its average by 1% on a given day, market turnover will increase by0.0029%. If , across the 48 Fama-French industries, the mean industry return deviates from themarket return by an additional 1%, the market turnover will decrease by 0.0022%. If, on average,each stock’s return deviates from the return of its Fama-French industry by an extra 1%, marketturnover will increase by 0.1577%.

The lesson to be drawn from Table IV is that it is individual stock volatility, not market-wide volatility that drives market turnover. A similar result is contained in Bessembinder, Chan,and Seguin (1996), but I believe that the finding deserves more emphasis and attention than ithas received. This result suggests that Gallant, Rossi, and Tauchen (1992), as well as most of thepapers surveyed in Karpoff (1987), miss the boat in trying to estimate the relation betweenvolatility and trading by using market volatility rather than individual firm volatility.

This finding also suggests that most trading associated with volatility is in response toinformation about specific companies. Indeed, this is the type of information, not informationabout entire industries or the market as a whole, that is likely to be private information for someinvestors. If re-weighting a portfolio was a primary reason for trading, I would expect to see astronger relation between industry volatility and turnover. If allocation between consumption and

13

savings were a major reason for the relation between volatility and trading, I would expectturnover to be especially sensitive to market-wide volatility. Instead, market turnover is drivenby firm specific volatility.

The last regression in the table omits all returns from October 1987. The market varianceon October 19, 1987 far exceeds that of any other day, and there are other days around the crashwith large volatilities as well. As can be seen in Table IV though, coefficient estimates are notaffected much by omitting the crash. The coefficient on the absolute value of abnormal stockreturns increases slightly from 0.1557 to 0.1669. Other coefficients decline slightly. It remainstrue that idiosyncratic stock return volatility is the most important determinant of marketturnover.

Panel B reports regressions that use variances rather than the absolute value of returndeviations as measures of volatility. These regressions do not appear to be as well specified.Adjusted R2's are much smaller, and, omitting the 1987 crash has a much bigger impact oncoefficients. It remains the case that the volatility of firm specific stock returns are far moreimportant in determining market turnover than either industry or market variance. Thecoefficient on the average idiosyncratic stock variance is 11.2 times as large as the marketvariance and almost 3.7 times as large as the industry variance.

B. How the Relation Between Volatility and Turnover has ChangedMarket-wide turnover increased eightfold over the 42 years from 1963 through 2004. If

the increase is due to more liquidity trading, we would expect the intercept from a regression ofturnover on volatility to increase over time. If increased liquidity allows investors to exploitprivate information by trading more, we would expect the coefficient on volatility to increaseover time. We would particularly expect the coefficient on firm specific volatility to increase.Since investors are more likely to have firm-specific private information than information aboutan industry or the market, it is firm specific volatility which is more likely to be related totrading on information.

I rerun the regressions from Table IV that include all variables, but now also includeinteractions between the explanatory variables and a linear trend variable measured as thenumber of trading days since the first CRSP return date. Here as before, I run Cochrane-Orcottregressions because residuals are positively autocorrelated even after the moving average of theprevious 100 days is subtracted from each variable. Results are shown in Table V. Coefficientsand t-statistics from the regression that uses absolute values of return deviations as a measure ofvolatility are shown in the first two columns of the table. The coefficient on the time trendvariable itself is positive and highly significant. Market-wide turnover that is not attributable tovolatility has been increasing over the sample period. There is greater turnover from liquiditytrading toward the end of the period, perhaps because of diminished trading costs.

Of more interest though is that the coefficients are positive for the interactions betweentime and each of the volatilities. Market turnover has become more sensitive to market, industry,and particularly to idiosyncratic stock volatility over 1963 - 2004. This could mean that moreinformation is being impounded in prices through trading, or, alternatively, that greater liquidityallows more trading on a given piece of information. When the trend variables are included, over43% of daily abnormal turnover is explained by volatilities, the January Dummy, and the elapseddays since the last trading day. Note that the estimated AR(1) parameter used in the Cochrane-

14

Orcott regressions was 0.4637, indicating significant remaining autocorrelation even aftersubtracting the moving average from turnover and every explanatory variable.

The last two columns of Table V report coefficients and t-statistics from the regressionthat uses the variance of returns as a measure of volatility. The adjusted R2 is 0.2836, much lessthat the adjusted R2 of 0.4348 when volatility is measured by the absolute value of returndeviations. The main conclusions from the first regression, however, also hold here. There ismore turnover that is unassociated with volatility, that is turnover from liquidity trading, andmarket turnover has grown significantly more sensitive to every kind of volatility over thesample period.

