Ilia D. Dichev
Emory University
Kelly Huang
Georgia State University
Dexin Zhou
Emory University
August 2, 2011
Abstract: This study investigates the effect of high trading volume on observed stock volatility.
The motivation is that volumes of U.S. trading have increased more than 30-fold over the last 50 years, truly transforming the marketplace. Given existing work that links volume and volatility as simultaneously driven by fundamental information, we are specifically interested in the effect of increased trading controlling for such information. We investigate a number of settings, including three natural experiments (exchange switches, S&P 500 changes, dual-class shares), the aggregate time-series of U.S. stocks since 1926, and the cross-section of U.S. stocks during the last 20 years.
Our main finding is that there is a economically substantial positive relation between volume of trading and stock volatility, especially when volume of trading is high. The conclusion is that stock trading can inject volatility above and beyond that based on fundamentals.
Comments welcome, please send to:
Ilia D. Dichev
1300 Clifton Road
Goizueta Business School, Emory University
Atlanta, GA, 30037
404-727-9353 idichev@emory.edu
We appreciate the helpful comments of workshop participants at Yale University, Florida State
University, Southern Methodist University, Wharton, Washington University, Norwegian School of
Economics and Business Administration (NHH), and especially those of Linda Bamber, Tarun
Chordia, Feng Li, Catherine Schrand, and Lasse Pedersen.
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1. Introduction
We investigate the effect of high volumes of trading on stock volatility. Given existing work that links volume and volatility as simultaneously driven by the flow of fundamental information (e.g., Karpoff 1987), we are specifically interested in the effect of high volumes of trading holding fundamental information constant. The motivation is that volume of stock trading has exploded during the last 50 years, increasing from an annualized value-weighted NYSE/AMEX turnover of less than 10 percent in 1960 to more than 300 percent in 2008-2009 (see evidence in
Figure 1). A change of this magnitude can be fairly characterized as transforming the marketplace, and it is important to carefully document and assess the parameters of this transformation. Note that dizzying growth in stock market trading is just one manifestation of a powerful trend of great increases in trading volume across a number of investment assets, including bonds, commodities, currencies, and many kinds of derivatives. Thus, the findings of this study have broad utility for the investment world at large.
There is much theory and empirical evidence about the effect of liquidity and volume on the level of stock prices and returns, see for example the review in Amihud, Mendelson, and Pedersen
(2005). Generally, the findings indicate that higher liquidity and volume are highly prized and rewarded by investors; they are correlated with lower transaction costs, easier creation and adjustment of investment positions, and lead to higher prices (e.g., Branch and Freed 1977; Jones
2002; Brennan, Chordia, and Subrahmanyam 1998). In contrast, there has been little attention on the effect of trading on the second moment of returns, especially controlling for fundamental information. Theoretically, there is a solid argument that higher investor participation and trading volume lead to better price discovery and therefore to prices that are closer to fundamental values; thus, more trading reduces estimation noise and reduces the volatility of returns . There are other
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factors, however, that confound this prediction. For example, the large presence of what is collectively known as noise traders can lead prices away from fundamentals, whiplashing them in temporary swings and reversals (Campbell, Grossman, and Wang 1993). The interplay of these two opposing forces is not understood well, and we have a poor idea of which effect dominates in practice, especially in view of the dramatic increase in trading during the last half century.
The most significant problem in this investigation is that both volume of trading and stock volatility are endogenously driven by information flow, where news drives both volatility and volume up (Schwert 1989). We address this problem in two ways. First, we identify a series of three natural experiments, where the setting controls for information flow and firm and business characteristics, while there is a significant exogenous variation in volume of trading. Specifically, we look at stock switches between major U.S. exchanges and S&P 500 index changes; both of these settings are characterized by substantial changes in volume, while there is little change in fundamentals, at least in the short windows surrounding the effective dates. We also examine dualclass U.S. stocks where typically the two classes have identical cash flow rights but different control rights and different liquidity. Our main finding is that in all of these settings increased volume of trading triggers a reliable increase in return volatility.
Second, we explore the relation between volume of trading and stock volatility in the aggregate time-series of U.S. stocks since 1926 and in the cross-section during the last 20 years, while controlling for information flow and other determinants of volatility. The advantage of this setting over the natural experiments is better calibration of the examined effects to the natural properties of the population of U.S. stocks; the disadvantage is losing some of the sharpness of the controls in the natural experiments. We find that the correlation between annual aggregate measures of volume and volatility is on the magnitude of 50 percent in the aggregate time-series, which is highly statistically significant and economically substantial. Thus, there is suggestive
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evidence that much of the historical variation in stocks is due to the widely different secular levels of trading over time. We also find a positive and convex relation between volume and volatility in the cross-section of stocks, where the relation is much clearer and stronger for high volumes of trading. In efforts to more precisely quantify and calibrate the effect of trading on volatility, we estimate that in recent years trading-induced volatility accounts for about a quarter of total observed stock volatility.
Summarizing, these results suggest that trading can create its own volatility above and beyond the volatility due to fundamentals. The implication is that the benefits of increased liquidity and trading are not a one-way street. Given that existing evidence on the benefits of liquidity is mostly for relatively low levels of trading, the combined impression with the results in this study is that there is perhaps a point (or range) of optimal levels of trading, and that there are very real costs of going beyond that. Considering the relentless march of trading volume up and up during the last several decades, such considerations raise troubling questions about the future and suggest a possible need to re-evaluate the institutional and regulatory framework of trading. Further research can help in answering these questions.
The remainder of the paper proceeds as follows. Section 2 presents the theory and existing findings. Section 3 provides the empirical design and the results for the three natural experiments, while Section 4 contains results for the broad sample of U.S. stocks. Section 5 discusses the results and suggests some research and policy implications. Section 6 concludes.
2. Theory and background
Our goal is to investigate the effect of high volumes of trading on stock volatility, with a particular emphasis on the effect of intense trading controlling for the flow of the underlying fundamental information. The motivation is that volume of stock trading has increased
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tremendously during the last 30 to 50 years (e.g., Baker and Stein 2004; Chordia, Roll, and
Subrahmanyam 2010). Figure 1 provides an illustration of this phenomenon for the full history of volume data on the major U.S. exchanges, 1926-2009 for NYSE/AMEX and 1983-2009 for
Nasdaq; specifically, Figure 1 plots annualized value-weighted turnover (volume/shares outstanding) over time.
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An examination of Figure 1 reveals a dizzying growth in trading with
NYSE/AMEX turnover of less than 10 percent a year during 1940-1970, a gradual and somewhat uneven rise during 1970-2000, and hitting a high of more than 300 percent in a pronounced spike of trading in the late 2000’s, a more than 30-fold increase in a relatively short period of time. The
Nasdaq time series, although much shorter, reveals a similar pattern of 6-fold increase but with a less pronounced spike in the most recent years. The magnitude of these increases is truly remarkable and has apparently transformed the marketplace. Simply put, a market in which securities change hands once in 10 years is likely to be qualitatively different from a market in which securities change hands three times a year, and this difference likely leads to qualitatively different outcomes in fundamental issues like security valuation, equity risk, and market efficiency.
Our study assesses some of these possibly material changes, concentrating on the effect of high volumes of trading on stock volatility.
There is a large existing literature which maps out a positive relation between volume and volatility. Generally speaking, this literature investigates the endogenous co-movement of volume and returns, where the basic message is that “volume moves prices,” see Karpoff (1987) for an early review. While this literature is rather broad, its unifying intuition is that new information sparks trades and triggers corresponding price revisions over relatively short horizons. There have been
1 AMEX volume data is available since 1963, here combined with the NYSE data series for parsimony. The value weighting is accomplished by calculating for each trading day the total dollar-value traded that day (aggregated over all stocks) and dividing it by aggregate market value outstanding as of that day. This measure is then annualized by multiplying the mean daily turnover for that year by the number of trading days in that year (approximately 250 days for most years).
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significant accomplishments in this line of research, which studies issues like the effects of private vs. public information, information asymmetry, and information with different precision on volume and security prices (Roll 1988; Morse 1980; Easley, Kiefer, and O’Hara 1996, 1997; Kandel and
Pearson 1995; Bamber, Barron, and Stober 1999).
In contrast, we are interested in the effect of high volumes of trading holding fundamental information constant. The large increases in trading in Figure 1 provide the motivation for pursuing such a perspective. It is possible that newer and faster information sources like the Internet lead to more news and more trading, and there is some evidence that fundamentally the economy today is more volatile than in the 1960’s (Wei and Zhang 2006; Irvine and Pontiff 2009). But it seems implausible that the more than 30-fold increase in trading since the 1960’s is purely driven by more information. Even more telling in this regard is actually the comparison of the 1940-1970 period with the 1926-1940 period in Figure 1. Note that the 1926-1940 period also represents a prolonged episode of heavy trading, and while its intensity is not as pronounced as in the most recent years, it is remarkable that annualized turnover both before and after the 1929 crash was over 100 percent a year, ten times as much as during the 1940-1970 period (which includes watershed information events like World War II and the Korean war). Differences of such magnitude are difficult to square with just differences in the amount of available information, and it is highly unlikely that information sources were better in the 1920s than two decades later.
In any case, in addition to the indirect and only suggestive evidence in Figure 1, there is more specific evidence that a great amount of trading is not driven by fundamental information, and that the amount of such trading has increased over time. One example of non-information trading is
“liquidity trading,” i.e., trading driven by needs like personal consumption or windfalls as opposed to stock fundamentals. Other trading can be thought of as triggered by a number of different reasons, which span a continuum between trading purely driven by fundamental information to
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trading purely driven by non-information motivations. In fact, much and maybe even most of trading seems to fall in the grey area between pure-information and non-information trading
(Chordia, Huh, and Subrahmanyam 2007). A vivid illustration of this grey area are various types of algorithmic trading, which apparently account for more than 70 percent of all trading today
(Hendershott, Jones, and Menkveld 2011). A trading algorithm based on momentum, for example, is based on information from the past pattern of security prices, essentially from past trading itself.
But since momentum trading also shapes prices, there is a lot of room for feedback loops and other interactions which affect prices but have nothing to do with actual fundamental information about the traded stocks. More generally, a lot of trading seems to be based on watching and reacting to the actions of other traders, and has little to do with true underlying fundamentals. It is the effect of this kind of trading and this type of effects that we want to capture in our investigation.
This trend towards algorithmic and technical-type trading has been turbocharged by the great reduction in transactions costs and improvements in technology during the last twenty to thirty years. Bid-ask spreads and commissions are an order of magnitude lower than they were just a generation ago, and that greatly expands the set of real or perceived profitable trades. Computing and communication technology has been a great enabler of the rising volumes in recent years, where traders can now execute thousands of orders a minute, often completely automated. In most likelihood, sentiment has also played considerable role in the increase of trading volume, where just a generation or two ago stock trading was a fairly arcane and specialized activity but has since become much more accepted and even embraced in society. Sentiment is also likely the chief driver of the early spike in volume of trading during the 1920s, when there is little room for the transaction cost and technology explanation.
Note that even for trading that is purely based on information there is likely a qualitative difference between the kinds of market and valuation equilibria that obtain when volume of trading
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differs by a factor of ten or more. The existing literature already offers evidence consistent with this conjecture, mainly on the effect of volume of trading on transaction costs and security prices.
A number of studies have documented that increased volume of trading is reliably related to decreased transaction costs (bid-ask spreads, brokerage fees, execution costs) where these two variables reinforce each other, and innovations in either one can lead to changes in the other
(Branch and Freed 1977; Copeland and Galai 1983) . Another reliable finding in the liquidity literature is that, everything else equal, higher liquidity leads to lower cost of capital and higher prices (Amihud and Mendelson 1986; Brennan, Chordia, and Subrahmanyam 1998; Liu 2006 ) .
Although in these studies volume of trading is usually just one of several liquidity variables, much of this literature can be thought of as examining the effect of trading on the first moment of prices, holding everything else constant.
More generally, a summary impression from the existing liquidity literature is that higher liquidity is an almost universally good thing. Since increased volume of trading and decreased transaction costs reinforce each other in a virtuous circle, it seems like higher liquidity is a real winwin for all parties involved. Investors like higher liquidity because it allows them to build and adjust investment positions easier, faster, and cheaper, and because it leads to lower cost of capital and higher asset prices. Market-makers also like liquidity because it generally makes their job easier and less risky. In addition, liquidity and demand for liquidity generally expand the size and the breadth of the market, both in terms of enhanced investor participation and in terms of new security offerings.
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In contrast to much research on the relation between liquidity and the level of asset prices, there is little evidence on the relation between volume of trading and the second moment of returns,
2 An exception to this generally positive view of the liquidity is a recent literature on stock bubbles documenting that market valuations which seem “too high” compared to fundamentals are typically accompanied by “overtrading” (Hong and Stein 2007), where euphoric investors bid up prices solely in anticipation of even further price appreciation.
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especially controlling for fundamentals, and this is the principal thrust of our investigation.
Theoretically, there is a straightforward argument that increased trading should lead to reduced volatility of stock returns because of the reduction of estimation risk in pricing company fundamentals. If trading leads to the incorporation of relevant fundamental information in security prices, and prices can be thought of as fundamental value plus estimation noise, then the evolution of prices depends on the innovations in both fundamental value and noise. Statistically, as the number of traders and trades goes up, the estimation noise is reduced, which leads to reduced volatility of stock returns. Empirically, there is some confirmatory evidence that more trading indeed reduces volatility. For example, Elyasiani, Hauser, and Lauterbach (2000) find that when stocks move from Nasdaq to NYSE, their volume of trading increases and their volatility decreases.
Such evidence, however, remains limited and is thus difficult to generalize.
In fact, other arguments and evidence suggest exactly the opposite prediction, that more trading induces higher stock volatility. Predictions along these lines have surfaced in various forms in the literature but essentially the idea is that trading produces trading noise, and this noise can lash prices away from fundamentals. For example, Shiller (1981) suggests that stock prices are “too volatile” given the variability of underlying fundamentals. Extending his argument further, if it is trading that produces return volatility above and beyond fundamentals, then a logical next step is to hypothesize that more trading produces more volatility. Cutler, Poterba, and Summers (1989) and
DeLong, Shleifer, Summers, and Waldmann (1990) argue that positive feedback investment strategies can result in excess volatility even in the presence of rational speculators. The fascinating finding that stock returns are on the magnitude of ten times more volatile during trading hours than during non-trading hours (French and Roll 1986) is also consistent with the view that trading
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produces its own volatility.
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A similar conclusion is reached by Black (1986), who argues that noise traders increase trading and simultaneously introduce noise in prices, and thus more trading and higher volatility go hand-in-hand. It is also possible that the relation between trading and volatility is non-linear and even changes sign depending on level of trading, e.g., perhaps elimination of estimation noise and reduction of volatility prevail with low levels of trading but high levels of trading indicate speculative overheating, “irrational exuberance,” and more volatility.
Finally, some observations from practice also suggest a potential link between trading and volatility. Stock exchanges often employ circuit-breakers, a policy of shutting down trading for a pre-specified amount of time after large price drops, either at the aggregate or at the individual security level. Such policies seem questionable and even counter-productive if one takes the view that large price drops indicate dramatic revisions of information, and that it is in precisely such times that trading and the associated pricing process are most needed and should be allowed to freely flow to their new equilibrium levels. The counterpoint is that such policies are likely not accidental and are really the evolutionary outcome of much historical trial-and-error, where the accumulated wisdom indicates that sometimes trading can go haywire for no particular reason related to fundamentals, and then a mandatory break allows everyone to cool off. Thus, such policies are consistent with the view that trading can produce its own volatility, and sometimes this volatility can get so out of hand that the simplest and most effective way to tame it is to completely shut down trading.
3. Natural experiments
We start with a series of natural experiments to investigate the effect of trading volume on stock volatility, holding fundamental information constant. The advantage of this approach is that
3 Note, however, that French and Roll find that trading noise accounts for only about 10 percent of this discrepancy and the rest is due to the more intense production and incorporation of private information during trading hours.
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when an appropriate setting is available, there is a natural and efficient control for potentially confounding variables. Here, as discussed earlier, the most important variables to control for are those related to information flow but an appropriate setting will also naturally control for other influential variables like firm size, profitability, nature of business, corporate governance, investor clientele variables, etc. On a philosophical level, we choose to pursue relatively simple research approaches and probe into multiple settings rather than a more involved investigation in just one setting. The reason is that we believe that no one setting is “perfect,” even after potential exhaustive controls and robustness checks. We also believe in the vital role of “triangulation,” i.e., cross-checking the findings in disparate and fairly independent research settings is the key to reliable conclusions.
There are essentially two types of settings where we can look for exogenous variation in trading while holding other factors constant. The first type of settings relies on temporal liquidity shocks, where we look at the effect of trading on volatility in narrow windows around a significant change-in-liquidity event. Examples include stocks listing and delisting on exchanges, inclusions and drops from popular indexes like the S&P 500, and adoption of significant new rules which promote or hinder trading. The assumption in these settings is that firm fundamentals are largely held constant around the narrow event windows, and that these significant liquidity events provide a substantial amount of exogenous variation in trading. The second type of settings rely on comparisons of essentially the same underlying security across different trading environments, which potentially provide enough exogenous variation in trading intensity while holding fundamentals constant. Examples include dual-stock firms, ADRs and the underlying stocks, and dual-listed shares.
3.1 Stocks switching exchanges
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Our first natural experiment uses the setting of stocks switching exchanges. Previous research finds reliable evidence that exchange switches result in material changes of trading volume. For example, Elyasiani, Hauser, and Lauterbach (2000) find that Nasdaq stocks that move to NYSE/AMEX experience an average increase in volume of 30 percent. Thus, the advantage of this setting is sharply defined events with material changes in liquidity, while the fundamentals of the firms are held largely the same during our narrow windows of investigation. A disadvantage of this setting is that the stock switch itself is an information event, and thus influences both the trading and volatility of stocks. A related shortcoming is that stock switches likely trigger changes in the investor clientele and changes in the information environment, including analyst and media coverage. We deal with these shortcomings in two ways. First, we examine windows which exclude the announcement and effective dates, and so avoid the periods with most informationladen trading. Second, we emphasize relative, within-sample results, which are less subject to the information-event and information-environment concerns. For example, we examine switches from
Nasdaq to NYSE, and rank on variation in trading within this sample.
Based on the Stocknames file on CRSP, we identify 3,611 firms that moved between the major U.S. stock exchanges (i.e., NYSE, AMEX, and Nasdaq) during 1962-2009 (AMEX data is available since 1962, with Nasdaq volume data becoming available in 1983).
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We collect daily trading volume, shares outstanding, and stock returns for these firms from the CRSP daily stock file. As detailed in Panel A of Table 1, after requiring firms to have nonmissing volume, shares outstanding, and return data over one-month before and one-month after listing on a new stock exchange, we are left with 2,860 observations for further analyses. Among these 2,860 switches,
951 moved between NYSE and AMEX, 1,573 firms moved from Nasdaq to NYSE/AMEX, and 336 moved from NYSE/AMEX to Nasdaq. Panel A also reveals that there is a reasonable distribution
4 We use historical exchange code (exchcd) in the Stocknames file to identify exchange switching and 1962 is the first year where we identify cases of exchange switching.
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of switches over time and that mean (median) market value is $546 (128) million. The resulting impression from the statistics in Panel A is that our sample captures the great majority of stock exchange switches and that these are economically important firms and events.
For stocks traded on NYSE and AMEX, daily share turnover is measured as daily trading volume divided by the number of shares outstanding on that day. For stocks traded on Nasdaq, the turnover computation is the same except trading volume is first scaled by two because of the double-counting of volume in dealer markets like Nasdaq (Anderson and Dyl 2005). Note that scaling by two is a rather heuristic correction for the different trading environment and volume statistics on Nasdaq’s dealer market vs. the auction markets on NYSE/AMEX, and the “true” correction is probably smaller and varies across firms and over time, please see the technical notes in Appendix A for fuller explanation. For our purposes, the bottom line from these more involved considerations is that volume comparisons between Nasdaq and NYSE/AMEX are prone to error, especially for estimating absolute levels of change in exchange switching. For this reason, while we present results for all switches, we emphasize the results for the cleaner subsample of stocks that moved between NYSE and AMEX.
For our main results, CH_VOLUME is the change of trading volume, measured as the difference between the average daily share turnover over trading days (-22, -1) and (0, 21), scaled by average daily share turnover over (-22, -1), where day 0 is the day when the firm was listed on the new stock exchange. Analogously, CH_STDRET is the change of stock volatility, measured as the scaled difference in the standard deviations of daily returns one trading month before and after the switch. Descriptive statistics about these two variables in Panel A reveal wide empirical variation in the test sample, which confirms impressions from existing research that exchange switches are a powerful setting to explore the effect of material changes in trading intensity within a short temporal window. The descriptive statistics also reveal that these two variables are highly
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non-normal, with large differences between means and medians and standard deviations greatly exceeding the interquartile range of the empirical distribution. Because of these pronounced nonnormalities, most of our subsequent tests rely on robust measures of central tendency (e.g., medians) and non-parametric tests.
We present two types of evidence to characterize the effect of volume of trading on volatility. First, we present the Spearman correlation between the changes in volume and the changes in volatility before and after the switch, providing a statistical measure of the strength and significance of this relation (results for Pearson correlations are similar). Second, within each test group, we sort change of turnover into quintiles and present the median of change of turnover and the median of change of return volatility for each quintile. One advantage of this portfolio specification is providing an intuitive and immediate estimate of the economic importance of the studied relation. Another advantage is the ability to identify possible non-linear relations between the two variables.
The main empirical results are presented in Panel B of Table 1, by the three types of available switches.
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An examination of Panel B reveals Spearman correlations on the magnitude of
0.23 to 0.35, all highly statistically significant (all p-values < 0.001), suggesting that increases in trading volume increase stock volatility. This impression is confirmed in the quintile portfolio specification, where for all three subsamples the ranking on change in volume produces a nearmonotonic ordering on change in volatility. The magnitude of difference across quintile medians also looks economically substantial; for the most reliable subsample of switches between NYSE and
AMEX, the differences between extreme quintiles suggest that an increase in turnover of about 156 percent produces an increase in volatility of 39 percent. If such magnitudes are anywhere close to a
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The results for a pooled sample of switches are very similar to those presented in Panel B.
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guide for what one can expect in more generalized settings, it is clear that the previously discussed
30-fold increases in volume likely have a pronounced effect on observed stock volatility.
In Panel C, we present the results for a robustness specification that employs the same main tests but uses (-45, -23) and (22, 45) trading windows around the exchange switch event. The advantage of this specification is that it excludes one trading month before and after the switch, so the results are less subject to concerns about unusual patterns of trading around the announcement and effective dates of the switch. Since results are similar across the three types of available switches, for parsimony we limit the additional results to the most reliable subsample of switches between NYSE and AMEX. We find that the tenor of the results remains nearly the same for this specification, with a similar Spearman correlation and similar range in volatility changes across extreme quintiles.
3.2 Stocks added or deleted from the S&P 500
The intuition and the characteristics for this setting are similar to those for exchange switches above. Essentially, the S&P 500 additions and deletions are significant liquidity events with little change in the underlying firm fundamentals, and so they provide another natural experiment to investigate the effects of trading intensity on stock volatility (Hegde and McDermott
2003). The S&P setting, though, has its own unique features, which are important to consider in test design and the interpretation of the results. The first such feature is that trading volume effects are strongly concentrated around the announcement and effective dates of index updates, while these dates span varying time windows over the years (Chen, Noronha, and Singal 2004). During
1976-1989, changes in the index were announced after the close of market on Wednesdays, and the change became effective on the next day at the market’s opening. With the growth of indexing and corresponding increasing re-shuffling and order imbalances on the effective date, Standard & Poors
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began pre-announcing changes in 1989, and the difference between announcement and effective day lengthened to typically a week or two but sometimes as much as a month. The second feature of the
S&P 500 setting is that index additions and deletions are highly asymmetric (Hegde and McDermott
2003; Chen, Noronha, and Singal 2004). Existing research finds reliable evidence that index additions are fairly “clean” good-news events, with a concentrated burst of trading and positive abnormal returns around the announcement and effective dates. In addition, the increased price persists over longer horizon, and there is a moderate increase in trading volume over the long run
(on the magnitude of 10 percent). In contrast, index deletions are a much more problematic and heterogeneous collection of events, often triggered by mergers, spin-offs, bankruptcy, and reorganization and restructuring, where the resulting firm and its stock are fundamentally changed.
As a result, it is much more difficult to derive clean, reasonably-sized samples and offer reliable conclusions for deletions; in fact, these problems are often so severe that many studies of index changes simply ignore deletions. The documented empirical patterns for deletions are also different from additions, with negative returns and increased trading at the announcement and effective dates but with no reliable changes in volume or price over longer horizons.
Our research design for the S&P 500 changes setting is similar to that for exchange switches. The change in volume and volatility variables are defined as before, and again we examine Spearman correlations and quintile rankings for these two variables to assess the strength of their relation. The trading windows are also the same, where the first change window spans trading day periods (-22, -1) and (0, 21), i.e., we examine the change in volume and volatility over one trading month before and after the effective date of the index change. Given the considerations above, this window includes the announcement and effective dates over the whole sample period, and we expect it to reflect the heavy trading accompanying the change event itself. A disadvantage of this window is that the trading also reflects the information content of the event itself, and also
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possible temporary order imbalances. The second time window we consider is changes over trading days (-45, -23) and (22, 45), i.e., one trading month on each side of the first trading window. The advantage of this window is that it reflects only long-term, permanent changes in trading patterns.
A disadvantage is that existing research indicates only small to moderate changes in long-term volume for the S&P 500 setting; recall, however, that since our tests rely to a large extent on withinsample variations in trading volume changes, the low average effects are not much of a problem if there is sufficient variation in changes in volume across firms.
Our sample is from Jeff Wurgler’s website, spanning 1976-2000, see Wurgler and
Zhuravskaya (2002) for sample selection criteria and more detailed properties. Brief descriptive statistics included in Panel A of Table 2 reveal a reasonably large sample of index additions (453) that are well-spread over the years, and much fewer index deletions (86). The results for S&P 500 additions are included in Table 2, Panel B. The Spearman correlations for the two return windows are on the magnitude of 34 and 38 percent respectively, highly significant, indicating a reliable positive relation between trading volume and stock volatility. This impression is confirmed in an examination of the quintile results, where the ranking on change in volume produces a strong and monotonic ranking on changes in volatility. The difference between extreme quintiles also suggests robust economic significance; taken literally, these results indicate that an increase in trading volume of 140 to 180 percent increases volatility by about 40 percent. Generally speaking, the pattern and even the magnitude of results for the S&P 500 additions are remarkably similar to those for exchange switches, indicating a plausible economic commonality behind these two settings.
The results for deletions are in Panel C of Table 2. For the (-22, -1) and (0, 21) window, there is a discernable positive association between changes in volume and volatility; this pattern, however, is statistically and economically weak, and much weaker than the corresponding relation for additions. The reasons for this weak association are not entirely clear but the asymmetric role of
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deletions and the small sample likely play a role. The evidence is much clearer for the (-45, -23) and (22, 45) event window, where there is again an emphatic positive relation between volume and volatility, with high statistical and economic significance. Overall, the evidence from S&P 500 changes is largely in line with the evidence from exchange switches, and indicates a reliable positive relation between trading volume and stock volatility.
3.3 Dual-class U.S. stocks
Our third natural experiment relies on a comparison of volatility across dual-class U.S. stocks, where the two classes usually have identical cash flow rights but different control rights
(e.g., A-class shares have 10 times the voting power of B-class shares) and often substantially different volumes of trading. The advantage of this setting is that it provides a near-perfect natural control for the flow of fundamental information, and thus it is closest to the theoretical constructs of our investigation. Consistent with this intuition, several previous studies use the same or similar settings to control for underlying cash flows. For example, Zingales (1994) uses dual-class firms to study the pricing of voting rights, while Gompers, Ishii and Metrick (2010) studies the difference in insiders’ cash flow rights and voting rights. There are, however, two limitations to the dual-class setting. The first limitation is that the two classes of shares are close substitutes, and thus arbitrage forces keep their returns and volatility of returns within fairly tight bounds. The second limitation is that there is usually a price difference between the two classes, which reflects the value of the control premium. Since the value of the control premium likely varies over time, it creates a separate source of return differences over time, possibly confounding our investigation. We have some priors, though, that the second limitation is unlikely to be critical. Lease, McConnell and
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Mikkelson (1983, 1984) document that superior voting shares generally have a small (5 percent) premium over inferior voting shares.
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Our sample of dual-class stocks is obtained by searching CRSP data from 1965 to 2009 for entries with the same PERMCO and company name but distinct PERMNOs. We also require that both issues are common stocks, are listed on the same major U.S. exchange (NYSE, Nasdaq, Amex or NYSE Arca), and have an overlap of at least four years of trading. The resulting sample has 59 firms and 118 issues, comparable to previous research, and with 7,322 firm-months available for the tests. Brief descriptive statistics in Panel A of Table 3 reveal that these are sizable firms with mean
(median) market cap of $1,789 million ($148 million). Correlations in monthly returns between the two share classes are high at about 80 percent, which confirms that the two classes are largely moved by the same underlying fundamental information. Still, the correlations are sufficiently different from perfect to allow the possible manifestation of disparate volatility effects.
Panel A also contains descriptive statistics for the test variables. For each available pairmonth we calculate the volume for each of the two issues, tag them as “high” and “low” within each pair, and create the variable DIF_VOLUME defined as the volume difference between high volume issue and low volume issue, scaled by the volume of low volume issue. Then, we create the variable DIF_STDRET defined as the stock volatility difference between high volume issue and low volume issue, scaled by the return volatility of low volume issue.
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An inspection of the empirical distributions of these variables in Panel A reveals that indeed there are large differences in liquidity between the two share classes, e.g., the median DIF_VOLUME is about 144.6%, which means that the median turnover for the high class exceeds the low one by close to 150 percent.
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In most cases, the articles of incorporation prohibit favorable dividend payout to the superior voting class shares.
However, inferior voting rights shares sometimes receive favorable dividend payout, where the magnitude of differential payout is generally small. Our sample has been reviewed for such differences, and firms with large differences in dividend payouts have been eliminated.
7
Similar results obtain if we scale by an average of stock volatility of low and high volume issues.
18

