The Changing Relation Between Stock Market Turnover and Volatility

Transcription

1 The Changing Relation Between Stock Market Turnover and Volatility Paul Schultz * October, 2006 * Mendoza College of Business, University of Notre Dame 1

2 Extensive research shows that for both individual stocks, and for market indices, volatility is positively correlated with trading volume or turnover. This correlation could arise from private information being impounded in prices through trading. It could also occur if investors re-weighted their portfolios in response to price changes. Finally, the correlation between volatility and trading could in part be mechanical. A price movement could trigger standing limit orders or stop-loss orders that would otherwise go unexecuted. The relation between volatility and trading volume has been changing over time. It is obvious to even casual observers that trading volume has increased dramatically. This is not just a result of more stocks and more outstanding shares though. I estimate that turnover, that is trading volume divided by outstanding shares, increased 700% between 1963 and I show further that the increase in turnover is not due to changes in the types of stocks that trade on the exchanges as turnover increases are similar for those stocks that trade over the entire period. I also show that the increase in turnover is also not attributable to an increase in the size of firms on the NYSE and Amex. But, while recent turnover is eight times as great as turnover forty years ago, volatility has hardly changed. Using the methodology of Campbell, Lettau, Malkiel, and Xu (2001), I estimate market-wide, industry, and firm-specific volatility. All three volatilities fluctuate significantly over the period, but none of them increases significantly between 1962 and This contrasts with Campbell et. al. s finding that firm-specific volatility has increased. The difference appears to be that I restrict my sample to NYSE and Amex stocks, while the Nasdaq stocks 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 remains unchanged. It is possible that investors now trade more frequently for liquidity reasons that are unrelated to stock returns. A second explanation for increasing turnover with constant volatility is that deeper equity markets may allow investors to trade more shares when they have information. Finally, it is possible that a larger proportion of information is being incorporated through trading on private information rather than through public disclosure. Of course, these explanations are not mutually exclusive. For example, an increase in liquidity trading would make it easier for informed investors to conceal their orders, and thus trade more shares in response to a piece of information. To examine the relation between turnover and volatility, I first estimate unexpected market turnover and volatilities by subtracting their mean values over the previous 100 days. I then regress unexpected turnover on the unexpected volatilities and other variables using the Cochrane-Orcott methodology to adjust for remaining autocorrelation. A key finding is that when all three volatilities are included, almost all of the explanatory power is due to firmspecific volatilities and very little to market-wide volatility or industry volatility. This has two implications. First, the relation between market turnover and market volatility documented in early 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 relation between turnover and volatility. Investors are much more likely to have private information about individual companies than about an industry or the market. On the other hand, if rebalancing of portfolios was behind the turnover-volatility relation, we would expect market and industry volatilities to have a big impact on turnover. The regressions are then rerun with time-trend variables and separately for subperiods. 2

3 This leads to several conclusions. First, turnover that is unrelated to volatility increases significantly over This indicates that the amount of liquidity trading has grown over the 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 the sample period. Finally, when firm-specific volatility is included in the regressions, a significant positive relation between market turnover and market-wide variance only appears in the latter part of the sample period. I also test whether the proportion of firm specific information that is incorporated into stock prices through trading increases over To do this, I regress the firm specific volatility measures on turnover for six subperiods. The R 2 's from the regressions increase over time, indicating that an increasingly large proportion of information is incorporated into prices through trading. At the same time though, the coefficients on the market turnover variables declines 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 volume and volatility is presented in Section I. Section II discusses the turnover and volatility data used here. The determinants of trading and the changing nature of the relation between turnover and volatility is examined in Section IV. Section V offers a summary of the paper and draws conclusions. I. Research on the Relation Between Volume and Volatility An excellent survey of the early literature on the relation between volume and volatility is provided by Karpoff (1987). He cites 18 articles published between 1966 and 1987 that find a positive relation between volume and the absolute value of price changes. The studies are robust to the use of daily or intraday data, and examine futures, individual stocks, and stock market aggregates. He also discusses several papers that find that volume is correlated with the size of the return as well as the size of the absolute value of the return. One reason given for this relation is that short-sale constraints may limit the volume associated with negative returns. The most sophisticated treatment of the topic from an econometric standpoint is provided by Gallant, Rossi, and Tauchen (1992). They use daily NYSE data for 1928 through 1987 and adjust for calendar regularities like the day of the week or month of the year that are known to affect volume or volatility. They also incorporate linear and quadratic trend terms. They then calculate 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 a wide range of below average volume. Bessembinder, Chan, and Seguin (1996) examine daily trading volume in S&P 500 futures contracts and NYSE stocks over May 1982 through December Volume and open interest figures are detrended by taking a 40-day moving average. In a regression, NYSE volume is positively affected by the absolute value of the market return, but more strongly with the mean deviation of individual stock returns from market returns. S&P 500 futures volume on the other hand is strongly positively related to absolute market return, but negatively related to the average deviation of individual stock returns from the market return. The conclusion they 3