It is difficult to capture precisely how the sensitivity of turnover has changed over timewith a simple, linear trend model. So, as another approach, I divide the 1963 - 2004 period intosix seven-year periods. The regressions of market turnover on market, industry, and stock-specific volatilities are reported in Table VI, with Panel A reporting regressions that use theabsolute value of return deviations to measure volatilities, and Panel B reporting regressionswith variances of returns. In Panel A, regression intercepts are much higher toward the end of thesample period, increasing from 0.0405 in 1963 - 1969 to 0.3025 in 1998 - 2004. Hence, assuggested in Table V, stocks turn over more rapidly toward the end of the period for liquiditypurposes. Adjusted R2's in Panel A increase over time from 0.2899 in 1963 - 1969 to 0.4788 over1998 - 2004. A larger portion of market turnover is explained by volatilities, the number of dayssince the last trading day, and January toward the end of the period than in the 1960's. Thecoefficient on the average absolute value of the stock returns increases from 0.0660 in 1963 -1969 steadily to 0.2015 in 1991 - 1997 before falling slightly to 0.1978 in 1998 - 2004. Thecoefficients on market and industry volatilities are actually negative in the first three subperiods,suggesting that after adjusting for firm-specific volatility increasing either market or industryvariance led to lower market-wide turnover. The coefficients on market volatility becomepositive and significant in the last three periods, suggesting that more market information isincorporated into prices through trading in the latter part of the sample period. As a whole, theregressions reported in Panel A of Table VI show that the association between turnover andvolatility became stronger over 1963 - 2004.

It is worth noting that in every subperiod, individual stock volatility is a more significantdeterminant of market turnover than either market or industry volatility. Again, turnover is dueto firm-specific returns, not market-wide returns.

Regressions using abnormal market, industry, and stock variances are reported in PanelB. These regressions do not seem to be as well-specified as the regressions in Panel A. AdjustedR2's are lower in every subperiod. Most of the same intertemporal patterns emerge though. Theintercept increases steadily over the six periods, showing that turnover irrespective of variancesis rising over time. The coefficient on abnormal market variance increases across the sixsubperiods, indicating that turnover becomes increasingly sensitive to market variance. Theintertemporal pattern for coefficients on industry and stock variance are not as clear. Thesecoefficients are generally higher toward the end of the sample period, but the increase is notmonotonic, with the coefficients declining from the 1991 - 1997 period to the 1998 - 2004period. So far, I have not explored the possibility that a larger portion of information isincorporated in prices through trading than in the past. If true, this could also explain why

15

( )(| & | | & | ) ( ) & & ( ) ( )

( ) ( )

, ,R R Turn Turn Days Days Jan Jan

WkDay WkDay

Stk t Stk t t t t t t t

n tn

n tn

t

− = − + − + − + −

+ ∑ − +

− − − −

= −

ρ α ρ α ρ α ρ α ρ

δ ρ ε

1 0 1 1 2 1 3 1

1

4

1

1

9

turnover has increased steadily over the last 40 years while stock return volatility in 2004 wassimilar to volatility in 1963.

To test this, I run Cochrane-Orcott regressions with the absolute value of the averageabnormal stock return as the dependent variable, and market turnover, dummy variables for theday of the week and for the first two weeks of January, and the number of calendar days thathave elapsed since the last trading day as explanatory variables. That is, I run the followingregression, with all variables defined as before:I use the average absolute value of the abnormal stock return, rather than industry or marketreturns because it is the volatility of individual stock returns that is most strongly associated withmarket turnover. The regression is run for each of the six consecutive seven year subperiods of1963 - 2004. If more information is being impounded in stock prices through trading, we wouldexpect R2's to increase over time.

Results are shown in Table VII. For the first six regressions, I drop all the explanatory

variables except market turnover. For these regressions, changes in R2's over time cannot beattributed to changes in the significance of other variables. Looking across the six subperiodsexamined in these regressions reveals that the adjusted R2's increase steadily from 0.2378 for1963-1969 to 0.3649 for 1998 - 2004. Considerably more of the individual stock volatilities areexplained by turnover at the end of the sample period. It is also interesting that while the R2'sincrease over the period, the coefficients on the abnormal market turnover fall from 4.0534 to1.8539. While turnover explains a larger portion of individual stock volatility, a given level ofturnover has a smaller impact on stock returns. Turnover explains more of stock return volatilitybecause there is more of it. At the same time, the market is more liquid.

The last six regressions in Table VII include the day of the week dummies, the dummyfor January, and the number of calendar days since the last trading day. In these regressions it isalso true that the adjusted R2's increase steadily over the sample period. As before, thecoefficient on market turnover declines across the subperiods.

