# Indexing and stock price efficiency.

Indexing has experienced substantial growth over the last two
decades because it is an effective way of holding a diversified
portfolio while minimizing trading costs and taxes. In this article, we
focus on one negative externality of indexing: the effect on the
efficiency of stock prices. Based on a sample of large and liquid US
stocks, we find that greater indexing leads to less efficient stock
prices, as indicated by stronger post-earnings-announcement drift and
greater deviations of stock prices from the random walk. We conjecture
that reduced incentives for information acquisition and arbitrage
induced by indexing and passive trading are probably the main causes for
degradation in price efficiency.

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The indexed investment sector, including index mutual funds, enhanced index funds, exchange-traded funds (ETFs), and closet indexers, has experienced rapid growth over the past two decades. (1) As of December 2013, the market share of broadly diversified index funds had reached 29.5% of the total investment in US equities in the mutual fund sector including ETFs. (2) The potential impact of indexing on the efficiency of equity markets, however, is an important but unexplored topic.

Previous studies have examined the impact of indexing on constituent stocks. In their model of institutional investors and index benchmarks, Basak and Pavlova (2013) find that institutional trades amplify stock market volatility and induce excess correlations among index stocks. The implications of the model are supported by Greenwood and Thesmar (2011) who find that institutional ownership increases volatility especially among markets or indexes. Another section of the literature examines the impact of institutional investors on stock prices. (3) Using a comprehensive sample of NYSE-listed stocks between 1983 and 2004, Boehmer and Kelley (2009) find that trading and ownership by institutional investors increase price efficiency. Specifically, institutional investors incorporate information into stock prices through their trading and their ownership facilitates informed arbitrage. Based on NYSE/AMEX stocks over 1989-1993, Bartov, Radhakrishnan, and Krinsky (2000) find that institutional holdings are negatively associated with the magnitude of post-earnings-announcement drift (PEAD), suggesting that investor sophistication may reduce stock return predictability. In contrast, Chen, Noronha, and Singal (2004) document that stock prices increase immediately after the announcement of additions to the S&P 500 index but reverse substantially after three months. They explain these findings by the temporary price pressure caused by index fund purchases of stocks newly added to the index. Goetzmann and Massa (2003) examine daily flows for three major S&P 500 index funds and find a strong contemporaneous correlation between inflows and returns. Similarly, Keim and Madhavan (1997) and Jones and Lipson (1999, 2001) find that index funds generate a larger price impact relative to active funds in the short period following their trading.

This article is at the intersection of these two literatures: the impact of indexing and the role of institutional investors in enhancing price efficiency. Despite extensive literatures on indexing and price efficiency, there has been no systematic study of the impact passive index investors may have on the informational efficiency of stock prices. Compared to their active peers, passive institutional investors have two unique characteristics. First, they generally hold a basket of stocks in certain indices passively, without active information acquisition and price discovery. Second, trading of passive funds is mostly driven by investor flows or index changes instead of private information. Both features raise concerns regarding a possible negative impact on price efficiency. As suggested by Grossman and Stiglitz (1980), price discovery relies on informed traders who actively acquire information and incorporate that information into stock prices by trading. An increase in passive (uninformed) investors and the consequent reduction in active traders can result in a proportionate increase in information costs and has the potential to move equilibrium to a less efficient level. In spirit, our article comes closest to Wurgler (2011) who points to the growing importance of indexing for investment and benchmarking such that it can distort markets and affect the real economy. In contrast, our focus is on a different consequence of the growth in indexing: assimilation of new information into stock prices, which is critical for an efficient market.

We empirically investigate the relation between indexed holdings and trading and price efficiency. Based on a sample of current S&P 500 index constituents and non-S&P 500 stocks with comparable size and turnover ratios, we find that prices become less efficient as indexed ownership grows, where price efficiency is measured by the magnitude of PEAD or by deviations of price from the random walk. It is robust to several alternative specifications. We also examine the impact of indexed ownership and passive trading separately, and find that indexed investments affect price efficiency only through indexed holdings, but passive trading by itself does not show any significant effect.

Our sample of passive institutional investors consists of 591 index funds, enhanced index funds, ETFs, and a number of closet indexers. The index and index-like funds are identified in several ways: keywords in fund names, "activeness" of funds based on deviations from index compositions, and fit from regressions of fund returns on index returns. For subsequent analysis, we measure each stock's passive ownership as the percentage of shares held by any fund in our sample at the end of each quarter, and we measure passive trading volume as the sum of absolute holding changes over that quarter.

We measure price efficiency in two ways. First, we view PEAD as an indicator of investors' under-reaction to public information and use it as a framework to study price inefficiency. Second, we assume that an efficient stock price should follow a random walk and use deviation of stock prices from random walk as proxy of price inefficiency. Specifically, we adopt normalized Hasbrouck's (1993) intraday pricing error volatility, absolute value of first-order autocorrelation in daily returns, and absolute value of weekly to daily variance ratio as our empirical measures of price inefficiency. We believe that an intraday measure, compared to daily or even longer horizon proxies, better captures deviation from efficient prices because of the relatively quick stock price adjustments by S&P 500 firms within each trading day (Chordia, Roll, and Subrahmanyam, 2005). Meanwhile, the daily measures ensure that potential price inefficiency in longer horizons is not omitted.

Our empirical tests use a sample period from 2002 to 2013, which is after the introduction of decimalization to avoid major institutional changes in price efficiency. We first test the magnitude of PEAD and find that PE AD increases along with passive ownership and, consistent with Bartov et al. (2000), decreases as (nonpassive) institutional ownership increases. These findings are robust to alternative definitions of price drift, different drift windows, and alternative measures of earnings surprise. Next, following Boehmer and Kelley (2009), we regress empirical measures of price efficiency on passive and nonpassive institutional ownership. Consistent with our hypothesis, the deviation of both intraday and daily stock prices from a random walk is positively correlated with passive ownership. We also reconfirm the inference of Boehmer and Kelley (2009) that (nonpassive) institutional investors may enhance price efficiency.

Our results could arise if passive ownership is higher for stocks that are characterized by price inefficiency. Though it could be significant in studies of active institutional investors, endogeneity is unlikely for indexed institutional investors where trading is driven by investor flows or index changes rather than through stock selection. Nevertheless, we confirm that endogeneity is a nonissue in two ways. First, we regress changes in passive ownership on lagged changes in price inefficiency. Second, we repeat cross-sectional analysis using a sample of passive index funds and ETFs, excluding discretionary index funds such as enhanced index funds and closet indexers. Results from neither test support evidence of endogeneity.

Among explanations for our results, further analysis reveals that information production, as measured by the number of analysts, is significantly and negatively associated with passive ownership but is positively related to nonpassive institutional ownership. This evidence is consistent with the expectation that as indexed investors have no incentive for information acquisition, arbitrage, and trading, information production will decline. Therefore, we believe that the reduced incentive for price discovery is primarily responsible for the negative impact of passive ownership on price efficiency. Moreover, passive investors may create limits to arbitrage through noise trader risk, which could deter or delay informed arbitrageurs from correcting the mispricing, thus reducing price efficiency indirectly.

This study illustrates that although indexing is beneficial for passive investors, it exerts a negative externality by making it more difficult for stock prices to reflect information efficiently. As the fraction of passive ownership increases, prices are likely to become less efficient. Taken to an improbable and theoretical extreme of 100% indexing, no one would have an incentive to make prices informationally efficient. Of course, the current fraction of passive ownership is relatively small; thus, its negative impact on market efficiency may not be striking or intuitive. However, given the likely rapid growth of indexing in the future, it is reasonable to be cautious about its negative influence on market efficiency.

The rest of this article is organized as follows. Section I describes the data sources and sample selection. Section II describes measures of price efficiency, liquidity, and other control variables. Section III presents our main results from PEAD and cross-sectional analyses, and corresponding robustness tests. Section IV explores potential underlying mechanisms to explain our findings. Section V concludes.

I. Sample

A. Sample of Passive Funds

Index funds and ETFs, which follow passive investment strategies, are the major passive institutional investors on the market. However, we do not restrict our sample to pure index funds and ETFs, but also include enhanced index funds and closet indexers to construct a more complete measure of passive ownership. Although these funds may strategically adjust weights of some holdings based on their predictions about future price movements, they track indices passively and closely. Thus, their impact on price efficiency is closer to index funds than to their active peers.

Institutional holdings data from the Center for Research in Security Prices (CRSP) Mutual Fund database and Thomson Reuters (13F filings) are used to create the passive fund sample in four steps. First, we merge the CRSP mutual fund database, which provides indicators for index funds and ETFs, with the 13F database to identify index mutual funds and index ETFs. Second, we screen remaining funds for index-related funds on both CRSP Mutual Fund and 13F databases using keywords in their names. A fund is classified as passive if it calls itself an index fund, enhanced index fund, or ETF. (4)

Third, we identify closet indexers in two ways. First, following Cremers and Petajisto (2009), we estimate the "active share" (AS hereafter) of each mutual fund from the 13F database. As suggested by Cremers and Petajisto (2009), any portfolio could be decomposed into a benchmark index portfolio plus a zero-net-value long-short portfolio. Thus, AS is a measure of the overall deviation of the weights of a fund's holdings from the benchmark index. For a pure index fund, AS will be close to zero, as the weight of each asset in the fund portfolio equals the asset weight in the benchmark index. (5) Second, we estimate a regression of daily fund returns on corresponding benchmark index returns to obtain [R.sup.2]. A fund with [R.sup.2] close to one is more likely to follow passive strategies. (6) Because the benchmark indices for closet indexers are not explicitly stated, we tested 10 indices for each fund and selected the lowest AS and the highest [R.sup.2] for each fund. The indices are: S&P 500 index, S&P 500 Growth index, S&P 500 Value index, S&P 400 Mid-Cap index, S&P 600 Small-Cap index, S&P 100 index, Russell 1000 index, Russell 2000 index, NASDAQ 100 index, and the whole market portfolio obtained from CRSP stock files. To be included in the passive fund sample as a closet indexer, a fund quarter must have AS less than 10% or [R.sup.2] above 99% in the prior year.

Finally, we exclude balanced funds, international funds, and bond funds from the sample. (7) The passive sample includes four types of passive institutional investors: 1) 255 open-end equity index funds that aim to replicate the performance of a specific equity index by holding the index constituents in the same proportions as the index, 2) 47 enhanced index funds that reserve certain flexibility on position size and investment strategies, 3) 289 ETFs that track an index and are traded on stock exchanges, (8) and 4) a number of closet indexers. Appendix A provides a detailed description of the procedure used to construct the sample.

B. Trends in Indexing

Table I shows the growth in indexing from 2002 to 2013. The US equity market grew from $11 trillion in 2002 to over $26 trillion in 2013. In the same period, the value of passive funds increased from $309 billion to $1865 billion. As a fraction of US equity mutual funds and ETFs, passive funds increased from 12.80% in 2002 to 27.52% in 2013, and as a portion of the equity market from 2.80% to 7.09%. Passive ownership for S&P 500 stocks increased steadily from 4.54% in 2002 to 9.62% in 2013. Unlike the steady increase in passive ownership, nonpassive institutional ownership increased from 57.80% of US equity in 2002 to 69.52% in 2007 before falling to 61.80% in 2013. The last column in Table I reports the difference between 100% and the holdings of institutional investors, and it represents the sum of holdings of insiders, individuals, and any errors in reporting.

C. Sample of Stocks

The primary empirical analysis in this article is based on S&P 500 stocks along with a control group of non-S&P 500 stocks of comparable size and turnover ratio. We choose a sample related to S&P 500 stocks for several reasons. First, the S&P 500 index is the most popular index by assets indexed and one of the most popular indexes by the percentage of assets indexed, which implies that S&P 500 stocks will exhibit a reasonable level of passive ownership. Meanwhile, non-S&P 500 stocks typically have fairly low, if not zero, passive ownership. This combined sample thus provides sufficient cross-sectional dispersion in passive ownership for empirical analysis. (9) Second, restricting the sample to S&P 500 constituents and comparable non-S&P 500 firms helps reduce the potential impact of infrequent trading, which could be severe in small firms. Third, the S&P 500 index represents the US equity market, and any effect found among its components is likely to be important for the entire market. Finally, restricting our sample to S&P 500 constituents and comparable non-S&P 500 firms generates a similar informational environment across stocks; thus, inferences about an association between indexed ownership and price efficiency will be more robust to potentially unobservable factors that may affect the informational environment of a firm.

We require all stocks to have prices of at least $2 at the beginning of a quarter to avoid severe market microstructure issues. Because the focus of our article is on price efficiency, we want to minimize the impact of external events. In particular, decimalization in 2001 has improved price efficiency considerably with an increase in liquidity that makes arbitrage less costly (Chordia, Roll, and Subrahmanyam, 2008). Accordingly, we begin our sample in 2002 to avoid the effect of decimalization.

It is critical that the control group of non-S&P 500 stocks is similar to the S&P 500 index. Fortunately and unlike the Russell 1000, which captures the largest eligible firms by market cap, the S&P 500 is more selective and need not select all large eligible firms. For example, as of December 31, 2013, among commercial airlines, only Delta Airlines ($23.5 billion) and Southwest Airlines ($13.1 billion) were included in the S&P 500. Two other airlines of similar size, American Airlines Group ($19.1 billion) and United Continental ($13.7 billion) were not S&P 500 constituents. (10) Similarly, among casinos and gaming, Wynn Resorts ($19.6 billion) is included in the index but a significantly larger Las Vegas Sands ($64.6 billion) and somewhat smaller but still large MGM Grand ($11.5 billion) are not in the index. It is these kinds of non-S&P 500 firms that we intend to capture in the control group.

The S&P 500 has very large firms (> $100 billion as of December 31,2013) but also relatively small firms as firms grow and shrink once added to the index. Larger firms are not ordinarily dropped from the index and small firms are dropped only with a delay. Because the smallest size decile of the S&P 500 may not represent the true nature of S&P 500 firms, we require all firms in the control group to be larger than firms in the smallest size decile. To be sure, the control group cannot replicate the S&P 500 in terms of all sectors adequately and is less likely to represent the top decile of the S&P 500 in terms of size. However we believe that the control group is a reasonable representation of the S&P 500 in terms of both security type and size.

We construct the sample as below. At the end of each quarter from 2002 to 2013, we sort all S&P 500 stocks into deciles by their market values following Fama and French (1992) and by their turnover ratios in the prior quarter. We select all stocks that are larger than any stock in the smallest S&P 500 size decile and with turnover greater than the smallest S&P 500 turnover ratio decile.

This procedure generates a sample of approximately 400 S&P 500 constituents and 130 non-S&P 500 stocks in each quarter. Sample characteristics are reported in Table II. Panel A shows that the control group, by construction, is extremely close to the S&P 500 in terms of security type as evidenced by the percentage of stocks in each share code. As with the S&P 500, about 94% of the control group consists of ordinary common shares of companies incorporated in the United States (share code 11). Between 2% and 3% of the companies incorporated outside the United States (share code 12) are deemed eligible for inclusion in the S&P 500 because their foreign incorporation is primarily for tax reasons, for example, Accenture, Garmin, Noble Energy, Transocean Drilling, Ingersoll Rand, and Seagate Technology. Finally, real estate investment trusts account for approximately 3-4% of the companies in the S&P 500 and the control group (share codes 18, 48).

Panel B of Table II shows the mean and median sizes of companies in the S&P 500 and the control group. Though the median size of the S&P 500 companies is about twice the size of the control group, we believe that the companies in both groups are large and that the control group reasonably represents firms in the S&P 500.

Daily stock price, return, trading volume, and shares outstanding are obtained from CRSP stock files, and intraday trade and quote data are obtained from NYSE Trade and Quote (TAQ) database. Information about earnings announcements are obtained from Compustat, and analyst earnings forecasts are obtained from Institutional Brokers Estimate System (IBES). We obtain constituents of the S&P indices from Compustat and of the Russell indices from Russell Investments. Total returns for the indexes are obtained from Bloomberg.