Note that the median DIF_STDRET is positive at 2.6 percent, which provides preliminary evidence that shares with higher turnover have higher volatility of returns as well. Finally, the descriptive statistics for both variables are again highly non-normal, which confirms the need for robust tests and non-parametric statistics.
For the main tests in Panel B, we aim to more fully use the natural variation in the sample by ranking the firm-month share pairs into within-firm quintiles on their DIF_VOLUME variable, and reporting the spread in DIF_STDRET across quintiles, where the formal test is on the difference in
DIF_STDRET medians between the two extreme quintiles. The results reveal a strong and monotonic positive relation between DIF_VOLUME and DIF_STDRET, where the difference in medians between the extreme quintiles is 4.2 percent, highly statistically significant. For completeness, we also compute Spearman correlations between DIF_VOLUME and DIF_STDRET for each firm in the sample; the resulting mean and median correlation across firms are reliably positive, confirming the quintile results. Summarizing, the results for dual-class shares are largely consistent with the results for exchange switches and S&P 500 changes. The identified differences in volatility, however, are much smaller for the dual-class setting, most likely due to the constraining effect of arbitrage.
8
4. Large-sample evidence for U.S. stocks
As previously discussed, the thorniest problem in investigating the hypothesized relation between trading volume and stock volatility is how to control for information flow. This is problematic because information flow follows a multitude of public and private channels and is thus difficult to observe and measure. The preceding section provides a series of natural experiments
8 Using similar variables and test design, we find similar results for a comparable setting, trading and volatility for
ADRs vs. the underlying stocks. The results are not tabulated for two reasons. First, we want to keep the paper to a reasonable length. Second, the ADR setting has some complications related to using cross-border data that do not mesh well with the rest of the tests in the paper, which rely on U.S. data.
19