All of the three explanations for the changing relation between turnover and volatilityreceive some support from the data. Liquidity trading seems to have increased. There alsoappears to be more trading associated with private information. Finally, it appears that moreinformation is being incorporated in prices through trading rather than disclosure. Which factoris more important in explaining the increase in turnover? I next breakdown turnover each dayinto turnover associated with volatility and turnover that is independent of it. To do so, I firstregress turnover each day on the different volatilities, a linear time trend, and interactionsbetween the time trend and volatilities. For this regression, I use a Cochrane-Orcott procedure toadjust for autocorrelation, but do not adjust the variables by subtracting out their movingaverages. To estimate the proportion of turnover attributable to volatility each day, I drop theintercept and time trend variables, and use the coefficients from the volatility variables and thevariables formed from interactions between the volatilities and time trend to predict turnover.

16

The 100-day moving average of turnover, and of the turnover due to volatility are show in Fig. 3.Fig. 3 shows that the turnover due to volatility has increased, roughly tripling over the

sample period. As market, industry, and firm volatilities are similar at the beginning and end ofthe sample period, it is the increased sensitivity of turnover to volatility that is behind theincrease in turnover from volatility. It is also clear from the graph that turnover from liquiditytrading is a larger part of turnover at the end of the period than at the beginning. The decline inturnover from volatility relative to total turnover after 2000 is striking in the graph, and isconsistent with casual observation. With the crash in technology stocks in 2000, both stockprices and volatility dropped sharply. Turnover, however, remained high. While it is clear thatliquidity trading increased since 2000, it is not entirely clear why. One candidate isdecimalization. NYSE stocks began trading in pennies in January 2001, and the resultingnarrowing of bid-ask spreads lowered trading costs for many investors. A second explanationcould be the continued growth of online trading. A definitive explanation for the recent increasein liquidity trading requires additional research.

IV. ConclusionsOver the years, a number of researchers have studied the relation between stock market

volatility and measures of trading activity like turnover. Almost all studies conclude thatvolatility and turnover are positively correlated. This could reflect information being impoundedin prices through trading, or portfolio rebalancing in response to stock price changes.

I show here that turnover has increased steadily over the past 40 years, and is nowroughly eight times as large as in the early 1960's. Turnover is positively correlated with bothmarket-wide volatility and, particularly with firm-specific volatility, but neither volatilityexhibits the growth displayed by turnover since the early 1960's. Hence the relation betweenvolatility and turnover has changed significantly over the last 40 years.

There are three ways in which the relation could change. Trading for liquidity reasons,that is reasons that are unrelated to information may have increased. We would expect this of forno other reason than that the cost of trading has declined over time. A second possibility is thatthe equity market liquidity has increased, and investors with information are able to takeadvantage of it by trading more now than in the past. Finally, it is possible that turnover hasincreased while volatility has not changed much since the 1960's because a larger proportion ofinformation, and hence volatility, is now impounded in stock prices through trading. Theseexplanations are not mutually exclusive. We would expect for example, that more liquiditytrading would allow informed investors to conceal their trades more easily, and therefore lead tomore trading on information.

I find support for all three explanations for the changing relation between volatility andturnover. Intercepts from regressions of turnover on volatility increase over time, as would beexpected if liquidity trading was increasing. The coefficient on the individual stock volatilitiesalso increases over time, suggesting more turnover associated with a given level of volatility inrecent years. Finally, the R2's from regressions of stock volatility on abnormal market turnoverincrease from 0.24 in 1963 - 1969 to 0.36 in 1998 - 2004. In recent years, more informationseems to be impounded in prices through trading rather than public announcements.

This paper raises questions that it does not attempt to answer. Of particular interest iswhy turnover has increased so much. Several possibilities are mentioned but not explored here.Trading costs have declined dramatically over the last 40 years. Tax rates on capital gains are far

17

lower than in the past. Institutions hold a much larger portion of publicly traded equities thanthey did in 1963. Derivatives trading has experienced explosive growth. All of these factorscould have a strong impact on turnover. Disentangling their effects is difficult though, and Ileave that for future work.

18

REFERENCES

Admati, Anat, and Paul Pfleiderer, 1988, A theory of intraday patterns: Volume and pricevariability, Review of Financial Studies 1, 3-40.

Anderson, Anne-Marie, and Edward Dyl, 2005, Market structure and trading volume, Journal ofFinancial Research 28, March.

Barber, Bradley, and Terry Odean, 2002, Online investors: Do the slow die first?, Review ofFinancial Studies 15, 455-489.

Bessembinder, Hendrik, Kalok Chan, and Paul Seguin, 1996, An empirical examination ofinformation, differences of opinion, and trading activity, Journal of Financial Economics 40,105-134.