II. Methodology

A. Measure of Relative Informational Efficiency of Prices

Measures of price efficiency fall into several groups. First, price efficiency could be measured by returns to trading strategies based on market anomalies, such as short-term reversals, momentum, and PEAD. Second, under the assumption that efficient price follows a random walk process, deviations of stock prices from random walk could be a measure of relative inefficiency. This group of measures includes return autocorrelations, variance ratios, and the Hasbrouck (1993) pricing error variance. Third, without an assumption about random walk, relative price inefficiency could be inferred by the delay of stock returns in response to market return (Hou and Moskowitz, 2005). Finally, price inefficiency could be measured by certain asset pricing models. For example, the Kalman filter estimation of mispricing used by Brennan and Wang (2010) is based on the assumption that the fundamental return follows an ex post version of the Fama and French (1993) three-factor model. In this article, we prefer the model-free assumption that efficient stock prices follow a random walk, and we measure price efficiency using two approaches: magnitude of PEAD and stock price deviation from a random walk.

1. Cumulative Abnormal Returns in the PEAD Analysis

We use cumulative abnormal returns (CARs) estimated from the companion-portfolio approach as measures of PEAD. Specifically, the CAR for the window ([t.sub.1], [t.sub.2]) is estimated as the daily abnormal return for firm i on date t as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (1)

where [R.sub.i,t] is the daily return of stock i and [R.sub.p,t] is the value-weighted daily return of a portfolio of stocks within the same size decile as stock i. (11)

Following Frazzini (2006), we use CAR(-2, 1), the cumulative abnormal return from two days preceding the announcement date to one day after, as the proxy for earnings surprise. Conventional measures of earnings surprise, such as the time-series model of actual earnings, or consensus forecasts may not truly measure the market's expectation. As suggested by Frazzini (2006), however, CAR around the announcement date is the actual market reaction and does not rely on assumptions underlying any forecasts. Nevertheless, we also use two alternative measures of unexpected earnings in robustness tests. First, following Ayers, Li, and Yeung (2011), we define standardized unexpected earnings (SUE) as the seasonal difference in actual earnings standardized by the stock price at the end of the previous fiscal quarter:

[SUE.sub.i,t] = [EPS.sub.i,t]-[EPS.sub.i,t-4]/[P.sub.i,t-1]. (2)

Second, we define analyst forecast error (AFE) as the difference between actual earnings per share and the mean of the most recent analyst forecasts, scaled by the stock price at the end of the previous fiscal quarter.

2. Deviation of Stock Price from the Random Walk

We adopt the pricing error of Hasbrouck (1993), the daily first-order autocorrelation in stock returns, and variance ratios of weekly returns to daily returns as our empirical measures of the deviation of stock prices from the random walk. We use pricing error as the principal measure, and the other two measures as robustness tests.

Compared to other measures of price inefficiency, Hasbrouck's (1993) pricing error has several advantages. First, Hasbrouck's (1993) measure is free from the asset pricing model. Mispricing proxies that rely on specific asset pricing models, such as the Kalman filter in Brennan and Wang (2010), the price delay in Hou and Moskowitz (2005), or measures based on momentum profit or PEAD, may suffer from model misspecification. Second, as suggested by Boehmer and Kelley (2009), Hasbrouck's (1993) measure only captures price deviation from random walk caused by uninformed trading, so that deviations caused by informed trading will not be mistakenly measured as price inefficiency. Variance ratio and autocorrelation, however, do not distinguish between information-induced and noninformation-induced deviations from random walk. Third, Hasbrouck's (1993) measure is estimated on a trade-to-trade basis, which captures most of the information involved in trading and places greater weight on periods with active information discovery. Variance ratio and autocorrelation, however, are measured with daily intervals, leading to loss of intraday information, and they place equal weight on periods with and without active price discovery. We expect that Hasbrouck's (1993) measure will provide more accurate and robust inferences compared to other empirical measures of price inefficiency.

The pricing error proposed by Hasbrouck (1993) measures the deviation between transaction prices and implicit efficient prices. (12) Specifically, the log transaction price, [p.sub.t], is defined as the efficient price, [m.sub.t], plus a transitory deviation, [s.sub.t]:

[p.sub.t] = [m.sub.t] + [s.sub.t], (3)

where t indexes either transactions or natural time, [m.sub.t] is the expectation of the stock value given all available public information and is assumed to follow a random walk, and [s.sub.t] measures the deviation of transaction price from the efficient price, [s.sub.t] is assumed to be a zero-mean covariance-stationary stochastic process with variance of [[sigma].sup.2.sub.t], where [[sigma].sup.2.sub.s] measures how closely the transaction price follows the efficient price. As [[sigma].sup.2.sub.s] is associated with price volatility, we follow Boehmer and Kelley (2009) and several other studies to normalize [[sigma].sup.2.sub.s], denoted as F(s), by the variance of log transaction prices, V(p), to form a measure of relative price efficiency, V(s)/V(p). Ln[V(s)/V(p)] is used as principal metrics in the cross-sectional analysis. (13)

Though the price adjustment process generally takes less than 60 minutes (Chordia et al., 2005) and should be well described by V(s)/V(p), we would like to capture potential price adjustment processes in longer horizons to enhance the robustness of our findings. The existence of long-horizon return anomalies, such as momentum, daily and weekly return autocorrelations, or PEAD, indicate the existence of inefficient stock prices beyond each trading day. Hence, we adopt two (inverse) efficiency measures based on daily and weekly returns. They are the absolute value of first-order daily return autocorrelation, [absolute value of AC(1)] and the absolute value of weekly-to-daily return variance ratio, [absolute value of 1 - VR(1,5)]. Both are associated with the magnitude of deviation of stock price from a random walk. Specifically, [absolute value of AC(1)] is estimated for each stock over each quarter by regressing daily returns on one-day lagged returns, and [absolute value of 1 - VR(1,5)] is estimated for each stock over each quarter as the absolute deviation of the ratio of weekly return variance to (five times) daily return variance from one, where the weekly returns are calculated from Wednesday to the next Tuesday to eliminate the weekend effect. All the daily and weekly returns are calculated by quote midpoints to eliminate potential bid-ask bounce.

Table III reports descriptive statistics of the five efficiency measures from 2002 to 2013. The average V(s)/V(p) of stocks in our sample is 0.007% and is decreasing over the sample period from 0.008% in early years to 0.004% in late years. [absolute value of AC(1)] and [absolute value of 1 - VR(1,5)] are relatively stable over time with average values of 0.105 and 0.222, respectively. Overall, the level of market efficiency does not change materially over the observation period.

B. Measures of Institutional Ownership and Trading

We define passive institutional ownership (PO) of a stock at the end of a quarter as the total shares held by any fund in the passive fund sample, scaled by total shares outstanding at the quarter end. Similarly, nonpassive institutional ownership (NPO) is defined as the total shares held by any institutional investor (who files a 13F form) that does not belong to the passive fund sample. (14) Therefore, PO represents the fraction of shares held by passive institutional investors, and NPO represents the fraction of shares held by active institutional investors.

Since the 13F database contains only positions held, we are not able to precisely estimate trading volumes of either passive or nonpassive institutional investors. Instead, we use changes in institutional holdings as a lower bound of institutional trading volume. Passive trading (PT) for each stock-quarter is estimated as the sum of absolute changes in passive holdings standardized by total shares outstanding, and nonpassive trading (NPT) is estimated as the sum of absolute changes in nonpassive holdings:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (4)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (5)

Table III reports the time-series average of quarterly cross-sectional means and standard deviations of ownership and trading variables. Average quarterly passive trading is 0.99% of total shares outstanding, which is equivalent to an annual turnover of 3.96%. In contrast, average quarterly nonpassive institutional trading is 19.92% of total shares outstanding, or an annual turnover of 79.68%. Average NPO (69.95%) is about 12 times average PO (6.16%), whereas average nonpassive trading is about 20 times average passive trading. As expected, nonpassive institutional investors trade much more than passive funds even after considering the difference in their ownership.

C. Control Variables

Chordia et al. (2008) find that liquidity stimulates arbitrage activities and enhances market efficiency. Four reverse measures for liquidity (ILLIQ) are used in the cross-sectional analysis: 1) trade-weighted relative effective spread (RES), estimated as two times the absolute distance between actual transaction price and corresponding quote midpoint, scaled by the quote midpoint, and weighted by trade size; 2) time-weighted relative quoted spread (RQS), estimated as the absolute distance between bid and ask price, scaled by the quote midpoint, and weighted by time intervals between two quotes; 3) Amihud (2002) price impact measure of illiquidity (Amihud), estimated as change in rate of stock returns per million dollar trade and adjusted by equity market inflation; and 4) Liu (2006) no-trade-day measure of illiquidity (Liu), estimated as number of zero-trade days in a quarter and adjusted by turnover ratio in that quarter. RES is preferred because it measures the actual (relative) transaction costs for traders. However, we recognize that RES may underestimate illiquidity because transactions are relatively infrequent during periods of low liquidity.

It is reasonable to expect that price efficiency is associated with stock size. Market value (MV) is measured as the number of shares outstanding multiplied by the closing price (CRSP items SHROUT and PRC) at the end of June of the previous year. We also control for dollar trading volume or turnover ratios, estimated as the dollar trading volume of a stock in a quarter scaled by total shares outstanding at the end of that quarter. Moreover, to control for the potential effect of price discreteness on price inefficiency, we control for stock price at the end of the previous quarter. In addition, we use number of analysts following (ANLY) as a proxy for information production. ANLY is measured as the total number of analysts that report quarterly earnings forecasts for a stock (IBES item FPI = 6).

III. Empirical Results

A. Impact of Indexed Ownership on PEAD

The following regression is estimated to study the relation between indexed ownership and PEAD:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (6)

Quarterly observations of earnings announcement are pooled across our stock sample from 2002 to 2013. Following Bartov et al. (2000) and Zhang (2012), among others, we use decile ranks of variables in our regression analysis. (15) In each calendar quarter, each of the independent variables is ranked into deciles based on the cutoff values from the previous quarter. (16) We then regress CARs on earnings surprises, an interaction term between earnings surprises and lagged indexed ownership (DPO), and an interaction term between earnings surprises and lagged nonpassive institutional ownership (DNPO). We choose four windows, (2, 5), (2, 15), (2, 30), and (2, 60), to better capture price drifts over short and long periods after an earnings announcement.

Control variables are constructed by interacting earnings surprises with the usual control variables such as market value of the stock at the end of the previous calendar year (DMV), share price at the end of the previous year (DPRC), average relative effective spread over the previous quarter (DRES), and dollar trading volume over the previous 12 months (DVOL). Because quarterly decile ranks of variables are used, any potential time fixed effects will automatically be controlled.

Table IV reports the main results. When earnings surprise is the only independent variable, CARs over all the four drift windows are positively and significantly associated with earnings surprise, clearly indicating the existence of PEAD. When PO and NPO (and other control variables) are included as independent variables, the positive relation between price drift after the earnings announcement and the earnings surprise is enhanced by PO while weakened by NPO. As the PEAD is generally considered an indication of investors' under-reaction to earnings news, the positive impact of indexed ownership on PEAD is consistent with our hypothesis that indexing reduces stock price efficiency. The negative impact of nonpassive institutional ownership on PEAD, in contrast, is consistent with findings in the literature that (nonpassive) institutional investors enhance stock price efficiency.

B. Alternative Specifications for PEAD Analysis

We adopt several alternative specifications as robustness tests. First, following Bartov et al. (2000), we use BM-adjusted CARs and size- and BM-adjusted CARs as alternative measures of PEAD. (17) These measures have a high fraction of missing values because of the nonavailability of BM ratios. Nevertheless, as shown in Panels A and B of Table V, the regression results are qualitatively unchanged when using these two measures. Next, we address the robustness of our findings to the definition of earnings surprise by using two alternative proxies of earnings surprise: SUE and APE. Both measures are widely used in the PEAD literature, so our findings based these two measures are easily comparable to previous studies. Panel C of Table V repeats our regression analysis but uses AFE to replace CAR(-2, 1). When earnings surprise is the only independent variable, CARs are always positively and significantly associated with earnings surprise, indicating the existence of PEAD. When PO and NPO are included as independent variables, the relation between postannouncement CAR and AFE is still positive, and is statistically significant for drift windows (2, 5), (2, 15), and (2, 60). NPO, in contrast, is negatively associated with postannouncement CAR. As shown in Panel D, using SUE generates qualitatively the same and quantitatively weaker results. The relation between postannouncement CAR and SUE is positive and significant for drift windows (2, 5) and (2, 15), but is not statistically significant for drift windows (2, 30) and (2, 60). Overall, our finding that indexed ownership enhances PEAD is robust to typical proxies of earnings surprise. Moreover, Panel E suggests that retaining only US common stocks in the sample has a negligible impact on our results. Finally, our findings are robust to alternative measures of illiquidity (results are not reported).

Another potential concern is the positive correlation in earnings surprises. Prior research, such as Bernard and Thomas (1990), has documented that earnings surprises show positive serial correlation for three quarters. Greater PEAD could thus be interpreted as either an indicator of delayed price response to earnings surprise or the result of forecasted positive earnings surprise in the subsequent quarter. If the second interpretation is true, the magnitude of PEAD may no longer be a valid proxy for price inefficiency. However, we believe that our regression results are not significantly affected by such a complication. If the magnitude of PEAD in one quarter is increased by the accurate forecast of future positive earnings surprise, the magnitude of PEAD in the following quarter)s) will be lowered. Overall, this may not significantly affect the regression coefficients.

C. Cross-Sectional Relation between Indexed Ownership and Price Efficiency

In addition to the PEAD analysis, we estimate a cross-section regression to directly investigate the relation between passive investments and stock price efficiency. We prefer a cross-sectional approach to a time-series approach because, as passive funds are indexed and index constitution changes slowly, time-series variation in passive ownership of an index stock is fairly small. In contrast, cross-sectional dispersions in passive ownership and trading are much greater. First, the S&P 500 constituents in our sample typically have much higher passive ownership than the non-S&P 500 stocks in the sample. Second, there is also some cross-sectional dispersion in passive ownership within the S&P 500 stocks, due to the presence of S&P 500 stocks in other indexes, such as the Russell and MSCI indexes, and the existence of impure index funds, such as closet indexers and enhanced indexers.

To formally examine the relation between indexed ownership and price efficiency, we estimate a multivariate cross-sectional regression following Fama and MacBeth (1973):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (7)

Specifically, one of the five price efficiency measures, [PE.sub.it], in each quarter is regressed on PO, NPO, and a lagged inefficiency measure from the previous quarter, while controlling for illiquidity (RES), market value of the stock (MV), stock price (Price) as of the end of the previous quarter, and turnover ratio (TO). All independent variables are lagged by one quarter to prevent potential reverse causality and to reduce the potential impact of passive ownership on contemporaneous explanatory variables. For example, if passive ownership has an effect on both price efficiency and liquidity, using contemporaneous illiquidity ([RES.sub.i,t]) as a control variable could lead to a downwardly biased coefficient on passive ownership ([[beta].sub.PO,t]). (18) Many control variables are log transformed to control for non-normality. The cross-sectional regression is estimated in each quarter of our sample period, and the time-series mean of the quarterly coefficient estimates is used for inference. The standard errors are adjusted for residual autocorrelation and heteroskedasticity by the Newey and West (1987) approach. To make the coefficient estimates in each quarter comparable across the entire sample period, we follow Kumar (2009) and standardize all dependent and independent variables to have zero-mean and unit standard deviation on a quarterly basis. (19,20)

Table VI reports the main results from the cross-sectional analysis. Controlling for nonpassive institutional ownership and other stock characteristics, each of the three inefficiency measures is positively and significantly related to passive ownership, indicating that indexed holdings are associated with greater deviation of stock price from a random walk. In contrast, nonpassive institutional ownership is negatively and significantly related to V(s)/V(p), indicating their potential role in enhancing market efficiency. The results are consistent with Boehmer and Kelley (2009) that (active) institutional investors contribute to efficient stock prices.

D. Endogeneity

A positive association between inefficiency measures and indexed fund ownership may, though unlikely, come from a self-selection bias rather than causality. If passive funds prefer to hold stocks with lower price efficiency, a cross-sectional negative relation between indexed holding and price efficiency is expected even if passive holdings generate no impact on price efficiency. Though this problem could be significant in studies of active institutional investors, it is likely to be less serious when studying indexed institutional investors whose trading is mostly driven by investor flows or index changes rather than preference to stocks with certain characteristics. Nevertheless, we adopt two approaches to preclude any possible self-selection bias. First, we exclude enhanced index funds and closet indexers from our passive fund sample, leaving only strictly passive index funds and ETFs, and repeat the cross-sectional regression. As presented in Panel A of Table VII, passive (strict index funds and ETFs) ownership is, again, associated with greater deviation of stock price from a random walk. Next, we regress changes in passive ownership on lagged changes in price inefficiency measures, controlling for lagged changes in passive ownership, effective spread, stock capitalization, turnover ratio, and two dummy variables indicating S&P 500 additions and deletions (SP_ADD and SP_DEL):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (8)

As reported in Panel B of Table VII, none of the five lagged inefficiency measure has a positive and significant relation to passive ownership. Therefore, there is no evidence of a self-selection bias.