that aim to control for information flow and to establish the existence and the direction of the trading/volatility relation. The disadvantage of these settings, however, is that by definition they are fairly specialized and limited, and thus there is a question about the generalizability and portability of these findings (especially their magnitudes) to the wider world of stock trading. In this section, we address this question by extending the investigation to the full universe of U.S. stocks.
Generally speaking, this extended investigation is more realistic and is well-calibrated to the naturally-occurring properties of the U.S. stock market; this benefit, however, comes at the cost of losing some of the sharp controls in the earlier specifications.
4.1 Evidence from the full time-series of U.S. stocks
The first type of evidence for the broad stock market looks at the long-run record for a sample of the 500 largest U.S. stocks over 1926-2009. We use 500 stocks because data availability is limited to about this number in the early years of the sample, and we want to preserve some measure of comparability over time. The evidence for this specification is presented in Figure 2 and
Table 4, based on annual observations of value-weighted turnover and stock return volatility. An inspection of Figure 2 reveals that the evolution of volatility has a perceptible synchronicity with the broad ebbs and flows of trading volume. When trading is lowest in the quiet years between
1940 and 1970, volatility is also lowest, never exceeding 2 percent (daily measure) over this extended period that includes World War II, the Korean War, and the various upheavals of the Cold
War. Volatility is the highest during the two periods with the most intense trading, peaking at over
4 percent during 1926-1940 and with the second and third highest peak occurring after the mid-
1990s. To be sure, the relation is far from lock-step and one can identify several instances where it is inadequate to describe the empirical behavior of volatility, e.g., volatility spikes during the recession of 1973-74 with no discernable change in volume of trading. The summary impression
20

