The Dark Side of Trading

Ilia D. DichevEmory University

Kelly HuangGeorgia State University

Dexin ZhouEmory 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. Dichev1300 Clifton RoadGoizueta Business School, Emory UniversityAtlanta, GA, 30037404-727-9353idichev@emory.edu

We appreciate the helpful comments of workshop participants at Yale University, Florida State University, Southern Methodist University, Wharton, Washington University, Norwegian School of Economics and Business Administration (NHH), and especially those of Linda Bamber, Tarun Chordia, Feng Li, Catherine Schrand, and Lasse Pedersen.

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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 dual-

class 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

significant accomplishments in this line of research, which studies issues like the effects of private 1 AMEX volume data is available since 1963, here combined with the NYSE data series for parsimony. The value weighting is accomplished by calculating for each trading day the total dollar-value traded that day (aggregated over all stocks) and dividing it by aggregate market value outstanding as of that day. This measure is then annualized by multiplying the mean daily turnover for that year by the number of trading days in that year (approximately 250 days for most years).

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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

trading purely driven by non-information motivations. In fact, much and maybe even most of

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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

differs by a factor of ten or more. The existing literature already offers evidence consistent with

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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 win-

win 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,

especially controlling for fundamentals, and this is the principal thrust of our investigation.

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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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

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

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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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

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

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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

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

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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 information-

laden 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

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.

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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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

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 non-

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normalities, 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 near-

monotonic 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

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.

5 The results for a pooled sample of switches are very similar to those presented in Panel B.

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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

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

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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 re-

organization 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

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

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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 within-

sample 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

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

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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

Mikkelson (1983, 1984) document that superior voting shares generally have a small (5 percent)

premium over inferior voting shares.6

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.

17

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 pair-

month 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.

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.

7 Similar results obtain if we scale by an average of stock volatility of low and high volume issues.

18

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

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,

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

we address this question by extending the investigation to the full universe of U.S. stocks.

Generally speaking, this extended investigation is more realistic and is well-calibrated to the

naturally-occurring properties of the U.S. stock market; this benefit, however, comes at the cost of

losing some of the sharp controls in the earlier specifications.

4.1 Evidence from the full time-series of U.S. stocks

The first type of evidence for the broad stock market looks at the long-run record for a

sample of the 500 largest U.S. stocks over 1926-2009. We use 500 stocks because data availability

is limited to about this number in the early years of the sample, and we want to preserve some

measure of comparability over time. The evidence for this specification is presented in Figure 2 and

Table 4, based on annual observations of value-weighted turnover and stock return volatility. An

inspection of Figure 2 reveals that the evolution of volatility has a perceptible synchronicity with

the broad ebbs and flows of trading volume. When trading is lowest in the quiet years between

1940 and 1970, volatility is also lowest, never exceeding 2 percent (daily measure) over this

extended period that includes World War II, the Korean War, and the various upheavals of the Cold

War. Volatility is the highest during the two periods with the most intense trading, peaking at over

4 percent during 1926-1940 and with the second and third highest peak occurring after the mid-

1990s. To be sure, the relation is far from lock-step and one can identify several instances where it

is inadequate to describe the empirical behavior of volatility, e.g., volatility spikes during the

recession of 1973-74 with no discernable change in volume of trading. The summary impression

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

20

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 time-

series 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,

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

21

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

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

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

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

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

23

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,

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

24

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.

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

25

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

(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

26

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

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

27

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

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

28

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 non-

existent 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

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

29

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

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

30

compare them to what we know about fundamentals-induced volatility. It is possible that trading-

based 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 re-

distribution of private gain based on specialized skills, resources, and access to information. With

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

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.

31

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

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

11 Data from the CIA World Factbook.

32

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

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

12 All data in this paragraph are from the Economist, July 17, 2010 (page 98); data provided by Standard and Poor’s.

33

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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38

Figure 1Value-Weighted Stock Trading Volume from 1926 to 2009

19261929

19321935

19381941

19441947

19501953

19561959

19621965

19681971

19741977

19801983

19861989

19921995

19982001

20042007

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

NYSE/AMEX NASDAQ

Ann

ualiz

ed T

radi

ng V

olum

e

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 2Trading Volume and Stock Volatility for Largest 500 U.S. Stocks from 1926 to 2009

19261928

19301932

19341936

19381940

19421944

19461948

19501952

19541956

19581960

19621964

19661968

19701972

19741976

19781980

19821984

19861988

19901992

19941996

19982000

20022004

20062008

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

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 3Actual/Implied Ratios for Largest 500 U.S. Stocks from 1926 to 2009