E. Alternative Specifications of Cross-Sectional Analysis

1. Alternative Liquidity Measures

As suggested by Chordia et al. (2008), liquidity stimulates arbitrage, which enhances market efficiency. Controlling for liquidity in our cross-sectional regression is important for two reasons. First, institutional investors, especially nonpassive institutional investors, may have a preference for liquid stocks because of their lower transaction costs. Thus, institutional holdings may be relatively efficiently priced simply because they are more liquid. Fortunately, this is not likely to be an important concern for indexed institutional investors who aim to track a specific stock index instead of actively looking for liquid stocks. Second, institutional trading and holdings may have an impact on liquidity, which in turn affects price efficiency. We estimate regressions similar to Table VI but use alternative liquidity measures: relative quoted spread (RQS), the Amihud (2002) price impact measure (Amihud) based on daily price movements and trading volume, and the Liu (2006) no-trade-day measure of illiquidity (Liu). Panel A of Table VIII reports the coefficient estimates for PO, NPO, and the illiquidity measure in the three specifications. Consistent with Table VI, PO is positively and significantly associated with most of the three price inefficiency measures under alternative liquidity specifications, whereas NPO generally has negative coefficients. Therefore, our conclusion is robust to the use of alternative liquidity measures.

2. Alternative Specifications

For the first alternative specification, we reconsider exclusion of liquidity and turnover ratio as control variables. If passive ownership has a positive impact on liquidity, controlling for liquidity and turnover ratio could make its negative impact on price efficiency look more pronounced. Second, if S&P 500 index constituents generally have lower price efficiency for reasons other than passive funds, the negative relation between passive ownership and price efficiency could be just a coincidence without implying causality. To eliminate such a possibility, we add a control variable that equals to 1 when a stock is a member of the S&P 500 index at that quarter, and 0 otherwise. Third, following Boehmer and Kelley (2009), we add the lagged dependent variable as an additional control variable, so that our results are more comparable with Boehmer and Kelley (2009). Fourth, we use contemporaneous independent variables instead of lagged variables. Fifth, instead of using the $2 filter, we remove stocks with a stock price of less than $5 at the beginning of a quarter to further eliminate potential microstructure biases. Finally, we keep only US common stocks in our sample. As presented in Panels B and C of Table VIII, each of the above specifications generates results that are qualitatively and quantitatively similar to Table VI. Moreover, using share trading volume or dollar trading volume to replace turnover ratio or using raw variables instead of standardized variables leads to similar results.

IV. Indexing and Price Efficiency: Potential Explanations

We consider three explanations for our results. First, higher indexed ownership possibly implies a reduced incentive for index investors to acquire information. Consequently, it may reduce the production of information and raise the cost of informed arbitrage for active investors. Second, as suggested by De Long et al. (1990), informed investors may not be willing to take risky positions to correct mispricing due to the existence of noise trader risk. The presence of passive investors, who may create noise trader risk, may reduce the incentive and effectiveness of informed investors' effort of price discovery, leading to more persistent price inefficiency. Finally, indexed ownership may serve as a proxy for passive trading, which is mostly uninformed. In addition, index-related trading due to index changes is unidirectional, which may cause prices to move away from fundamentals (Harris and Gurel, 1986; Chen et al., 2004).

A. Reduced Information Production

Analyst following has been used in the literature as a source of information production about a firm. For example, Hong, Lim, and Stein (2000) find that analyst coverage accelerates the transmission of firm-specific information to the public, and Elgers, Lo, and Pfeiffer (2001) report that lower analyst coverage leads to a delayed price response. However, analyst following is not exogenous and may be affected by institutional ownership. O'Brien and Bhushan (1990) find that institutional demand for information could affect the number of analysts following a firm because institutional willingness to pay for information provides an incentive for analysts to follow that firm.

By contrast, indexed or passive shareholders have no desire to pay for information because they do not trade based on information generated by analysts. These investors rely on index providers such Standard & Poor's, Russell Investments, and MSCI to make changes to an index as necessary. They are interested in matching the index, not in earning abnormal returns. In addition, holding a basket of securities could reduce the incentive, or say necessity, of informed arbitrage because random mispricing in index stocks is likely to cancel out: lower returns from overpriced stocks are set off against higher returns from underpriced stocks. Therefore, passive shareholders holding indexed stocks may reduce analyst following and information production due to their lack of trading and limited need for new information.

To test the above hypothesis, we regress the number of analysts against passive ownership and nonpassive ownership based on all stocks in our sample:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

where MV is the market value of the stock estimated by the Fama and French (1992) approach, and TO is the turnover ratio over the previous year. As index additions are associated with a significant increase in number of analysts (Yu, 2008) as well as a significant increase in passive ownership, controlling for index membership is crucial to eliminate any false positive relation between passive ownership and number of analysts. Therefore, we add two dummy variables indicating current memberships in the S&P 500 index (SP500D) or the Russell 1000 index (R1000D).

Consistent with our conjecture, the number of analysts is negatively related to passive ownership in all three regression specifications in Table IX, implying that less information is being produced for firms with greater fractions of passive investors because these investors exhibit limited incentive for information acquisition. (21) Moreover, consistent with O'Brien and Bhushan (1990) and Brennan and Subrahmanyam (1995), the number of analysts is positively related to nonpassive ownership, indicating that nonpassive institutions indirectly facilitate information production.

B. Lowered Incentive of Arbitrage

The reduction in information production may be inconsequential for price discovery as long as there exists a group of smart investors with easy access to superior information because the negative impact of indexed investors on price efficiency could be largely offset by arbitrage activities of such informed traders. However, as suggested by De Long et al. (1990), informed investors may not be willing to take risky positions against noise traders (indexed investors) because of the existence of noise trader risk, so that the mispricing caused by noise traders could become even more extreme before its disappearance. The presence of passive investors, therefore, may reduce the incentive and effectiveness of informed investors' price discovery efforts. For example, Morck and Yang (2001) suggest that the increasing demand for S&P 500 stocks from passive funds induces ever-increasing overpricing in these stocks. If this finding is true, short selling is not a rational strategy even if informed investors recognize the existence of overpricing, as increasing demand from indexed investors will push index stocks to become more overpriced instead of converging to fundamental values, at least in the short term.

C. Consequences of Passive Trading

Similar to noise trading, passive trading conveys no information about individual stocks or industries. Passive funds trade based on flows initiated by investors who may, at best, convey market-wide information. Passive funds also trade around index changes, which is not only uninformed but can cause herding among passive investors and temporarily move prices away from fundamentals (Harris and Gurel, 1986; Lynch and Mendenhall, 1997; Chen et al., 2004). Though trading by passive investors has the potential to move prices, average passive trading volume is only 5% of average nonpassive trading volume as reported in Table III. Therefore, whether passive trading could generate a significant negative impact on price efficiency becomes an empirical question.

To evaluate the effect of passive ownership on price efficiency, PE, we examine the relation between passive trading on price efficiency using the following cross-sectional regression:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (10)

If the negative relation between passive ownership and price efficiency is caused by passive trading, the coefficient on [PT.sub.i,t] in Equation (10) should be positive and significant. We use contemporaneous trading instead of lagged trading because the impact of trading on stock prices should take place immediately, and as mentioned earlier, there is no evidence of endogeneity between passive ownership and price efficiency.

The results in Table X suggest no significant impact of PT on price efficiency. None of the three measures of price inefficiency has a positive and significant coefficient, but the variance ratio is negatively and significantly related to PT. In addition, PO is positively related to all three price inefficiency measures even after controlling for PT. These results suggest that passive trading does not seem to be a source of indexed investors' negative impact on price efficiency. Of course, our measure of passive trading, which is based on absolute changes in quarterly holdings, is likely to underestimate actual trading volume. More precise data on institutional trading volume, if available, may deliver more reliable results.

V. Conclusion

Index funds and indexed investing have been promoted by academics and practitioners over the last 50 years as an inexpensive and effective way to hold a diversified portfolio. As a result, the indexed investment sector has grown and today accounts for more than 7% of the total equity market and more than 29% of the US equity mutual fund sector. Although advantages of index investing are significant, there are negative externalities that passive investors impose on other market participants and the economy by making stock prices less efficient. Active traders produce information and trade to earn abnormal returns. In the process, they contribute to market efficiency. Index investors, in contrast, use these efficient prices to invest but without directly contributing to making those prices efficient. Their trades are primarily liquidity-driven, information-less trades motivated either by index changes or by investor flows.

Consistent with the above notion and based on a sample of large and liquid US stocks from 2002 to 2013, we find that indexing reduces informational efficiency of stock prices, and stocks with a higher level of indexing, as measured by passive ownership and passive trading, have less informative prices. We examine explanations for the decrease in price efficiency. We find that the relation is not explained by persistence in price efficiency, size, or endogeneity. The relation is robust to several intraday and daily price efficiency measures and alternate liquidity measures. We distinguish between the effects of indexed ownership and passive trading on price efficiency, and find that indexing affects price efficiency probably through reduced information acquisition and arbitrage. We also argue that indexed investors may indirectly lower price efficiency by reducing informed investors' incentive to arbitrage.

Appendix A: Selection of Index Funds and ETFs

In the first step, we pick up all funds that are classified as either an index fund or an ETF by the CRSP index fund and ETF indicators. To identify potential index funds and ETFs that are not marked by the indicators, we then screen fund names in the 13F database by keywords. For index funds, we look for the following keywords: "INDEX," "IND"IDX," INDE," "S&P 500 I," "S&P 5001," "S&P 400 I," "S&P 4001," "S&P 600 I," "S&P 6001," "S&P500IND," "S&P400IND," "S&P600IND," "RUSSELL 1000," "RUSSELL 2000," "RUSSELL 3000," and "VANGUARD." For ETFs, we look for the following keywords: "EXCHANGE TRADED," "EXCHANGE-TRADED," "ETF," "ISHARES," "POWERSHARES," "PROFUNDS," "SPDR S&P" "SPDR DOW," "SPDR DJ," "RYDEX," "SPA MG," "MARKET GRADER," and "QQQ."

To exclude bond funds, balanced funds, and funds that substantially hold derivatives from our sample, we remove funds with the following keywords in their names: "BOND," "INFLATION," "TREASURY," "BD," "LEHMAN," "BARCLAY," "OPTION," "HEDGE," "BALANCE," "ALLOC," "ASSET AL," "MULTI ASSET," and "PRINCIPAL PROTECTION,"

To exclude international funds, we require that the country code in 13F be either blank or "UNITED STATES." Furthermore, we remove funds with the following keywords in their names: "EURO," "FRANCE," "GERMAN," "CANADA," "CANADIAN," "HK," "JAPAN," "SING," "INDA," "INDU," "INDI," "INDO," "NETH," "SWITZ," "ITALY," "SPAIN," "ASIA," "GLOBAL," "NIKKEI," "FT-SE," "FTSE," "EM," "EMER," "BRIC," "EUR," "UK," "ENT," "AUSTRLA," "JAP," "CNDN," "CDN," "PACIF," "TRU," "LATIN," "EMER," "EMG," "EMRG," "LAT AME," "KINDOM," "CHILE," "JPN," "TURKEY," "DEVELOPE," "ENERGY," "BRAZIL," "KOREA," "BELG," "MALAYSIA," "SWEDEN," "AUSTRIA," "EMU," "SOUTH AFR," "TAIWAN," "INDONESIA," "STOXX," "THAI," "EX US," "INDEKS," "NIKKO," "TOKYO," "HANG SENG," "JPA," "SIMCAV" "TOPIX," "EAFE," "SPHINX," "WARBURG," "FOND," "TSX," "AMER EXEMPT," "TSE," "GOLDEN DRAGO," "AVENIR ALIZES," "FINORD INDEX AMERIQUE," and "ASX."

Finally, we manually check the investment objective and strategies of each fund from its prospectus and remove funds that are not passive equity funds. We remove funds with the following ID number in the 13F database: 526, 583, 697, 787, 792, 1366, 1469, 1588, 1884, 2231, 2373, 2468, 2518, 2637, 2676, 2875, 2882, 2887, 2965, 3300, 3300, 5040, 7679, 12065, 12065, 12096, 12707, 12760, 12877, 13000, 13143, 13235, 13256, 14266, 14499, 16561, 16570, 16598, 18009, 18252, 20075, 21002, 21888, 22461,22616, 23300, 23645, 26775, 28900, 28908, 29093, 34560, 36077, 36578, 36593, 45638, 47191,47224, 47959, 48003, 48160, 49335, 51143, 51527, 51652, 51894, 53700, 53705, 53800, 53900, 53933, 54440, 55633, 56500, 58099, 58852, 60100, 61423, 63079, 64362, 64635, 64635, 64803, 64804, 64805, 64816, 64960, 66970, 67996, 68391, 68392, 70032, 71917, 72523, 72986, 73268, 73290, 73424, 73695,73695, 74147, 74285, 75703, 75704, 75708, 76021, 76021, 76734, 77497, 77498, 77889, 77941, 78219, 78580, 79882, 80729, 80730, 80811, 80857, 80859, 81110, 81200, 83285, and 83380.

Appendix B: Estimation of Hasbrouck's (1993) Pricing Error

Intraday trade and quote data obtained from the NYSE TAQ database are used for estimation of as. Following Boehmer and Kelly (2009), we use quotes and trades that are within the regular trading hours (9:30 a.m.-4:00 p.m.) and ignore overnight price changes. A quote is removed if the ask price is lower than the bid price, if the bid price is lower than $0.10, or if the bid-ask spread is higher than 25% of the quote midpoint. To be eligible for estimation, a trade is required to have a value of zero in TAQ's CORR field; marked as "@," "@F," "F," "B," "E," "J," "K," or blank in TAQ's COND field; and have a positive trade size and price. A trade is removed if its price differs by more than 30% from the previous trade. We ignore the natural times but view transactions as untimed sequences. This approach is preferable because it gives more weight to periods with heavier price discovery activities, represented by more transactions, and uses information delivered from every single transaction. Following Flasbrouck (1993), we estimate the lower bound for [[sigma].sub.s] using a vector autoregression (VAR) model with five lags over the four-variable set [X.sub.t] = ([r.sub.t], [x.sub.t])', where [r.sub.t] = [p.sub.t] - [p.sub.t-1] and [x.sub.t] is a 3 x 1 vector of the following trade variables: 1) sign of trading direction that equals 1 if the transaction is buyer initiated, -1 if it is seller initiated, and 0 if it is a quote midpoint transaction; 2) signed trading volume; and 3) signed square root of trading volume. Following Harris (1989) and Lee and Ready (1991), we classify a trade as buyer initiated (seller initiated) if the transaction price is above (below) the prevailing quote midpoint. The inclusion of square root of trading volume aims to allow for concave dependencies in both [m.sub.t] and [s.sub.t]. In each month, we estimate L(s) for stocks that have at least 100 trades during that month. Specifically, the joint process of [X.sub.t] is described by a five-lag VAR model:

[X.sub.t] = [B.sub.1][X.sub.t-1] + [B.sub.2][X.sub.t-2] + [B.sub.3][X.sub.t-3] + [B.sub.4][X.sub.t-4] + [B.sub.5][X.sub.t-5] + [u.sub.t], (B. 1)

where [B.sub.k] is the 4 x 4 coefficient matrix for lag k, and [u.sub.t] is a 1 x 4 vector of zero-mean error terms with E ([u.sub.i,t], [U.sub.j,t]) = 0. The VAR model is then transformed into a five-lag approximation of vector moving average (VMA) representation: (22)

[X.sub.t] = [u.sub.t] + [A.sub.1][u.sub.t-1] + [A.sub.2][u.sub.t-2] + [A.sub.3][u.sub.t-2] + [A.sub.4][U.sub.t-4] + [A.sub.5][u.sub.t-5]. (B.2)

Variance of pricing error is expressed by:

[[sigma].sub.s.sup.2] =[4.summation over (j=0)] [[[gamma].sub.1,j] [[gamma].sub.2,j] [[gamma].sub.3,j] [[gamma].sub.4,j]] Cov(u) [[[gamma].sub.1,j] [[gamma].sub.2,j] [[gamma].sub.3,j] [[gamma].sub.4,j]], (B.3)

where

[[gamma].sub.i,j] = - [5.summation over (k=j+1)] [A.sub.k,1,i] (B.4)

and Cov(m) is the residual covariance matrix from the VAR model. We use the average of the monthly estimates of [[sigma].sub.s.sup.2] in a quarter as the pricing error variance of that quarter.