from Figure 2, however, is that even at this broad-brush graphical level volume of trading and volatility are substantially positively related. This impression is confirmed by the statistical test in
Table 4, with a Spearman correlation of 0.54 between these two variables, which is highly statistically significant and seems economically rather substantial. We also explore a changes specification based on the intuition that levels tests are often subject to confounding influences of other variables, and a simple way to control for these confounding effects is to conduct the same test in the innovations of the variables of interest. The Spearman correlation between the timeseries changes in volume and volatility is 0.32 in Table 4, again with high statistical and economic significance, confirming the hypothesized relation.
By necessity, the evidence in the long-run sample is limited because we lack data to control for fundamental information, e.g., earnings data is only available since the 1960’s. However, we provide one additional analysis that helps to sharpen the long-run evidence, and is perhaps the most direct evidence that high volumes of trading induce noise in stock returns. This analysis is based on the intuition that noise in stock returns eventually has to revert, and thus in the presence of noise long-window stock returns will be less volatile than short-window stock returns. The major difficulty in implementing this intuition is deciding on the horizon of noise reversals, and here we use the technology and results in French and Roll (1986) as a guide. Specifically, we construct a ratio of Actual/Implied volatility for our sample at weekly and monthly horizons. The Actual volatility in the numerator is the standard deviation of weekly and monthly returns measured over each calendar year. The Implied volatility in the denominator is the hypothetical weekly and monthly volatility implied by daily volatility assuming serial independence of returns, i.e., the standard deviation of daily returns over a year multiplied by the square root of the number of trading days in a week or a month. The resulting Actual/Implied ratio has some nice properties and intuitive appeal. Under the null of no noise, which means no negative autocorrelation of returns,
21

this ratio should be close to one, and the magnitude of deviation from this null indicates the magnitude of trading noise.
The results for the Actual/Implied specification are presented in Figure 3 (means across our
500 firms) in two lines corresponding to the weekly and monthly horizons of noise reversals. In addition to the jagged lines linking the actual observations, we also present the same results after a second-order polynomial smoothing. An examination of Figure 3 reveals that the Actual/Implied ratio is mostly less than one, and thus indicates the presence of negative autocorrelations in returns and therefore trading noise. In addition, the graph reveals a distinct inverted-U shape over time, i.e., the ratio approaches its peak and the theoretical ideal of one in the low-volume middle years of the sample, and drops away from that level in the high-volume early and late years in the sample.
Note that this inverted-U shape in Figure 3 is precisely the opposite of the U-shape observed for volume in Figure 2. The implication is that high volumes of trading induce trading noise that makes short-horizon returns considerably more volatile than long-horizon returns. The magnitudes of the
Actual/Implied ratio also allow an estimate of the amount of trading noise in short-horizon returns.
Using the estimates from the smoothed monthly line, trading noise accounts for as much as 15 to 25 percent of the volatility of daily returns in the early years of the sample and 10 to 15 percent in the late years.
9
4.2 Evidence from the cross-section of U.S. stocks over the last 20 years
The second type of evidence for the broad stock market is based on the cross-sectional variation in trading intensity during recent years; specifically, we use a sample of all NYSE-AMEX
9 Note that the well-known bid-ask bounce that causes a negative autocorrelation in stock returns is unlikely to account for these temporal patterns; if anything, a correction for the bid-ask bounce is likely to reveal a more pronounced evidence of trading noise in high-volume environments, especially for the late years in the sample. The reason is that bid-ask spreads have dramatically declined during the last 20 to 30 years in the sample. Thus, the decline in the
Actual/Implied ratio in the late years of Figure 3 is the opposite of what one would expect based on the decline in the bid-ask spreads over this period; therefore, a correction for the bid-ask decline can only make the decline in the
Actual/Implied ratio more pronounced.
22

stocks over 1988-2007. For this set of tests, we avoid Nasdaq stocks because of the previously discussed problems in measuring Nasdaq volume and the need to maintain within-sample comparability. We start with a simple specification that examines the univariate relation between volume and volatility. Stocks are sorted annually into deciles based on their annualized daily volume turnover, and we report median turnover and volatility by decile in Panel A of Table 5. An inspection of Panel A reveals that there is a substantial cross-sectional variation in turnover, with a low of about 10 percent for the bottom decile and a high of 235 percent for the top decile. There is also a substantial spread in volatility between the extreme deciles, from about 2 percent (daily volatility) in the bottom decile to about 3 percent in the top decile, which is both statistically significant and economically substantial. A closer look at the results also reveals that this increase is not monotonic, and indeed there is little reliable variation in volatility from the first decile until about the seventh decile, followed by a quick rise and hitting a high in the top decile. The combined impression from these observations is that while the relation between volume and volatility is generally positive, it is also decidedly non-linear, with volatility only clearly rising in the extremes of high trading.
Of course, the simple analysis in Panel A is inadequate because it does not control for variation in volatility related to fundamentals. Broadly speaking, stock volatility due to fundamentals can come from two sources, changes in expectations about future cash flows and changes in the discount rate. We make no formal attempt to control for discount rate changes because our volatility observations are at the firm-year level, while the empirical variation in discount rates within a year is likely small; in addition, discount rates are notoriously difficult to measure (Elton 1999). We control for changes in expectations about future cash flows by using realized earnings variability over current and future periods as a proxy; specifically, for any firm i and year t, we use the standard deviation of realized quarterly earnings over the current and two
23

future years (i.e., years t, t+1, and t+2). Earnings are defined as earnings before extraordinary items, scaled by the average of beginning and ending total assets, where earnings and asset data are from Compustat. Given much previous evidence of non-normality in the underlying variables and non-linearities in the examined relations, we rely on a portfolio specification to map out the relation between trading volume and stock volatility, controlling for fundamentals volatility. Specifically, we first sort the sample annually on fundamentals variability into deciles, and then within these portfolios sort on volume into deciles. The result is a 10X10 matrix in Panel B of Table 5, with each cell reporting median stock volatility for that portfolio; variation down the columns captures the effect of fundamental variability on stock volatility, and variation across the columns captures the effect of trading volume on stock volatility, controlling for fundamental variability.
An examination of the results in Panel B reveals that fundamental variability is the primary driver of observed stock volatility. The bottom line in Panel B captures differences in the extreme deciles down the columns; while these differences vary, they average 2.5 percent (daily volatility).
This magnitude clearly dominates the corresponding numbers for the effect of trading volume, captured in the extreme-right column, which average about 0.8 percent. Of course, the dominance of fundamental variability is not surprising; in fact, in an efficient market fundamental variability should be the only variable that affects stock volatility. What is more remarkable, actually, is that the effect of trading intensity remains economically large after controlling for fundamental variability. If one thinks of total stock volatility as the sum of volatility due to fundamental variability and volatility due to trading intensity, a literal reading of the results in Panel B suggests that differences in trading intensity account for about a quarter of total stock volatility, a rather significant amount. A closer look at the results in Panel B also reveals the same non-linear pattern in the trading/volatility relation first observed for the univariate specification in Panel A. Moving across columns, there is little reliable variation in volatility from column 1 until about column 7,
24

