Effects of Passive Intensity on Aggregate Price

Dynamics

Sina Ehsani and Donald Lien∗

August 14, 2014

Abstract

We find that passive intensity (PI), measured by the passive-linked share of to-

tal stock market trading volume, is strongly related to the overall pattern of stock

price movements. A one-standard deviation increase in PI is associated with 8 per-

cent higher price synchronicity. We further investigate the channels through which

this relation is established by separately analyzing its impact on aggregate systematic

and idiosyncratic volatility of stock returns. PI has a positive effect on systematic

volatility and a negative impact on firm-specific volatility. Consistent with the effect

of passive-trading on price dynamics, we find evidence that PI is negatively associated

with mutual funds alpha dissimilarity. After controlling for market and idiosyncratic

volatility, a one-standard deviation increase in PI corresponds to a 0.20% decrease in

fund dissimilarity. Our findings are robust after controlling for various macro and cor-

porate factors known to affect systematic or firm-specific volatilities.

JEL Code: G10, G14

Key words: passive investment, price dynamics, comovement, synchronism, systematic

volatility, idiosyncratic volatility

∗University of Texas at San Antonio; email:don.lien@utsa.edu or sina.ehsani@utsa.edu. All errors are

ours.

1

1 Introduction

According to traditional finance theories, stock price is the risk-adjusted present value of

future expected cash flows. In this framework, asset returns are correlated because the

variations in intrinsic value of assets (e.g. future expected cash flows) are correlated and

frictions or the trading behavior of a portion of investors does not affect price comovement.

Researchers have found patterns inconsistent with this argument and have proposed several

explanations to why asset returns exhibit different regimes of comovement over time and

across countries. Barberis and Shleifer (2003) and Barberis, Shleifer and Wurgler (2005)

suggest that comovement may be detached from fundamentals because of frictions or irra-

tional behavior of investors. Several theoretical and empirical studies suggest a variety of

factors from corporate finance to business cycle for possible candidates. In this paper, we

show that passive intensity (PI) measured by passive-linked share of total trading volume is

one possible factor: it is strongly related to time-series behavior of aggregate stock return

synchronicity, systematic volatility and aggregate idiosyncratic volatility.

Demand for low-cost diversification has given rise to the creation of index funds. A

passive product such as Exchange Traded Fund (ETF) is typically designed to replicate the

performance of an index or a segment (e.g. small cap stocks, value stocks, etc.) of the

market by investing a specific amount in each of the underlying securities. In addition to

diversification, ETFs have lower managerial expenses, are tax efficient, can be traded like a

stock throughout the day, and the creation/redemption mechanism allows them to be traded

in line with the fund’s underlying net asset value. Unlike a stock price that is determined

by supply and demand, a passive product’s price should only reflect the underlying basket:

local supply/demand or trading volume does not change its fundamental value and should

not affect its price. Consequently, price or trading volume of a passive product should not

affect the price dynamics of the underlying stocks and the market. Passive instruments are

intended to follow the price of the underlying basket, and should not be associated with

price discovery of the underlying securities.

The most popular ETF, ’SPY’ was introduced in January 1993 to track the performance

2

of the S&P500 index. In 1993, SPY’s daily dollar volume was on average smaller than 10

million dollars and two decades later, it has surpassed $20 billion. From 2006 to 2012, the

average trading turnover of SPY accounts for roughly 10% of total trading volume of the

U.S. stocks, making it the most heavily traded security in the world.1 ETFs’ total dollar

turnover has increased at a very fast pace of 78% annually until 2007, compared to total

stock market dollar turnover growth of 20%. Figure 1 displays the number of ETFs and their

share of total daily trading volume drawn from the CRSP database. ETFs’ share of total

trading, has increased from less than 1% in 1993 to 30% in 2007 and has been fluctuating

in the 25%-40% range since then.

[Insert figure 1 around here]

Wurgler (2011) notes that the broad economic consequences of index-linked2 investment

are blurred. As passive instruments continue to take over a larger share of the market,

they could eventually affect the underlying securities and the stock market. A relevant

literature explores the short and long term effects of major indices compositional changes on

share prices and comovement. Event studies (e.g. Harris and Gurel (1986), Shleifer (1986),

Benish and Whaley (1996), Wurgler and Zhuravskaya (2002), and Petajisto (2011)) test

the short-term effect of inclusion or deletion on the underlying stock price. Vijh (1994) and

Barberis, Shleifer and Wurgler (2005) examine the changes in correlations and betas of newly

listed/delisted stocks and find that stocks added to S&P500 follow the index more closely

and their betas are higher relative to matched similar stocks. In general, these studies focus

1Most passive securities have experienced exponential upward trend in inflows and trading volume, and

continue to receive a large portion of total stock market inflow. In 2012, passive securities absorbed 41%

of total net flows. (Morningstar, “2012: Annual Global Flows Report”). According to a report available at

http://www.etftrends.com/2013/11/etf-asset-flows-reveal-investors-love-for-stocks/, US ETF net inflow was

$156.4 billion during the first 10 months of 2013, with total assets reaching $1.641 trillion by the end of

October 2013. There were 1,524 ETFs in U.S. at the time of this study in November 2013.2Because most ETFs and passive products follow an index or a segment of the market, we use the words

passive intensity, passive trading, ETF trading, index trading and indexing interchangeably.

3

on a segment of the market (for example, the underlying stocks of S&P500 vs. the others),

and argue that uninformed demand affects the price dynamics of the exposed stocks.

A second strand of literature examines how passive investment may affect the aggre-

gate stock market. Wurgler (2011) argues that index-linked products ‘are no longer mere

carriers of information’ but have become a new underlying force of the stock market. Ben-

David, Franzoni and Moussawi (2012) conjecture that ETFs can increase systematic risk via

arbitrage activity between the ETF and the underlying securities. They show that ETFs

increase the exposure of the underlying securities to non-fundamental shocks and convey

more volatility to the market. Clifford, Fulkerson and Jordan (2014) find that ETF fund

flow is related to measures of activity such as turnover and past performance while they

find no association between flows and future performance. Da and Shive (2013) relate ETF

activity to higher return comovement at the firm level, with the effect being larger for small

and illiquid stocks. Sullivan and Xiong (2012) find that pairwise correlations between stock

returns have amplified threefold for both S&P500 listed and non-listed stocks over the last

two decades. They suggest that growth in passive investment can explain the observed jump

in price commonality.

Most previous studies examine the effects of indexing using firm level data and do not

provide sufficient evidence to generalize the observed consequences of passive investment to

the aggregate stock market. The purpose of this study is to complement prior findings by

investigating the relationship between passive trading and price synchronism, idiosyncratic

volatility and systematic volatility at the aggregate level. We show that passive intensity

loads positively on systematic volatility and negatively on aggregate firm-specific volatility,

resulting in a very strong correlation with price comovement. Although firm-specific risk

can be diversified away and therefore should not be priced according to modern asset pricing

theory, it has attracted a lot of attention from academicians and practitioners. Fama (1970)

calls a market ‘efficient’ if prices always fully reveal available information. French & Roll

(1986) and Morck, Yeung and Yu (2000), among others, argue that the central creating

forces of firm-specific variation are the arrival of new information and the intensity that new

4

information is incorporated into prices. Therefore, higher idiosyncratic volatility indicates

that prices reflect the changes in firm-specific fundamentals faster. All else equal, this signals

higher market efficiency. From an investment point of view, idiosyncratic volatility is a

source of stock differentiation and potential alpha. Active managers have a greater chance

of outperforming or underperforming a benchmark when idiosyncratic volatility is high and a

smaller chance of realizing a significant alpha when other investors exhibit ‘herd behavior’.3

Idiosyncratic volatility is also relevant in pricing options because option prices depend on

both systematic and idiosyncratic volatilities of the underlying stock.