4 draw from this is that people with market-wide information trade the futures, while investors with information on individual stocks trade in the spot market. These results also hold when the sample period is split into May October 1987, and November December When firms are divided into size quintile portfolios, volume is positively and significantly related to market return for only the portfolio of largest firms. Some recent work attempts to model the relation between volatility and trading volume as arising endogenously as a result of optimal decisions by investors. In Wang (1994), some investors have more information about a stock s value than others. In his model, informed investors also have private investment opportunities that prevent uninformed investors from extracting their information by observing their trades. Wang shows that under these circumstances, there is a positive correlation between the absolute value of price changes and volume. When information asymmetries are greater, uninformed investors demand a greater price concession to trade with the informed, and hence the correlation between volume and price changes is higher. In this model, investors also trade in response to new public information because 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: to rebalance portfolios and to speculate on private information. Portfolio rebalancing leads to negative return autocorrelation while information trading results in positive autocorrelation as information is gradually released. Llorente, Michaely, Saar, and Wang test their model using individual NYSE/Amex stocks over They regress daily returns on the prior day s returns and the product of the prior days return and log turnover. For small firms, firms with large bid-ask spreads, and firms with little analyst coverage, the coefficient on this product is usually 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 used as proxies for firms with few information asymmetries. In regressions for these firms, the coefficient 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 primary reason 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 at changes in the motivation for trading. They build on the insight of Lo and Wang (2000) that if two-fund separation holds, turnover should be identical for all stocks. They run cross-sectional regressions each month of the log of trading volume on the log of the number of shares outstanding. If all investors indexed and two-fund separation held, the R 2 from the regression should be one. So, a measure of the maximum proportion of trading that can be explained by stock picking is 1- R 2. Bhattacharya and Galpin (2005) report that stock picking is declining all over the world. Of the 43 countries in their sample, 38 have a lower portion of stock picking in than in For the United States, stock picking declined from over 0.7 in the mid-1960's to less than 0.25 after This suggests more indexing by investors and less trading on firm-specific information than in the past. II. Data 4

5 The data used in this paper comes from the CRSP daily files and includes the period from July 1962 through December Only NYSE/Amex stocks are included because trading volume for listed and Nasdaq stocks is not directly comparable. 1 SIC codes from CRSP are used to assign stocks to 48 industries as defined in Fama and French (1997), and to two-digit SIC code industries. Volatility and trading volume measures are calculated daily. A. Market Turnover Turnover, the measure of trading volume used here, is intuitively meaningful. For a single stock, it is the proportion of shares that trade on a particular day. The value-weighted market turnover used here is the proportion of the market s value that will trade that day. An advantage 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 an implication of the intertemporal capital asset pricing model is that turnover ratios should be equal across stocks. Thus market turnover, unlike market volume, should provide information about the trading of individual stocks as well. Lo and Wang (2000) consider the implications of portfolio theory for trading volume. With k+1 fund separation, Lo and Wang show that the turnover of each stock should be approximated by a k-factor linear structure. Lo and Wang sort stocks into ten portfolios on the basis of the coefficient of the stock turnover on the market turnover. A principle components analysis is then used to show that turnover is almost completely explained by a two-factor model. For each day from July 1962 through 2004 I calculate the turnover of each stock that traded 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 moving averages based on the prior 100 days. Fig. 1a depicts the 100-day moving average of market turnover. There is a clear upward trend in turnover over the 1963 through 2004 period. During 1963, 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/Amex share traded eight times as frequently in 2004 as in 1963 or Had Fig.1a shown trading volume instead, the increase would have been even more dramatic because the number of outstanding shares has increased steadily for NYSE/Amex stocks over this period. It is natural to ask whether the increase in outstanding shares and capitalizations of NYSE/Amex stocks is behind the increase in turnover. To answer this, I calculate daily turnover for all firms with market capitalizations of $50 million to $400 million at the beginning of each year. I use capitalizations fixed in nominal rather than real terms because commission schedules and tick sizes were set in nominal terms. A firm with a capitalization of $50 million ranged from the 14 th to the 66 th size percentile over the sample period and was at the 37 th percentile on average. A firm with a capitalization of $400 million ranged from the 38 th to the 91 st size percentile. On average it was at the 70 th percentile. 1 See Anderson and Dyl (2005) 5