and then a clear and pronounced increase over the remaining columns, always hitting a high in column 10.
We extend the analysis of the cross-sectional relation between volatility and volume using a multivariate regression. The advantage of the regression specification is that it allows for simultaneous control for a number of variables that have been shown to be determinants of stock volatility. The disadvantage is the normality and linearity assumptions, which are clearly violated in this setting, as shown in previous results. We make appropriate adjustments to variable and regression specification to overcome these limitations; there are residual difficulties however, in the interpretation of the results, especially for their economic magnitude.
Specifically, for the period 1988-2007, we estimate coefficients in the following regression:
STDRET i,t
= β
0
+ β
1
HIGH i,t
+ β
2
VOLUME i,t
+ β
3
VOLUME*HIGH i,t
+ β
4
STDRET i,t-1
+
β
5
RET i,t
+ β
6
STDEARN i,t+2
+ β
7
SIZE i,t-1
+ β
8
AGE i,t-1
+ β
9
LEVERAGE i,t-1
+
β
10
BTM i,t-1
+ ε i,t
Where STDRET is the standard deviation of daily stock returns, HIGH is an indicator variable set to
1 if volume is in the top quartile in year t, VOLUME is the annualized volume turnover, RET is the compounded daily return in year t. STDEARN is the standard deviation of quarterly earnings scaled by the average total assets over years t, t+1, and t+2 with a minimum requirement of eight quarters. SIZE is proxied by the market value of common equity, AGE is the number of years since the firm first appeared in the CRSP database, LEVERAGE is the ratio of debt to assets, and BTM is the book to market ratio.
We introduce the HIGH variable to account for the convex relation between volatility and volume shown in Table 5; thus we expect a positive sign on HIGH*VOLUME. Control variables are from Wei and Zhang (2006) and Brandt, Brav, Graham, and Kumar (2010). Briefly, lagged value of STDRET is included because volatility is known to be positively autocorrelated, and essentially as a catch-all variable that captures omitted variables and other misspecifications.
25

Contemporaneous return is included following the intuition that expected return and risk are positively correlated, and so are their realizations. As above, STDEARN controls for volatility related to fundamentals, we expect a positive sign. The rest of the variables are commonly found in asset pricing tests, and the predicted signs are clear, except for BTM. We replace the original values of all variables with their percentile ranks to control for non-normalities in their distributions and to allow for direct comparison of their strength across variables. Thus, the regression coefficients can be interpreted as the percentage change in volatility for one percent change in the corresponding variable (controlling for all other variables).
The regression results are presented in Table 6, where regressions (1) through (3) use a
Fama-MacBeth specification to control for cross-sectional dependencies in the residuals. We start with baseline specifications (1) and (2), which include only VOLUME and then VOLUME interacted with HIGH. Consistent with the results in Table 5, regression (1) confirms that there is a positive relation between volatility and volume, while the positive and significant coefficient on
VOLUME*HIGH in regression (2) clarifies that this relation is convex, i.e., it is much stronger for high levels of volume. The main results are in regression (3), which includes all control variables.
An inspection of regression (3) reveals that the relation between volatility and volume remains statistically significant and economically substantial after the controls, with sizable coefficients on both VOLUME and VOLUME*HIGH. In fact, the coefficients on VOLUME are larger than those of any other variable except lagged volatility, dominating even the coefficients on SIZE and
STDEARN. A disadvantage of the Fama-MacBeth specification in regressions (1) to (3) is that it essentially assumes time-series stationarity in the volume/volatility relation, and ignores much of the meaningful increase in volume over time. We address this limitation in regression (4), which uses a panel specification with standard errors clustered by firm and year as suggested by Petersen
26

(2009). The results of this panel regression largely remain the same as those for the main specification (3), confirming that these findings are reliable.
4.3 Extensions and robustness checks
We perform a number of extensions and robustness checks for the large-sample results; for parsimony, these results are discussed only briefly and are not tabulated. First, there is a concern that since both volume and volatility are endogenously determined, the hypothesized causality in the volume/volatility relation may run in the opposite direction; specifically, the concern is that environments of high stock volatility are also those with the highest potential for speculative profits, and thus attract more traders and trading. While this story has intuitive appeal, it omits the consideration of opposing forces, namely as uncertainty and volatility go up, market-makers widen the spreads to protect themselves against informed trading, which kills volume. In any case, to further sort out these alternative stories, we perform Granger causality tests in our time-series sample, where we regress current volatility and volume on lagged yearly volatility and volume. Not surprisingly, both volume and volatility have a strong positive autoregressive component but it is the cross-variable cross-lag loadings that are of more interest here. Lagged volume loads up positive and significant on current volatility (coefficient of 0.12 with t-stat of 2.47) but lagged volatility has a negative relation with current volume (coefficient of -0.30, t-stat of -3.85). Overall, the Granger causality evidence suggests that volume drives volatility; the converse relation, if it exists, seems rather weak and may be even reversed.
Another direction in which we extend the results is implementing the Actual/Implied volatility specification used in the time-series analysis (in Section 4.1) for the cross-section of stocks (in Section 4.2), where the expectation is to find lower Actual/Implied ratios for the stocks with the highest trading volume. The cross-sectional results yield a more complicated and nuanced
27

picture; in fact, we find that the Actual/Implied ratio increases with volumes of trading for smaller stocks and for most years. However, the Actual/Implied ratio decreases with volumes of trading for larger stocks and when the most recent years are included. These findings are consistent with the earlier conjecture about the non-monotonic benefits of trading. Taken as a whole, the results imply that increased volumes of trading reduce trading noise and are beneficial for smaller stocks and for comparatively low levels of trading. But after a certain point, this relation reverses and higher volumes of trading lead to more trading noise for large stocks and for the most recent years. One caveat in interpreting these results is that the behavior of trading noise and its reversals are more complicated and cover longer horizons than the ones considered here. For example, momentum is a continuation of existing return trends at intermediate horizons (up to a year), and thus any reversals of momentum “noise” have to happen at rather long horizons, much longer than the weekly and monthly horizons considered here. We leave a more comprehensive investigation of the parameters and horizons of noise reversals for future research.
As another implication of our results, we also explore for a “gone fishing” reduction in summer volatility. Hong and Yu (2009) document a “gone fishing” effect in trading activity, where stock turnover is significantly lower during summer vacation months (July-September) as compared to the rest of the year. We use this finding as providing a natural setting for exogenous variation in trading volume, and investigate whether the lower trading volumes in summer leads to lower stock volatility as well. We first confirm that volume of trading is lower during summer months; specifically, this pattern exists in 64 out of 84 years for our long-term sample. Then, we find that stock volatility is also lower during summer months as opposed to the rest of the year, in 65 out of
84 years. Finally, we take the differences in summer/non-summer volume and volatility, and document a Spearman correlation of 0.45 between them, which is highly statistically significant and
28

economically large. Summarizing, seasonal effects in volume of trading are reliably associated with seasonal effect in stock volatility, consistent with the main results in the paper.
5. Discussion of results
While the results in this paper span a number of specifications and offer many nuances, they seem to converge on some key themes. We find economically substantial evidence that more intensive stock trading is accompanied by increased return volatility. This relation is weak to nonexistent at low to moderate levels of trading but becomes increasingly strong as volume of trading increases. These findings are robust over a number of specifications, and hold after controlling for fundamental information and other relevant firm and business characteristics. The combined impression from these results is that high volumes of trading can be destabilizing, injecting a sizable layer of trading-induced volatility over and above the unavoidable fundamentals-based volatility.
Two recent studies offer evidence that is largely in line with our findings. Foucalt, Sraer, and Thesmar (2011) explores the effects of a reform in the French stock market that triggers a drop in retail trading activity, and find that the daily return volatility of stocks falls by twenty basis points. This evidence suggests that (noise) traders indeed affect the volatility of stock returns, and is essentially a demonstration of the same forces documented here, only in reverse, and in a more limited setting. Zhang (2010) investigates the effect of high-frequency trading on price discovery, and finds that it has some harmful effects, including inducing higher volatility in stocks. While these findings have more specialized motivations and methodologies, the general agreement in the results provides further confidence in our more general findings.
In considering the larger meaning of these results, it is useful to remember that existing research documents a number of benefits from security liquidity and trading (Brennan, Chordia, and
Subrahmanyam 1998; Chordia and Swaminathan 2000; Fang, Noe, and Tice 2009). There is
29

reliable evidence that traded assets command higher valuations, lower transaction costs, and wider investor recognition, and that these benefits increase with higher levels of trading. To be able to reconcile the disparate messages of this study and existing research, note that much of the previously documented benefits of liquidity come from environments with low trading intensity e.g., newly listed stocks experience a substantial increase in price and decrease in bid-ask spread
(Kadlec and McConnel 1994). In contrast, the evidence in this study comes almost exclusively from the largest, most-traded environments and stocks of all time; generally, we examine prominent companies on the major U.S. stock exchanges, often during the unprecedented surge in trading activity over the last 20 years.
The totality of evidence suggests that the benefits of trading in financial markets are not a one-way street. While benefits to investors dominate at low to medium levels of trading, there is possibly an inflection point or range, beyond which some of the benefits of trading stagnate, new problems appear, and some of the remaining benefits become more concentrated and accrue only to a small circle of traders. For an example of benefits that are likely to stagnate beyond a certain level of trading, consider the normal trading of typical individual investors or longer-term institutional investors. Everything else equal, whether their orders are executed in 1 minute or 1 second is unlikely to matter a whole lot for those who are investing for long-term goals like retirement. Whether transaction costs are on the magnitude of $10 or $1 per trade does not matter that much either for the returns on a typical round-lot transaction. Whether such investors adjusts their portfolios once a month or 10 times a month is unlikely to improve performance (and in fact there is evidence that the opposite is true, e.g., Barber and Odean 2000) and trading once a month is more than enough to fund liquidity needs or invest excess cash.
The results in this study provide an example of the new problems that start appearing with the intensification of trading. Higher levels of trading seem to generate their own volatility, with all
30