The evidence provided in our study suggests that the growth in passive-linked trading

increases price synchronicity by reducing firm-specific variation, which in turn affects price

informativeness and managers who seek to outperform a benchmark. We run a series of

robustness checks and conclude that the results cannot be attributed to possible economical

and statistical concerns. Our findings shed new light on the broad economic consequences

of proliferation of passive products.

2 Data

Daily returns for all US stocks over the period 1963-2012 and ETFs (share code of 73) over

the period 1993-2012 are drawn from The Center for Research in Security Prices (CRSP). We

exclude alternative, volatility, bond, commodity, real estate and currency ETFs according to

the classification provided by etfdb.com in order to restrict the sample to equity ETFs. Since

information is eventually impounded into price through trading, aggregate trading volume

of passive products is a natural indicator of activity in the passive space. We define passive

intensity (PI) by the portion of total trading that is associated with passive trading, and

is calculated by the ratio of daily dollar-volume of all equity-ETFs to dollar-volume of all

3The tendency of individuals to respond uniformly to new news is usually described as herd behavior.

When investors herd, stocks respond to new news homogeneously and idiosyncratic volatility drops. As we

show in section 4, in times of low firm-specific volatility active managers have little opportunity to realize

returns that are significantly different from their peers.

5

common stocks in the CRSP database.4 Following Morck, Yeung and Yu (2000), we drop

firm-months with less than 12 daily observations and truncate 0.5% returns on both ends

to mitigate data errors. We use the market model regression to construct proxies of price

synchronicity. The following regression is run every month for each stock:

ri,t = αi,m + βi,mrM,t + εi,t, (1)

where ri,t is the excess return of stock i in day t and rM,t is the return of the market portfolio

less the risk free rate in day t. We record monthly R2 and daily residuals for all stocks.

Roll (1988) notes that the R2 of regression (1) captures the portion of total variance that

is explained by systematic risk. Obviously, a higher R2 means that a larger part of the

variation in a stock’s returns is related to market variations because in univariate regressions

such as (1), R2 is the squared of the correlation coefficient between the dependent variable

(stock return) and the independent variable (market return). Using this logic, we construct

a time-series representing aggregate price commonality, the value weighted R2, (from here

on referred to as synchronicity) as follows:

Sync.m =n∑i=1

wi,mR2i,m (2)

where R2i,m is the R2 of equation (1) for stock i in month m and wi,m is the weight (based

on the beginning month’s market capitalization) of stock i in month m.

We use Bekaert, Hodrick and Zhang (2012) approach to compute aggregate idiosyncratic

4While the ETF market contains a minority of actively managed funds, it is mostly concentrated in passive

products. The trading volume of all the ETFs in the CRSP universe provides a decent representation of

passive trading activity.

6

variance:5

σ2idio.,m =

n∑i=1

wi,mσ2εi,m

(3)

where σ2εi,m

is the variance of residuals of stock i in month m. Also, let σ2M,m denote the

variance of market returns in month m. The top graph of Figure 2 displays idiosyncratic and

market volatilities over the period January 1963 to December 2012. Idiosyncratic volatility

is defined as the square root of (3) and market volatility is the defined by the standard

deviation of daily market returns over a month. Synchronicity and the ratio of systematic

to total variance (σ2M,m

σ2M,m+σ2

idio.,m) are plotted in the bottom graph. For individual stocks, the

ratio of systematic to total variance is equivalent to R2 if a stock’s beta is one. The graph

shows that this ratio is a good approximation for synchronicity at the aggregate level,6 the

ratio tracks the value-weighted R2 trend very closely (the two time-series have a correlation

of 0.97) and we can analyze return commonality by only focusing on market and aggregate

firm-specific volatilities.

The first graph demonstrates that the well-known upward trend of idiosyncratic risk

(Campbell, Lettau, Malkei and Xu, 2001) ends in late 1990s and reverses sharply after-

wards, whereas market volatility does not exhibit any significant regime change. Indeed,

during the past decade, market variance has been at historical maximum relative to idiosyn-

cratic variance. The second graph confirms this observation; US stocks have become more

synchronous over time as systematic variance to total variance exhibits an increasing trend

5We have also employed the Fama-French three factor model to estimate residuals and compute idiosyn-

cratic volatility as in Ang, Hodrick, Xing and Zhang (2006) and Bekaert, Hodrick and Zhang (2012). Those

results are consistent with the results presented in this paper and are available upon request. For another

robustness check, we used Bali, Cakici and Levy (2008) model-free measure of aggregate idiosyncratic volatil-

ity. That measure also has a correlation of 0.98 with the one used for this study and generates the same

patterns and results.6To achieve a better approximation of aggregate R2, we computed market-wide variation defined by the

monthly average of β2i,mσ

2M,m (instead of σ2

M,m), where β2i,m is the beta of stock i in month m from (1). The

resulting approximated R2 was slightly superior to our approximation above in terms of tracking the actual

synchronicity. We decided to use market variance since market-wide variation depends on the interaction of

betas and market variance which adds more complexity to interpretations

7

starting in 1990s and in late 2007 reaches levels that were unseen before. The systematic

portion of total variation of stock returns has never been at this high for such a long period.

High levels of aggregate R2 indicates that most of the volatility is systematic and a smaller

portion of total volatility can be diversified.

[Insert figure 2 around here]

Initial evidence on the link between price synchronicity and passive intensity is presented

in Table 1. Statistics of the top fifteen months of our sample sorted by synchronicity are

reported. The column ‘Passive intensity rank’ reports the rank in our sample of 240 months

based on that month’s PI.7 There are several observations worth mentioning. First, except

for the crash of October 1987, months with highest price commonality occurred in recent

years. Second, in recent years, times of high price commonality may happen in any market

condition. For example, during September 2011 market plunged more than 8% due to worries

about European debt and synchronicity was 62%, the seventh highest in fifty years. One

month later in October 2011 when the stock market had one of its best months in almost two

decades (the market portfolio return was 11.34%), stock returns were still highly correlated.

Synchronicity was 57%, the eleventh highest in our sample. Finally, and most important for

our study, ten of the top-fifteen high synchronicity observations are also in top-fifteen high

passive trading months, times of high price commonality are associated with heavy passive

trading.

[Insert table 1 around here]

Figure 3 reveals how this relation is established. The first graph displays the positive

synchronicity-PI relationship in a univariate setting. The regression line shown on the graph

indicates a statistically significant association with an R2 of 0.56. Omitting 5% extreme

observations from synchronicity, PI or both does not affect the association between the

7Our US stock sample covers 50 years (1963-2012). The first ETF was introduced in January 1993,

limiting the sample with passive-trading data to 20 years.