6 Fig. 1b shows the 100-day moving average of turnover for a value-weighted portfolio of stocks with $50 million to $400 million in market capitalization. The large capitalization firms that dominated the value-weighted turnover in Fig.1a are now excluded, so this is, in effect, a different sample of smaller firms. Just as in Fig. 1a though, turnover increases significantly over the sample period, rising from less than 0.10% in 1963, to over 0.50% at the end of the sample period. The stocks listed on the exchanges changed over , so it is interesting to ask if the changes in aggregate turnover occurred because stock turnovers increased, or because different stocks with higher turnovers came to be listed on the NYSE and Amex. There are (42 x 41)/2 = 866 pairs of calendar years for the sample period. For each of these pairs, I find 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 traded 200 days in both 1963 and I calculate the average daily turnover of each stock in both years of the pair. I then calculate average daily turnovers for the stocks each year by taking equal-weighted averages of the stock turnovers, and value-weighted averages where the weight of the stock for each year is the proportion of the market value of that portfolio at the beginning of the year. Finally, I calculate the ratio of the turnover in the latter year to the ratio of the turnover 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 and every 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 (fourth column) turned over times as frequently in 1994 as in The portfolio of stocks that traded in both 1963 and 2004 (first row and seventh column) turned over times as frequently at the end of the sample period as at the beginning. For almost all combinations of years, the ratios exceed one. Turnover has been steadily increasing. When the years are a decade or more apart, the ratios far exceed one. The increase in aggregate turnover has occurred because individual stock turnovers are increasing, not because the market now contains more stocks that turn over rapidly. Panel B reports the ratios for equal-weighted portfolios. The main results of Panel A also hold here. The great majority of the ratios are above one. Turnover has increased steadily when equal-weighted portfolios are used. When a long time separates the years, the ratio is typically two or higher. Stocks that traded both in 1963 and 2004 turned over an average of times as frequently in the latter year. A comparison on Panels A and B indicates though that ratios are usually much larger when value-weighted portfolios are used. The growth in turnover has been greater for large stocks than small ones. There are a number of potential exogenous changes in the markets that could be behind the increase in turnover. One is the dramatic decline in commissions. For most of the NYSE s history, commissions were based solely on the price of the traded stock, and were the same amount per share regardless of the number of shares traded. In 1968, in response to pressures from the SEC and institutional investors, volume discounts were built into the commission scale for orders of more than 1,000 shares. Fixed trade commissions, which had been industry practice since 1792, were ended entirely by the Securities Acts Amendments of Negotiated trade commissions became legal on May 1, 1975, and many institutional investors immediately began 6