Bhattacharya, Utpal, and Neal Galpin, 2005, Is stock picking declining around the world,Working paper, Indiana University.

Campbell, John, Grossman, Sanford, and Jiang Wang, 1993, Trading volume and serialcorrelation in stock returns, Quarterly Journal of Economics 108, 905-939.

Campbell, John, Martin Lettau, Burton Malkiel, and Yexiao Xu, 2001, Have individual stocksbecome more volatile? An empirical exploration of idiosyncratic risk, Journal of Finance 56, 1-43.

Christie, William, and Roger Huang, 1994, Equity return dispersions, Working paper, VanderbiltUniversity.

Christie, William, and Roger Huang, 1995, Following the pied piper: Do individual returns herdaround the market, Financial Analysts Journal, July-August, 1995, 31-37.

French, Kenneth, and Richard Roll, 1986, Stock return variances: The arrival of information andthe reaction of traders, Journal of Financial Economics 17, 5-26.

Gallant, A. Ronald, Peter Rossi, and George Tauchen 1992, Stock prices and volume, Review ofFinancial Studies 5, 199-242.

Griffin, John, Federico Nardari, and René Stulz, 2005, Do investors trade more when stocks haveperformed well? Evidence from 46 countries, Working paper, Ohio State University.

Hasbrouck, Joel, 1991a, Measuring the information content of stock trades, Journal of Finance46, 179-207.

Hasbrouck, Joel, 1991b, The summary informativeness of stock trades: An econometric analysis,

19

Review of Financial Studies 4, 571-595.

Karpoff, Jonathan, 1987, The relation between price changes and trading volume: A survey,Journal of Financial and Quantitative Analysis 22, 109-126.

Lo, Andrew, and Jiang Wang, 2000, Trading volume: Definitions, data analysis, andimplications of portfolio theory, Review of Financial Studies 13, 257-300.

Llorente, Guillermo, Roni Michaely, Gideon Saar, and Jiang Wang, 2002, Dynamic volume-return relationship of individual stocks, Review of Financial Studies 15, 1005-1047.

Ofer, Aharon and Arie Melnick, 1978, Price deregulation in the brokerage industry: Anempirical analysis, Bell Journal of Economics 9, 633-641.

Roll, Richard, 1988, R2, Journal of Finance 43, 541-566.

Tkac, Paula, 1999, A trading volume benchmark: Theory and evidence, Journal of Financial andQuantitative Analysis 34, 89 - 114.

Wang, Jiang, 1994, A model of competitive stock trading volume, Journal of Political Economy102, 127 - 168.

20

Table I. Ratios of Turnover in Latter Years to Turnover in Earlier Years for Stocks that Traded in BothFor each combination of years, the average daily turnover is calculated for each stock that tradedin both years. A portfolio turnover is calculated each year in a year pair by averaging theturnover of individual stocks. The table report the ratio of turnover in the latter year to turnoverin the earlier year. Panel A: Portfolio turnovers are a value-weighted average of stock turnovers, where the valuesare the market capitalizations at the beginning of each year.

1970 1976 1982 1988 1994 2000 2004

1963 1.604 2.163 4.666 7.563 6.700 11.428 12.543

1965 1.611 2.139 4.741 7.764 7.143 12.863 13.848

1967 1.025 1.331 3.000 4.925 4.666 7.988 8.796

1969 0.975 1.207 2.682 4.261 3.977 6.920 7.608

1971 1.194 2.595 4.026 3.714 6.430 6.897

1973 1.273 2.744 4.136 3.737 6.224 6.795

1975 1.236 2.617 3.759 3.359 5.492 6.081

1977 2.293 3.262 2.953 4.837 5.255

1979 1.758 2.524 2.323 3.924 4.278

1981 1.363 1.911 1.758 2.895 3.141

1983 1.183 1.090 1.802 1.928

1985 1.048 0.966 1.565 1.725

1987 0.787 0.739 1.157 1.243

1989 0.979 1.537 1.663

1991 1.127 1.777 1.907

1993 1.026 1.619 1.941

1995 1.403 1.712

1997 1.316 1.559

1999 1.204 1.447

2001 1.152

2003 1.050

21

Table I (Continued.)Panel B. Portfolio turnovers are an equal-weighted average of the individual stock turnovers.