8

two as the R2 of univariate regressions remains above 0.45 in all cases. The next two graphs

demonstrate that PI has a negative influence on idiosyncratic volatility and a positive impact

on market volatility. We discuss these findings in more details in the following section.

[Insert figure 3 around here]

3 Exploring price synchronicity, systematic volatility and firm-specific

volatility

As mentioned in the previous section, the relation between R2 and any explanatory variable

depends on how that variable correlates with firm-specific or market variance. A variable

may correlate with R2 because it correlates with market variance, firm-specific variance or

both. A plausible argument is that high return comovement is attributed to the changes

in any of the studied determinants of volatility. Perhaps not the increase in PI but higher

macroeconomic uncertainty explains the trend in volatility that consequently leads to the

upsurge in price commonality. We briefly explore the literature on several determinants of

volatility that will be used in this study.

A large strand of research suggests different reasons to why volatility (both firm-specific

and market) is itself volatile over time. Merton (1980) specifies a relationship between ex-

pected returns and market volatility by assuming market volatility is a sufficient statistic for

risk. French, Schwert, and Stambaugh (1987) provide empirical support for this hypothesis.

Goyal and Santa-Clara (2003) present empirical evidence that idiosyncratic volatility pre-

dicts returns. We proxy for expected returns by calculating the next month’s value weighted

return of the stocks in the CRSP database.

Officer (1973) links changes in stock return volatility to macroeconomic variables. Bekaert,

et. al (2012) show empirically that business cycles impact firm-specific volatility through

changes in macroeconomic uncertainty. Business cycle variables proxy for firm-level earn-

ing and overall economy condition that may lead to changes in firm-specific and market

9

volatility. Following Bekaert et. al (2012) we control for growth in industrial production,

default spread (difference between yields on AAA and BAA bonds), dispersion in survey

forecast (standard deviation across growth forecasts), variance premium (difference between

the square of VIX index and the physical variance of the S&P500 index), term spread (the

yields spread between 10 year and one year treasury bonds) and market volatility.8

Numerous studies suggest corporate variables as the potential determinants of stock

volatility. Wei and Zhang (2006) document that return-on-equity, the ratio of earning to

book-value of equity, explains the trend in average stock return volatility over the 1976-2000

period. We use all the stocks in the Compustat universe to compute an equally weighted

return on equity. Cao, Simin and Zhao (2008) show theoretically and empirically that

growth options available to managers are related to idiosyncratic volatility. We follow their

procedure and use the ratio of market value to book value of assets to proxy for corporate

growth options. Chun, Kim, Morck and Yeung (2008) suggest that intensified creativity as

a result of high productivity growth leads to higher firm-specific stock return. To construct

a measure of research intensity, we use Bekaert et. al (2012) approach and compute both a

value weighted average and a cross-sectional variance of firm-level R&D expenditure where

R&D expenditure is defined as the ratio of R&D expense to total revenue.9

Our main dependent variables as well as the proxy for passive intensity are constructed

on a monthly basis while the accounting data is reported on a quarterly basis. These reports

are dispersed all over the year but more reports are available in some months. Irvine and

Pontiff (2008) and Bekaert et. al (2012) suggest calculating a three month moving average

8Industrial production, yields on ten and one year Treasury bonds, AAA and BAA bonds and historical

VIX index are collected from Federal Reserve Bank of St. Louis website. Corporate earnings forecasts are

drawn from The Survey of Professional Forecasters; this data is reported over a quarterly basis. We linearly

interpolate through time to construct a monthly estimate of uncertainty regarding corporate earnings.9We have controlled for other variables such as aggregate tangibility, cash and short-term investments,

profitability, debt maturity, and leverage as in Bartram, Brown and Stulz (2012). These variables exhibit

very little correlation with aggregate R2 and does not change the quality of the results in Table 2. We have

omitted those controls in interest of conciseness.

10

(current month and the previous two months) to have monthly measures that represent the

full sample of firms. We have followed their procedure for computing monthly corporate

variables.

Table 2 presents the main results of our paper. Because ETFs were born in 1993, our

number of observations is 240 (20 years) in the following tests. The first three columns of

table 2 present pairwise correlations between each independent variable and the dependent

variables. Passive intensity correlates significantly with market and firm-specific volatil-

ity in opposite directions, resulting in a solid correlation with synchronicity. The pairwise

correlation coefficient between PI and synchronicity is 0.76 which is comparable to that of

market volatility. This is an important observation when we consider that market volatility

is directly related (numerator) to R2 of a market model regression. Multivariate regres-

sion results in specifications 1 through 6 provide supporting evidence. For each dependent

variable, we first run a regression that contains all independent variables. Since a model

with all variables may include irrelevant variables and would be inappropriate because of

possible multicollinearity, we exclude regressors that are not significant at the 10% level in

the first specification and rerun the regressions. These results are presented in specifications

2, 4 and 6. The control variables that survive this procedure are growth options (MABA),

default spread (DFLT), variance premium (VP), physical market volatility (MVOL) and the

recession indicator (RECESSION). The relation between PI and dependent variables seems

robust to inclusion or exclusion of additional control variables. After controlling for other

well-known determinants of volatility, PI continues to load positively (significant at the 10%

level) on market volatility and negatively (significant at 1% level) on aggregate firm-specific

volatility and is the only variable that exhibits such behavior. The PI coefficient in columns

1 and 2 implies that a one-standard deviation increase in passive trading is associated with

an 8% increase in the level of synchronicity, an economically significant result considering

that the mean level of synchronicity is around 29% in this sample. This association is a

result of the coefficients reported in column 3 through 6. A one-standard deviation increase

in PI corresponds to a 2% increase in market volatility and a 4% decrease in idiosyncratic

11

volatility, both associations magnify the positive synchronicity-PI relationship.

[Insert table 2 around here]

After obtaining a significant relation between PI and comovement at the monthly fre-

quency, we now examine the consistency of this finding by testing this relation on a daily

basis. Morck et al (2000) suggest a measure of price synchronism that can be computed on

a daily basis:

ft =max[nupt , n

downt ]

nupt + ndownt

(4)

where nupt and ndownt are the number of stocks whose prices rise and fall on date t, respectively.

The measure computes daily comovement of stock returns by using the maximum number of

stocks that go up or down each day. ft takes a value of 0.5 when the number of stocks that

lost value equals to the number of stocks whose price increased and reaches a maximum value

of 1 when all stocks go down or up on a day. Our daily measure of market volatility is the

VIX index and we compute the daily cross-sectional standard deviation of all stock returns

in the CRSP database to proxy for idiosyncratic volatility. Figure 4 displays scatter plots

and the estimated linear relations between these variables and indexing. The fitted lines

show that PI performance is consistent with our previous findings: it is positively related

with market volatility and negatively with idiosyncratic volatility.10 The interaction of the

two effects results in a high impact on price commonality.

[Insert figure 4 around here]

Because most corporate and macroeconomic control variables are not available on a daily

basis, we use the daily return on the market portfolio as a control variable that indicates

the general state of the economy. Table 3 presents the results for multivariate regressions

10The proxies for monthly and daily price synchronicity are bounded within the [0,1] and [0,0.5] range,

respectively. As in Morck et al (2000), we have applied logistic transformations to map the measures to the

whole real domain and found consistent results with those presented in this paper. Thus, we settle on the

raw measures since interpretations are more apparent.