19261929

19321935

19381941

19441947

19501953

19561959

19621965

19681971

19741977

19801983

19861989

19921995

19982001

20042007

0.650000000000003

0.750000000000003

0.850000000000003

0.950000000000003

1.05

1.15

Weekly Polynomial (Weekly) Monthly Polynomial (Monthly)

Act

ual/I

mpl

ied

Rat

io

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

Between NYSE and

AMEX

From Nasdaq to

NYSE/AMEX

From NYSE/AMEX

to NasdaqFull

SampleInitial sample 989 2,217 405 3,611Final sample 951 1,573 336 2,860

By year1962-1970 163 - - 1631971-1980 249 - - 2491981-1990 153 576 16 7451991-2000 204 842 120 1,1662001-2009   182   155   200   537

Mean STD 10% 25% 50% 75% 90%MVE 546 1,877 23 47 128 392 1,066

CH_VOLUME100.4

%1,160.5

% -55.0% -30.1% 6.0% 63.3% 189.9%CH_STDRET 4.8% 73.9% -52.6% -35.9% -10.6% 21.9% 73.3%

This panel reports sample composition and descriptive statistics of stocks that switched between three major U.S. stock exchanges (i.e., NYSE, AMEX, and Nasdaq). The initial sample consists of all switches between the three exchanges from 1962-2009 based on the Stockname file on CRSP. The final sample consists of switching stocks with nonmissing daily volume, shares outstanding, and stock price over one month before and after exchange switch. MVE is the market value of equity ($million) on the effective date of switch, calculated as closing price multiplied by closing shares outstanding. CH_VOLUME is the change of trading volume, measured as the difference between the average daily volume before and after the switch, scaled by the average daily volume before the switch. For NYSE/AMEX stocks, daily volume is daily trading volume divided by daily closing shares outstanding. For Nasdaq stocks, daily volume turnover is scaled by two. CH_STDRET is the change of stock volatility, measured as the difference between the standard deviations of daily stock returns before and after the switch, scaled by the standard deviation of returns before the switch. Windows (-22, -1) and (0, 21) are used as measurement windows before and after the switch, respectively, where day 0 is the effective date of switch.

42

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_VOLUME

(Low to High)

 

CH_VOLUME

 

CH_STDRET

 

Spearman Corr. (CH_VOLUME, CH_STDRET)

Between NYSE and

AMEX (N = 951)

Q1 -44.1% -25.4%Q2 -21.6% -15.2%Q3 0.8% -4.5%Q4 34.0% 2.9%Q5 111.8% 13.7%

Q5 - Q1 Diff. 155.9%* 39.1%* 0.352*

From Nasdaq to

NYSE/AMEX (N = 1,573)

Q1 -47.1% -34.4%Q2 -11.4% -20.8%Q3 23.6% -10.9%Q4 69.2% -4.3%Q5 258.7% -7.8%

Q5 - Q1 Diff. 305.8%* 26.6%* 0.234*

From NYSE/AMEX

to Nasdaq (N = 336)

Q1 -77.8% -6.7%Q2 -64.9% -2.6%Q3 -45.4% 21.4%Q4 -18.7% 4.4%Q5 55.3% 44.0%

Q5 - Q1 Diff.   133.1%*   50.7%*   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)   CH_VOLUME   CH_STDRET  

Spearman Corr. (CH_VOLUME, CH_STDRET)

Q1 -57.1% -21.2%Q2 -25.9% -16.1%Q3 -0.6% -4.2%Q4 41.6% 6.7%Q5 157.6% 19.8%

Q5 - Q1 Diff.   214.7% *   41.0% *   0.342*

This panel reports median CH_VOLUME and CH_STDRET across quintiles formed by CH_VOLUME and spearman correlations between CH_VOLUME and CH_STDRET measured over windows (-45, -23) and (22, 45). CH_VOLUME and CH_STDRET are defined as in Table 1 Panel A with the exception that windows (-45, -23) and (22, 45) are used as measurement windows before and after the switch, respectively, where day 0 is the effective date of switch. * denotes significance at the 1% level. The p-value for the difference between the top and bottom quintiles (Q5-Q1 Diff.) is based on Wilcoxon z-statistics.