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Nan Qin and Vijay Singal *

We thank participants at the 2013 Financial Management Association annual meetings and at Virginia Tech for comments and suggestions.

* Nan Qin is an Assistant Professor of Finance from the Luter School of Business at Christopher Newport University in Newport News, VA. Vijay Singal is the J. Gray Ferguson Professor of Finance from the Pamplin College of Business at Virginia Tech in Blacksburg, VA.

(1) Closet indexers are "active" mutual funds that actually track an index.

(2) Source: 2014 ICI Factbook. The total amount in broad-based equity ETFs ($762 billion) and US equity index mutual funds ($1,213 billion) was $1,975 billion. The total amount in US equity mutual funds and ETFs was $6,694 billion, comprising $964 billion in ETFs and $5,730 billion in mutual funds.

(3) Shu (2007) finds that price anomalies, including return momentum, PEAD, and value premium, are much stronger in stocks with relatively low institutional trading volume.

(4) Details of the keyword search are reported in Appendix A.

(5) Theoretically, AS for a pure index fund with very low tracking error should be close to zero. However, as 13F filings generally ignore small holdings, the estimated AS will be higher than the actual value. The average estimate of AS over the life of an index fund in our sample could be as large as approximately 20%.

(6) We do not require the beta to be close to 1 because a passively inclined fund may intentionally maintain a beta different from 1.00 by using leverage or by holding cash.

(7) Balanced funds, international funds, and bond funds are identified mainly by their names and country code provided in the 13F database. We also manually screen the sample to remove any of these funds. We check the fund prospectus for fund objective and strategies. Typically, a fund is removed from the sample when its investment strategy states that the manager actively chooses undervalued stocks.

(8) This number is smaller than the actual number of US equity ETFs for several reasons. First, we exclude ETFs that hold a significant percentage of international equities. Second, ETFs that are reported jointly with index mutual funds are identified as index funds instead of ETFs in the sample. An example is Vanguard 500 Index Funds, which has both investor shares and ETF shares. Third, the 13F database does not provide an ETF indicator, and the ETF indicators from CRSP are not able to identify all ETFs in the 13F database because the MFLINKS data set does not provide a complete linkage between the CRSP mutual fund database and the 13F database.

(9) A sample with only S&P 500 stocks has relatively low cross-sectional dispersion in passive ownership, as all S&P 500 index funds will hold each S&P stock in the same proportion.

(10) All market caps are as of December 31,2013.

(11) At the beginning of each quarter, we sort all stocks in our sample into deciles by their size, which is estimated by the same approach as Fama and French (1992). We then construct 10 value-weighted benchmark portfolios and use their returns to estimate CARs of the stocks within the same size deciles at that quarter. We also use book-to-market (BM)-adjusted and size- and BM-adjusted CARs for robustness tests.

(12) A detailed analysis is provided in Appendix B.

(13) Boehmer, Saar, and Yu (2005) use this measure to study the effect of the increased pretrade transparency on stock price efficiency. Boehmer and Kelley (2009) use this measure to study the effect of institutional ownership on stock price efficiency. Boehmer and Wu (2012) use this measure to examine the relation between short selling and the price discovery process. Hotchkiss and Ronen (2002) use a variant of this measure, MQ = 1 - 2[[sigma].sup.2.sub.s]/[[sigma].sup.2.sub.p], to examine the informational efficiency of corporate bond price.

(14) Institutional holdings are obtained from the 13F database, and data on total shares outstanding are obtained from the CRSP stock files. For stock-quarters that report more institutional holdings than total shares outstanding, we set institutional ownership to 100% and calculate PO and NPO accordingly, provided the institutional ownership in the previous or the following quarter is above 80%. Otherwise, we consider it to be an invalid observation.

(15) The use of decile ranks has become typical methodology in the PEAD literature and makes our results more comparable to prior work.

(16) Each variable takes the values of 0.05 for the smallest decile and 0.95 for the largest decile.

(17) Estimation of BM-adjusted CARs is similar to that of size-adjusted CARs. To estimate size- and BM-adjusted CARs, we sort all stocks in our sample into quintiles by their size and BM ratios at the beginning of each quarter, and construct 5x5 value-weighted benchmark portfolios. We then use their returns to estimate CARs of the stocks within the same size and BM quintiles at that quarter.

(18) Using contemporaneous variables leads to qualitatively and quantitatively similar regression results.

(19) The results are similar without variable standardization.

(20) Several dependent and independent variables suffer from heteroskedasticity over the sample period. There are noticeable increases in the cross-sectional standard deviations of PO and PT, and decreases in the standard deviations of the normalized pricing error volatility, V(s)/V(p), and illiquidity measures, RES, Amihud, and Liu. Because the cross-sectional volatility of the dependent variables (i.e., V(s)/V(p)) are moving in the opposite direction compared to the volatility of the independent variables (i.e., PO and PT), coefficient estimates of PO and PT tend to have larger magnitudes in early years than in recent years, leading to the Fama and MacBeth (1973) regression results being more influenced by early years.

(21) Yu (2008) finds that analyst coverage is negatively associated with earnings management because, in addition to their role in information production, analysts serve as external monitors. Therefore, lower analyst coverage induced by indexing may encourage the firms to intentionally create information asymmetry by earnings management, resulting lower price efficiency.

(22) VMA lags beyond five are assumed to have little impact and are ignored to simplify the estimation process. As mentioned by Hasbrouck (1993), more lags generally increase the estimates of pricing error variance but make little change in the cross-sectional ranking.

**********

The indexed investment sector, including index mutual funds, enhanced index funds, exchange-traded funds (ETFs), and closet indexers, has experienced rapid growth over the past two decades. (1) As of December 2013, the market share of broadly diversified index funds had reached 29.5% of the total investment in US equities in the mutual fund sector including ETFs. (2) The potential impact of indexing on the efficiency of equity markets, however, is an important but unexplored topic.

Previous studies have examined the impact of indexing on constituent stocks. In their model of institutional investors and index benchmarks, Basak and Pavlova (2013) find that institutional trades amplify stock market volatility and induce excess correlations among index stocks. The implications of the model are supported by Greenwood and Thesmar (2011) who find that institutional ownership increases volatility especially among markets or indexes. Another section of the literature examines the impact of institutional investors on stock prices. (3) Using a comprehensive sample of NYSE-listed stocks between 1983 and 2004, Boehmer and Kelley (2009) find that trading and ownership by institutional investors increase price efficiency. Specifically, institutional investors incorporate information into stock prices through their trading and their ownership facilitates informed arbitrage. Based on NYSE/AMEX stocks over 1989-1993, Bartov, Radhakrishnan, and Krinsky (2000) find that institutional holdings are negatively associated with the magnitude of post-earnings-announcement drift (PEAD), suggesting that investor sophistication may reduce stock return predictability. In contrast, Chen, Noronha, and Singal (2004) document that stock prices increase immediately after the announcement of additions to the S&P 500 index but reverse substantially after three months. They explain these findings by the temporary price pressure caused by index fund purchases of stocks newly added to the index. Goetzmann and Massa (2003) examine daily flows for three major S&P 500 index funds and find a strong contemporaneous correlation between inflows and returns. Similarly, Keim and Madhavan (1997) and Jones and Lipson (1999, 2001) find that index funds generate a larger price impact relative to active funds in the short period following their trading.

This article is at the intersection of these two literatures: the impact of indexing and the role of institutional investors in enhancing price efficiency. Despite extensive literatures on indexing and price efficiency, there has been no systematic study of the impact passive index investors may have on the informational efficiency of stock prices. Compared to their active peers, passive institutional investors have two unique characteristics. First, they generally hold a basket of stocks in certain indices passively, without active information acquisition and price discovery. Second, trading of passive funds is mostly driven by investor flows or index changes instead of private information. Both features raise concerns regarding a possible negative impact on price efficiency. As suggested by Grossman and Stiglitz (1980), price discovery relies on informed traders who actively acquire information and incorporate that information into stock prices by trading. An increase in passive (uninformed) investors and the consequent reduction in active traders can result in a proportionate increase in information costs and has the potential to move equilibrium to a less efficient level. In spirit, our article comes closest to Wurgler (2011) who points to the growing importance of indexing for investment and benchmarking such that it can distort markets and affect the real economy. In contrast, our focus is on a different consequence of the growth in indexing: assimilation of new information into stock prices, which is critical for an efficient market.

We empirically investigate the relation between indexed holdings and trading and price efficiency. Based on a sample of current S&P 500 index constituents and non-S&P 500 stocks with comparable size and turnover ratios, we find that prices become less efficient as indexed ownership grows, where price efficiency is measured by the magnitude of PEAD or by deviations of price from the random walk. It is robust to several alternative specifications. We also examine the impact of indexed ownership and passive trading separately, and find that indexed investments affect price efficiency only through indexed holdings, but passive trading by itself does not show any significant effect.

Our sample of passive institutional investors consists of 591 index funds, enhanced index funds, ETFs, and a number of closet indexers. The index and index-like funds are identified in several ways: keywords in fund names, "activeness" of funds based on deviations from index compositions, and fit from regressions of fund returns on index returns. For subsequent analysis, we measure each stock's passive ownership as the percentage of shares held by any fund in our sample at the end of each quarter, and we measure passive trading volume as the sum of absolute holding changes over that quarter.

We measure price efficiency in two ways. First, we view PEAD as an indicator of investors' under-reaction to public information and use it as a framework to study price inefficiency. Second, we assume that an efficient stock price should follow a random walk and use deviation of stock prices from random walk as proxy of price inefficiency. Specifically, we adopt normalized Hasbrouck's (1993) intraday pricing error volatility, absolute value of first-order autocorrelation in daily returns, and absolute value of weekly to daily variance ratio as our empirical measures of price inefficiency. We believe that an intraday measure, compared to daily or even longer horizon proxies, better captures deviation from efficient prices because of the relatively quick stock price adjustments by S&P 500 firms within each trading day (Chordia, Roll, and Subrahmanyam, 2005). Meanwhile, the daily measures ensure that potential price inefficiency in longer horizons is not omitted.

Our empirical tests use a sample period from 2002 to 2013, which is after the introduction of decimalization to avoid major institutional changes in price efficiency. We first test the magnitude of PEAD and find that PE AD increases along with passive ownership and, consistent with Bartov et al. (2000), decreases as (nonpassive) institutional ownership increases. These findings are robust to alternative definitions of price drift, different drift windows, and alternative measures of earnings surprise. Next, following Boehmer and Kelley (2009), we regress empirical measures of price efficiency on passive and nonpassive institutional ownership. Consistent with our hypothesis, the deviation of both intraday and daily stock prices from a random walk is positively correlated with passive ownership. We also reconfirm the inference of Boehmer and Kelley (2009) that (nonpassive) institutional investors may enhance price efficiency.

Our results could arise if passive ownership is higher for stocks that are characterized by price inefficiency. Though it could be significant in studies of active institutional investors, endogeneity is unlikely for indexed institutional investors where trading is driven by investor flows or index changes rather than through stock selection. Nevertheless, we confirm that endogeneity is a nonissue in two ways. First, we regress changes in passive ownership on lagged changes in price inefficiency. Second, we repeat cross-sectional analysis using a sample of passive index funds and ETFs, excluding discretionary index funds such as enhanced index funds and closet indexers. Results from neither test support evidence of endogeneity.

Among explanations for our results, further analysis reveals that information production, as measured by the number of analysts, is significantly and negatively associated with passive ownership but is positively related to nonpassive institutional ownership. This evidence is consistent with the expectation that as indexed investors have no incentive for information acquisition, arbitrage, and trading, information production will decline. Therefore, we believe that the reduced incentive for price discovery is primarily responsible for the negative impact of passive ownership on price efficiency. Moreover, passive investors may create limits to arbitrage through noise trader risk, which could deter or delay informed arbitrageurs from correcting the mispricing, thus reducing price efficiency indirectly.

This study illustrates that although indexing is beneficial for passive investors, it exerts a negative externality by making it more difficult for stock prices to reflect information efficiently. As the fraction of passive ownership increases, prices are likely to become less efficient. Taken to an improbable and theoretical extreme of 100% indexing, no one would have an incentive to make prices informationally efficient. Of course, the current fraction of passive ownership is relatively small; thus, its negative impact on market efficiency may not be striking or intuitive. However, given the likely rapid growth of indexing in the future, it is reasonable to be cautious about its negative influence on market efficiency.

The rest of this article is organized as follows. Section I describes the data sources and sample selection. Section II describes measures of price efficiency, liquidity, and other control variables. Section III presents our main results from PEAD and cross-sectional analyses, and corresponding robustness tests. Section IV explores potential underlying mechanisms to explain our findings. Section V concludes.

I. Sample

A. Sample of Passive Funds

Index funds and ETFs, which follow passive investment strategies, are the major passive institutional investors on the market. However, we do not restrict our sample to pure index funds and ETFs, but also include enhanced index funds and closet indexers to construct a more complete measure of passive ownership. Although these funds may strategically adjust weights of some holdings based on their predictions about future price movements, they track indices passively and closely. Thus, their impact on price efficiency is closer to index funds than to their active peers.

Institutional holdings data from the Center for Research in Security Prices (CRSP) Mutual Fund database and Thomson Reuters (13F filings) are used to create the passive fund sample in four steps. First, we merge the CRSP mutual fund database, which provides indicators for index funds and ETFs, with the 13F database to identify index mutual funds and index ETFs. Second, we screen remaining funds for index-related funds on both CRSP Mutual Fund and 13F databases using keywords in their names. A fund is classified as passive if it calls itself an index fund, enhanced index fund, or ETF. (4)

Third, we identify closet indexers in two ways. First, following Cremers and Petajisto (2009), we estimate the "active share" (AS hereafter) of each mutual fund from the 13F database. As suggested by Cremers and Petajisto (2009), any portfolio could be decomposed into a benchmark index portfolio plus a zero-net-value long-short portfolio. Thus, AS is a measure of the overall deviation of the weights of a fund's holdings from the benchmark index. For a pure index fund, AS will be close to zero, as the weight of each asset in the fund portfolio equals the asset weight in the benchmark index. (5) Second, we estimate a regression of daily fund returns on corresponding benchmark index returns to obtain [R.sup.2]. A fund with [R.sup.2] close to one is more likely to follow passive strategies. (6) Because the benchmark indices for closet indexers are not explicitly stated, we tested 10 indices for each fund and selected the lowest AS and the highest [R.sup.2] for each fund. The indices are: S&P 500 index, S&P 500 Growth index, S&P 500 Value index, S&P 400 Mid-Cap index, S&P 600 Small-Cap index, S&P 100 index, Russell 1000 index, Russell 2000 index, NASDAQ 100 index, and the whole market portfolio obtained from CRSP stock files. To be included in the passive fund sample as a closet indexer, a fund quarter must have AS less than 10% or [R.sup.2] above 99% in the prior year.

Finally, we exclude balanced funds, international funds, and bond funds from the sample. (7) The passive sample includes four types of passive institutional investors: 1) 255 open-end equity index funds that aim to replicate the performance of a specific equity index by holding the index constituents in the same proportions as the index, 2) 47 enhanced index funds that reserve certain flexibility on position size and investment strategies, 3) 289 ETFs that track an index and are traded on stock exchanges, (8) and 4) a number of closet indexers. Appendix A provides a detailed description of the procedure used to construct the sample.