12

using the daily sample and complements our findings in table 2. PI is significantly related

to synchronicity, market and idiosyncratic volatilities on a daily basis.

[Insert table 3 around here]

4 The effect on alpha commonality

An actively managed fund seeks to outperform an index or his peers through superior security

selection. The manager expects a larger risk-adjusted alpha (positive or negative) if he invests

in a portfolio that includes less “common” securities. Studies such as Amihud and Goyenko

(2013) show that funds that choose to invest in unique securities, measured by the R2 of

a multifactor model, outperform otherwise similar funds. Since the main benchmark for

a manager’s skill is the realized alpha, we test whether risk-adjusted alpha commonality

is associated with passive trading intensity. Our measure is the cross-sectional standard

deviation of monthly realized risk-adjusted alphas (σα) where alpha of each fund is the

intercept of Fama-French-Carhart four-factor model.

Daily gross returns and assets under management of mutual funds are drawn from

Bloomberg. We download the data for both active and inactive equity funds that are mainly

invested in the US stock market. We exclude ETFs and passive funds and limit the sample

to those mutual funds that are classified as ‘US EQUITY’ and are dollar denominated. The

final sample includes 2,510 funds of which 89 have disappeared by the end of 2012. For each

fund, every month we regress daily gross returns on the Fama-French-Carhart four-factor

model:

rf,t = αf,m + βf,mMKTRFt + βf,SMB,mSMBt + βf,HML,mHMLt

+βf,UMD,mUMDt + εf,t

(5)

where rf,t is the excess return of fund f in day t and MKTRF , SMB, HML and UMD

are the daily risk factors obtained from Kenneth French website. We record the intercepts

to calculate the cross-sectional variation of alphas.

13

Table 4 provides an overview and descriptive statistics of the sample. There are 488

funds in 1993 and this number increases to 2,398 by the end of 2012. Funds tend to be

smaller in the initial years of the sample compared to recent years. While individual fund

returns exhibit a large cross-sectional variation, a time-series market model regression with

the average return of all funds as the dependent variable yields a R2 of 98%, indicating that

a portfolio of all the funds in the sample is broad and well diversified

[Insert table 4 around here]

Figure 5 plots the time-series of average monthly and the monthly cross-sectional standard

deviation of alphas (σα). σα has a mean of 2.56% and standard deviation of 1.03%. Average

annualized alpha is 0.42% which implies that the net management fee alpha is negative over

our sample period. Also, there is no significant association between alpha dissimilarity and

average alpha. Alpha dissimilarity is highly volatile over our sample period and is the highest

in the dot-com boom (bust) and peaks again during the recent financial crisis.

[Insert figure 5 around here]

Columns 1 and 4 of Table 5 report the results for contemporaneous and predictive uni-

variate regressions of alpha dissimilarity on PI.11 In column 3, we control for the subgroup

of variables that were significant in table 2 as well as idiosyncratic volatility. As expected,

aggregate idiosyncratic volatility has the highest statistical and economical association with

alpha dissimilarity among all variables. Nevertheless, PI remains significant when we control

for idiosyncratic volatility and other control variables. A one-standard deviation increase in

PI is associated with 0.15 to 0.39 percent less variation across alphas. Coefficients in columns

11The ‘alpha dissimilarity’ used in the regressions is adjusted for the fact that the number of observations

affect sample variance. Kenney and Keeping (1951) show that if s is the sample’s standard deviation, then

sb(N) is an unbiased estimator of the actual standard deviation. Note that b(N) =

√2N

Γ( N2 )

Γ( N−12 )

, N is the

number of observations and Γ(.) is a gamma function. In our sample, N (number of funds) is always a large

figure and the adjustment factor b(N) is very close to one. Thus, the adjusted standard deviation is close to

the sample’s standard deviation.

14

4 through 6 are obtained when independent variables at month t are used to predict alpha

dissimarility at month t + 1 and are in line with contemporaneous results. The results are

consistent with the argument that passive trading is positively associated with alpha com-

monality and may deteriorate the well-known procedures used to distinguish between skilled

and unskilled managers.

[Insert table 5 around here]

5 Robustness

5.1 Endogeneity problem

An alternative explanation for our findings might be the endogenous causation link between

correlation and index trading. Figure 1 concedes that price commonality increases dur-

ing times of high uncertainty. When uncertainty regarding the economy rises, market-wide

variation explains a large part of stock variation and stock returns tend to have smaller dif-

ferences, leading to high levels of price synchronism. Being aware of this, investors may find

less value in picking stocks and invest in passive funds. Therefore one can argue that large

PI is a result of high synchronicity rather than causing the synchronicity. We attempted to

address the above endogeneity problem by controlling for economy risk in Tables 2 and 3

and showed that PI has additional explanatory power. Besides, multivariate specifications of

table 2 reveal that PI affects idiosyncratic volatility more than systematic volatility (statisti-

cally), hence the link between PI and synchronicity is through both market and firm-specific

volatilities.

To provide formal evidence for our argument, we show that passive intensity is related to

future price synchronism and its components and perform both unconditional and conditional

Vector Autoregression (VAR) analysis for synchronicity and passive intensity. In table 6, we

regress synchronicity, market and idiosyncratic volatilities on lagged PI and control variables.

Results in Panel A are economically and statistically consistent with the contemporaneous

15

regressions of table 2. Similarly, in Panel B we test the predictive power of PI on a daily

basis and obtain results parallel to those of table 3. We conclude that greater PI in a period

is associated with higher price synchronicity in the following period.

[Insert table 6 around here]

Table 7 reports the VAR analysis results. In the first specification, synchronicity is a

function of its own lags and PI lags. Coefficients in the first column demonstrate that the

second and third lags of PI are positively related to return comovement, while other lags are

statistically insignificant. On the other hand, results in the second column with PI as the

dependent variable show that the first lag of synchronicity is positively (but not statistically

significant) related to PI and that impact is more than offset by the large negative impact

of the third, fourth and fifth lags. The total effects of all lags demonstrate that higher

PI results in higher synchronicity and in contrast higher synchronicity seems to result in

lower passive trading. The bottom rows of table 7 displays the F and p-values of Granger

causality tests with five lags. The null hypothesis that a time-series is not useful in forecasting

another is rejected for both variables. We also run conditional VAR tests and the last two

columns summarize those results. Specifically, we test for causality between synchronicity

and PI while controlling for both VIX and cross-sectional volatility. Results are similar to

those of unconditional tests with the exception that in the last column, all synchronicity

lagged coefficients become negative compared to results in the second column where the first

coefficient was positive. Altogether, we conclude that causality is likely not unidirectional

nor a positive feedback process and the direction is more from PI to synchronicity than

otherwise.

[Insert table 7 around here]

5.2 Stationarity

According to figure 1, trading volume of passive products exhibits a relatively monotonic

increasing trend for the initial years of our sample. One important question to be addressed

16

is whether the above results are biased because a non-stationary stochastic process can pro-

duce spurious regression results with inflated t-statistics. To transform PI into a white noise,

we fit an autoregressive integrated moving average (ARIMA) with 3,1 and 2 for the orders

of autoregressive, difference and moving average, respectively. We take the first difference

for other variables and repeat the OLS specifications of table 2. Table 8 presents the results.