ensuing consequences, including possible shifts in investor risk preferences and risk management behavior, and possible destabilization of the market. At this point, these possibilities are just conjectures, and it will be useful to explore them further in future research. For example, it will be interesting to examine more closely the origin and dynamics of trading-induced volatility and compare them to what we know about fundamentals-induced volatility. It is possible that tradingbased volatility is much more endogenous, prone to feedback loops, and hard to predict and anticipate, and thus more dangerous and damaging than fundamentals-based volatility. A related theme is further study of the possible destabilization role of trading-induced volatility. The variable used in this study, standard deviation of returns, is a fairly bland proxy for destabilization risk, and more targeted work can be done for extreme environments and events, which are of special interest to investors and regulators.
It is also useful to think more closely about the parties who derive the most benefits from the current high-trading environment. It seems that while the early gains from trading and liquidity are widespread, the benefits at very high levels of trading are much more specialized, accrue to a smaller circle of people, and lean in the direction of re-distribution rather than the creation of new wealth. While it is helpful to be able to buy and sell sizable investment positions promptly, the race to trade on slivers of new information a fraction of a second faster than anybody else is more questionable as a value-enhancing activity at the society level. For the economy as a whole, the primary function of the stock market is to facilitate the flow of capital into and out of the real activities of firms through stock issues and repurchases and various forms of stock-enabled corporate reorganizations. This primary function can be fulfilled at fairly low levels of trading, and indeed it has been satisfied for quite some time. The high intensity of trading we observe today is strictly on the secondary market of existing shares, and is much more about the splitting and redistribution of private gain based on specialized skills, resources, and access to information. With
31

the increasing volumes and speed of trading, and the attendant increase in volatility documented here, the potential for concentration of profits likely increases as well.
10
Another question is whether market-makers and regulators need to be more cognizant and proactive about the fact that high trading leads to high volatility. To a certain extent, such reactions already exist, e.g., circuit-breakers dampen extreme price moves by halting trading, which is essentially a forced and extreme reversal of the forces documented in this study. There are also other ideas about possible reactions, and some of them have a long history. For example, Ripley
(1911) reviews a massive wave of speculation in major U.S. railroad stocks at the turn of the last century, where annual turnover for several stocks reached magnitudes of 10 to 20, very high even by our modern standards of hyperactive trading. Ripley suggests that one way to dampen such speculative excesses is to impose taxes on trading, with the side benefit of raising government funds. Similar ideas are developed in Summers and Summers (1989), who argue that imposing a small security transaction tax will curb speculation and reduce the diversion of resources into the financial sector of the economy. While these ideas remain controversial, there is little doubt that the underlying issue is important, and can be a fruitful field for future research.
Another interesting direction for research is to investigate the volume/volatility relation in investment assets beyond stocks. Corporate and government bonds, closed-end funds, commodities, currencies – all these instruments provide potential testing ground for the effects documented here. Currency trading, for example, has grown 10-fold during the last 20 years, and today at $4 trillion/day is arguably much higher than needs tied to the real economy (e.g., total annual global trade is $25 trillion and global money stock is only $12 trillion as of 2009).
11
Another intriguing and topical research opportunity is real estate investments, where for a long time most
10 News reports in May 2010 revealed that Goldman Sachs made trading profits on every single day of its first fiscal quarter. Such consistency in profits suggests that some traders have clear trading (and/or information) advantages over other market participants.
11 Data from the CIA World Factbook.
32

homes and the associated mortgages were both held as long-term investments and either not traded or traded chiefly for needs as relocation or changing family needs and preferences. Perhaps it is not accidental that the great price appreciation in the early to mid 2000s and the ensuing crash coincided with the re-assessment of real estate as a tradable and speculative asset, with much
“flipping” of homes and re-packaging and continuous re-trading of mortgages and home-equity loans.
Finally, it is useful to consider the implications of the trading/volatility results for other investor environments and stock exchanges. The U.S. evidence is important in its own right since the U.S. stock market at $15 trillion is by far the largest, accounting for about a third of world market cap of $47 trillion as of the end of 2009.
12
But it is also important because the U.S. experience in volume of trading is ahead of the curve and the rest of the world seems to be moving in the same direction. Specifically, while volumes of trading have been rising world-wide for the last 20 years, the annualized U.S. turnover of 300 percent as of the end of 2009 is the highest in the world, and far above the second-highest at 150 percent (China). Most developed markets (Japan,
U.K., Germany) have turnover on the magnitude of 100 percent, and developing markets (Australia,
Brazil, Hong Kong) tend to be even lower at around 50 percent. As illustrated in Figure 1, U.S. markets start registering turnovers around 50 percent in the late 1980s, and around 100 percent in the late 1990’s. The implication is that, if history is any guide, the U.S. experience is 10 to 20 years ahead of the curve, and thus lessons from this high-volume trading environment are likely to be portable and useful around the world.
6. Conclusion
12 All data in this paragraph are from the Economist, July 17, 2010 (page 98); data provided by Standard and Poor’s.
33

This study investigates the effect of high trading volume on observed stock volatility controlling for fundamental information. The motivation is that volumes of U.S. trading have increased more than 30-fold over the last 50 years, truly transforming the marketplace, and it is important to map out the effects of such a momentous change. First, we employ a series of three natural experiments to examine the existence and direction of this relation, while controlling for fundamental information that endogenously drives both volume and volatility. We use exchange switches, S&P 500 index changes, and dual-class stocks as settings with substantial variation in trading but good natural controls for underlying fundamentals. Our main finding is that in all three settings volume of trading is reliably positively correlated with stock volatility, and this relation seems economically substantial. Second, we examine the aggregate time-series of U.S. stocks since
1926 and the cross-section of stocks during the last 20 years to better calibrate the economic parameters of the identified relation. Using annual measures, volume and volatility are correlated on the magnitude of 50 percent in the aggregate time-series, suggesting that much of the historical variation in volatility is driven by the prevailing volumes of trading. Tests in the cross-section confirm the positive volume/volatility relation but also reveal a pronounced convexity, where the relation is weak to non-existent for low levels of trading and becomes much clearer and stronger for high levels of trading. Efforts quantifying the volume effect reveal that trading-induced volatility accounts for about a quarter of total observed stock volatility today. The combined impression from these results is that stock trading injects an economically substantial layer of volatility above and beyond that based on fundamentals, especially at high levels of trading.
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There are a number of difficulties and complications in determining Nasdaq share volume, which hamper the comparability of not only Nasdaq volume with volume from other exchanges but also within Nasdaq’s own time-series of data. We refer the interested reader to Anderson and Dyl
(2005) for a full account of these problems, and here provide only a brief summary, which suffices for our purposes. The most well-known problem with Nasdaq volume arises because Nasdaq is a dealer market, and thus end-customer to end-customer transactions pass through a dealer, and are thus double counted in volume; the usual solution to this problem is to divide Nasdaq volume by two (Atkins and Dyl 1997), and we employ this adjustment. Unfortunately, there are several other factors that complicate the interpretation of Nasdaq volume, and there is no easy way to control for them. First, Nasdaq has much inter-dealer trading, which varies in intensity across stocks; since these transactions are counted in, reported volume is further increased, and the increase varies cross-sectionally. Second, electronic communication networks (ECNs) have accounted for increasing volumes of trade on Nasdaq. Since ECN’s transactions are counted only once in volume, double-counting is eliminated but data on ECN participation over time and across stocks is not readily available. Third, in 1997 regulators changed several important rules about the reporting of
Nasdaq volume, which eliminated double-counting for some transactions, see Anderson and Dyl
(2005) for full details. These changes also hamper volume comparability across exchanges, stocks, and time.
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38

4,0
3,5
3,0
2,5
2,0
1,5
1,0
0,5
0,0
NYSE/AMEX NASDAQ
This figure shows the annualized value-weighted trading volume turnover for NYSE/AMEX (solid line) from 1926 to 2009 and Nasdaq (patterned line) from
1983 to 2009. Annualized value-weighted volume turnover is the average daily value-weighted market volume turnover for calendar year t multiplied by the number of trading days in year t (approximate 250 days for most years). Daily value-weighted volume turnover is measured as dollar-value traded (volume * price) on a trading day aggregated over all stocks on the corresponding exchanges divided by aggregate market value (price*shrout) outstanding as of that day.
Volume for stocks traded on Nasdaq is volume on CRSP scaled by two.
39

4,0
3,5
3,0
2,5
2,0
1,5
1,0
0,5
0,0
VOLUME STDRET
This figure shows trading volume (solid line) and stock volatility (dotted line) for the largest 500 stocks on NYSE/AMEX from 1926 to 2009. VOLUME is annualized value-weighted trading volume as defined in figure 1 with the exception that the calculation is based on the largest 500 U.S. stocks. STDRET is the value-weighted average of stock volatility (multiplied by 50 for scaling), measured as the sum of stock volatility for each of the 500 stocks multiplied by its corresponding weight. Stock volatility for firm i is the standard deviation of its daily stock returns in year t and weight for firm i is the average of its beginning and ending market values in year t divided by the total market values of the 500 stocks in year t.
40