1970 1976 1982 1988 1994 2000 2004

1963 1537 1.151 2.091 3.016 2.898 4.774 6.246

1965 1.083 0.839 1.461 2.111 2.170 3.591 5.005

1967 0.660 0.528 0.952 1.428 1.517 2.709 3.712

1969 0.863 0.689 1.209 1.787 1.900 3.316 4.517

1971 0.706 1.227 1.688 1.749 3.166 4.205

1973 1.071 1.845 2.442 2.436 4.026 5.322

1975 1.192 1.999 2.580 2.592 4.316 5.797

1977 1.713 2.217 2.237 3.719 4.983

1979 1.234 1.581 1.649 2.821 3.863

1981 1.134 1.411 1.482 2.504 3.378

1983 0.918 0.946 1.565 2.051

1985 0.963 1.002 1.629 2.158

1987 0.702 0.747 1.200 1.668

1989 1.005 1.572 2.081

1991 1.074 1.620 2.198

1993 0.914 1.343 1.799

1995 1.182 1.654

1997 0.733 0.962

1999 1.078 1.498

2001 1.089

2003 0.620

22

Table IICorrelations of daily value-weighted market turnover and measures of market, industry, and individual stock volatilities.Market turnover is the capitalization-weighted average of each NYSE/Amex stock’s trading volume divided by its outstanding shares. F2

Mkt is the squareddifference between the market return and it’s time series average. F2

FF Ind is obtained by calculating a capitalization - weighted average of the squared differencesbetween the 48 Fama-French industry returns and the market. F2

SIC Ind is analogous but uses two-digit SIC code industries. F2FF Stkis a capitalization-weighted

average squared difference between stock returns and the return of their Fama-French industry. F2SIC Stk uses two-digit SIC coed instead. |RFF Ind|, |RFF Stk|, |RSIC Ind|,

|RSIC Stk| are analogous measures of volatility based on the absolute values of return differences rather than squared return differences.

Turn Mkt F2Mkt F2

FF Ind F2FF Stk F2

SIC Ind F2SIC Stk |RFF Ind| |RFF Stk| |RSIC Ind| |RSIC Stk|

Turn Mkt 1.0000

F2Mkt 0.1629 1.0000

F2FF Ind 0.4212 0.2646 1.0000

F2FF Stk 0.3549 0.4217 0.7547 1.0000

F2SIC Ind 0.4249 0.2609 0.9804 0.7423 1.0000

F2SIC Stk 0.3497 0.4184 0.7586 0.9947 0.7260 1.0000

|RFF Ind| 0.5104 0.2615 0.8794 0.7499 0.8733 0.7463 1.0000

|RFF Stk| 0.3869 0.3598 0.7027 0.9037 0.7013 0.8940 0.8106 1.0000

|RSIC Ind| 0.5184 0.2619 0.8738 0.7417 0.8835 0.7300 0.9846 0.8065 1.0000

|RSIC Stk| 0.3751 0.3573 0.7084 0.9007 0.6917 0.8990 0.8143 0.9934 0.7994 1.0000

23

Table IIIAutocorrelations and partial autocorrelations of daily market turnover and measures of market,industry, and firm-specific volatility.

1 2 3 4 5 6 7

Market Turnover

Autocorrelations 0.9437 0.9196 0.9107 0.9082 0.9070 0.8980 0.8898

Partial Autocorrelations 0.9437 0.2654 0.2239 0.1906 0.1549 0.0410 0.0380

Market Variance

Autocorrelations 0.1322 0.2343 0.1414 0.0547 0.1869 0.0624 0.0463

Partial Autocorrelations 0.1322 0.2206 0.0942 -0.0203 0.1426 0.0161 -0.0336

Absolute Value of Excess Market Returns

Autocorrelations 0.2140 0.2209 0.2244 0.2053 0.2344 0.1852 0.1889

Partial Autocorrelations 0.2140 0.1836 0.1589 0.1160 0.1367 0.0645 0.0660

Industry Variance

Autocorrelations 0.5501 0.4477 0.4124 0.4202 0.4255 0.4224 0.4144

Partial Autocorrelations 0.5501 0.2081 0.1543 0.1627 0.1398 0.1141 0.0929

Absolute Value of Excess Industry Returns

Autocorrelations 0.6863 0.6342 0.6074 0.6076 0.6081 0.5930 0.5862

Partial Autocorrelations 0.6864 0.3086 0.1980 0.1839 0.1557 0.0983 0.0888

Stock Variance

Autocorrelations 0.7314 0.5763 0.5242 0.5193 0.5100 0.4900 0.4889

Partial Autocorrelations 0.7316 0.0889 0.1630 0.1555 0.1011 0.0697 0.1011

Absolute Value of Excess Stock Returns

Autocorrelations 0.8423 0.7588 0.7283 0.7199 0.7067 0.6922 0.6822

Partial Autocorrelations 0.8427 0.1704 0.1942 0.1676 0.0998 0.0796 0.0747

24

Table IV.Cochrane-Orcott Regressions of Daily Market Turnover on Volatility for 1963 - 2004.Each day, abnormal market turnover and abnormal volatilities are obtained by subtracting the average value of the variable over thelast 100 days from the current realization. A Cochrane-Orcott regression, which assumes the residuals follow an AR(1) process is thenrun. Other variables include the number of calendar days since the last trading day, a dummy variable that takes a value of one duringthe first half of January, and dummy variables for Monday, Tuesday, Thursday, and Friday.