MABA and DFLT become insignificant while PI, VP and MVOL remain significant. Coef-

ficients of table 8 imply that an increase in PI is associated with increases in synchronicity

and market volatility and a decrease in idiosyncratic volatility. Once again, the sign and the

statistical significance of the coefficients are consistent with our results in table 2.

[Insert table 8 around here]

5.3 Monetary policies

An important systematic factor in recent years is the US Federal Reserve’s monetary policies.

Shortly after the recent financial crisis, US Federal Reserve implemented an unconventional

monetary policy by increasing the money supply, lowering interest rates and term-premiums

to stimulate the economy and increase employment. Since the beginning of quantitative

easing in late 2008 until the time of this study, Federal Reserve’s holdings of Treasury and

mortgage backed securities has increased more than $3 trillion. Several studies document a

significant relation between large scale asset purchases (LSAPs) and economy-wide factors

such as Treasury yields.12 D’Amico, English, Lopez-Salido and Nelson (2012) estimate that

the first and second rounds of LSAPs pushed down long term yields by 35 and 45 basis

points, respectively. The decline in interest rates coupled with the exogenous excess liq-

uidity impact stock market investors and companies in different ways. Corporations may

find incentives to borrow at cheap long-term rates to invest in projects or buy-back shares,

investors may increase their stock holdings because the risk-adjusted future dividends are

discounted at a lower rate and the expected returns on bonds are lower. Given that asset

12For example, see Krishnamurthy and Vissing-Jorgensen (2011), Swanson (2011) and D’Amico and King

(2012)

17

purchases take place gradually, its impacts on stock prices happen over time. Any exogenous

phenomenon that affects all assets simultaneously might be a candidate for explaining the

existing high correlation among stock returns. However, the relation between LSAPs and re-

turn comovement depends on several factors. When the cost of debt declines, some projects

with negative NPV turn out to be positive and more projects become feasible. According

to Chun, Kim, Morck and Yeung (2008), if companies undertake more projects, we expect

to see a higher dispersion in cash flows and performance over a long term. On the other

hand, Federal Reserve injects liquidity over a lengthy period of time through open market

operations. This regularly injected extra liquidity supports the demand side of most assets

including stocks, thereby inducing a common factor in the returns of these securities.

To summarize, it seems that the possible negative effect of LSAPs (through higher cor-

porate investments) on price synchronicity happens over a long period while excess liquidity

has short-term local demand impact that is attributable to a broad class of assets. We

control for FED’s monetary policy by including a QE dummy variable that takes a value of

one in months with QE operations and zero otherwise. We add the QE dummy to the OLS

regressions of table 2 (specifications 2, 4 and 6) and find that the PI coefficients remain the

same; a one standard deviation increase in PI is associated with 0.08 (t = 15.55) increase in

synchronicity, 0.02 (t = 2.17) increase in systematic volatility and 0.04 (t = -7.39) decrease

in idiosyncratic volatility. The QE dummy is insignificant in all three specifications and

the rest of the coefficients are omitted in interest of brevity as they were qualitatively and

quantitatively similar to those of Table 2. Moreover, according to graph 1, passive trading

has been in a narrow range since the beginning of QE in 2008 and even though QE may

contribute to return comovement, its impact on the indexing-synchronicity link seems to be

minimal.

18

6 Summary

The overall pattern of stock price movements since early-2000s exhibits very high synchronic-

ity. This means certain factors are common among most stocks. The evidence provided in

this study suggests that the increase in passive intensity, the passive-linked share of total

trading volume, is one possible factor. PI has increased from negligible levels since its in-

troduction in 1993 to more than 30% of U.S. market total trading volume. High levels of

PI affects price dynamics at the aggregate level; it diminishes the difference between stocks

by reducing idiosyncratic volatility and increasing price commonality. After controlling for

economy and corporate level variables, a one-standard deviation increase in PI corresponds

to 2% higher systematic volatility, 4% lower idiosyncratic volatility and 8% higher price

synchronicity. Similar relationships hold when PI is used to predict future levels of volatility

and price commonality.

According to Fama (1970), French and Roll (1986) and Roll (1988), a market is more

efficient when price capitalizes information more quickly to new events. Any factor that

reduces idiosyncratic volatility, and thus narrows the difference between stocks, may disturb

information efficiency. Changes in idiosyncratic volatility also affect active managers who

seek to outperform a benchmark by picking stocks with potential positive alpha. We find

that the cross-sectional similarity in mutual fund alphas is positively associated with passive

intensity which directly affects investors who seek to identify skilled managers. Our findings

suggest that investors should consider passive products’ trading volume in decision making

because it affects the basic dynamics of price discovery.

References

Amihud, Y. and Goyenko, R. (2013). Mutual fund’s R2 as predictor of performance. Review

of Financial Studies, 26(3):667–694.

19

Bali, T. G., Cakici, N., and Levy, H. (2008). A model-independent measure of aggregate

idiosyncratic risk. Journal of Empirical Finance, 15(5):878–896.

Barberis, N. and Shleifer, A. (2003). Style investing. Journal of Financial Economics,

68(2):161–199.

Barberis, N., Shleifer, A., and Wurgler, J. (2005). Comovement. Journal of Financial

Economics, 75(2):283–317.

Bartram, S. M., Brown, G., and Stulz, R. M. (2012). Why are U.S. stocks more volatile?

Journal of Finance, 67(4):1329–1370.

Bekaert, G., Hodrick, R. J., and Zhang, X. (2012). Aggregate idiosyncratic volatility. Journal

of Financial and Quantitative Analysis, 47(6):1155–1185.

Ben-David, I., Franzoni, F., and Moussawi, R. (2012). ETFs, arbitrage, and contagion.

Working paper.

Beneish, M. and Whaley, R. (1996). An anatomy of the S&P game: The effect of changing

the rules. Journal of Finance, 51(5):1909–1930.

Campbell, J. Y., Lettau, M., Malkiel, B., and Xu, Y. (2001). Have individual stocks become

more volatile? an empirical exploration of idiosyncratic risk. Journal of Finance, 56(1):1–

43.

Cao, C., Simin, T., and Zhao, J. (2008). Can growth options explain the trend in idiosyncratic

risk? Review of Financial Studies, 21(6):2599–2633.

Chun, H., Kim, J. W., Morck, R., and Yeung, B. (2008). Creative destruction and firm-

specific performance heterogeneity. Journal of Financial Economics, 89(1):109–135.

Clifford, C. P., Fulkerson, J. A., and Jordan, B. D. (2014). What drives ETF flows? The

Financial Review, 49(3):619–642.

20

Da, Z. and Shive, S. (2013). When the bellwether dances to noise: Evidence from exchange-

traded funds. Working paper.

D’Amico, S., English, W., Lopez-Salido, D., and Nelson, E. (2012). The Federal Re-

serve’s large-scale asset purchase programs: Rationale and effects. The Economic Journal,

122(564):415–446.

D’Amico, S. and King, T. B. (2013). Flow and stock effects of large-scale treasury purchases:

Evidence on the importance of local supply. Journal of Financial Economics, 108(2):425–

448.

Fama, E. (1970). Efficient capital markets: A review of theory and empirical work. Journal

of Finance, 25(2):383–417.

French, K. and Roll, R. (1986). Stock return variances: The arrival of information and the

reaction of traders. Journal of Financial Economics, 17(1):5–26.