B. Trends in Indexing

Table I shows the growth in indexing from 2002 to 2013. The US equity market grew from $11 trillion in 2002 to over $26 trillion in 2013. In the same period, the value of passive funds increased from $309 billion to $1865 billion. As a fraction of US equity mutual funds and ETFs, passive funds increased from 12.80% in 2002 to 27.52% in 2013, and as a portion of the equity market from 2.80% to 7.09%. Passive ownership for S&P 500 stocks increased steadily from 4.54% in 2002 to 9.62% in 2013. Unlike the steady increase in passive ownership, nonpassive institutional ownership increased from 57.80% of US equity in 2002 to 69.52% in 2007 before falling to 61.80% in 2013. The last column in Table I reports the difference between 100% and the holdings of institutional investors, and it represents the sum of holdings of insiders, individuals, and any errors in reporting.

C. Sample of Stocks

The primary empirical analysis in this article is based on S&P 500 stocks along with a control group of non-S&P 500 stocks of comparable size and turnover ratio. We choose a sample related to S&P 500 stocks for several reasons. First, the S&P 500 index is the most popular index by assets indexed and one of the most popular indexes by the percentage of assets indexed, which implies that S&P 500 stocks will exhibit a reasonable level of passive ownership. Meanwhile, non-S&P 500 stocks typically have fairly low, if not zero, passive ownership. This combined sample thus provides sufficient cross-sectional dispersion in passive ownership for empirical analysis. (9) Second, restricting the sample to S&P 500 constituents and comparable non-S&P 500 firms helps reduce the potential impact of infrequent trading, which could be severe in small firms. Third, the S&P 500 index represents the US equity market, and any effect found among its components is likely to be important for the entire market. Finally, restricting our sample to S&P 500 constituents and comparable non-S&P 500 firms generates a similar informational environment across stocks; thus, inferences about an association between indexed ownership and price efficiency will be more robust to potentially unobservable factors that may affect the informational environment of a firm.

We require all stocks to have prices of at least $2 at the beginning of a quarter to avoid severe market microstructure issues. Because the focus of our article is on price efficiency, we want to minimize the impact of external events. In particular, decimalization in 2001 has improved price efficiency considerably with an increase in liquidity that makes arbitrage less costly (Chordia, Roll, and Subrahmanyam, 2008). Accordingly, we begin our sample in 2002 to avoid the effect of decimalization.

It is critical that the control group of non-S&P 500 stocks is similar to the S&P 500 index. Fortunately and unlike the Russell 1000, which captures the largest eligible firms by market cap, the S&P 500 is more selective and need not select all large eligible firms. For example, as of December 31, 2013, among commercial airlines, only Delta Airlines ($23.5 billion) and Southwest Airlines ($13.1 billion) were included in the S&P 500. Two other airlines of similar size, American Airlines Group ($19.1 billion) and United Continental ($13.7 billion) were not S&P 500 constituents. (10) Similarly, among casinos and gaming, Wynn Resorts ($19.6 billion) is included in the index but a significantly larger Las Vegas Sands ($64.6 billion) and somewhat smaller but still large MGM Grand ($11.5 billion) are not in the index. It is these kinds of non-S&P 500 firms that we intend to capture in the control group.

The S&P 500 has very large firms (> $100 billion as of December 31,2013) but also relatively small firms as firms grow and shrink once added to the index. Larger firms are not ordinarily dropped from the index and small firms are dropped only with a delay. Because the smallest size decile of the S&P 500 may not represent the true nature of S&P 500 firms, we require all firms in the control group to be larger than firms in the smallest size decile. To be sure, the control group cannot replicate the S&P 500 in terms of all sectors adequately and is less likely to represent the top decile of the S&P 500 in terms of size. However we believe that the control group is a reasonable representation of the S&P 500 in terms of both security type and size.

We construct the sample as below. At the end of each quarter from 2002 to 2013, we sort all S&P 500 stocks into deciles by their market values following Fama and French (1992) and by their turnover ratios in the prior quarter. We select all stocks that are larger than any stock in the smallest S&P 500 size decile and with turnover greater than the smallest S&P 500 turnover ratio decile.

This procedure generates a sample of approximately 400 S&P 500 constituents and 130 non-S&P 500 stocks in each quarter. Sample characteristics are reported in Table II. Panel A shows that the control group, by construction, is extremely close to the S&P 500 in terms of security type as evidenced by the percentage of stocks in each share code. As with the S&P 500, about 94% of the control group consists of ordinary common shares of companies incorporated in the United States (share code 11). Between 2% and 3% of the companies incorporated outside the United States (share code 12) are deemed eligible for inclusion in the S&P 500 because their foreign incorporation is primarily for tax reasons, for example, Accenture, Garmin, Noble Energy, Transocean Drilling, Ingersoll Rand, and Seagate Technology. Finally, real estate investment trusts account for approximately 3-4% of the companies in the S&P 500 and the control group (share codes 18, 48).

Panel B of Table II shows the mean and median sizes of companies in the S&P 500 and the control group. Though the median size of the S&P 500 companies is about twice the size of the control group, we believe that the companies in both groups are large and that the control group reasonably represents firms in the S&P 500.

Daily stock price, return, trading volume, and shares outstanding are obtained from CRSP stock files, and intraday trade and quote data are obtained from NYSE Trade and Quote (TAQ) database. Information about earnings announcements are obtained from Compustat, and analyst earnings forecasts are obtained from Institutional Brokers Estimate System (IBES). We obtain constituents of the S&P indices from Compustat and of the Russell indices from Russell Investments. Total returns for the indexes are obtained from Bloomberg.

II. Methodology

A. Measure of Relative Informational Efficiency of Prices

Measures of price efficiency fall into several groups. First, price efficiency could be measured by returns to trading strategies based on market anomalies, such as short-term reversals, momentum, and PEAD. Second, under the assumption that efficient price follows a random walk process, deviations of stock prices from random walk could be a measure of relative inefficiency. This group of measures includes return autocorrelations, variance ratios, and the Hasbrouck (1993) pricing error variance. Third, without an assumption about random walk, relative price inefficiency could be inferred by the delay of stock returns in response to market return (Hou and Moskowitz, 2005). Finally, price inefficiency could be measured by certain asset pricing models. For example, the Kalman filter estimation of mispricing used by Brennan and Wang (2010) is based on the assumption that the fundamental return follows an ex post version of the Fama and French (1993) three-factor model. In this article, we prefer the model-free assumption that efficient stock prices follow a random walk, and we measure price efficiency using two approaches: magnitude of PEAD and stock price deviation from a random walk.

1. Cumulative Abnormal Returns in the PEAD Analysis

We use cumulative abnormal returns (CARs) estimated from the companion-portfolio approach as measures of PEAD. Specifically, the CAR for the window ([t.sub.1], [t.sub.2]) is estimated as the daily abnormal return for firm i on date t as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (1)

where [R.sub.i,t] is the daily return of stock i and [R.sub.p,t] is the value-weighted daily return of a portfolio of stocks within the same size decile as stock i. (11)

Following Frazzini (2006), we use CAR(-2, 1), the cumulative abnormal return from two days preceding the announcement date to one day after, as the proxy for earnings surprise. Conventional measures of earnings surprise, such as the time-series model of actual earnings, or consensus forecasts may not truly measure the market's expectation. As suggested by Frazzini (2006), however, CAR around the announcement date is the actual market reaction and does not rely on assumptions underlying any forecasts. Nevertheless, we also use two alternative measures of unexpected earnings in robustness tests. First, following Ayers, Li, and Yeung (2011), we define standardized unexpected earnings (SUE) as the seasonal difference in actual earnings standardized by the stock price at the end of the previous fiscal quarter:

[SUE.sub.i,t] = [EPS.sub.i,t]-[EPS.sub.i,t-4]/[P.sub.i,t-1]. (2)

Second, we define analyst forecast error (AFE) as the difference between actual earnings per share and the mean of the most recent analyst forecasts, scaled by the stock price at the end of the previous fiscal quarter.

2. Deviation of Stock Price from the Random Walk

We adopt the pricing error of Hasbrouck (1993), the daily first-order autocorrelation in stock returns, and variance ratios of weekly returns to daily returns as our empirical measures of the deviation of stock prices from the random walk. We use pricing error as the principal measure, and the other two measures as robustness tests.

Compared to other measures of price inefficiency, Hasbrouck's (1993) pricing error has several advantages. First, Hasbrouck's (1993) measure is free from the asset pricing model. Mispricing proxies that rely on specific asset pricing models, such as the Kalman filter in Brennan and Wang (2010), the price delay in Hou and Moskowitz (2005), or measures based on momentum profit or PEAD, may suffer from model misspecification. Second, as suggested by Boehmer and Kelley (2009), Hasbrouck's (1993) measure only captures price deviation from random walk caused by uninformed trading, so that deviations caused by informed trading will not be mistakenly measured as price inefficiency. Variance ratio and autocorrelation, however, do not distinguish between information-induced and noninformation-induced deviations from random walk. Third, Hasbrouck's (1993) measure is estimated on a trade-to-trade basis, which captures most of the information involved in trading and places greater weight on periods with active information discovery. Variance ratio and autocorrelation, however, are measured with daily intervals, leading to loss of intraday information, and they place equal weight on periods with and without active price discovery. We expect that Hasbrouck's (1993) measure will provide more accurate and robust inferences compared to other empirical measures of price inefficiency.

The pricing error proposed by Hasbrouck (1993) measures the deviation between transaction prices and implicit efficient prices. (12) Specifically, the log transaction price, [p.sub.t], is defined as the efficient price, [m.sub.t], plus a transitory deviation, [s.sub.t]:

[p.sub.t] = [m.sub.t] + [s.sub.t], (3)

where t indexes either transactions or natural time, [m.sub.t] is the expectation of the stock value given all available public information and is assumed to follow a random walk, and [s.sub.t] measures the deviation of transaction price from the efficient price, [s.sub.t] is assumed to be a zero-mean covariance-stationary stochastic process with variance of [[sigma].sup.2.sub.t], where [[sigma].sup.2.sub.s] measures how closely the transaction price follows the efficient price. As [[sigma].sup.2.sub.s] is associated with price volatility, we follow Boehmer and Kelley (2009) and several other studies to normalize [[sigma].sup.2.sub.s], denoted as F(s), by the variance of log transaction prices, V(p), to form a measure of relative price efficiency, V(s)/V(p). Ln[V(s)/V(p)] is used as principal metrics in the cross-sectional analysis. (13)

Though the price adjustment process generally takes less than 60 minutes (Chordia et al., 2005) and should be well described by V(s)/V(p), we would like to capture potential price adjustment processes in longer horizons to enhance the robustness of our findings. The existence of long-horizon return anomalies, such as momentum, daily and weekly return autocorrelations, or PEAD, indicate the existence of inefficient stock prices beyond each trading day. Hence, we adopt two (inverse) efficiency measures based on daily and weekly returns. They are the absolute value of first-order daily return autocorrelation, [absolute value of AC(1)] and the absolute value of weekly-to-daily return variance ratio, [absolute value of 1 - VR(1,5)]. Both are associated with the magnitude of deviation of stock price from a random walk. Specifically, [absolute value of AC(1)] is estimated for each stock over each quarter by regressing daily returns on one-day lagged returns, and [absolute value of 1 - VR(1,5)] is estimated for each stock over each quarter as the absolute deviation of the ratio of weekly return variance to (five times) daily return variance from one, where the weekly returns are calculated from Wednesday to the next Tuesday to eliminate the weekend effect. All the daily and weekly returns are calculated by quote midpoints to eliminate potential bid-ask bounce.

Table III reports descriptive statistics of the five efficiency measures from 2002 to 2013. The average V(s)/V(p) of stocks in our sample is 0.007% and is decreasing over the sample period from 0.008% in early years to 0.004% in late years. [absolute value of AC(1)] and [absolute value of 1 - VR(1,5)] are relatively stable over time with average values of 0.105 and 0.222, respectively. Overall, the level of market efficiency does not change materially over the observation period.

B. Measures of Institutional Ownership and Trading

We define passive institutional ownership (PO) of a stock at the end of a quarter as the total shares held by any fund in the passive fund sample, scaled by total shares outstanding at the quarter end. Similarly, nonpassive institutional ownership (NPO) is defined as the total shares held by any institutional investor (who files a 13F form) that does not belong to the passive fund sample. (14) Therefore, PO represents the fraction of shares held by passive institutional investors, and NPO represents the fraction of shares held by active institutional investors.

Since the 13F database contains only positions held, we are not able to precisely estimate trading volumes of either passive or nonpassive institutional investors. Instead, we use changes in institutional holdings as a lower bound of institutional trading volume. Passive trading (PT) for each stock-quarter is estimated as the sum of absolute changes in passive holdings standardized by total shares outstanding, and nonpassive trading (NPT) is estimated as the sum of absolute changes in nonpassive holdings:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (4)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (5)

Table III reports the time-series average of quarterly cross-sectional means and standard deviations of ownership and trading variables. Average quarterly passive trading is 0.99% of total shares outstanding, which is equivalent to an annual turnover of 3.96%. In contrast, average quarterly nonpassive institutional trading is 19.92% of total shares outstanding, or an annual turnover of 79.68%. Average NPO (69.95%) is about 12 times average PO (6.16%), whereas average nonpassive trading is about 20 times average passive trading. As expected, nonpassive institutional investors trade much more than passive funds even after considering the difference in their ownership.

C. Control Variables

Chordia et al. (2008) find that liquidity stimulates arbitrage activities and enhances market efficiency. Four reverse measures for liquidity (ILLIQ) are used in the cross-sectional analysis: 1) trade-weighted relative effective spread (RES), estimated as two times the absolute distance between actual transaction price and corresponding quote midpoint, scaled by the quote midpoint, and weighted by trade size; 2) time-weighted relative quoted spread (RQS), estimated as the absolute distance between bid and ask price, scaled by the quote midpoint, and weighted by time intervals between two quotes; 3) Amihud (2002) price impact measure of illiquidity (Amihud), estimated as change in rate of stock returns per million dollar trade and adjusted by equity market inflation; and 4) Liu (2006) no-trade-day measure of illiquidity (Liu), estimated as number of zero-trade days in a quarter and adjusted by turnover ratio in that quarter. RES is preferred because it measures the actual (relative) transaction costs for traders. However, we recognize that RES may underestimate illiquidity because transactions are relatively infrequent during periods of low liquidity.

It is reasonable to expect that price efficiency is associated with stock size. Market value (MV) is measured as the number of shares outstanding multiplied by the closing price (CRSP items SHROUT and PRC) at the end of June of the previous year. We also control for dollar trading volume or turnover ratios, estimated as the dollar trading volume of a stock in a quarter scaled by total shares outstanding at the end of that quarter. Moreover, to control for the potential effect of price discreteness on price inefficiency, we control for stock price at the end of the previous quarter. In addition, we use number of analysts following (ANLY) as a proxy for information production. ANLY is measured as the total number of analysts that report quarterly earnings forecasts for a stock (IBES item FPI = 6).

III. Empirical Results

A. Impact of Indexed Ownership on PEAD

The following regression is estimated to study the relation between indexed ownership and PEAD:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (6)

Quarterly observations of earnings announcement are pooled across our stock sample from 2002 to 2013. Following Bartov et al. (2000) and Zhang (2012), among others, we use decile ranks of variables in our regression analysis. (15) In each calendar quarter, each of the independent variables is ranked into deciles based on the cutoff values from the previous quarter. (16) We then regress CARs on earnings surprises, an interaction term between earnings surprises and lagged indexed ownership (DPO), and an interaction term between earnings surprises and lagged nonpassive institutional ownership (DNPO). We choose four windows, (2, 5), (2, 15), (2, 30), and (2, 60), to better capture price drifts over short and long periods after an earnings announcement.

Control variables are constructed by interacting earnings surprises with the usual control variables such as market value of the stock at the end of the previous calendar year (DMV), share price at the end of the previous year (DPRC), average relative effective spread over the previous quarter (DRES), and dollar trading volume over the previous 12 months (DVOL). Because quarterly decile ranks of variables are used, any potential time fixed effects will automatically be controlled.

Table IV reports the main results. When earnings surprise is the only independent variable, CARs over all the four drift windows are positively and significantly associated with earnings surprise, clearly indicating the existence of PEAD. When PO and NPO (and other control variables) are included as independent variables, the positive relation between price drift after the earnings announcement and the earnings surprise is enhanced by PO while weakened by NPO. As the PEAD is generally considered an indication of investors' under-reaction to earnings news, the positive impact of indexed ownership on PEAD is consistent with our hypothesis that indexing reduces stock price efficiency. The negative impact of nonpassive institutional ownership on PEAD, in contrast, is consistent with findings in the literature that (nonpassive) institutional investors enhance stock price efficiency.