7 paying lower trading costs, particularly on large trades. Ofer and Melnick (1978) examine trades of ten banks trust departments in the first year following deregulation and find that they paid, on average, 36% less in commissions than under the old fixed-price schedule. Commissions did not decline as quickly for retail investors. Nevertheless, trades that would have cost a retail investor hundreds 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, trading volume 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. In 1982, the Kansas City Board of Trade launched the first stock index future, a contract on the Value-line index. The success of that contract led the Chicago Board of Trade to introduce options on the S&P 500 contract. Options on indices followed in 1983 when the CBOE introduced options on the CBOE 100 index, which later became the S&P 100 index. All of these contracts can create additional demand to trade stocks. All of them can be used to hedge risks in the market, or can be used in conjunction with stocks to create alternative payoffs. Arbitrage between futures and stock markets also leads to increased trading. Another change is the growing importance of institutional investors. According to the 2001 NYSE fact book, institutional investors held only 7.2% of U.S. equities at the end of At the end of 1970, institutional holdings made up 28.2% of U.S. equities. Holdings reached 45.8% at the end of 2000, and continues to grow. This affects turnover because institutions trade more frequently than individuals. One reason they trade more frequently is that trading costs for institutions tend to be lower than for retail investors. In addition, many do not pay taxes and are unconcerned about triggering capital gains through trading. A fourth change in the equity markets has been the move to finer price increments. The minimum price increment, or tick, for NYSE stocks had been $0.125 since In June of 1997, the tick was halved to $ In January 2001, decimalization began and the tick was reduced 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 the beginning 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 and convenience of online trading usually encourages people to trade more (Barber and Odean (2002)). For institutions, program trading involving dozens or even hundreds of stocks, is commonplace now but was impossible in the 1960's. B. Volatility I calculate separate measures of market, industry, and firm-specific volatility. The methodology I use to calculate these measures is similar to that of Campbell et. al. For the market, I calculate two measures of volatility. The market variance for day t is the square of the difference between the return of the value-weighted index on day t, and the average return of the value-weighted index over the entire period. That is, 2 = ( R R ) 2 ( 1) σ Mkt, t Mkt, t Mkt 7

8 The absolute value of the market return deviation on day t is the absolute value of the difference between the value-weighted index on day t and the average return of the value-weighted index over the entire period. The value-weighted index in each case is composed of NYSE and Amex stocks only. R = R R ( 2) Mktt, Mktt, Mkt I next calculate analogous measures of industry volatility for each of the forty-eight Fama and French (1997) industries. The industry variance for industry i on day t is the squared difference between the industry return on that day and the market return. The absolute value of the return deviation for industry i on day t is the absolute value of the difference between the industry return on day t and the market return on day t. I then take weighted averages of the industry variances and absolute values of industry return deviations using industry capitalizations as weights to produce aggregate industry measures. That is, σ = ω ( R R ) ( 3) Ind, t i i, t Mkt, t i= 1 R = ω R R ( 4) Ind, t i i, t Mkt, t i= 1 Whereω = the percentage of market capitalization in industry i i 48 Finally, analogous measures of idiosyncratic stock volatility are calculated for each day. I first calculate the squared difference between each stock j s return and its industry return for day t and the absolute value of the difference between stock j s return and its industry return that day. I then compute aggregate measures of idiosyncratic stock volatility for each day by taking weighted averages of individual stocks squared differences between return and industry return and the absolute value of the differences between individual stocks returns and the returns of their industries. Weights are the capitalizations of each individual stock. The measures of individual stock volatility can be written as This procedure is used in Christie and Huang (1995) to decompose volatilities. It is also used in σ N 2 2 Stk, t J J, t i ( J ), t J = 1 = ϖ ( R R ) ( 5) N R = ϖ R R ( 6) Whereϖ = Stk, t J J, t i ( J ), t i = 1 J the percentage of industry i' s capitalization in firm J Campbell et. al. (2001). They observe that individual industry and individual stock measures of volatility may be off if the industry beta with respect to the market differs from one, or if the 8