French, K., Schwert, W., and Stambaugh, R. F. (1987). Expected stock returns and volatility.

Journal of Financial Economics, 19(1):3–29.

Goyal, A. and Santa-Clara, P. (2003). Idiosyncratic risk matters! Journal of Financial

Economics, 58(3):975–1007.

Harris, L. and Gurel, E. (1986). Price and volume effects associated with changes in the S&P

500: New evidence for the existence of price pressures. Journal of Finance, 41(4):815–829.

Irvine, P. J. and Pontiff, J. (2009). Idiosyncratic return volatility, cash flows, and product

market competition. Review of Financial Studies, 22(3):1149–1177.

Kenney, J. F. and Keeping, E. S. (1951). Mathematics of Statistics. Princeton, second

edition.

Krishnamurthy, A. and Vissing-Jorgensen, A. (2011). The effects of quantitative easing

on interest rates: Channels and implications for policy. Brookings Papers on Economic

Activity, (3):215–265.

21

Merton, R. C. (1980). On estimating the expected return on the market: An exploratory

investigation. Journal of Financial Economics, 8(4):323–361.

Morck, R., Yeung, B., and Yu, W. (2000). The information content of stock market: Why

do emerging markets have synchronous stock price movements? Journal of Financial

Economics, 58(1):215–260.

Officer, R. R. (1973). The variability of the market factor of the new york exchange. Journal

of Business, 46(3):434–453.

Petajisto, A. (2011). The index premium and its hidden cost for index funds. Journal of

Empirical Finance, 18(2):271–288.

Roll, R. (1988). R2. Journal of Finance, 43(3):541–566.

Shleifer, A. (1986). Do demand curves for stocks slope down? Journal of Finance, 41(3):579–

590.

Sullivan, R. N. and Xiong, J. X. (2012). How index trading increases market vulnerability.

Financial Analyst Journal, 68(2):70–84.

Swanson, E. T. (2011). Let’s twist again: A high-frequency event-study analysis of operation

twist and its implications for QE2. Brookings Papers on Economic Activity, pages 151–188.

Vijh, A. (1994). S&P 500 trading strategies and stock betas. Review of Financial Studies,

7(1):215–251.

Wei, S. X. and Zhang, C. (2006). Why did individual stocks become more volatile? Journal

of Business, 79(1):259–292.

Wurgler, J. (2011). On the economic consequences of index-linked investing. Challenges to

Business in the Twenty-First Century: The Way Forward. Edited by W.T. Allen and R.

Khurana and J. W. Lorsch, and G. Rosenfeld. Cambridge, Mass.: American Academy of

Arts and Sciences.

22

Wurgler, J. and Zhuravskaya, K. (2002). Does arbitrage flatten demand curves for stocks?

Journal of Business, 75(4):583–608.

23

0

100

200

300

400

500

600

700

800

900

1000

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

35.00%

40.00%

45.00%

50.00%

Jan-93 Jan-98 Jan-03 Jan-08 Dec-12

Number of traded ETFs Passive intensity

Figure 1: Number of traded ETFs and ETF share of total trade volume between 1993 and

2012.

Graph displays the daily time-series of the number of traded equity-ETFs (shaded area) and their share of

stock market dollar-volume (solid line) from January-1993 to December-2012.

24

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Jan-63 Jan-68 Jan-73 Jan-78 Jan-83 Jan-88 Jan-93 Jan-98 Jan-03 Jan-08

Idiosyncratic volatility

Market volatility

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Jan-63 Jan-68 Jan-73 Jan-78 Jan-83 Jan-88 Jan-93 Jan-98 Jan-03 Jan-08

Value weighted R-Sqaured

Market variance / Total variance

Figure 2: Firm specific volatility, market volatility and price synchronicity between 1963 and

2012.

The top graph displays the time-series for annualized market and idiosyncratic volatilities over the period

January 1963 to December 2012 for U.S. companies. Market volatility is the monthly standard deviation

of market portfolio returns. Idiosyncratic volatility is the square root of aggregate idiosyncratic variance

defined in (3). Market and aggregate idiosyncratic volatilities are annualized. The second graph plots the

time-series for aggregate US stock comovement. Value weighted R2 is defined in (2) and is the R2s of the

market model regressions weighted by market capitalization. Total variance is defined as the summations

of market variance and aggregate idiosyncratic variance. Shaded area represents recession as determined by

the National Bureau of Economic Research (NBER).

25

Synchronicity = 0.173 + 0.918 × PI (R2 =0.57 )

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

Market volatility = 0.121 + 0.360 × PI (R2 =0.16)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

Idiosyncratic volatility = 0.333 - 0.209 × PI (R2 =0.05 )

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

Figure 3: Scatter plots of monthly synchronicity, market and idiosyncratic volatilities as a

function of PI.

Graphs display the scatter plot of each variable as the function of PI. Fitted OLS lines and their equations

are displayed on each graph.

26

Synchronicity = 0.601 + 0.248 × PI (R2 =0.10 )

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

Market volatility = 0.174 + 0.271 × PI (R2 =0.13)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Idiosyncratic volatility = 0.049 - 0.049 × PI (R2 =0.15 )

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Figure 4: Scatter plots of daily synchronicity, market and idiosyncratic volatilities as a function

of PI.

Graphs display the scatter plot of each variable as the function of PI. Fitted OLS lines and their equations

are displayed on each graph.

27

-2

-1

0

1

2

3

4

5

6

7

Jan-93 Jan-98 Jan-03 Jan-08

Alpha Alpha dissimilarity

Figure 5: Alpha and Alpha dissimilarity.

This figure plots monthly average and cross-sectional standard deviation of alphas. Alpha is the intercept

of the Fama-French-Carhart four-factor model and is computed every month and for each fund. The sample

period is from January 1993 to December 2012.

28

Table 1: Summary statistics of the sample and selected months with highest price commonality.

Table reports the summary statistics for the sample and the fifteen months with highest price synchronicity.

Synchronicity is the value weighted R2 of market model regressions. Idiosyncratic and market variances are

annualized. PI (Passive intensity) is the ETF share (in percentage) of total stock market dollar-volume. PI

rank is the position of the corresponding month in our sample. Return is the return (in percentage) on the

market portfolio.

Year Month Sync. Idio. var. Market var. PI (%) PI rank Return (%)

2011 8 0.76 0.080 0.236 32 9 -5.96

2011 11 0.70 0.058 0.101 31 13 -0.89

2010 5 0.68 0.058 0.108 32 8 -8.12

2008 11 0.66 0.341 0.482 39 1 -8.74

1987 10 0.65 0.370 0.623 N.A. N.A. -22.73

2008 10 0.62 0.479 0.605 37 2 -18.61

2011 9 0.62 0.063 0.089 32 10 -8.66

2010 6 0.61 0.051 0.069 29 19 -5.25

2008 9 0.58 0.269 0.27 33 7 -9.97

2008 12 0.58 0.212 0.241 36 3 1.90

2011 10 0.57 0.080 0.097 32 11 11.34

2009 3 0.57 0.230 0.237 35 6 8.83

2012 6 0.57 0.043 0.045 27 37 3.85

2003 3 0.55 0.070 0.069 12 107 1.06

2011 12 0.53 0.045 0.038 30 17 0.86

Mean (1963-2012) 0.25 0.081 0.025 N.A. 0.64

Mean (1993-2012) 0.29 0.106 0.039 12 0.61

29

Table 2: Analysis of the monthly relation between indexing and synchronicity, market volatility or firm-specific volatility.