B. Alternative Specifications for PEAD Analysis

We adopt several alternative specifications as robustness tests. First, following Bartov et al. (2000), we use BM-adjusted CARs and size- and BM-adjusted CARs as alternative measures of PEAD. (17) These measures have a high fraction of missing values because of the nonavailability of BM ratios. Nevertheless, as shown in Panels A and B of Table V, the regression results are qualitatively unchanged when using these two measures. Next, we address the robustness of our findings to the definition of earnings surprise by using two alternative proxies of earnings surprise: SUE and APE. Both measures are widely used in the PEAD literature, so our findings based these two measures are easily comparable to previous studies. Panel C of Table V repeats our regression analysis but uses AFE to replace CAR(-2, 1). When earnings surprise is the only independent variable, CARs are always positively and significantly associated with earnings surprise, indicating the existence of PEAD. When PO and NPO are included as independent variables, the relation between postannouncement CAR and AFE is still positive, and is statistically significant for drift windows (2, 5), (2, 15), and (2, 60). NPO, in contrast, is negatively associated with postannouncement CAR. As shown in Panel D, using SUE generates qualitatively the same and quantitatively weaker results. The relation between postannouncement CAR and SUE is positive and significant for drift windows (2, 5) and (2, 15), but is not statistically significant for drift windows (2, 30) and (2, 60). Overall, our finding that indexed ownership enhances PEAD is robust to typical proxies of earnings surprise. Moreover, Panel E suggests that retaining only US common stocks in the sample has a negligible impact on our results. Finally, our findings are robust to alternative measures of illiquidity (results are not reported).

Another potential concern is the positive correlation in earnings surprises. Prior research, such as Bernard and Thomas (1990), has documented that earnings surprises show positive serial correlation for three quarters. Greater PEAD could thus be interpreted as either an indicator of delayed price response to earnings surprise or the result of forecasted positive earnings surprise in the subsequent quarter. If the second interpretation is true, the magnitude of PEAD may no longer be a valid proxy for price inefficiency. However, we believe that our regression results are not significantly affected by such a complication. If the magnitude of PEAD in one quarter is increased by the accurate forecast of future positive earnings surprise, the magnitude of PEAD in the following quarter)s) will be lowered. Overall, this may not significantly affect the regression coefficients.

C. Cross-Sectional Relation between Indexed Ownership and Price Efficiency

In addition to the PEAD analysis, we estimate a cross-section regression to directly investigate the relation between passive investments and stock price efficiency. We prefer a cross-sectional approach to a time-series approach because, as passive funds are indexed and index constitution changes slowly, time-series variation in passive ownership of an index stock is fairly small. In contrast, cross-sectional dispersions in passive ownership and trading are much greater. First, the S&P 500 constituents in our sample typically have much higher passive ownership than the non-S&P 500 stocks in the sample. Second, there is also some cross-sectional dispersion in passive ownership within the S&P 500 stocks, due to the presence of S&P 500 stocks in other indexes, such as the Russell and MSCI indexes, and the existence of impure index funds, such as closet indexers and enhanced indexers.

To formally examine the relation between indexed ownership and price efficiency, we estimate a multivariate cross-sectional regression following Fama and MacBeth (1973):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (7)

Specifically, one of the five price efficiency measures, [PE.sub.it], in each quarter is regressed on PO, NPO, and a lagged inefficiency measure from the previous quarter, while controlling for illiquidity (RES), market value of the stock (MV), stock price (Price) as of the end of the previous quarter, and turnover ratio (TO). All independent variables are lagged by one quarter to prevent potential reverse causality and to reduce the potential impact of passive ownership on contemporaneous explanatory variables. For example, if passive ownership has an effect on both price efficiency and liquidity, using contemporaneous illiquidity ([RES.sub.i,t]) as a control variable could lead to a downwardly biased coefficient on passive ownership ([[beta].sub.PO,t]). (18) Many control variables are log transformed to control for non-normality. The cross-sectional regression is estimated in each quarter of our sample period, and the time-series mean of the quarterly coefficient estimates is used for inference. The standard errors are adjusted for residual autocorrelation and heteroskedasticity by the Newey and West (1987) approach. To make the coefficient estimates in each quarter comparable across the entire sample period, we follow Kumar (2009) and standardize all dependent and independent variables to have zero-mean and unit standard deviation on a quarterly basis. (19,20)

Table VI reports the main results from the cross-sectional analysis. Controlling for nonpassive institutional ownership and other stock characteristics, each of the three inefficiency measures is positively and significantly related to passive ownership, indicating that indexed holdings are associated with greater deviation of stock price from a random walk. In contrast, nonpassive institutional ownership is negatively and significantly related to V(s)/V(p), indicating their potential role in enhancing market efficiency. The results are consistent with Boehmer and Kelley (2009) that (active) institutional investors contribute to efficient stock prices.

D. Endogeneity

A positive association between inefficiency measures and indexed fund ownership may, though unlikely, come from a self-selection bias rather than causality. If passive funds prefer to hold stocks with lower price efficiency, a cross-sectional negative relation between indexed holding and price efficiency is expected even if passive holdings generate no impact on price efficiency. Though this problem could be significant in studies of active institutional investors, it is likely to be less serious when studying indexed institutional investors whose trading is mostly driven by investor flows or index changes rather than preference to stocks with certain characteristics. Nevertheless, we adopt two approaches to preclude any possible self-selection bias. First, we exclude enhanced index funds and closet indexers from our passive fund sample, leaving only strictly passive index funds and ETFs, and repeat the cross-sectional regression. As presented in Panel A of Table VII, passive (strict index funds and ETFs) ownership is, again, associated with greater deviation of stock price from a random walk. Next, we regress changes in passive ownership on lagged changes in price inefficiency measures, controlling for lagged changes in passive ownership, effective spread, stock capitalization, turnover ratio, and two dummy variables indicating S&P 500 additions and deletions (SP_ADD and SP_DEL):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (8)

As reported in Panel B of Table VII, none of the five lagged inefficiency measure has a positive and significant relation to passive ownership. Therefore, there is no evidence of a self-selection bias.

E. Alternative Specifications of Cross-Sectional Analysis

1. Alternative Liquidity Measures

As suggested by Chordia et al. (2008), liquidity stimulates arbitrage, which enhances market efficiency. Controlling for liquidity in our cross-sectional regression is important for two reasons. First, institutional investors, especially nonpassive institutional investors, may have a preference for liquid stocks because of their lower transaction costs. Thus, institutional holdings may be relatively efficiently priced simply because they are more liquid. Fortunately, this is not likely to be an important concern for indexed institutional investors who aim to track a specific stock index instead of actively looking for liquid stocks. Second, institutional trading and holdings may have an impact on liquidity, which in turn affects price efficiency. We estimate regressions similar to Table VI but use alternative liquidity measures: relative quoted spread (RQS), the Amihud (2002) price impact measure (Amihud) based on daily price movements and trading volume, and the Liu (2006) no-trade-day measure of illiquidity (Liu). Panel A of Table VIII reports the coefficient estimates for PO, NPO, and the illiquidity measure in the three specifications. Consistent with Table VI, PO is positively and significantly associated with most of the three price inefficiency measures under alternative liquidity specifications, whereas NPO generally has negative coefficients. Therefore, our conclusion is robust to the use of alternative liquidity measures.

2. Alternative Specifications

For the first alternative specification, we reconsider exclusion of liquidity and turnover ratio as control variables. If passive ownership has a positive impact on liquidity, controlling for liquidity and turnover ratio could make its negative impact on price efficiency look more pronounced. Second, if S&P 500 index constituents generally have lower price efficiency for reasons other than passive funds, the negative relation between passive ownership and price efficiency could be just a coincidence without implying causality. To eliminate such a possibility, we add a control variable that equals to 1 when a stock is a member of the S&P 500 index at that quarter, and 0 otherwise. Third, following Boehmer and Kelley (2009), we add the lagged dependent variable as an additional control variable, so that our results are more comparable with Boehmer and Kelley (2009). Fourth, we use contemporaneous independent variables instead of lagged variables. Fifth, instead of using the $2 filter, we remove stocks with a stock price of less than $5 at the beginning of a quarter to further eliminate potential microstructure biases. Finally, we keep only US common stocks in our sample. As presented in Panels B and C of Table VIII, each of the above specifications generates results that are qualitatively and quantitatively similar to Table VI. Moreover, using share trading volume or dollar trading volume to replace turnover ratio or using raw variables instead of standardized variables leads to similar results.

IV. Indexing and Price Efficiency: Potential Explanations

We consider three explanations for our results. First, higher indexed ownership possibly implies a reduced incentive for index investors to acquire information. Consequently, it may reduce the production of information and raise the cost of informed arbitrage for active investors. Second, as suggested by De Long et al. (1990), informed investors may not be willing to take risky positions to correct mispricing due to the existence of noise trader risk. The presence of passive investors, who may create noise trader risk, may reduce the incentive and effectiveness of informed investors' effort of price discovery, leading to more persistent price inefficiency. Finally, indexed ownership may serve as a proxy for passive trading, which is mostly uninformed. In addition, index-related trading due to index changes is unidirectional, which may cause prices to move away from fundamentals (Harris and Gurel, 1986; Chen et al., 2004).

A. Reduced Information Production

Analyst following has been used in the literature as a source of information production about a firm. For example, Hong, Lim, and Stein (2000) find that analyst coverage accelerates the transmission of firm-specific information to the public, and Elgers, Lo, and Pfeiffer (2001) report that lower analyst coverage leads to a delayed price response. However, analyst following is not exogenous and may be affected by institutional ownership. O'Brien and Bhushan (1990) find that institutional demand for information could affect the number of analysts following a firm because institutional willingness to pay for information provides an incentive for analysts to follow that firm.

By contrast, indexed or passive shareholders have no desire to pay for information because they do not trade based on information generated by analysts. These investors rely on index providers such Standard & Poor's, Russell Investments, and MSCI to make changes to an index as necessary. They are interested in matching the index, not in earning abnormal returns. In addition, holding a basket of securities could reduce the incentive, or say necessity, of informed arbitrage because random mispricing in index stocks is likely to cancel out: lower returns from overpriced stocks are set off against higher returns from underpriced stocks. Therefore, passive shareholders holding indexed stocks may reduce analyst following and information production due to their lack of trading and limited need for new information.

To test the above hypothesis, we regress the number of analysts against passive ownership and nonpassive ownership based on all stocks in our sample:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

where MV is the market value of the stock estimated by the Fama and French (1992) approach, and TO is the turnover ratio over the previous year. As index additions are associated with a significant increase in number of analysts (Yu, 2008) as well as a significant increase in passive ownership, controlling for index membership is crucial to eliminate any false positive relation between passive ownership and number of analysts. Therefore, we add two dummy variables indicating current memberships in the S&P 500 index (SP500D) or the Russell 1000 index (R1000D).

Consistent with our conjecture, the number of analysts is negatively related to passive ownership in all three regression specifications in Table IX, implying that less information is being produced for firms with greater fractions of passive investors because these investors exhibit limited incentive for information acquisition. (21) Moreover, consistent with O'Brien and Bhushan (1990) and Brennan and Subrahmanyam (1995), the number of analysts is positively related to nonpassive ownership, indicating that nonpassive institutions indirectly facilitate information production.

B. Lowered Incentive of Arbitrage

The reduction in information production may be inconsequential for price discovery as long as there exists a group of smart investors with easy access to superior information because the negative impact of indexed investors on price efficiency could be largely offset by arbitrage activities of such informed traders. However, as suggested by De Long et al. (1990), informed investors may not be willing to take risky positions against noise traders (indexed investors) because of the existence of noise trader risk, so that the mispricing caused by noise traders could become even more extreme before its disappearance. The presence of passive investors, therefore, may reduce the incentive and effectiveness of informed investors' price discovery efforts. For example, Morck and Yang (2001) suggest that the increasing demand for S&P 500 stocks from passive funds induces ever-increasing overpricing in these stocks. If this finding is true, short selling is not a rational strategy even if informed investors recognize the existence of overpricing, as increasing demand from indexed investors will push index stocks to become more overpriced instead of converging to fundamental values, at least in the short term.

C. Consequences of Passive Trading

Similar to noise trading, passive trading conveys no information about individual stocks or industries. Passive funds trade based on flows initiated by investors who may, at best, convey market-wide information. Passive funds also trade around index changes, which is not only uninformed but can cause herding among passive investors and temporarily move prices away from fundamentals (Harris and Gurel, 1986; Lynch and Mendenhall, 1997; Chen et al., 2004). Though trading by passive investors has the potential to move prices, average passive trading volume is only 5% of average nonpassive trading volume as reported in Table III. Therefore, whether passive trading could generate a significant negative impact on price efficiency becomes an empirical question.

To evaluate the effect of passive ownership on price efficiency, PE, we examine the relation between passive trading on price efficiency using the following cross-sectional regression:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (10)

If the negative relation between passive ownership and price efficiency is caused by passive trading, the coefficient on [PT.sub.i,t] in Equation (10) should be positive and significant. We use contemporaneous trading instead of lagged trading because the impact of trading on stock prices should take place immediately, and as mentioned earlier, there is no evidence of endogeneity between passive ownership and price efficiency.

The results in Table X suggest no significant impact of PT on price efficiency. None of the three measures of price inefficiency has a positive and significant coefficient, but the variance ratio is negatively and significantly related to PT. In addition, PO is positively related to all three price inefficiency measures even after controlling for PT. These results suggest that passive trading does not seem to be a source of indexed investors' negative impact on price efficiency. Of course, our measure of passive trading, which is based on absolute changes in quarterly holdings, is likely to underestimate actual trading volume. More precise data on institutional trading volume, if available, may deliver more reliable results.

V. Conclusion

Index funds and indexed investing have been promoted by academics and practitioners over the last 50 years as an inexpensive and effective way to hold a diversified portfolio. As a result, the indexed investment sector has grown and today accounts for more than 7% of the total equity market and more than 29% of the US equity mutual fund sector. Although advantages of index investing are significant, there are negative externalities that passive investors impose on other market participants and the economy by making stock prices less efficient. Active traders produce information and trade to earn abnormal returns. In the process, they contribute to market efficiency. Index investors, in contrast, use these efficient prices to invest but without directly contributing to making those prices efficient. Their trades are primarily liquidity-driven, information-less trades motivated either by index changes or by investor flows.

Consistent with the above notion and based on a sample of large and liquid US stocks from 2002 to 2013, we find that indexing reduces informational efficiency of stock prices, and stocks with a higher level of indexing, as measured by passive ownership and passive trading, have less informative prices. We examine explanations for the decrease in price efficiency. We find that the relation is not explained by persistence in price efficiency, size, or endogeneity. The relation is robust to several intraday and daily price efficiency measures and alternate liquidity measures. We distinguish between the effects of indexed ownership and passive trading on price efficiency, and find that indexing affects price efficiency probably through reduced information acquisition and arbitrage. We also argue that indexed investors may indirectly lower price efficiency by reducing informed investors' incentive to arbitrage.

Appendix A: Selection of Index Funds and ETFs

In the first step, we pick up all funds that are classified as either an index fund or an ETF by the CRSP index fund and ETF indicators. To identify potential index funds and ETFs that are not marked by the indicators, we then screen fund names in the 13F database by keywords. For index funds, we look for the following keywords: "INDEX," "IND"IDX," INDE," "S&P 500 I," "S&P 5001," "S&P 400 I," "S&P 4001," "S&P 600 I," "S&P 6001," "S&P500IND," "S&P400IND," "S&P600IND," "RUSSELL 1000," "RUSSELL 2000," "RUSSELL 3000," and "VANGUARD." For ETFs, we look for the following keywords: "EXCHANGE TRADED," "EXCHANGE-TRADED," "ETF," "ISHARES," "POWERSHARES," "PROFUNDS," "SPDR S&P" "SPDR DOW," "SPDR DJ," "RYDEX," "SPA MG," "MARKET GRADER," and "QQQ."