9 stock beta with respect to the industry differs from one. Campbell et al. note that these deviations, however, will cancel out when aggregate measures of industry or return volatilities are calculated. Christie and Huang (1994) examine monthly idiosyncratic volatilities over They find that idiosyncratic volatilities vary over time, and are greater during economic downturns. They also demonstrate that idiosyncratic volatilities are much larger for small firms than for large firms. Campbell et. al. examine volatilities of U.S. stocks over Most of the volatility is 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. Put another way, the correlation of returns of individual stocks with each other is declining over time. Campbell et. al. also look more closely at the ten largest industries. For each industry, firm specific volatility increases over their sample period. Campbell et. al. propose several possible reasons for increasing volatility over time. One is a trend toward breaking up conglomerates. Another is the tendency of firms to go public earlier. A third is that granting stock options to executives provides an incentive for more risk taking. Finally, Campbell et. al. suggest that the growth of derivative markets could also be behind the increase in firm-specific volatility, but note that most earlier work finds that introducing derivatives decreases volatility. For the market, industry, and firm volatility series, like the market turnover series, I calculate 100-day moving averages. The 100 day moving average of the value-weighted market variance 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 I truncate the volatility from the 1987 market crash because, at 0.008, it is very large relative to the volatility for the rest of the sample period. The 100-day moving average of the Fama-French industry variance is shown in Fig 2b. Like the moving average of the market variance, it has no trend. Industry variances are correlated with market variances, but are generally lower and do not fluctuate as much. Industry variance is particularly high in 1999 and 2000 when the technology and telecommunications sectors were variable relative to the market as a whole. Moving averages of individual stock variances are shown in Fig. 2c. With the exception of the 1987 crash, 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 In most ways, my findings on the intertemporal behavior of volatilities are similar to those of Campbell et. al.. Like them, I find firm-specific variances to be larger than the market variance, which is, in turn larger than the average industry variance. Also, like Campbell et. al., I find that all three volatilities are positively correlated. A major difference between this paper and theirs is that I find no evidence of a trend in the firm-specific variance series. This may be because my sample period ends in 2004 while Campbell et. al. s. ends several years earlier in A more significant difference though is that my sample is restricted to NYSE/Amex stocks while Campbell et. al. also include Nasdaq stocks. Nasdaq stocks appear in CRSP at the end of 1972, almost ten years into the sample period. Nasdaq stocks make up increasing proportions of both the number and capitalization of stocks over the sample period. It seems likely that much of the increase in firm-specific volatility that Campbell et. al. document arises from the inclusion of more volatile stocks in the universe of publicly traded firms. Unfortunately, trading volume and 9

10 hence turnover are not directly comparable across NYSE/Amex and Nasdaq stocks. Hence I confine my sample to NYSE/Amex stocks only. III. The Changing Relation Between Turnover and Volatility A. The Determinants of Turnover So, 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 and volatility. One is that there is now much more trading for liquidity purposes. It would not be surprising if investors were more likely to sell stock for consumption purposes since the costs of trading have declined significantly over the past forty years. Increased liquidity trading could show 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 increased liquidity in recent years allows investors to better exploit private information by trading more shares. We would see this in the data as increases in the turnover generated by a given level of volatility. This could occur in conjunction with increased liquidity trading, as liquidity trading makes 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 more information is being incorporated into prices through trading, rather than as result of public announcements. It has been long-established that much information is incorporated in stock prices 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 open than 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 by market or industry returns, or by public news announcements. Both articles point to trading on private information as the primary source of stock returns. Numerous microstructure papers (e.g. Hasbrouck (1991a) and Hasbrouck (1991b)) demonstrate this more directly. Buy orders are followed by permanent price increases while sell orders are accompanied by permanent price declines. If the proportion of information that is incorporated through trading increases over the sample period, we would expect higher regression R 2 's in later years when volatility is regressed on turnover. Table II reports correlations between the daily market turnover and daily measures of market, industry, and individual stock volatilities. Market turnover is correlated with all of the volatility measures, but the correlation is higher with measures of industry volatility than with measures of individual stock or particularly market volatility. The correlation between turnover and the variance of market returns is lowest at In general, measures of volatility based on absolute values of return deviations have slightly higher correlations with market turnover than do variances. For example, the correlation between the market turnover and the variance of Fama-French industry returns is , while the correlation between market turnover and the average absolute value of the difference between the market and the Fama-French industry return is Volatility measures based on Fama-French and two-digit SIC codes are very highly correlated. For example, the correlation between the mean absolute value of the two-digit SIC 10