First three columns of Table 2 report the pairwise correlation coefficients between each regressor and the dependent variables. The corresponding

p-value is reported below each correlation coefficient. Specifications 1-6 report the values from the multivariate OLS regressions with synchronicity,

market volatility or idiosyncratic volatility as the dependent variable. All coefficients are estimated using monthly data between 1993 and 2012.

Independent variables (except Expected return) are standardized, therefore the coefficients represent the effect of a one-standard deviation increase in

the independent variable on the dependent variable. PI is the passive intensity and is defined by the monthly share of ETFs total turnover from total

stock market turnover. ROE is the aggregate return-on-equity. MABA is the market value to book values of assets. RD is the value weighted average

of firm-level R&D expenditure. CVRD is the cross-sectional variance of firm-level R&D expenditure. INDGRO is the growth in industrial production.

DFLT is the difference between the rate of the AAA and BAA corporate bonds. DISP is the dispersion in analyst forecasts about corporate earnings.

VP is the variance premium. TS is is the difference between the rate of the 10-year and one-year Treasury notes. E[Rm] is the next month return of

the market portfolio. MVOL is the standard deviation of daily market portfolio returns over a month. RECESSION is a dummy that takes one in

recessions as determined by the National Bureau of Economic Research (NBER) and zero otherwise. Corporate and macro explanatory variables are

explained in detail in section 3. t-statistics are reported in parenthesis. Standard errors are corrected using Newey-West procedure with 12 lags (one

year). Number of observations is 240 in all tests. * represent statistical significance at 10% level.

30

Pairwise correlations OLS Multivariate specifications

Synchronicity Market vol. Idio. vol. Synchronicity Market vol. Idio. vol.

(1) (2) (3) (4) (5) (6)

PI 0.76 0.41 -0.23 0.08* 0.08* 0.02* 0.02* -0.04* -0.04*

0.00 0.00 0.00 (8.53) (12.56) (1.86) (1.86) (-4.42) (-7.63)

ROE -0.26 -0.24 -0.10 -0.00 0.01 0.00

0.00 0.00 0.12 (-0.55) (1.49) (0.12)

MABA -0.33 0.13 0.69 -0.03* -0.03* 0.02* 0.03* 0.04* 0.04*

0.00 0.04 0.00 (-3.33) (-7.69) (2.31) (4.31) (4.68) (12.41)

RD 0.09 0.34 0.54 -0.00 0.03* 0.01

0.18 0.00 0.00 (-0.27) (2.39) (0.37)

CVRD 0.17 0.02 -0.06 0.01 -0.02* -0.00

0.01 0.80 0.33 (0.87) (-1.98) (-0.44)

INDGRO -0.14 -0.31 -0.25 0.08 0.16 -0.11

0.03 0.00 0.00 (0.39) (1.08) (-0.80)

DFLT 0.58 0.63 0.20 -0.04* -0.04* 0.04* 0.04* 0.02* 0.02*

0.00 0.00 0.00 (-6.50) (-5.97) (6.15) (5.49) (4.01) (3.83)

DISP 0.23 0.20 -0.03 -0.00 -0.00 -0.00

0.00 0.00 0.61 (-0.45) (-0.32) (-0.35)

VP -0.26 -0.56 -0.34 0.03* 0.03* -0.04* -0.04* -0.01 -0.01*

0.00 0.00 0.00 (5.85) (5.99) (-5.47) (-4.71) (-1.18) (-1.67)

TS 0.34 0.12 -0.24 0.01 0.01 -0.00

0.00 0.06 0.00 (0.73) (1.16) (-0.28)

E[RM ] -0.02 -0.12 -0.12 0.02 0.11* -0.06

0.70 0.06 0.06 (0.26) (1.76) (-0.65)

MVOL 0.70 1.00 0.63 0.10* 0.10* 0.04* 0.04*

0.00 0.00 (13.40) (13.21) (5.68) (6.04)

RECESSION 0.27 0.48 0.34 -0.06* -0.07* 0.03 0.03 0.04* 0.05*

0.00 0.00 0.00 (-3.91) (-4.21) (1.25) (1.40) (2.37) (2.92)

INTERCEPT 0.26* 0.27* 0.13* 0.15* 0.27* 0.27*

(15.09) (42.68) (10.35) (17.04) (18.99) (59.32)

Adj. R2 0.86 0.86 0.69 0.67 0.85 0.85

31

Table 3: Analysis of the daily relation between indexing and synchronicity, market or idiosyn-

cratic volatility.

Table reports the coefficients of a multivariate OLS regression with price synchronicity, market or idiosyn-

cratic volatility as the dependent variable. Coefficients are estimated using daily data between 1993 and

2012. Daily price synchronicity is from Morck et. al (2000) and is defined in (4). Market volatility is the VIX

index. Idiosyncratic volatility is the cross-sectional standard deviation of daily returns of all stocks in the

CRSP database. Independent variables are standardized therefore the OLS coefficients represent the effect

of a one standard deviation increase in the independent variable. PI is the daily ETF share of total stock

market turnover. MKTRF is the return on the market portfolio. t-statistics are reported in parenthesis.

Standard errors are corrected using Newey-West procedure with 5 lags. * represent statistical significance

at 10% level. Number of observations is 5,018 in all tests.

Synchronicity Market vol. Idio. vol

(1) (2) (3) (4) (5) (6)

PI 0.03* 0.02* 0.03* 0.03* -0.01* -0.01*

(18.75) (16.81) (8.37) (8.33) (-9.78) (-32.87)

VIX 0.01* 0.01*

(7.67) (27.12)

MKTRF -0.02* -0.01* 0.001*

(-13.36) (-4.77) (8.48)

INTERCEPT 0.63* 0.63* 0.21* 0.21* 0.04* 0.04*

(450.96) (504.02) (76.86) (77.22) (103.32) (169.09)

Adj. R2 0.10 0.22 0.13 0.15 0.15 0.59

32

Table 4: Summary statistics of the mutual fund sample.

This table reports descriptive statistics for the mutual fund sample over our sample period from January

1993 to December 2012. The first three columns show the average assets under management, number of

funds and number of observations, which equals the number of alphas in each year. The fourth column shows

the average monthly four-factor alpha of funds. The last column presents average alpha dissimilarity (σα)

defined by the cross-sectional standard deviation. The bottom row shows the average for each parameter

over our total sample.

