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The Dark Side of Trading
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
[email protected]
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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The Dark Side of Trading
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.1 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
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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.2
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.3 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).4 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.5 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
5
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
17
Mikkelson (1983, 1984) document that superior voting shares generally have a small (5 percent)
premium over inferior voting shares.6
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.7 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.
6
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 mid1990s. 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 = β0 + β1HIGHi,t + β2VOLUMEi,t + β3VOLUME*HIGHi,t + β4STDRETi,t-1 +
β5RETi,t + β6STDEARNi,t+2 + β7SIZEi,t-1 + β8AGEi,t-1 + β9LEVERAGEi,t-1 +
β10BTMi,t-1 + εi,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.
34
Appendix A
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.
35
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Figure 1
Value-Weighted Stock Trading Volume from 1926 to 2009
4.0
Annualized Trading Volume
3.5
3.0
2.5
2.0
1.5
1.0
0.5
1926
1928
1930
1932
1934
1936
1938
1940
1942
1944
1946
1948
1950
1952
1954
1956
1958
1960
1962
1964
1966
1968
1970
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
2006
2008
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
Figure 2
Trading Volume and Stock Volatility for Largest 500 U.S. Stocks from 1926 to 2009
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
1926
1928
1930
1932
1934
1936
1938
1940
1942
1944
1946
1948
1950
1952
1954
1956
1958
1960
1962
1964
1966
1968
1970
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
2006
2008
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
Figure 3
Actual/Implied Ratios for Largest 500 U.S. Stocks from 1926 to 2009
1.15
Actual/Implied Ratio
1.05
0.95
0.85
0.75
1926
1928
1930
1932
1934
1936
1938
1940
1942
1944
1946
1948
1950
1952
1954
1956
1958
1960
1962
1964
1966
1968
1970
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
2006
2008
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
Table 1
Stocks Switching Exchanges
Panel A: Sample composition and descriptive statistics
Initial sample
Final sample
By year
1962-1970
1971-1980
1981-1990
1991-2000
2001-2009
MVE
CH_VOLUME
CH_STDRET
Between
NYSE and
AMEX
989
951
From
Nasdaq to
NYSE/AMEX
2,217
1,573
From
NYSE/AMEX
to Nasdaq
405
336
Full
Sample
3,611
2,860
163
249
153
204
182
576
842
155
16
120
200
163
249
745
1,166
537
Mean
STD
10%
546
1,877
23
100.4% 1,160.5% -55.0%
4.8%
73.9%
-52.6%
25%
47
-30.1%
-35.9%
50%
128
6.0%
-10.6%
75%
392
63.3%
21.9%
90%
1,066
189.9%
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
Table 1 (continued)
Panel B: Change of trading volume and stock volatility over windows (-22, -1) and
(0, 21) for three types of switches
Quintiles
Formed by
CH_
Spearman Corr.
VOLUME
CH_
CH_
(CH_VOLUME,
(Low to High)
VOLUME
STDRET
CH_STDRET)
Q1
-44.1%
-25.4%
Between
Q2
-21.6%
-15.2%
NYSE and
Q3
0.8%
-4.5%
AMEX
Q4
34.0%
2.9%
(N = 951)
Q5
111.8%
13.7%
From
Nasdaq to
NYSE/AMEX
(N = 1,573)
From
NYSE/AMEX
to Nasdaq
(N = 336)
Q5 - Q1 Diff.
155.9%*
39.1%*
Q1
Q2
Q3
Q4
Q5
-47.1%
-11.4%
23.6%
69.2%
258.7%
-34.4%
-20.8%
-10.9%
-4.3%
-7.8%
Q5 - Q1 Diff.
305.8%*
26.6%*
Q1
Q2
Q3
Q4
Q5
-77.8%
-64.9%
-45.4%
-18.7%
55.3%
-6.7%
-2.6%
21.4%
4.4%
44.0%
Q5 - Q1 Diff.
133.1%*
50.7%*
0.352*
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
Table 1 (continued)
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)
Q1
Q2
Q3
Q4
Q5
CH_VOLUME
-57.1%
-25.9%
-0.6%
41.6%
157.6%
CH_STDRET
-21.2%
-16.1%
-4.2%
6.7%
19.8%
Q5 - Q1 Diff.
214.7% *
41.0% *
Spearman Corr.