11 code industry return and the mean absolute value of the Fama-French industry return is Because they are so highly correlated, in the rest of the paper I focus exclusively on industry and firm-specific volatilities as defined by Fama-French industries. Table III provides autocorrelations and partial autocorrelations of daily market turnover and daily measures of market, industry, and firm variance. All of these series exhibit positive autocorrelation. The first order autocorrelation of market turnover is , and all of the first five 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 returns and industry returns, the first order autocorrelation is Autocorrelations remain high for many lags, and remain above 0.68 after seven days. Industry volatilities are also highly autocorrelated with first order autocorrelations of when industry volatility is measured as the average absolute value of the difference between industry and market returns. Market volatility is also significantly autocorrelated, although the autocorrelations are smaller than either industry or individual firm volatility. The autocorrelations in Table III underscore the difficulty in measuring the relation between turnover and volatility. Lo and Wang (2000) show that weekly turnover is highly autocorrelated 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 quadratic detrending as well as first differences, but none seem completely successful in producing a stationary series. Hence, they employ the raw turnover data in most of their tests. I follow the example of Bessembinder, Chan, and Seguin (1996) who subtract the average turnover from the previous forty days to calculate a daily abnormal turnover. I subtract the mean market turnover from the previous 100 days from turnover and the mean volatility from the past 100 days from each volatility measure to calculate abnormal turnovers and volatilities. To examine the relation between 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 day of the week dummies, and a dummy variable that takes a value of one if the day is in the first half of January. Even when abnormal turnover and volatilities are used, regression residuals remain highly autocorrelated. Hence, Cochrane-Orcott regressions, which assume the residuals follow an AR(1) process are estimated as: Turn & ρturn & = α ( 1 ρ) + α ( & σ ρσ& ) + α ( & σ ρσ& ) + α ( & σ ρσ& ) t t Mt, Mt, 1 2 Indt, Indt, 1 3 Jt, Jt, 1 n n + α ( Days ρdays ) + α ( Jan ρjan ) + δ ( WkDay ρwkday ) + ε ( 7) 4 t t 1 4 t t 1 n t t 1 n= 1 Where Turn t is the market turnover on day t, D is the coefficient from the AR(1) process, F M,t is the standard deviation of the market on day t, F Ind,,t is the weighted average of the industry standard deviations for day t, F J,,t is the weighted average of each stock J s standard deviation on day t, Days is the number of calendar days since the last trading day, Jan is a dummy variable Turn & ρturn & = α ( 1 ρ) + α ( R & ρ R & ) + α ( R & ρ R & ) + α ( R & ρ R & ) t t Mkt, t Mkt, t 1 2 Ind, t Ind, t 1 3 Stk, t Stk, t 1 n n + α ( Days ρdays ) + α ( Jan ρjan ) + δ ( WkDay ρwkday ) + ε ( 8) 4 t t 1 4 t t 1 n t n= t 1 t t 11

12 that takes a value of one for days in the first half of January, and WkDay is a serious of for dummy variables that take values of one on Monday, Tuesday, Thursday, and Friday. In calculating weighted averages, weights are the proportion of market capitalization represented by the stock or industry on that day t. In (7) and (8), a dot over a variable signifies the difference between the variable and its average value over the previous 100 days. WkDay n is a dummy variable that takes a value of one if the day of the week is day n, where the 1-4 represent Monday, Tuesday, Thursday, and Friday. Panel A of Table IV reports regression results when volatilities are measured as the average absolute value of the return deviation. The first row reports the regression when all days are included, but the average absolute value of the deviation between the market return and its average return is the only volatility measure. In the regression, the coefficient on the number of trading days is and is highly significant. All else equal, there is less turnover on Mondays and following holidays than on other days. The coefficient on the January dummy is positive 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 , with a t-statistic of Greater market volatility is associated with greater market turnover. The next two rows report regressions that include, respectively, the average absolute value of industry return deviations only, and the average absolute value of stock return deviations only. The adjusted R 2 goes from when only market volatility is used to when only industry volatility is used, to when only firm-specific volatility is used. The regression reported in the fourth row of the table includes all volatility measures and observations from the entire sample period. The adjusted R 2 is , not much different from the value of obtained when only firm-specific volatility is included. In other words, firmspecific volatility is the principle determinant of market turnover. Neither market-wide volatility nor industry volatility has much impact on share turnover. This can also be seen by comparing the coefficients on the three volatility types. At , the coefficient on the firm-specific volatility is 54 times as large as the coefficient on the market volatility. The coefficient on the abnormal industry return is actually negative, albeit an insignificant So, if the market return deviates from its average by 1% on a given day, market turnover will increase by %. If, across the 48 Fama-French industries, the mean industry return deviates from the market return by an additional 1%, the market turnover will decrease by %. If, on average, each stock s return deviates from the return of its Fama-French industry by an extra 1%, market turnover will increase by %. The lesson to be drawn from Table IV is that it is individual stock volatility, not marketwide 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 it has received. This result suggests that Gallant, Rossi, and Tauchen (1992), as well as most of the papers surveyed in Karpoff (1987), miss the boat in trying to estimate the relation between volatility and trading by using market volatility rather than individual firm volatility. This finding also suggests that most trading associated with volatility is in response to information about specific companies. Indeed, this is the type of information, not information about entire industries or the market as a whole, that is likely to be private information for some investors. If re-weighting a portfolio was a primary reason for trading, I would expect to see a stronger relation between industry volatility and turnover. If allocation between consumption and 12