Panel A. Volatility measures are based on absolute values of differences between expected and actual returns.

Intercept x1,000

Absolute ValueAbnormal

Market Return

Absolute ValueAbnormal

Industry Returns

Absolute ValueAbnormal Stock

Returns

Days Since LastTrading Day x

1,000

JanuaryDummy x

1,000

Day-of-Week

DummiesAdj.R2

1963 - 2004 0.1802(13.13)

0.0152(26.61)

-0.0601(-7.16)

0.1503(4.19)

Yes 0.1294

1963 - 2004 0.1778(13.85)

0.0829(39.97)

-0.0731(-8.80)

0.1226(3.73)

Yes 0.1907

1963 - 2004 0.1751(15.70)

0.1611(72.16)

-0.0799(-10.72)

0.0874(3.15)

Yes 0.3741

1963 - 2004 0.1773(15.89)

0.0029(5.29)

-0.0022(-0.88)

0.1577(51.67)

-0.0807(-10.83)

0.0881(3.17)

Yes 0.3753

1963 - 2004: Omit Oct. 1987

0.1776(16.03)

0.0017(3.04)

-0.0030(-1.23)

0.1669(51.62)

-0.0817(-11.04)

0.0839(3.05)

Yes 0.3653

25

Table IV (continued).Cochrane-Orcott Regressions of Daily Market Turnover on Volatility for 1963 - 2004.

Panel B. Volatility measures are based on squared differences between expected and actual returns.

Intercept x1,000

AbnormalMarket Variance

Abnormal FFIndustryVariance

Abnormal FFStock Variance

Days Since LastTrading Day x

1,000

JanuaryDummy x

1,000

Day-of-Week

DummiesAdj.R2

1963 - 2004 0.1713(12.26)

0.1685(17.99)

-0.0536(-6.29)

0.1630(4.45)

Yes 0.0989

1963 - 2004 0.1728(12.94)

1.6276(30.30)

-0.0622(-7.38)

0.1391(4.20)

Yes 0.1440

1963 - 2004 0.1767(14.27)

1.5707(47.95)

-0.0698(-8.54)

0.1402(4.49)

Yes 0.2337

1963 - 2004 0.1802(14.67)

0.1202(13.40)

0.3685(5.71)

1.3494(32.48)

-0.0725(-8.96)

0.1362(4.39)

Yes 0.2478

1963 - 2004: Omit Oct. 1987

0.1872(15.61)

0.2189(11.00)

0.2427(3.76)

1.7712(35.82)

-0.0800(-10.00)

0.1289(4.32)

Yes 0.2573

26

Table V.Cochrane-Orcott Regressions of Turnover on Volatilities, and Volatilities Interacted with Time.Time is measured as the number of days since the first trading day on CRSP/1,000. Each day,abnormal market turnover and abnormal volatilities are obtained by subtracting the averagevalue of the variable over the last 100 days from the current realization. Other variables includethe number of calendar days since the last trading day, a dummy variable that takes a value ofone during the first half of January, and dummy variables for Monday, Tuesday, Thursday, andFriday.

Coefficient T-statistic Coefficient T-statistic

Intercept x 1,000 0.0203 (0.93) 0.0184 (0.74)

Time 0.000029 (8.24) 0.000030 (7.52)

Absolute Value of Abnormal Market Return -0.0043 (-3.11)

Absolute Value of Abnormal Market Return x Time 0.0013 (6.75)

Absolute Value of Abnormal Industry Return -0.0108 (-1.83)

Absolute Value of Abnormal Industry Return x Time 0.0007 (0.94)

Absolute Value of Abnormal Stock Return 0.0527 (7.36)

Absolute Value of Abnormal Stock Return x Time 0.0166 (16.27)

Variance of Abnormal Market Return -0.1945 (-4.08)

Variance of Abnormal Market Return x Time 0.0494 (6.87)

Variance of Abnormal Industry Return 0.3978 (1.50)

Variance of Abnormal Industry Return x Time -0.0253 (-0.84)

Variance of Abnormal Stock Return 0.3258 (2.48)

Variance of Abnormal Stock Return x Time 0.1590 (8.99)