To exclude bond funds, balanced funds, and funds that substantially hold derivatives from our sample, we remove funds with the following keywords in their names: "BOND," "INFLATION," "TREASURY," "BD," "LEHMAN," "BARCLAY," "OPTION," "HEDGE," "BALANCE," "ALLOC," "ASSET AL," "MULTI ASSET," and "PRINCIPAL PROTECTION,"

To exclude international funds, we require that the country code in 13F be either blank or "UNITED STATES." Furthermore, we remove funds with the following keywords in their names: "EURO," "FRANCE," "GERMAN," "CANADA," "CANADIAN," "HK," "JAPAN," "SING," "INDA," "INDU," "INDI," "INDO," "NETH," "SWITZ," "ITALY," "SPAIN," "ASIA," "GLOBAL," "NIKKEI," "FT-SE," "FTSE," "EM," "EMER," "BRIC," "EUR," "UK," "ENT," "AUSTRLA," "JAP," "CNDN," "CDN," "PACIF," "TRU," "LATIN," "EMER," "EMG," "EMRG," "LAT AME," "KINDOM," "CHILE," "JPN," "TURKEY," "DEVELOPE," "ENERGY," "BRAZIL," "KOREA," "BELG," "MALAYSIA," "SWEDEN," "AUSTRIA," "EMU," "SOUTH AFR," "TAIWAN," "INDONESIA," "STOXX," "THAI," "EX US," "INDEKS," "NIKKO," "TOKYO," "HANG SENG," "JPA," "SIMCAV" "TOPIX," "EAFE," "SPHINX," "WARBURG," "FOND," "TSX," "AMER EXEMPT," "TSE," "GOLDEN DRAGO," "AVENIR ALIZES," "FINORD INDEX AMERIQUE," and "ASX."

Finally, we manually check the investment objective and strategies of each fund from its prospectus and remove funds that are not passive equity funds. We remove funds with the following ID number in the 13F database: 526, 583, 697, 787, 792, 1366, 1469, 1588, 1884, 2231, 2373, 2468, 2518, 2637, 2676, 2875, 2882, 2887, 2965, 3300, 3300, 5040, 7679, 12065, 12065, 12096, 12707, 12760, 12877, 13000, 13143, 13235, 13256, 14266, 14499, 16561, 16570, 16598, 18009, 18252, 20075, 21002, 21888, 22461,22616, 23300, 23645, 26775, 28900, 28908, 29093, 34560, 36077, 36578, 36593, 45638, 47191,47224, 47959, 48003, 48160, 49335, 51143, 51527, 51652, 51894, 53700, 53705, 53800, 53900, 53933, 54440, 55633, 56500, 58099, 58852, 60100, 61423, 63079, 64362, 64635, 64635, 64803, 64804, 64805, 64816, 64960, 66970, 67996, 68391, 68392, 70032, 71917, 72523, 72986, 73268, 73290, 73424, 73695,73695, 74147, 74285, 75703, 75704, 75708, 76021, 76021, 76734, 77497, 77498, 77889, 77941, 78219, 78580, 79882, 80729, 80730, 80811, 80857, 80859, 81110, 81200, 83285, and 83380.

Appendix B: Estimation of Hasbrouck's (1993) Pricing Error

Intraday trade and quote data obtained from the NYSE TAQ database are used for estimation of as. Following Boehmer and Kelly (2009), we use quotes and trades that are within the regular trading hours (9:30 a.m.-4:00 p.m.) and ignore overnight price changes. A quote is removed if the ask price is lower than the bid price, if the bid price is lower than $0.10, or if the bid-ask spread is higher than 25% of the quote midpoint. To be eligible for estimation, a trade is required to have a value of zero in TAQ's CORR field; marked as "@," "@F," "F," "B," "E," "J," "K," or blank in TAQ's COND field; and have a positive trade size and price. A trade is removed if its price differs by more than 30% from the previous trade. We ignore the natural times but view transactions as untimed sequences. This approach is preferable because it gives more weight to periods with heavier price discovery activities, represented by more transactions, and uses information delivered from every single transaction. Following Flasbrouck (1993), we estimate the lower bound for [[sigma].sub.s] using a vector autoregression (VAR) model with five lags over the four-variable set [X.sub.t] = ([r.sub.t], [x.sub.t])', where [r.sub.t] = [p.sub.t] - [p.sub.t-1] and [x.sub.t] is a 3 x 1 vector of the following trade variables: 1) sign of trading direction that equals 1 if the transaction is buyer initiated, -1 if it is seller initiated, and 0 if it is a quote midpoint transaction; 2) signed trading volume; and 3) signed square root of trading volume. Following Harris (1989) and Lee and Ready (1991), we classify a trade as buyer initiated (seller initiated) if the transaction price is above (below) the prevailing quote midpoint. The inclusion of square root of trading volume aims to allow for concave dependencies in both [m.sub.t] and [s.sub.t]. In each month, we estimate L(s) for stocks that have at least 100 trades during that month. Specifically, the joint process of [X.sub.t] is described by a five-lag VAR model:

[X.sub.t] = [B.sub.1][X.sub.t-1] + [B.sub.2][X.sub.t-2] + [B.sub.3][X.sub.t-3] + [B.sub.4][X.sub.t-4] + [B.sub.5][X.sub.t-5] + [u.sub.t], (B. 1)

where [B.sub.k] is the 4 x 4 coefficient matrix for lag k, and [u.sub.t] is a 1 x 4 vector of zero-mean error terms with E ([u.sub.i,t], [U.sub.j,t]) = 0. The VAR model is then transformed into a five-lag approximation of vector moving average (VMA) representation: (22)

[X.sub.t] = [u.sub.t] + [A.sub.1][u.sub.t-1] + [A.sub.2][u.sub.t-2] + [A.sub.3][u.sub.t-2] + [A.sub.4][U.sub.t-4] + [A.sub.5][u.sub.t-5]. (B.2)

Variance of pricing error is expressed by:

[[sigma].sub.s.sup.2] =[4.summation over (j=0)] [[[gamma].sub.1,j] [[gamma].sub.2,j] [[gamma].sub.3,j] [[gamma].sub.4,j]] Cov(u) [[[gamma].sub.1,j] [[gamma].sub.2,j] [[gamma].sub.3,j] [[gamma].sub.4,j]], (B.3)

where

[[gamma].sub.i,j] = - [5.summation over (k=j+1)] [A.sub.k,1,i] (B.4)

and Cov(m) is the residual covariance matrix from the VAR model. We use the average of the monthly estimates of [[sigma].sub.s.sup.2] in a quarter as the pricing error variance of that quarter.

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Nan Qin and Vijay Singal *

We thank participants at the 2013 Financial Management Association annual meetings and at Virginia Tech for comments and suggestions.

* Nan Qin is an Assistant Professor of Finance from the Luter School of Business at Christopher Newport University in Newport News, VA. Vijay Singal is the J. Gray Ferguson Professor of Finance from the Pamplin College of Business at Virginia Tech in Blacksburg, VA.

(1) Closet indexers are "active" mutual funds that actually track an index.

(2) Source: 2014 ICI Factbook. The total amount in broad-based equity ETFs ($762 billion) and US equity index mutual funds ($1,213 billion) was $1,975 billion. The total amount in US equity mutual funds and ETFs was $6,694 billion, comprising $964 billion in ETFs and $5,730 billion in mutual funds.

(3) Shu (2007) finds that price anomalies, including return momentum, PEAD, and value premium, are much stronger in stocks with relatively low institutional trading volume.

(4) Details of the keyword search are reported in Appendix A.

(5) Theoretically, AS for a pure index fund with very low tracking error should be close to zero. However, as 13F filings generally ignore small holdings, the estimated AS will be higher than the actual value. The average estimate of AS over the life of an index fund in our sample could be as large as approximately 20%.

(6) We do not require the beta to be close to 1 because a passively inclined fund may intentionally maintain a beta different from 1.00 by using leverage or by holding cash.

(7) Balanced funds, international funds, and bond funds are identified mainly by their names and country code provided in the 13F database. We also manually screen the sample to remove any of these funds. We check the fund prospectus for fund objective and strategies. Typically, a fund is removed from the sample when its investment strategy states that the manager actively chooses undervalued stocks.

(8) This number is smaller than the actual number of US equity ETFs for several reasons. First, we exclude ETFs that hold a significant percentage of international equities. Second, ETFs that are reported jointly with index mutual funds are identified as index funds instead of ETFs in the sample. An example is Vanguard 500 Index Funds, which has both investor shares and ETF shares. Third, the 13F database does not provide an ETF indicator, and the ETF indicators from CRSP are not able to identify all ETFs in the 13F database because the MFLINKS data set does not provide a complete linkage between the CRSP mutual fund database and the 13F database.

(9) A sample with only S&P 500 stocks has relatively low cross-sectional dispersion in passive ownership, as all S&P 500 index funds will hold each S&P stock in the same proportion.

(10) All market caps are as of December 31,2013.

(11) At the beginning of each quarter, we sort all stocks in our sample into deciles by their size, which is estimated by the same approach as Fama and French (1992). We then construct 10 value-weighted benchmark portfolios and use their returns to estimate CARs of the stocks within the same size deciles at that quarter. We also use book-to-market (BM)-adjusted and size- and BM-adjusted CARs for robustness tests.

(12) A detailed analysis is provided in Appendix B.

(13) Boehmer, Saar, and Yu (2005) use this measure to study the effect of the increased pretrade transparency on stock price efficiency. Boehmer and Kelley (2009) use this measure to study the effect of institutional ownership on stock price efficiency. Boehmer and Wu (2012) use this measure to examine the relation between short selling and the price discovery process. Hotchkiss and Ronen (2002) use a variant of this measure, MQ = 1 - 2[[sigma].sup.2.sub.s]/[[sigma].sup.2.sub.p], to examine the informational efficiency of corporate bond price.

(14) Institutional holdings are obtained from the 13F database, and data on total shares outstanding are obtained from the CRSP stock files. For stock-quarters that report more institutional holdings than total shares outstanding, we set institutional ownership to 100% and calculate PO and NPO accordingly, provided the institutional ownership in the previous or the following quarter is above 80%. Otherwise, we consider it to be an invalid observation.

(15) The use of decile ranks has become typical methodology in the PEAD literature and makes our results more comparable to prior work.

(16) Each variable takes the values of 0.05 for the smallest decile and 0.95 for the largest decile.

(17) Estimation of BM-adjusted CARs is similar to that of size-adjusted CARs. To estimate size- and BM-adjusted CARs, we sort all stocks in our sample into quintiles by their size and BM ratios at the beginning of each quarter, and construct 5x5 value-weighted benchmark portfolios. We then use their returns to estimate CARs of the stocks within the same size and BM quintiles at that quarter.

(18) Using contemporaneous variables leads to qualitatively and quantitatively similar regression results.

(19) The results are similar without variable standardization.

(20) Several dependent and independent variables suffer from heteroskedasticity over the sample period. There are noticeable increases in the cross-sectional standard deviations of PO and PT, and decreases in the standard deviations of the normalized pricing error volatility, V(s)/V(p), and illiquidity measures, RES, Amihud, and Liu. Because the cross-sectional volatility of the dependent variables (i.e., V(s)/V(p)) are moving in the opposite direction compared to the volatility of the independent variables (i.e., PO and PT), coefficient estimates of PO and PT tend to have larger magnitudes in early years than in recent years, leading to the Fama and MacBeth (1973) regression results being more influenced by early years.

(21) Yu (2008) finds that analyst coverage is negatively associated with earnings management because, in addition to their role in information production, analysts serve as external monitors. Therefore, lower analyst coverage induced by indexing may encourage the firms to intentionally create information asymmetry by earnings management, resulting lower price efficiency.

(22) VMA lags beyond five are assumed to have little impact and are ignored to simplify the estimation process. As mentioned by Hasbrouck (1993), more lags generally increase the estimates of pricing error variance but make little change in the cross-sectional ranking.