13 savings were a major reason for the relation between volatility and trading, I would expect turnover to be especially sensitive to market-wide volatility. Instead, market turnover is driven by firm specific volatility. The last regression in the table omits all returns from October The market variance on October 19, 1987 far exceeds that of any other day, and there are other days around the crash with large volatilities as well. As can be seen in Table IV though, coefficient estimates are not affected much by omitting the crash. The coefficient on the absolute value of abnormal stock returns increases slightly from to Other coefficients decline slightly. It remains true that idiosyncratic stock return volatility is the most important determinant of market turnover. Panel B reports regressions that use variances rather than the absolute value of return deviations as measures of volatility. These regressions do not appear to be as well specified. Adjusted R 2 's are much smaller, and, omitting the 1987 crash has a much bigger impact on coefficients. It remains the case that the volatility of firm specific stock returns are far more important in determining market turnover than either industry or market variance. The coefficient on the average idiosyncratic stock variance is 11.2 times as large as the market variance and almost 3.7 times as large as the industry variance. B. How the Relation Between Volatility and Turnover has Changed Market-wide turnover increased eightfold over the 42 years from 1963 through If the increase is due to more liquidity trading, we would expect the intercept from a regression of turnover on volatility to increase over time. If increased liquidity allows investors to exploit private information by trading more, we would expect the coefficient on volatility to increase over 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 about an industry or the market, it is firm specific volatility which is more likely to be related to trading on information. I rerun the regressions from Table IV that include all variables, but now also include interactions between the explanatory variables and a linear trend variable measured as the number of trading days since the first CRSP return date. Here as before, I run Cochrane-Orcott regressions because residuals are positively autocorrelated even after the moving average of the previous 100 days is subtracted from each variable. Results are shown in Table V. Coefficients and t-statistics from the regression that uses absolute values of return deviations as a measure of volatility are shown in the first two columns of the table. The coefficient on the time trend variable itself is positive and highly significant. Market-wide turnover that is not attributable to volatility has been increasing over the sample period. There is greater turnover from liquidity trading 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 between time and each of the volatilities. Market turnover has become more sensitive to market, industry, and particularly to idiosyncratic stock volatility over This could mean that more information is being impounded in prices through trading, or, alternatively, that greater liquidity allows more trading on a given piece of information. When the trend variables are included, over 43% of daily abnormal turnover is explained by volatilities, the January Dummy, and the elapsed days since the last trading day. Note that the estimated AR(1) parameter used in the Cochrane- 13