Days Since Last Trading Day x 1,000 -0.0123 (-0.82) -0.0066 (-0.40)

Days Since Last Trading Day x 1,000 x Time -0.0001 (-5.10) -0.00001 (-4.47)

January Dummy x 1,000 -0.0615 (-1.19) -0.0638 (-1.06)

January Dummy x 1,000 x Time 0.00003 (3.46) 0.00003 (3.89)

Observations 10,597 10,597

D 0.4637 0.4947

Adjusted R2 0.4348 0.2836

27

Table VI.Cochrane-Orcott Regressions of Turnover on Volatilities for Seven-Year Subperiods.Each day, abnormal market turnover and abnormal volatilities are obtained by subtracting the average value of the variable over thelast 100 days from the current realization. A Cochrane-Orcott regression, which assumes the residuals follow an AR(1) process is thenrun. Other variables include the number of calendar days since the last trading day, a dummy variable that takes a value of one duringthe first half of January, and dummy variables for Monday, Tuesday, Thursday, and Friday.

Panel A. Volatility measures based on absolute values of differences between actual and expected returns.

Intercept x1,000

Absolute ValueAbnormal

Market Return

Absolute ValueAbnormal

Industry Returns

Absolute ValueAbnormal Stock

Returns

Days Since LastTrading Day x

1,000

JanuaryDummy x

1,000

Day-of-Week

Dummies Adj.R2

1963 - 1969 0.0403(4.38)

-0.0015(-2.25)

-0.0075(-2.86)

0.0660(20.71)

-0.0100(-1.94)

-0.0678(-2.86)

Yes 0.2899

1970 - 1976 0.0773(6.02)

-0.0017(-3.63)

-0.0051(-2.14)

0.0723(23.53)

-0.0378(-6.10)

-0.0079(-0.25)

Yes 0.3908

1977 - 1983 0.1772(8.72)

-0.0045(-4.37)

-0.0116(-2.96)

0.1492(25.17)

-0.0646(-5.27)

0.0398 (0.72)

Yes 0.3957

1984 - 1990 0.2312(6.58)

0.0097(7.00)

-0.0130(-1.20)

0.1715(19.39)

-0.1307(-5.38)

0.0655(0.75)

Yes 0.4387

1991 - 1997 0.2201(8.24 )

0.0074(4.48)

0.0183(2.31)

0.2015(21.15)

-0.1018(-5.34 )

0.2002(3.23)

Yes 0.4461

1998 - 2004 0.3025(8.19 )

0.0062(4.12)

-0.0015(-0.27)

0.1978(25.30)

-0.1206(-4.93 )

0.2750(2.95)

Yes 0.4788

28

Table VI (continued).Cochrane-Orcott Regressions of Turnover on Volatilities for Seven-Year Subperiods.

Panel B. Volatility measures based on squared differences between actual and expected returns.

Intercept x1,000

AbnormalMarket Variance

Abnormal FFIndustryVariance

Abnormal FFStock Variance

Days Since LastTrading Day x

1,000

JanuaryDummy x

1,000

Day-of-Week

DummiesAdj.R2

1963 - 1969 0.0421(4.44)

-0.1595(-4.00)

-0.0006(-0.00)

1.1010(16.01)

-0.0098(-1.78)

-0.0481(-1.97)

Yes 0.2234

1970 - 1976 0.0754(5.73)

-0.0773(-4.25)

0.1336(1.32)

1.0957(17.93)

-0.0381(-5.73)

-0.0088(-0.26)

Yes 0.3083

1977 - 1983 0.1978(8.46)

0.1161(2.80)

0.3378(1.93)

1.0554(12.25)

-0.0702(-5.11)

0.0954(1.51)

Yes 0.2258

1984 - 1990 0.2263(5.63)

0.1151(8.29)

0.0079(0.02)

1.1450(7.86)

-0.1148(-4.14)

0.1246(1.24)

Yes 0.2617

1991 - 1997 0.2326(8.00)

0.2179(3.44)

1.7826(6.01)

2.9311(15.51)

-0.0993(-4.82)

0.2572(3.72)

Yes 0.3406

1998 - 2004 0.3081(7.42)

0.3263(6.98)

-0.0003(-0.00)

2.0268(18.53)

-0.1175(-4.38)

0.3454(3.20)

Yes 0.3442

29

( )(| & | | & |) ( ) & & ( ) ( ) ( ), ,R R Turn Turn Days Days Jan Jan WkDay WkDayStk t Stk t t t t t t t n tn

ntn

t− = − + − + − + − + ∑ − +− − − −=

−ρ α ρ α ρ α ρ α ρ δ ρ ε1 0 1 1 2 1 3 11

4

11

Table VII.Regressions of the Average Absolute Value of Individual Stock Returns on Abnormal Market TurnoverThe following regression is run using daily observations:

Here, RStk,t is the value-weighted mean absolute value of the difference between individual stock returns and thereturn of their Fama-French industry. Turn is the value-weighted market turnover. Days is the number of calendardays since the last trading day, Jan is a dummy that takes a value of one for the first two weeks of January, WkDayare dummy variables for the day of the week. A dot over the variable indicates that it was first adjusted bysubtracting out its mean for the previous 100 days.