44

Table 2 Stocks Added and Deleted from the S&P 500 Index

Panel A: Sample composition and descriptive statistics

Additions Deletions Full SampleInitial sample 590 565 1,155Final sample 453 86 539

By year1976-1980 44 2 461981-1990 207 18 2251991-2000   202   66   268

Mean STD 10% 25% 50% 75% 90%MVE 4,248 8,166 244 607 1,424 5,311 8,830

CH_VOLUME 26.7% 70.4% -40.3% -19.0% 9.3% 55.5% 104.5%CH_STDRET 11.8% 50.6% -39.8% -21.9% 1.8% 36.1% 73.3%

This panel reports sample composition and descriptive statistics of stocks that were added and deleted from the S&P 500 index. The initial sample is obtained from Jeff Wurgler’s website, spanning from 1976 – 2000. The final sample excludes additions and deletions as a result of merges, spin-offs, bankruptcy, re-organization, 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

CH_VOLUME (Low to High)  

CH_VOLUME  

CH_STDRET  

Spearman Corr. (CH_VOLUME,CH_STDRET)

Window (-22,-1) (0,21)

Q1 -13.4% -12.1%Q2 22.0% -3.4%Q3 53.2% 2.7%Q4 88.9% 8.2%Q5 164.8% 29.8%

Q5 - Q1 Diff. 178.2%* 41.9%* 0.344*

Window (-45,-23) (22,45)

Q1 -39.0% -17.7%Q2 -11.4% -9.1%Q3 8.5% 0.1%Q4 42.6% 14.6%Q5 101.0% 20.1%

Q5 - Q1 Diff.   140.0%*   37.8%*   0.380*

Panel C: Change of trading volume and return volatility for S&P 500 deletions Quintiles by

CH_VOLUME (Low to High)  

CH_VOLUME  

CH_STDRET  

Spearman Corr. (CH_VOLUME,CH_STDRET)

Window (-22,-1) (0,21)

Q1 -11.8% 0.2%Q2 57.4% 2.7%Q3 84.8% -2.3%Q4 134.9% 8.6%Q5 198.6% 5.7%

Q5 - Q1 Diff. 210.4%* 5.5% 0.181***

Window (-45,-23) (22,45)

Q1 -43.7% -24.4%Q2 -23.4% -10.6%Q3 13.2% 7.1%Q4 47.9% 7.8%Q5 143.5% 47.8%

Q5 - Q1 Diff.   187.2%*   72.2%*   0.422*This panel reports median CH_VOLUME and CH_STDRET across quintiles formed by CH_VOLUME and spearman correlations between the two variables. CH_VOLUME and CH_STRET are defined in Panel A Table 2. *, **, and *** denotes significance at the 1%, 5%, and 10% levels, respectively. The p-value for the difference between the top and bottom quintiles (Q5-Q1 Diff.) is based on Wilcoxon z-statistics.

46

Table 3: Evidence from Dual-Class Firms

Panel A: Sample composition and descriptive statisticsNumber of firms 59Number of share classes 118Firm-month pairs 7,322

Mean 10% 25% 50% 75% 90%MVE 1,789 11 53 148 419 2,212DIF_VOLUME 4,546.5% 16.4% 48.3% 144.6% 522.5% 2,361.9%DIF_STDRET 20.9% -37.3% -16.5% 2.6% 28.5% 69.5%

Panel B: Difference in trading volume and stock volatilityQuintiles by

DIF_VOLUME(Sorted at Firm Level) DIF_VOLUME DIF_STDRET

1 17.2% 0.0%2 59.2% 2.0%3 121.2% 2.4%4 254.6% 3.7%5 743.6% 4.2%

Q5-Q1 Diff. 726.1%* 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*

YearVOLUME

STDRET Year

VOLUME

STDRET Year

VOLUME

STDRET

1926 114.6% 0.014 1954 12.0% 0.011 1982 49.8% 0.0201927 113.1% 0.013 1955 11.9% 0.014 1983 57.0% 0.0171928 147.4% 0.016 1956 9.6% 0.012 1984 58.9% 0.0161929 130.4% 0.029 1957 8.8% 0.013 1985 66.4% 0.0141930 77.4% 0.023 1958 9.8% 0.012 1986 75.4% 0.0171931 60.6% 0.032 1959 9.6% 0.013 1987 85.9% 0.0261932 52.4% 0.043 1960 8.5% 0.014 1988 67.5% 0.0161933 61.4% 0.037 1961 9.6% 0.013 1989 65.7% 0.0141934 24.2% 0.021 1962 10.1% 0.017 1990 55.8% 0.0171935 24.7% 0.018 1963 10.0% 0.011 1991 55.8% 0.0161936 26.2% 0.016 1964 9.3% 0.010 1992 54.7% 0.0151937 22.9% 0.024 1965 10.1% 0.011 1993 62.1% 0.0151938 18.1% 0.024 1966 14.8% 0.015 1994 63.8% 0.0151939 15.7% 0.020 1967 16.0% 0.014 1995 69.9% 0.0141940 11.6% 0.018 1968 17.0% 0.015 1996 72.5% 0.0161941 9.2% 0.014 1969 15.6% 0.015 1997 79.4% 0.0191942 7.1% 0.014 1970 15.3% 0.018 1998 82.9% 0.0231943 11.9% 0.012 1971 17.2% 0.014 1999 93.3% 0.0241944 10.7% 0.010 1972 16.2% 0.013 2000 111.9% 0.0311945 14.4% 0.012 1973 16.0% 0.019 2001 110.9% 0.0241946 14.7% 0.018 1974 14.6% 0.023 2002 129.3% 0.0261947 10.0% 0.013 1975 18.6% 0.018 2003 124.7% 0.0161948 11.5% 0.013 1976 22.8% 0.014 2004 124.2% 0.0131949 9.3% 0.011 1977 20.5% 0.012 2005 138.0% 0.0131950 16.4% 0.013 1978 24.9% 0.014 2006 159.8% 0.0131951 12.5% 0.011 1979 28.3% 0.014 2007 224.2% 0.0161952 9.2% 0.010 1980 38.4% 0.020 2008 360.5% 0.0371953 9.0% 0.010 1981 36.3% 0.018 2009 277.3% 0.028