(CH_VOLUME,
CH_STDRET)
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
Table 2
Stocks Added and Deleted from the S&P 500 Index
Panel A: Sample composition and descriptive statistics
Initial sample
Final sample
By year
1976-1980
1981-1990
1991-2000
MVE
CH_VOLUME
CH_STDRET
Mean
4,248
26.7%
11.8%
Additions
590
453
Deletions
565
86
Full Sample
1,155
539
44
207
202
2
18
66
46
225
268
STD
8,166
70.4%
50.6%
10%
244
-40.3%
-39.8%
25%
607
-19.0%
-21.9%
50%
1,424
9.3%
1.8%
75%
5,311
55.5%
36.1%
90%
8,830
104.5%
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
Table 2 (continued)
Panel B: Change of trading volume and stock volatility for S&P 500 additions
Quintiles by
Spearman Corr.
CH_VOLUME
CH_
CH_
(CH_VOLUME
(Low to High)
VOLUME
STDRET
,CH_STDRET)
Q1
-13.4%
-12.1%
Q2
22.0%
-3.4%
Q3
53.2%
2.7%
Window
Q4
88.9%
8.2%
(-22,-1) (0,21)
Q5
164.8%
29.8%
Window
(-45,-23) (22,45)
Q5 - Q1 Diff.
178.2%*
41.9%*
Q1
Q2
Q3
Q4
Q5
-39.0%
-11.4%
8.5%
42.6%
101.0%
-17.7%
-9.1%
0.1%
14.6%
20.1%
Q5 - Q1 Diff.
140.0%*
37.8%*
0.344*
0.380*
Panel C: Change of trading volume and return volatility for S&P 500 deletions
Quintiles by
Spearman Corr.
CH_VOLUME
CH_
CH_
(CH_VOLUME
(Low to High)
VOLUME
STDRET
,CH_STDRET)
Q1
-11.8%
0.2%
Q2
57.4%
2.7%
Q3
84.8%
-2.3%
Window
Q4
134.9%
8.6%
(-22,-1) (0,21)
Q5
198.6%
5.7%
Window
(-45,-23) (22,45)
Q5 - Q1 Diff.
210.4%*
5.5%
Q1
Q2
Q3
Q4
Q5
-43.7%
-23.4%
13.2%
47.9%
143.5%
-24.4%
-10.6%
7.1%
7.8%
47.8%
Q5 - Q1 Diff.
187.2%*
72.2%*
0.181***
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
Table 3: Evidence from Dual-Class Firms
Panel A: Sample composition and descriptive statistics
Number of firms
59
Number of share classes
118
Firm-month pairs
7,322
MVE
DIF_VOLUME
DIF_STDRET
Mean
1,789
4,546.5%
20.9%
10%
11
16.4%
-37.3%
25%
53
48.3%
-16.5%
50%
148
144.6%
2.6%
Panel B: Difference in trading volume and stock volatility
Quintiles by
DIF_VOLUME
(Sorted at Firm Level)
DIF_VOLUME
1
17.2%
2
59.2%
3
121.2%
4
254.6%
5
743.6%
Q5-Q1 Diff.