0,95
0,85
0,75
1,15
1,05
0,65
Weekly Monthly
This figure shows the mean weekly Actual/Implied ratios (solid line) and monthly Actual/Implied ratios (dotted line) for the largest 500 stocks on NYSE/AMEX from 1926 to 2009. Weekly (Monthly) Actual/Implied ratio for stock i in year t is the actual weekly (monthly) stock volatility divided by the implied weekly
(monthly) stock volatility. Actual weekly (monthly) stock volatility is the standard deviation of weekly (monthly) returns in year t. Implied weekly (monthly) stock volatility is the standard deviation of daily returns multiplied by the square root of the number of trading days in a week (month). The smooth trend lines are obtained from the second-order polynomial function.
41

Panel A: Sample composition and descriptive statistics
Between
NYSE and
AMEX
From
Nasdaq to
NYSE/AMEX
From
NYSE/AMEX to Nasdaq
Full
Sample
Initial sample
Final sample
By year
1962-1970
1971-1980
1981-1990
1991-2000
2001-2009
989
951
163
249
153
204
182
2,217
1,573
-
-
576
842
155
405
336
-
-
16
120
200
3,611
2,860
163
249
745
1,166
537
MVE
Mean
546
STD
1,877
10%
23
25%
47
50%
128
75%
392
90%
1,066
CH_VOLUME 100.4% 1,160.5% -55.0% -30.1% 6.0% 63.3% 189.9%
CH_STDRET 4.8% 73.9% -52.6% -35.9% -10.6% 21.9% 73.3%
This panel reports sample composition and descriptive statistics of stocks that switched between three major U.S. stock exchanges (i.e., NYSE, AMEX, and Nasdaq). The initial sample consists of all switches between the three exchanges from 1962-2009 based on the Stockname file on CRSP. The final sample consists of switching stocks with nonmissing daily volume, shares outstanding, and stock price over one month before and after exchange switch. MVE is the market value of equity ($million) on the effective date of switch, calculated as closing price multiplied by closing shares outstanding. CH_VOLUME is the change of trading volume, measured as the difference between the average daily volume before and after the switch, scaled by the average daily volume before the switch. For NYSE/AMEX stocks, daily volume is daily trading volume divided by daily closing shares outstanding. For Nasdaq stocks, daily volume turnover is scaled by two. CH_STDRET is the change of stock volatility, measured as the difference between the standard deviations of daily stock returns before and after the switch, scaled by the standard deviation of returns before the switch. Windows (-22, -1) and (0, 21) are used as measurement windows before and after the switch, respectively, where day 0 is the effective date of switch.
42

Panel B: Change of trading volume and stock volatility over windows (-22, -1) and
(0, 21) for three types of switches
Between
NYSE and
AMEX
(N = 951)
From
Nasdaq to
NYSE/AMEX
(N = 1,573)
From
NYSE/AMEX to Nasdaq
(N = 336)
Quintiles
Formed by
CH_
VOLUME
(Low to High)
Q1
Q2
Q3
CH_
VOLUME
-21.6%
0.8%
CH_
STDRET
-44.1% -25.4%
-15.2%
-4.5%
Q4 34.0% 2.9%
Q5 111.8% 13.7%
Q5 - Q1 Diff. 155.9%* 39.1%*
Spearman Corr.
(CH_VOLUME,
CH_STDRET)
0.352*
Q1
Q2
Q3
Q4
-47.1%
-11.4%
-34.4%
-20.8%
23.6% -10.9%
69.2% -4.3%
Q5 258.7% -7.8%
Q5 - Q1 Diff. 305.8%* 26.6%*
Q1 -77.8% -6.7%
Q2
Q3
-64.9% -2.6%
-45.4% 21.4%
Q4 -18.7% 4.4%
Q5 55.3% 44.0%
Q5 - Q1 Diff. 133.1%* 50.7%*
0.234*
0.247*
This panel reports median CH_VOLUME and CH_STDRET across quintiles formed by CH_VOLUME and spearman correlations between CH_VOLUME and CH_STDRET measured over windows (-22, -1) and (0, 21). CH_VOLUME and CH_STDRET are defined in Table 1 Panel A. * denotes significance at the
1% level. The p-value for the difference between the top and bottom quintiles (Q5-Q1Diff.) is based on
Wilcoxon z-statistics.
43

Panel C: Change of trading volume and stock volatility over windows (-45, -23) and (22, 45) for the switches between NYSE and AMEX
Quintiles Formed by
CH_VOLUME
(Low to High) CH_VOLUME CH_STDRET
Spearman Corr.
(CH_VOLUME,
CH_STDRET)
Q1
Q2
Q3
-57.1%
-25.9%
-0.6%
-21.2%
-16.1%
-4.2%
Q4
Q5
41.6%
157.6%
6.7%
19.8%
Q5 - Q1 Diff. 214.7% * 41.0% * 0.342*
This panel reports median CH_VOLUME and CH_STDRET across quintiles formed by CH_VOLUME and spearman correlations between CH_VOLUME and CH_STDRET measured over windows (-45, -23) and (22, 45). CH_VOLUME and CH_STDRET are defined as in Table 1 Panel A with the exception that windows (-45, -23) and (22, 45) are used as measurement windows before and after the switch, respectively, where day 0 is the effective date of switch. * denotes significance at the 1% level. The p-value for the difference between the top and bottom quintiles (Q5-Q1 Diff.) is based on Wilcoxon z-statistics.
44

Panel A: Sample composition and descriptive statistics
Additions Deletions Full Sample
Initial sample
Final sample
By year
1976-1980
1981-1990
1991-2000
590
453
44
207
202
565
86
2
18
66
1,155
539
46
225
268
MVE
Mean
4,248
STD 10%
8,166 244
25%
607
50%
1,424
75%
5,311
90%
8,830
CH_VOLUME 26.7% 70.4% -40.3% -19.0% 9.3% 55.5% 104.5%
CH_STDRET 11.8% 50.6% -39.8% -21.9% 1.8% 36.1% 73.3%
This panel reports sample composition and descriptive statistics of stocks that were added and deleted from the S&P 500 index. The initial sample is obtained from Jeff Wurgler’s website, spanning from 1976 –
2000. The final sample excludes additions and deletions as a result of merges, spin-offs, bankruptcy, reorganization, restructuring, and stocks with missing CRSP data to calculate CH_VOLUME and
CH_STDRET. MVE is the market value of equity ($million) on the effective date of change, calculated as closing price multiplied by closing shares outstanding. CH_VOLUME is the change of trading volume, measured as the difference between average daily volume before and after the S&P change, scaled by average daily volume before the S&P change. For NYSE/AMEX stocks, daily volume is daily trading volume divided by daily closing shares outstanding. For Nasdaq stocks, daily volume is scaled by two.
CH_STDRET is the change of stock volatility, measured as the difference between the standard deviations of daily stock returns before and after the change, scaled by the standard deviation of returns before the change. Windows (-45, -23) and (22, 45) are used as measurement windows before and after the S&P 500 addition or deletion, respectively, where day 0 is the effective date of change.
45

Panel B: Change of trading volume and stock volatility for S&P 500 additions
Window
(-22,-1) (0,21)
Quintiles by
CH_VOLUME
(Low to High)
Q1
Q2
Q3
Q4
Q5
CH_
VOLUME
CH_
STDRET
-13.4% -12.1%
22.0% -3.4%
53.2% 2.7%
88.9% 8.2%
Spearman Corr.
(CH_VOLUME
,CH_STDRET)
164.8% 29.8%
Window
(-45,-23) (22,45)
Q5 - Q1 Diff. 178.2%* 41.9%*
Q1 -39.0% -17.7%
Q2
Q3
-11.4% -9.1%
8.5% 0.1%
Q4
Q5
42.6% 14.6%
101.0% 20.1%
0.344*
Q5 - Q1 Diff. 140.0%* 37.8%* 0.380*
Panel C: Change of trading volume and return volatility for S&P 500 deletions
Window
(-22,-1) (0,21)
Window
(-45,-23) (22,45)
Quintiles by
CH_VOLUME
(Low to High)
Q1
Q2
CH_
VOLUME
CH_
STDRET
-11.8% 0.2%
57.4% 2.7%
Spearman Corr.
(CH_VOLUME
,CH_STDRET)
Q3
Q4
Q5
Q1
84.8%
134.9%
-2.3%
8.6%
198.6% 5.7%
Q5 - Q1 Diff. 210.4%* 5.5%
-43.7% -24.4%
0.181***
Q2
Q3
Q4
-23.4%
13.2%
47.9%
-10.6%
7.1%
7.8%
Q5 143.5% 47.8%
Q5 - Q1 Diff. 187.2%* 72.2%* 0.422*
This panel reports median CH_VOLUME and CH_STDRET across quintiles formed by CH_VOLUME and spearman correlations between the two variables. CH_VOLUME and CH_STRET are defined in Panel
A Table 2. *, **, and *** denotes significance at the 1%, 5%, and 10% levels, respectively. The p-value for the difference between the top and bottom quintiles (Q5-Q1 Diff.) is based on Wilcoxon z-statistics.
46

Panel A: Sample composition and descriptive statistics
Number of firms
Number of share classes
Firm-month pairs
59
118
7,322
Mean 10% 25% 50% 75% 90%
MVE 1,789 11 53 148 419 2,212
DIF_VOLUME 4,546.5% 16.4% 48.3% 144.6% 522.5% 2,361.9%
DIF_STDRET 20.9% -37.3% -16.5% 2.6% 28.5% 69.5%
Panel B: Difference in trading volume and stock volatility
Quintiles by
DIF_VOLUME
(Sorted at Firm Level) DIF_VOLUME
1
2
17.2%
59.2%
3
4
5
Q5-Q1 Diff.
121.2%
254.6%
743.6%
726.1%*
DIF_STDRET
0.0%
2.0%
2.4%
3.7%
4.2%
4.2%*
Panel A reports sample composition and descriptive statistics of dual-class stocks listed on the same major
U.S. exchanges (i.e., NYSE, Nasdaq, Amex or NYSE Arca) during 1965-2009. MVE is the market value of equity ($million). For each firm-month, shares in a pair are split into high and low groups based on their corresponding trading volume. DIF_VOLUME is the trading volume difference between high volume issue and low volume issue for each firm-month, scaled by the volume of the low volume issue. Trading volume for a given issue is calculated as total volume divided by total share outstanding in a month. DIF_STDRET is the stock volatility difference between high volume issue and low volume issue for each firm-month, scaled by the stock volatility of the low volume issue. Stock volatility is measured as the standard deviation of daily returns in a month. Panel B reports median DIF_VOLUME and DIF_STDRET across
DIF_VOLUME quintiles sorted at the firm level. * denotes significance at the 1% level. The p-value for the difference between the top and bottom quintiles (Q5-Q1 Diff.) is based on Wilcoxon z-statistics.
47