14 Orcott regressions was , indicating significant remaining autocorrelation even after subtracting the moving average from turnover and every explanatory variable. The last two columns of Table V report coefficients and t-statistics from the regression that uses the variance of returns as a measure of volatility. The adjusted R 2 is , much less that the adjusted R 2 of when volatility is measured by the absolute value of return deviations. The main conclusions from the first regression, however, also hold here. There is more turnover that is unassociated with volatility, that is turnover from liquidity trading, and market turnover has grown significantly more sensitive to every kind of volatility over the sample period. It is difficult to capture precisely how the sensitivity of turnover has changed over time with a simple, linear trend model. So, as another approach, I divide the period into six seven-year periods. The regressions of market turnover on market, industry, and stockspecific volatilities are reported in Table VI, with Panel A reporting regressions that use the absolute value of return deviations to measure volatilities, and Panel B reporting regressions with variances of returns. In Panel A, regression intercepts are much higher toward the end of the sample period, increasing from in to in Hence, as suggested in Table V, stocks turn over more rapidly toward the end of the period for liquidity purposes. Adjusted R 2 's in Panel A increase over time from in to over A larger portion of market turnover is explained by volatilities, the number of days since the last trading day, and January toward the end of the period than in the 1960's. The coefficient on the average absolute value of the stock returns increases from in steadily to in before falling slightly to in The coefficients 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 industry variance led to lower market-wide turnover. The coefficients on market volatility become positive and significant in the last three periods, suggesting that more market information is incorporated into prices through trading in the latter part of the sample period. As a whole, the regressions reported in Panel A of Table VI show that the association between turnover and volatility became stronger over It is worth noting that in every subperiod, individual stock volatility is a more significant determinant of market turnover than either market or industry volatility. Again, turnover is due to firm-specific returns, not market-wide returns. Regressions using abnormal market, industry, and stock variances are reported in Panel B. These regressions do not seem to be as well-specified as the regressions in Panel A. Adjusted R 2 's are lower in every subperiod. Most of the same intertemporal patterns emerge though. The intercept increases steadily over the six periods, showing that turnover irrespective of variances is rising over time. The coefficient on abnormal market variance increases across the six subperiods, indicating that turnover becomes increasingly sensitive to market variance. The intertemporal pattern for coefficients on industry and stock variance are not as clear. These coefficients are generally higher toward the end of the sample period, but the increase is not monotonic, with the coefficients declining from the period to the period. So far, I have not explored the possibility that a larger portion of information is incorporated in prices through trading than in the past. If true, this could also explain why 14

15 turnover has increased steadily over the last 40 years while stock return volatility in 2004 was similar to volatility in To test this, I run Cochrane-Orcott regressions with the absolute value of the average abnormal stock return as the dependent variable, and market turnover, dummy variables for the day of the week and for the first two weeks of January, and the number of calendar days that have elapsed since the last trading day as explanatory variables. That is, I run the following regression, with all variables defined as before: I use the average absolute value of the abnormal stock return, rather than industry or market returns because it is the volatility of individual stock returns that is most strongly associated with market turnover. The regression is run for each of the six consecutive seven year subperiods of If more information is being impounded in stock prices through trading, we would expect R 2 's to increase over time. Results are shown in Table VII. For the first six regressions, I drop all the explanatory ( ) ( R & ρ R & ) = α ( 1 ρ) + α Turn & ρturn & + α ( Days ρdays ) + α ( Jan ρjan ) Stk, t Stk, t t t 1 2 t t 1 3 t t 1 4 n n + δ ( WkDay ρwkday ) + ε ( 9) n= 1 n t t 1 variables except market turnover. For these regressions, changes in R 2 's over time cannot be attributed to changes in the significance of other variables. Looking across the six subperiods examined in these regressions reveals that the adjusted R 2 's increase steadily from for to for Considerably more of the individual stock volatilities are explained by turnover at the end of the sample period. It is also interesting that while the R 2 's increase over the period, the coefficients on the abnormal market turnover fall from to While turnover explains a larger portion of individual stock volatility, a given level of turnover has a smaller impact on stock returns. Turnover explains more of stock return volatility because 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 dummy for January, and the number of calendar days since the last trading day. In these regressions it is also true that the adjusted R 2 's increase steadily over the sample period. As before, the coefficient on market turnover declines across the subperiods. All of the three explanations for the changing relation between turnover and volatility receive some support from the data. Liquidity trading seems to have increased. There also appears to be more trading associated with private information. Finally, it appears that more information is being incorporated in prices through trading rather than disclosure. Which factor is more important in explaining the increase in turnover? I next breakdown turnover each day into turnover associated with volatility and turnover that is independent of it. To do so, I first regress turnover each day on the different volatilities, a linear time trend, and interactions between the time trend and volatilities. For this regression, I use a Cochrane-Orcott procedure to adjust for autocorrelation, but do not adjust the variables by subtracting out their moving averages. To estimate the proportion of turnover attributable to volatility each day, I drop the intercept and time trend variables, and use the coefficients from the volatility variables and the variables formed from interactions between the volatilities and time trend to predict turnover. t 15