726.1%*
75%
419
522.5%
28.5%
90%
2,212
2,361.9%
69.5%
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
Table 4
Trading Volume and Stock Volatility for Largest 500 U.S. Stocks
from 1926 - 2009
Spearman Corr. (VOLUME, STDRET) = 0.541*
Spearman Corr. (CH_VOLUME, CH_STDRET) = 0.321*
Year
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
VOL
UME
114.6%
113.1%
147.4%
130.4%
77.4%
60.6%
52.4%
61.4%
24.2%
24.7%
26.2%
22.9%
18.1%
15.7%
11.6%
9.2%
7.1%
11.9%
10.7%
14.4%
14.7%
10.0%
11.5%
9.3%
16.4%
12.5%
9.2%
9.0%
STD
RET
0.014
0.013
0.016
0.029
0.023
0.032
0.043
0.037
0.021
0.018
0.016
0.024
0.024
0.020
0.018
0.014
0.014
0.012
0.010
0.012
0.018
0.013
0.013
0.011
0.013
0.011
0.010
0.010
Year
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
VOL
UME
12.0%
11.9%
9.6%
8.8%
9.8%
9.6%
8.5%
9.6%
10.1%
10.0%
9.3%
10.1%
14.8%
16.0%
17.0%
15.6%
15.3%
17.2%
16.2%
16.0%
14.6%
18.6%
22.8%
20.5%
24.9%
28.3%
38.4%
36.3%
STD
RET
0.011
0.014
0.012
0.013
0.012
0.013
0.014
0.013
0.017
0.011
0.010
0.011
0.015
0.014
0.015
0.015
0.018
0.014
0.013
0.019
0.023
0.018
0.014
0.012
0.014
0.014
0.020
0.018
Year
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
VOL
UME
49.8%
57.0%
58.9%
66.4%
75.4%
85.9%
67.5%
65.7%
55.8%
55.8%
54.7%
62.1%
63.8%
69.9%
72.5%
79.4%
82.9%
93.3%
111.9%
110.9%
129.3%
124.7%
124.2%
138.0%
159.8%
224.2%
360.5%
277.3%
STD
RET
0.020
0.017
0.016
0.014
0.017
0.026
0.016
0.014
0.017
0.016
0.015
0.015
0.015
0.014
0.016
0.019
0.023
0.024
0.031
0.024
0.026
0.016
0.013
0.013
0.013
0.016
0.037
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
Table 5
Stock Volatility Across Trading Volume Portfolios
Panel A: Stock volatility formed on the basis of trading volume
VOLUME deciles (low to high)
D1
D2
D3
D4
D5
D6
D7
D8
9.7%
22.4%
35.0%
47.3%
59.2%
70.7%
84.2%
104.9%
0.020
0.021
0.020
0.019
0.019
0.019
0.020
0.022
D9
136.4%
D10
244.8%
D10 - D1
235.1%*
0.025
0.031
0.011*
Panel B: Stock volatility formed on the basis of both earnings volatility and trading volume
STDEARN
deciles
(low
to
high)
D1
D2
D3
D4
D5
D6
D7
D8
D9
D10
0.001
0.003
0.004
0.006
0.008
0.011
0.014
0.021
0.036
0.096
D10-D1 0.095*
D1
9.7%
D2
22.2%
D3
34.7%
VOLUME deciles (low to high)
D4
D5
D6
D7
D8
D9
D10
46.5% 58.5% 71.0% 86.0% 107.6% 139.3% 235.0%
0.014
0.015
0.017
0.018
0.019
0.020
0.022
0.025
0.028
0.037
0.015
0.016
0.017
0.019
0.019
0.021
0.022
0.026
0.033
0.043
0.015
0.014
0.017
0.018
0.018
0.020
0.021
0.025
0.031
0.042
0.015
0.015
0.016
0.017
0.018
0.019
0.022
0.024
0.029
0.047
0.015
0.015
0.016
0.017
0.018
0.018
0.020
0.024
0.029
0.040
0.016
0.015
0.017
0.017
0.019
0.019
0.021
0.024
0.028
0.041
0.016
0.016
0.018
0.018
0.020
0.021
0.023
0.023
0.028
0.043
0.018
0.018
0.019
0.020
0.021
0.022
0.024
0.026
0.029
0.040
0.018
0.019
0.021
0.021
0.024
0.025
0.026
0.028
0.031
0.039
0.021
0.023
0.024
0.026
0.027
0.028
0.030
0.033
0.036
0.046
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
Table 6
The Cross-Sectional Relation between Stock Volatility and Trading Volume,
Controlling for Other Factors
STDRET i,t = β0 + β1HIGHi,t + β2VOLUMEi,t + β3VOLUME*HIGHi,t + β4STDRETi,t-1
+ β5RETi,t + β6STDEARNi,t+2 + β7SIZEi,t-1 + β8AGEi,t-1 +
β9LEVERAGEi,t-1 + β10BTMi,t-1 + εi,t
Intercept
Predicted
Sign
+
HIGH
VOLUME
VOLUME*HIGH
STDRETt-1
RET
STDEARN
+
(4)
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)*
(2.12)**
0.663
0.666
(58.46)*
(20.49)*
-0.071
-0.117
(-3.51)*
(-4.88)*
0.103
0.114
(19.17)*
(9.17)*
-0.148
-0.141
(-8.35)*
(-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
+
+
AGE
-
(Average) Number of
Observations
(Average) Adjusted R2
(3)
17.515
+
-
BTM
(2)
44.550
-
SIZE
LEVERAGE
(1)
38.377
+
?
1,916
0.055
1,916
0.096
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 R2 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.
52