Year
Spearman Corr. (VOLUME, STDRET) = 0.541*
Spearman Corr. (CH_VOLUME, CH_STDRET) = 0.321*
VOL
UME
STD
RET Year
VOL
UME
STD
RET Year
VOL
UME
STD
RET
1926 114.6% 0.014 1954 12.0% 0.011 1982 49.8% 0.020
1927 113.1% 0.013 1955 11.9% 0.014 1983 57.0% 0.017
1928 147.4% 0.016 1956 9.6% 0.012 1984 58.9% 0.016
1929 130.4% 0.029 1957 8.8% 0.013 1985 66.4% 0.014
1930 77.4% 0.023 1958 9.8% 0.012 1986 75.4% 0.017
1931 60.6% 0.032 1959 9.6% 0.013 1987 85.9% 0.026
1932 52.4% 0.043 1960 8.5% 0.014 1988 67.5% 0.016
1933 61.4% 0.037 1961 9.6% 0.013 1989 65.7% 0.014
1934 24.2% 0.021 1962 10.1% 0.017 1990 55.8% 0.017
1935 24.7% 0.018 1963 10.0% 0.011 1991 55.8% 0.016
1936 26.2% 0.016 1964 9.3% 0.010 1992 54.7% 0.015
1937 22.9% 0.024 1965 10.1% 0.011 1993 62.1% 0.015
1938 18.1% 0.024 1966 14.8% 0.015 1994 63.8% 0.015
1939 15.7% 0.020 1967 16.0% 0.014 1995 69.9% 0.014
1940 11.6% 0.018 1968 17.0% 0.015 1996 72.5% 0.016
1941 9.2% 0.014 1969 15.6% 0.015 1997 79.4% 0.019
1942 7.1% 0.014 1970 15.3% 0.018 1998 82.9% 0.023
1943 11.9% 0.012 1971 17.2% 0.014 1999 93.3% 0.024
1944 10.7% 0.010 1972 16.2% 0.013 2000 111.9% 0.031
1945 14.4% 0.012 1973 16.0% 0.019 2001 110.9% 0.024
1946 14.7% 0.018 1974 14.6% 0.023 2002 129.3% 0.026
1947 10.0% 0.013 1975 18.6% 0.018 2003 124.7% 0.016
1948 11.5% 0.013 1976 22.8% 0.014 2004 124.2% 0.013
1949 9.3% 0.011 1977 20.5% 0.012 2005 138.0% 0.013
1950 16.4% 0.013 1978 24.9% 0.014 2006 159.8% 0.013
1951 12.5% 0.011 1979 28.3% 0.014 2007 224.2% 0.016
1952 9.2% 0.010 1980 38.4% 0.020 2008 360.5% 0.037
1953 9.0% 0.010 1981 36.3% 0.018 2009 277.3% 0.028
This table reports trading volume and stock volatility for the largest 500 stocks on NYSE/AMEX from
1926 to 2009. VOLUME and STDRET are defined in Figure 2. CH_VOLUME (CH_STDRET) is the difference of VOLUME (STDRET) in year t and t-1. * denotes significance at the 1% level.
48

Panel A: Stock volatility formed on the basis of trading volume
D1 D2
VOLUME deciles (low to high)
D3 D4 D5 D6 D7 D8 D9 D10 D10 - D1
9.7% 22.4% 35.0% 47.3% 59.2% 70.7% 84.2% 104.9% 136.4% 244.8% 235.1%*
0.020 0.021 0.020 0.019 0.019 0.019 0.020 0.022 0.025 0.031 0.011*
Panel B: Stock volatility formed on the basis of both earnings volatility and trading volume
D1 0.001
VOLUME deciles (low to high)
D1 D2 D3 D4 D5 D6 D7 D8 D9 D10
9.7% 22.2% 34.7% 46.5% 58.5% 71.0% 86.0% 107.6% 139.3% 235.0%
0.014 0.015 0.015 0.015 0.015 0.016 0.016 0.018 0.018 0.021
STD-
EARN deciles
(low
to high)
D2 0.003
D3 0.004
D4 0.006
D5 0.008
D6 0.011
0.015 0.016 0.014 0.015 0.015 0.015 0.016 0.018 0.019 0.023
0.017 0.017 0.017 0.016 0.016 0.017 0.018 0.019 0.021 0.024
0.018
0.019
0.020
0.019
0.019
0.021
0.018
0.018
0.020
0.017
0.018
0.019
0.017
0.018
0.018
0.017
0.019
0.019
0.018
0.020
0.021
0.020
0.021
0.022
0.021
0.024
0.025
0.026
0.027
0.028
D7 0.014
D8 0.021
0.022 0.022 0.021 0.022 0.020 0.021 0.023 0.024 0.026 0.030
0.025 0.026 0.025 0.024 0.024 0.024 0.023 0.026 0.028 0.033
D9 0.036 0.028 0.033 0.031 0.029 0.029 0.028 0.028 0.029 0.031 0.036
D10 0.096 0.037 0.043 0.042 0.047 0.040 0.041 0.043 0.040 0.039 0.046
D10-D1 0.095* 0.023* 0.027* 0.027* 0.032* 0.025* 0.025* 0.026* 0.023* 0.021* 0.024*
D10-D1
225.3%*
0.007*
0.008*
0.007*
0.008*
0.008*
0.008*
0.008*
0.008*
0.008*
0.009*
49

This table reports median stock volatility for portfolios formed on the basis of trading volume (both earnings volatility and earnings volatility) in Panel A (Panel
B). The sample consists of 40,577 firm-year observations from all NYSE/AMEX stocks over 1988-2007 with available CRSP and Compustat data to calculate trading volume, stock volatility, and earnings volatility at the firm-year level. Trading volume (VOLUME) is the annualized volume turnover, calculated as average daily volume turnover (volume/shares outstanding) multiplied by 250 for firm i in year t. Stock volatility (STDRET) is the standard deviation of daily stock returns for firm i in year t. Earnings volatility (STDEARN) is the standard deviation of quarterly earnings for firm i over years t, t + 1, and t + 2. Quarterly earnings are earnings before extraordinary items, scaled by the average of beginning and ending total assets (Compustat data8/data44). In Panel A all sample firms are sorted into deciles based on trading volume each year. In panel B all sample firms are sorted into deciles based on earnings volatility each year and within each earnings volatility decile firms are further sorted into deciles based on trading volume. * denotes significance at the 1% level. The p-value of the difference between the top and bottom deciles (D10-D1 Diff.) is based on Wilcoxon z-statistics.
50

STDRET i,t
= β
0
+ β
1
HIGH i,t
+ β
2
VOLUME i,t
+ β
3
VOLUME*HIGH i,t
+ β
4
STDRET i,t-1
+ β
5
RET i,t
+ β
6
STDEARN i,t+2
+ β
7
SIZE i,t-1
+ β
8
AGE i,t-1
+
β
9
LEVERAGE i,t-1
+ β
10
BTM i,t-1
+ ε i,t
Intercept
HIGH
VOLUME
VOLUME*HIGH
STDRET t-1
RET
STDEARN
SIZE
AGE
LEVERAGE
BTM
(Average) Number of
Observations
(Average) Adjusted R 2
Predicted
Sign
+
(1) (2) (3) (4)
38.377 44.550 17.515 18.112
-
(45.28)* (54.50)* (12.65)* (6.02)*
-69.782 -20.425 -13.697
(-21.43)* (-9.06)* (-2.11)**
0.225 0.011 0.105 0.133 +
+
+
-
+
(13.13)* (0.63) (10.31)* (5.93)*
1.004 0.274 0.170
(23.21)* (10.33)*
0.663
(2.12)**
0.666
(58.46)* (20.49)*
-0.071 -0.117
(-3.51)* (-4.88)*
0.103 0.114
-
-
+
?
1,916
0.055
1,916
0.096
(19.17)*
-0.148
(-8.35)*
(9.17)*
-0.141
(-4.84)*
-0.028 -0.032
(-2.87)* (-2.75)*
0.005 0.014
(0.88) (2.15)**
0.001 -0.009
(0.10) (-0.71)
1,916
0.752
38,322
0.706
51

This table reports cross-sectional regressions of stock volatility on trading volume along with control variables at the firm level for NYSE/AMEX firms over the period 1988-2007. STDRET is the standard deviation of returns for stock i in year t. VOLUME is the annualized trading volume turnover. HIGH is an indicator variable coded as 1 if volume is in the top quartile of the sample. STDRET t-1
is the standard deviation of returns for stock i in year t-1. RET is the compounded daily return for stock i in year t.
STDEARN is the standard deviation of quarterly earnings scaled by average total assets(Compustat data8/data44) over years t, t+1, and t+2 with a minimum requirement of eight quarters. SIZE is proxied by the market value of common equity (Compustat data25*data199). AGE is the number of years since the firm first appears in the CRSP database. LEVERAGE is the ratio of debt to assets ((data9+data34)/data6).
BTM is the book to market ratio (data25*data199/data60). Regressions (1) through (3) report the estimates from Fama-MacBeth cross-sectional regressions. The t-values in parentheses are based on Fama-MacBeth standard errors and the number of observations and R 2 are the averages across the twenty annual regressions. Regression (4) reports estimates from pooled-cross sectional regression to gauge the effect of increasing volume over time on stock volatility. The t-values reported in parentheses are based on standard errors clustered by firm and year as suggested by Petersen (2009). To control for non-normalities in their distributions and to allow for direct comparison of their strength across variables, all variables in regressions (1) through (3) are ranked into percentiles by year and all variables in regression (4) are ranked into percentiles without sorting by year. * and ** denote significance at the 1% and 5% levels, respectively.
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