This table reports trading volume and stock volatility for the largest 500 stocks on NYSE/AMEX from 1926 to 2009. VOLUME and STDRET are defined in Figure 2. CH_VOLUME (CH_STDRET) is the difference of VOLUME (STDRET) in year t and t-1. * denotes significance at the 1% level.

48

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 D9 D10 D10 - D19.7% 22.4% 35.0% 47.3% 59.2% 70.7% 84.2% 104.9% 136.4% 244.8%   235.1%*

0.020 0.021 0.020 0.019 0.019 0.019 0.020 0.022 0.025 0.031 0.011*

Panel B: Stock volatility formed on the basis of both earnings volatility and trading volume

VOLUME deciles (low to high)D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 D10-D1

9.7% 22.2% 34.7% 46.5% 58.5% 71.0% 86.0%107.6

% 139.3%235.0

%  

225.3%*

STD-EARN deciles (low to

high)

D1 0.001 0.014 0.015 0.015 0.015 0.015 0.016 0.016 0.018 0.018 0.021 0.007*D2 0.003 0.015 0.016 0.014 0.015 0.015 0.015 0.016 0.018 0.019 0.023 0.008*D3 0.004 0.017 0.017 0.017 0.016 0.016 0.017 0.018 0.019 0.021 0.024 0.007*D4 0.006 0.018 0.019 0.018 0.017 0.017 0.017 0.018 0.020 0.021 0.026 0.008*D5 0.008 0.019 0.019 0.018 0.018 0.018 0.019 0.020 0.021 0.024 0.027 0.008*D6 0.011 0.020 0.021 0.020 0.019 0.018 0.019 0.021 0.022 0.025 0.028 0.008*D7 0.014 0.022 0.022 0.021 0.022 0.020 0.021 0.023 0.024 0.026 0.030 0.008*D8 0.021 0.025 0.026 0.025 0.024 0.024 0.024 0.023 0.026 0.028 0.033 0.008*D9 0.036 0.028 0.033 0.031 0.029 0.029 0.028 0.028 0.029 0.031 0.036 0.008*

D10 0.096 0.037 0.043 0.042 0.047 0.040 0.041 0.043 0.040 0.039 0.046 0.009*

 D10-D1 0.095*   0.023 0.027* 0.027 0.032* 0.025 0.025* 0.026* 0.023* 0.021* 0.024*    

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* * *

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.

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Table 6The 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

 Predicted

Sign   (1)   (2)   (3)   (4)Intercept + 38.377 44.550 17.515 18.112

(45.28)* (54.50)* (12.65)* (6.02)*HIGH - -69.782 -20.425 -13.697

(-21.43)* (-9.06)* (-2.11)**VOLUME + 0.225 0.011 0.105 0.133

(13.13)* (0.63) (10.31)* (5.93)*VOLUME*HIGH + 1.004 0.274 0.170

(23.21)* (10.33)* (2.12)**STDRETt-1 + 0.663 0.666

(58.46)* (20.49)*RET - -0.071 -0.117

(-3.51)* (-4.88)*STDEARN + 0.103 0.114

(19.17)* (9.17)*SIZE - -0.148 -0.141

(-8.35)* (-4.84)*AGE - -0.028 -0.032

(-2.87)* (-2.75)*LEVERAGE + 0.005 0.014

(0.88) (2.15)**BTM ? 0.001 -0.009

(0.10) (-0.71)

(Average) Number of Observations 1,916 1,916 1,916 38,322(Average) Adjusted R2   0.055   0.096   0.752   0.706

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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.

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