Year Net assets ($Bil) No. of funds No. of obs. Ave. α ( %) σα (%)

1993 0.10 488 5,385 0.25 2.68

1994 0.11 555 6,320 -0.04 2.45

1995 0.14 625 7,051 -0.22 2.52

1996 0.17 711 8,005 -0.13 2.44

1997 0.22 863 9,608 -0.19 3.09

1998 0.26 991 11,257 0.00 3.41

1999 0.33 1,096 12,628 0.32 3.89

2000 0.34 1,232 13,976 0.32 4.62

2001 0.33 1,335 15,491 -0.15 3.31

2002 0.97 1,418 16,474 -0.10 2.99

2003 1.29 1,493 17,440 0.00 2.04

2004 1.55 1,587 18,502 0.20 1.84

2005 1.70 1,702 19,620 0.23 1.68

2006 1.90 1,816 21,208 -0.10 1.71

2007 2.07 1,919 22,427 0.17 2.05

2008 1.68 2,043 23,915 -0.20 2.83

2009 1.27 2,109 24,897 0.13 2.41

2010 1.46 2,232 26,066 0.06 1.85

2011 1.57 2,333 27,527 -0.18 1.77

2012 1.60 2,398 28,349 0.05 1.58

Average 0.95 1,447 16,807 0.02 2.56

33

Table 5: Analysis of the relation between indexing and mutual fund alpha dissimilarity

Table reports the coefficients of regressions with the mutual fund alpha dissimilarity measured by cross-

sectional standard deviation (σα) of monthly Fama-French-Carhart four-factor alphas as the dependent

variables. The coefficients are reported in percentages and are estimated using monthly data between 1993

and 2012. The rest of the variables are defined in table 2. Newey-West adjusted t-statistics with 12 lags

are reported in parenthesis. * represents statistical significance at 10% level. Number of observations is 240

(239) in contemporaneous (predictive) tests.

Contemporaneous Predictive

(1) (2) (3) (4) (5) (6)

PI -0.39* -0.20* -0.16* -0.40* -0.28* -0.27*

(-2.38) (-2.31) (-2.14) (-2.46) (-2.77) (-3.24)

MVOL -0.03 0.13 0.03 0.18*

(-0.31) (1.48) (0.34) (1.98)

IVOL 0.59* 0.47* 0.47* 0.16

(9.37) (-5.60) (5.40) (1.07)

MABA 0.15* 0.34*

(1.91) (2.80)

DFLT -0.01 0.07

(-0.16) (0.75)

VP 0.18* 0.10

(4.32) (1.35)

RECESSION -0.10 0.19

(-0.77) (0.95)

INTERCEPT 2.56* 2.31* 2.26* 2.56* 2.34* 2.26*

(16.20) (48.71) (52.07) (16.18) (37.50) (37.52)

Adj. R2 0.14 0.62 0.66 0.14 0.50 0.55

34

Table 6: Predictive regressios.

Table reports the coefficients from predictive multivariate regressions with synchronicity, market volatility

or idiosyncratic volatility as the dependent variable. Panel A correspond to the results obtained from the

monthly sample. Coefficients in Panel B are estimated using the daily sample. Independent variables are

lagged and standardized. The remainder of the procedure is the same as in tables 2 and 3. t-statistics are

reported in parenthesis. Standard errors are corrected using Newey-West procedure with 12 lags for the

monthly and with 5 lags for the daily estimations. * represent statistical significance at 10% level.

Synchronicity Market Vol. Idio. Vol.

Panel A. Monthly sample

PI 0.08* 0.03* -0.03*

(9.15) (2.50) (-5.07)

MABA -0.02* 0.03* 0.05*

(-3.49) (5.09) (10.10)

DFLT -0.02* 0.03* 0.02*

(-2.43) (2.88) (3.32)

VP 0.03* -0.01 0.00

(5.24) (-0.91) (0.97)

MVOL 0.07* 0.03*

(9.30) (5.23)

RECESSION -0.04* 0.06* 0.06*

(-1.99) (2.75) (2.43)

INTERCEPT 0.27* 0.15* 0.27*

(33.21) (16.99) (53.08)

Adj. R2 0.64 0.44 0.72

Panel B. Daily sample

PI 0.02* 0.03* -0.01*

(14.78) (8.28) (-32.85)

VIX 0.01* 0.01*

(5.47) (26.70)

MKTRF -0.01* -0.01* 0.001*

(-6.95) (-3.95) (4.47)

INTERCEPT 0.63* 0.21* 0.04*

(475.57) (77.24) (168.71)

Adj. R2 0.10 0.14 0.58

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Table 7: Vector auto-regression (VAR) analysis of synchronicity and PI (daily sample).

Table reports the results for a VAR analysis up to the fifth lag between synchronicity and passive intensity

using the daily sample. Sync.t is price synchronicity of day t and is defined in (4). PIt is the ratio of ETFs

total dollar turnover to total stock market dollar turnover on day t. t-statistics are reported in parenthesis.

* represent statistical significance at 10% level. Number of observations is 5,013 in all tests.

Unconditional Conditional

Sync.t PIt Sync.t PIt

Sync.t−1 0.05* 0.04 0.03 -0.06*

(3.57) (1.54) (1.64) (-2.23)

Sync.t−2 0.07* -0.01 0.07* -0.04

(5.00) (-0.59) (4.33) (-1.35)

Sync.t−3 0.06* -0.07* 0.05* -0.09*

(4.02) (-2.75) (3.36) (-3.20)

Sync.t−4 0.05* -0.08* 0.06* -0.04

(3.52) (-2.88) (3.83) (-1.39)

Sync.t−5 0.07* -0.04 0.07* -0.02

(4.66) (-1.43) (4.47) (-0.75)

PIt−1 -0.01 0.42* -0.02* 0.37*

(-1.07) (28.84) (-2.24) (25.22)

PIt−2 0.02* 0.23* 0.02* 0.22*

(2.32) (14.34) (2.25) (13.97)

PIt−3 0.02* 0.10* 0.02* 0.11*

(2.19) (6.17) (2.72) (7.13)

PIt−4 -0.01 0.11* -0.01 0.12*

(-1.43) (6.70) (-1.07) (7.61)

PIt−5 0.00 0.15* 0.00 0.17*

(-0.15) (10.39) (0.07) (11.70)

Constant 0.44* 0.10* 0.46* 0.15*

(25.22) (3.27) (23.31) (4.50)

R2 0.11 0.98 0.12 0.98

Total effect of PI on sync. 0.02* 0.02*

(12.51) (8.28)

Total effect of sync. on PI -0.16* -0.24*

(-3.23) (-4.67)

Granger Causality testsH0: No causality

from PI to sync.

H0: No causality

from sync. to PI

H0: No causality

from PI to sync.

H0: No causality

from sync. to PI

F-value 33.24 4.49 82.69 24.73

p-value 0.00 0.00 0.00 0.00

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Table 8: Stationarized sample.

Table reports OLS regression results for the stationarized dependent and independent variables using the

monthly sample. The remainder of the procedure is the same as in Table 2. t-statistics are reported in

parenthesis. Standard errors are corrected using Newey-West procedure with 12 lags (one year). * represent

statistical significance at 10% level.

Synchronicity Market Vol. Idio. Vol.

PI 0.36* 0.23* -0.15*

(2.70) (2.82) (-2.36)

MABA -0.00 0.01 -0.00

(-0.16) (1.31) (-0.12)

DFLT -0.02 0.03* 0.00

(-1.30) (2.98) (0.11)

VP 0.03* -0.04* -0.01

(5.38) (-8.83) (-1.06)

MVOL 0.11* 0.03*

(9.57) (5.22)

RECESSION 0.01 -0.00 -0.00

(0.98) (-0.32) (-0.96)

INTERCEPT -0.00* -0.00 0.00

(-1.88) (-0.99) (1.08)

Adj. R2 0.64 0.55 0.41

37