Intercept x1,000

AbnormalMarket

Turnover

Days SinceLast TradingDay x 1,000

JanuaryDummy x

1,000

Day-of-Week

DummiesAdj. R2

1963 - 1969 0.0180(0.45)

4.0534(23.44)

0.2378

1970 - 1976 -0.0868(-1.05)

4.2930(26.26)

0.2804

1977 - 1983 -0.0785(-1.65)

2.3373(30.09)

0.3093

1984 - 1990 -0.0392(-0.41)

1.6404(29.52)

0.3011

1991 - 1997 -0.0259(-0.65)

1.3342(26.69)

0.2868

1998 - 2004 -0.2009(-2.45)

1.8539(31.80)

0.3649

1963 - 1969 -0.4272(-6.01)

4.1619(24.19)

0.3718(8.26)

0.4818(2.70)

Yes 0.2939

1970 - 1976 -0.3434(-3.18)

4.7181(27.49)

0.1794(3.30)

0.2475(0.92)

Yes 0.3024

1977 - 1983 -0.3701(-4.62)

2.5097(31.11)

0.1622(3.21)

0.2942(1.42)

Yes 0.3317

1984 - 1990 -0.3612(-2.93)

1.7932(31.50)

0.1992(3.11)

-0.0269(-0.08)

Yes 0.3303

1991 - 1997 -0.1898(-2.62)

1.5025(29.65)

0.1466(3.03)

0.0507(0.28)

Yes 0.3653

1998 - 2004 -0.6367(-5.05)

1.9445(32.93)

0.3896(5.29)

0.3142(0.91)

Yes 0.4048

30

0

0.001

0.002

0.003

0.004

0.005

0.00619

6211

26

1966

1125

1971

0106

1975

0103

1978

1229

1982

1227

1986

1219

1990

1214

1994

1209

1998

1207

2002

1211

Market Turnover (MA)

Figure 1a. 100-day moving average of market turnover, 1963 - 2004.

31

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

1962

1123

1966

1123

1971

0105

1975

0102

1978

1228

1982

1223

1986

1218

1990

1213

1994

1208

1998

1204

2002

1210

Turnover (100 Day MA)

Figure 1b. Turnover of stocks with market capitalizations between $50 million and $400 million.

32

0

0.0001

0.0002

0.0003

0.0004

0.0005

1962

1126

1966

1125

1971

0106

1975

0103

1978

1229

1982

1227

1986

1219

1990

1214

1994

1209

1998

1207

2002

1211

Market Variance (MA)

0

0.0001

0.0002

0.0003

0.0004

0.0005

1962

1126

1966

1125

1971

0106

1975

0103

1978

1229

1982

1227

1986

1219

1990

1214

1994

1209

1998

1207

2002

1211

Industry Variance (MA)

Fig 2a. Market Variance

Fig 2b. Industry Variance

33

0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0.0007

0.0008

1962

1126

1966

1125

1971

0106

1975

0103

1978

1229

1982

1227

1986

1219

1990

1214

1994

1209

1998

1207

2002

1211

Idiosyncratic Stock Variance (MA)

Fig. 2c. Idiosyncratic Stock Variances

34

0

0.001

0.002

0.003

0.004

0.005

0.00619

6304

19

1967

0420

1971

0528

1975

0528

1979

0523

1983

0518

1987

0514

1991

0509

1995

0504

1999

0503

2003

0507

Volatility Turnover

Total Turnover

Fig. 3. Total turnover and turnover explained by market, industry, and firm volatility. Changes inthe relation between volatility and turnover are modeled with linear interaction terms betweendays since July 2, 1962 and volatility measures. Turnover measures are 100-day movingaverages.

Turnover from volatility = - 0.0039305 x |RMkt,t - E(RMkt)| + 0.00000117 x days x RMkt,t - E(RMkt)| - 0.0163417 x |RInd,t- E(RInd)| + 0.00000109 x days x |RInd,t - RMkt,t| +0.0537823 x |RStk,t - RInd,t| + 0.0000141 x days x |RStk,t - RInd,t| + gt