Table I. Summary Statistics of Passive Funds Sample The sample of passive funds includes a total of 591 US equity index funds, enhanced index funds, exchange-traded funds (ETFs), and closet indexers over the sample period 2002-2013. Values of passive funds and institutional investors are estimated from their reported (in 13F files) holdings and the corresponding stock price. Institutional investors include all institutions that file quarterly 13F reports. Column (2) reports the total capitalization of the US equity market (obtained from the Center for Research in Security Prices [CRSP]). Column (3) shows the total capitalization of US equity mutual funds and ETFs (obtained from Investment Company Institute). Column (4) reports the total number of funds in the sample each year, and Column (5) reports the total value of passive fund holdings (obtained from Thomson Reuters and CRSP Mutual Funds). Column (6) reports the total value of holdings of US institutional investors who file 13F forms. Column (7) reports the market share of the passive fund sample, measured as total passive fund holdings divided by total US equity market capitalization. Column (8) reports the fraction of market capitalization of all passive funds in the total capitalization of the US equity market (Columns (5)/(2)). Column (9) presents the percentage of passive funds in US mutual fund and ETF sector (Columns (5)/(3)). Column (10) reports the nonpassive institutional share of the US equity market (Columns (6)/(2) minus (8)). Column (11) contains the percent equity held by noninstitutional holders such as insiders and individuals (1 minus Columns (8) and (10)). Year Size of Size of No. of Total Total US Equity US Equity Passive Value of Value of Market ($ Mutual Funds Passive Inst. billion) Funds and Funds ($ Investors ETFs ($ billion) ($ billion) billion) (1) (2) (3) (4) (5) (6) 2002 11026.99 2414.81 260 309.11 6682.16 2003 14577.77 3320.30 261 443.34 9190.98 2004 16449.40 3906.15 279 586.04 10603.06 2005 17369.92 4260.92 279 614.94 11838.86 2006 19599.79 4890.89 271 735.51 13810.55 2007 20190.51 5204.80 426 830.09 14867.53 2008 12128.88 3135.86 461 619.45 8496.12 2009 15804.56 4033.89 432 822.73 10939.38 2010 18490.48 4626.20 416 1007.63 12770.74 2011 17886.66 4470.97 405 1042.10 12031.24 2012 20352.31 4965.17 390 1265.24 13535.10 2013 26285.95 6776.20 377 1864.70 18110.28 Year % PO of % Market Fraction % Market Other S&P 500 Cap of of Passive Cap of Investors Stocks Passive Funds in Nonpassive as % of Funds US Equity Inst. market Mutual Funds Investors Cap and ETFs (1) (7) (8) (9) (10) (11) 2002 4.54% 2.80% 12.80% 57.80% 39.40% 2003 4.86% 3.04% 13.35% 60.01% 36.95% 2004 5.07% 3.56% 15.00% 60.90% 35.54% 2005 5.01% 3.54% 14.43% 64.62% 31.84% 2006 5.19% 3.75% 15.04% 66.71% 29.54% 2007 6.02% 4.11% 15.95% 69.52% 26.36% 2008 8.55% 5.11% 19.75% 64.94% 29.95% 2009 7.85% 5.21% 20.40% 64.01% 30.78% 2010 8.31% 5.45% 21.78% 63.62% 30.93% 2011 9.92% 5.83% 23.31% 61.44% 32.74% 2012 8.50% 6.22% 25.48% 60.29% 33.50% 2013 9.62% 7.09% 27.52% 61.80% 31.10% Table II. Summary Statistics of the Stocks Sample On average, the sample has 400 S&P 500 stocks and 130 non-S&P 500 stocks in each quarter. Panel A reports the composition of the sample. The sample consists of US common stocks (share codes 10 and 11), eligible foreign stocks (share code 12), real estate investment trusts (share codes 18 and 48), American depositary receipts (share code 31), and units (share code 72). Panel B shows average number and size of sample stocks by year. Panel A. Composition of the Sample Share S&F 500 Stocks Code Percentage Mean Median Size Size ($ billion) ($ billion) 10 0.02% 11.73 13.42 11 94.57% 20.65 10.99 12 2.49% 20.39 12.13 18 1.88% 11.86 9.97 31 0.01% 42.47 42.47 48 0.82% 11.56 11.78 72 0.22% 24.52 23.38 Share Non-S&F 500 Stocks Code Percentage Mean Median Size Size ($ billion) ($ billion) 10 0.02% 4.44 4.44 11 93.81% 5.80 4.46 12 2.82% 26.15 24.93 18 2.08% 8.05 7.47 31 0.03% 26.78 26.78 48 0.99% 4.96 4.46 72 0.26% 6.15 5.94 Panel B. Number and Size of Sample Stocks in Each Quarter Year S&P 500 Stocks Number Mean Median of Size Size Stocks ($ billion) ($ billion) 2002 394 15.42 7.84 2003 400 15.34 8.21 2004 400 18.41 10.33 2005 401 20.24 11.67 2006 399 23.14 13.34 2007 402 24.74 14.08 2008 401 19.84 10.26 2009 399 15.86 7.93 2010 401 19.17 10.29 2011 401 21.01 11.58 2012 402 23.56 12.74 2013 401 28.07 15.51 Year Non-S&P 500 Stocks Total Number Mean Median Number Mean of Size Size of Size Stocks ($ billion) ($ billion) Stocks ($ billion) 2002 158 4.02 3.08 551 12.14 2003 156 4.29 3.29 556 12.22 2004 158 5.59 4.12 558 14.78 2005 151 6.63 4.85 552 16.53 2006 139 7.22 5.07 538 19.03 2007 119 8.54 5.88 520 21.03 2008 134 6.35 4.18 535 16.55 2009 133 4.58 3.24 532 13.09 2010 96 6.20 4.73 497 16.67 2011 95 8.00 5.62 497 18.53 2012 114 8.40 6.08 515 20.22 2013 109 10.42 7.78 510 24.29 Table III. Descriptive Statistics of Price Efficiency Measures and Control Variables The quarterly sample includes S&P 500 constituents and non-S&P 500 stocks that meet the minimum requirements for size and turnover ratio. PO is the fraction of shares outstanding of a stock owned by passive funds. NPO is the fraction of shares outstanding of a stock owned by nonpassive institutional investors. PT is the sum of absolute passive holding changes of a stock during a quarter scaled by the total shares outstanding. NPT is the sum of absolute nonpassive institutional holding changes of a stock during a quarter scaled by the total shares outstanding. F(s) is the pricing error of Hasbrouck (1993) estimated over a quarter and V(s)-V(p) is the relative pricing error (scaled by standard deviation of log price, V(p), over that quarter). AC(1) is the first-order autocorrelation of daily stock return. KR(l,5) is the ratio of weekly stock return variance to five times daily stock return variance. CAR(-2, 1) is the cumulative abnormal return for a four-day window around an earnings announcement. CAR(2, 60) is the cumulative abnormal return from the 2nd to the 60th days after an earnings announcement. SUE is the standardized unexpected earnings. AFE is the standardized analyst earnings forecast error. RES is size-weighted relative effective spread, and RQS is time-weighted relative quote spread. Amihud is the Amihud (2002) price impact measure of illiquidity. Liu is the Liu (2006) no-trade-day measure. MV is the market value of stock. TO is the turnover ratio of the previous quarter. PRC is the share price at quarter end. ANLY is number of analysts. 2002-2013 Mean Std. Dev. Average number of stocks per quarter 530 Measures of efficiency V(s)/V(p) (x [10.sup.-3]) 0.07 0.09 [absolute value of AC(1)] 0.10 0.08 [absolute value of 1-VR(1,5)] 0.22 0.15 Ownership and trading PO 6.16% 2.65% NPO 69.95% 14.17% Quarterly PT 0.99% 1.21% Quarterly NPT 19.92% 12.03% Post-earnings-ann. drift CAR(-2, 1) 0.15% 6.14% CAR(2, 60) 0.13% 12.19% SUE -0.01% 2.47% AFE 0.07% 0.41% Other variables Illiquidity RES 0.17% 0.13% RQS 0.67% 0.44% Amihud (x [10.sup.-2]) 1.22 1.32 Liu (x [10.sup.-5]) 1.34 0.74 MV ($ billion) 16.76 23.16 PRC ($) 47.42 49.96 TO (/quarter) 69.07% 48.69% ANLY 14.83 7.67 2002-2007 Mean Std. Dev. Average number of stocks per quarter 546 Measures of efficiency V(s)/V(p) (x [10.sup.-3]) 0.08 0.10 [absolute value of AC(1)] 0.11 0.08 [absolute value of 1--VR(1,5)] 0.22 0.16 Ownership and trading PO 4.56% 1.57% NPO 69.37% 15.01% Quarterly PT 0.73% 0.89% Quarterly NPT 19.75% 12.12% Post-earnings-ann. drift CAR(-2, 1) 0.24% 5.83% CAR(2, 60) -0.01% 12.01% SUE 0.10% 2.10% AFE 0.05% 0.36% Other variables Illiquidity RES 0.20% 0.15% RQS 0.72% 0.45% Amihud (x [10.sup.-2]) 1.39 1.44 Liu (x [10.sup.-5]) 1.61 0.81 MV ($ billion) 15.61 22.03 PRC ($) 43.90 36.28 TO (/quarter) 57.55% 43.90% ANLY 13.28 7.11 2008-2013 Mean Std. Dev. Average number of stocks per quarter 514 Measures of efficiency V(s)/V(p) (x [10.sup.-3]) 0.04 0.07 [absolute value of AC(1)] 0.10 0.08 [absolute value of 1--VR(1,5)] 0.23 0.15 Ownership and trading PO 7.95% 2.45% NPO 70.60% 13.14% Quarterly PT 1.28% 1.43% Quarterly NPT 20.12% 11.92% Post-earnings-ann. drift CAR(-2, 1) 0.04% 6.47% CAR(2, 60) 0.30% 12.39% SUE -0.15% 2.82% AFE 0.08% 0.47% Other variables Illiquidity RES 0.13% 0.10% RQS 0.62% 0.43% Amihud (x [10.sup.-2]) 1.02 1.14 Liu (x [10.sup.-5]) 1.04 0.50 MV ($ billion) 18.04 24.29 PRC ($) 51.31 61.43 TO (/quarter) 81.84% 50.53% ANLY 16.56 7.89 Table IV. Impact of Passive Ownership on Post-Earnings-Announcement Drift Observations of quarterly earnings announcements are pooled from 2002 to 2013 based on a stock sample including S&P 500 constituents and non-S&P 500 stocks that meet the minimum requirements for size and turnover ratio. The cumulative abnormal returns (CAR) from the 2nd to the 5th, 15th, 30th, and 60th days after an earnings announcement are regressed on earnings surprise and its interaction term with other variables. Abnormal returns are defined as size-adjusted returns. The quarterly decile rank of cumulative abnormal return for a four-day window around an earnings announcement, DCAR(-2, 1), is used as proxy for earnings surprise. DPO, DNPO, DMV, DPRC, DRES, and DVOL are the decile portfolios of PO, NPO, MV, PRC, RES and VOL of the prior quarter, respectively. All decile portfolios are scaled to range between zero and one. Dependent CAR CAR CAR CAR Variable (2, 5) (2, 15) (2, 30) (2, 60) (1) (2) (3) (4) Panel A. Independent Variable Includes Only Announcement Returns DCAR(-2, 1) 0.25 *** 0.50 *** 1.03 *** 1 22 t-statistic 3.21 3.76 5.45 4.35 Adj. [R.sup.2] 0.000 0.001 0.001 0.001 N 23,470 23,453 23,433 23,242 Panel B. Institutional Ownerships Added to Control Variables DCAR(-2, 1) 0.16 0.44 ** 1 27 t-statistic 1.27 1.99 3.74 2.78 DCAR(-2, 1) * DPO 0.38 *** 0.71 *** 0.54 * 1.02 ** t-statistic 3.16 3.38 1.85 2.33 DCAR(-2, 1) * DNPO -0.22 * -0.57 *** -0.73 ** -1.07 ** t-statistic -1.76 -2.62 -2.39 -2.36 Adj. [R.sup.2] 0.001 0.001 0.002 0.001 N 23,470 23,453 23,433 23,242 Panel C. Stock Characteristics Also Added as Control Variables DCAR(-2, 1) 0.40 ** 0.92 *** 1.23 *** 0.84 t-statistic 2.15 2.79 2.66 1.22 DCAR(-2, 1) * DPO 0.36 *** 0 73 0.65 ** 1.16 *** t-statistic 2.96 3.46 2.18 2.60 DCAR(-2, 1) * DNPO -0.19 -0.59 ** -0.84 *** -1.05 ** t-statistic -1.42 -2.56 -2.58 -2.17 DCAR(-2, 1) * DMV 0.08 -0.02 -0.54 0.51 t-statistic 0.39 -0.04 -1.06 0.67 DCAR(-2, 1) * DPRC -0.01 -0.08 -0.19 -0.05 t-statistic -0.07 -0.34 -0.62 -0.11 DCAR(-2, 1) * DRES -0.18 -0.14 0.42 0.41 t-statistic -1.49 -0.65 1.39 0.92 DCAR(-2, 1) * DVOL -0.03 -0.51 0.34 -0.63 t-statistic -0.16 -1.34 0.63 -0.79 DCAR(-2, 1) * DANLY -0.29 * -0.10 -0.19 0.40 t-statistic -1.91 -0.38 -0.52 0.73 Adj. [R.sup.2] 0.001 0.002 0.002 0.001 N 23,330 23,313 23,294 23,104 *** Significant at the 0.01 level. ** Significant at the 0.05 level. * Significant at the 0.10 level. Table V. Robustness Tests on Post-Earnings-Announcement Drift Observations of quarterly earnings announcements are pooled from 2002 to 2013. DCAR, DRET, DPO, DNPO, DMV, DPRC, DRES, DVOL, DAFE, and DSUE are the decile portfolios of CAR, RET, PO, NPO, MV, PRC, RES, VOL, AFE, and SUE of the prior quarter, respectively. All of the decile portfolios are scaled to range between zero and one. In Panel A, abnormal return is defined as book-to-market-adjusted returns. In Panel B, abnormal return is defined as size-and book-to-market- adjusted returns. In Panel C, analyst forecast error (AFE) is used as proxy for earnings surprise. In Panel D, standardized unexpected earnings (SUE), defined as seasonal difference in announced earnings standardized by stock price at the end of the previous fiscal quarter, is used as proxy for earnings surprise. In Panel E, only US common stocks are included in the sample. Dependent CAR (2, 5) CAR (2, 15) Variable (1) (2) (3) (4) Panel A. CAR Based on Book-to-Market-Adjusted Returns DCAR(-2, 1) 0.20 ** 0.41 ** 0.44 *** 1.02 *** t-statistic 2.50 2.10 3.19 3.03 DCAR(-2, 1) * DPO 0.35 *** 0.71 *** t-statistic 2.78 3.28 DCAR(-2, 1) * DNPO -0.22 -0.48 ** t-statistic -1.62 -2.02 Panel B. CAR Based on Size- and Book-to-Market-Adjusted Returns DCAR(-2, 1) 0.24 *** 0.46 ** 0.50 *** 1.06 *** t-statistic 3.03 2.38 3.62 3.12 DCAR(-2, 1) * DPO 0.30 ** 0.68 *** t-statistic 2.43 3.11 DCAR(-2, 1) * DNPO -0.14 -0.42 * t-statistic -1.03 -1.74 Panel C. Earnings Surprise Measured by AFE DAFE 0.52 *** 0.92 *** 0.60 *** 1 24 t-statistic 6.88 4.97 4.50 3.81 DAFE * DPO 0.26 ** 0.50 ** t-statistic 2.12 2.36 DAFE * DNPO -0.13 -0.63 *** t-statistic -0.97 -2.72 Panel D. Earnings Surprise Measured by SUE DSUE 0.43 *** 0.55 *** 0.41 *** 1.07 *** t-statistic 5.61 3.01 3.08 3.32 DSUE * DPO 0.35 *** 0.47 ** t-statistic 2.91 2.20 DSUE * DNPO -0.06 -0.59 ** t-statistic -0.46 -2.58 Panel E. Retain Only US Common Stocks DCAR(-2, 1) 0.24 *** 0.29 0.47 *** 0.74 ** t-statistic 3.06 1.51 3.39 2.20 DCAR(-2, 1) * DPO 0.43 *** 0.75 *** t-statistic 3.51 3.46 DCAR(-2, 1) * DNPO -0.13 -0.51 ** t-statistic -0.99 -2.14 Dependent CAR (2, 30) CAR (2, 60) Variable (5) (6) (7) (8) Panel A. CAR Based on Book-to-Market-Adjusted Returns DCAR(-2, 1) 0.85 *** 1.49 *** 0.73 ** 0.81 t-statistic 4.39 3.13 2.53 1.15 DCAR(-2, 1) * DPO 0.46 1.00 ** t-statistic 1.51 2.19 DCAR(-2, 1) * DNPO -0.60 * -0.68 t-statistic -1.80 -1.37 Panel B. CAR Based on Size- and Book-to-Market-Adjusted Returns DCAR(-2, 1) 1.03 *** 1.55 *** 0.87 *** 0.55 t-statistic 5.28 3.25 2.98 0.77 DCAR(-2, 1) * DPO 0.38 0.97 ** t-statistic 1.24 2.11 DCAR(-2, 1) * DNPO -0.40 -0.49 t-statistic -1.19 -0.98 Panel C. Earnings Surprise Measured by AFE DAFE 0.64 *** 1.06 ** 0.71 ** 0.04 t-statistic 3.42 2.34 2.56 0.06 DAFE * DPO 0.48 1.31 *** t-statistic 1.61 2.95 DAFE * DNPO _Q QJ -0.99 ** t-statistic -2.80 -2.04 Panel D. Earnings Surprise Measured by SUE DSUE 0.47 ** 0.89 ** 0.80 *** 0.26 t-statistic 2.48 1.97 2.83 0.39 DSUE * DPO 0.35 0.70 t-statistic 1.17 1.59 DSUE * DNPO -0.88 *** -1.19 ** t-statistic -2.72 -2.46 Panel E. Retain Only US Common Stocks DCAR(-2, 1) 0.97 *** 1.12 ** 1.12 *** 0.87 t-statistic 5.02 2.37 3.86 1.23 DCAR(-2, 1) * DPO 0.54 * 0.93 ** t-statistic 1.77 2.04 DCAR(-2, 1) * DNPO -0.84 ** -1.19 ** t-statistic -2.53 -2.40 *** Significant at the 0.01 level. ** Significant at the 0.05 level. * Significant at the 0.10 level. Table VI. Cross-Sectional Relation between Passive Ownership and Price Efficiency The quarterly sample includes S&P 500 constituents and non-S&P 500 stocks that meet the minimum requirements for size and turnover ratio from 2002 to 2013. Measure of price efficiency is regressed on lagged passive ownership (PO) and control variables. Following the Fama and MacBeth (1973) approach, cross-sectional regressions are estimated in each quarter and the mean coefficients are reported. V(s) is the pricing error of Hasbrouck (1993) estimated over a quarter and V(s)/ V(p) is the relative pricing error (scaled by standard deviation of log price, V(p), over that quarter,). AC(1) is the first-order autocorrelation of daily stock return. VR(1,5) is the ratio of weekly stock return variance to five times daily stock return variance. [PO.sub.t-1] is the percentage of shares outstanding held by our passive fund sample at the end of the previous quarter. [NPO.sub.t- 1] is the percentage of shares outstanding held by nonpassive institutional investors at the end of the previous quarter. [RES.sub.t-1] the trade-weighted relative effective spread estimated from the previous quarter. [TO.sub.t-1] is the turnover ratio over the previous quarter. MV is the market value estimated by the approach of Fama and French (1992). [PRC.sub.t-1] is the stock price at the end of the previous quarter. All variables are standardized to have zero-mean and unit standard deviation in each quarter. The significance level is based on the time-series variation in the quarterly regression coefficients over the sample period. The standard errors are adjusted for residual autocorrelation and heteroskedasticity based on Newey and West (1987). Dependent Ln[V(s) [absolute value [absolute value Variable /V(p)] of AC(1)] of 1 - VR (1,5)] Intercept 0.00 0.00 * 0.00 ** t-statistic -0.58 -1.89 -2.07 [PO.sub.t-1] 0.04 *** 0.03 ** 0.03 *** t-statistic 2.79 2.52 2.73 [NPO.sub.t-1] -0.12 *** -0.01 -0.01 t-statistic -9.62 -0.65 -0.65 [Ln[RES.sub.t-1]] 0.08 0.00 -0.02 *** t-statistic 1.64 -0.22 -3.10 Ln[MV] 0.04 * -0.01 -0.02 ** t-statistic 2.00 -1.19 -2.53 Ln[[PRC.sub.t-1]] -0.54 *** -0.01 -0.01 t-statistic -22.51 -0.97 -0.73 Ln[[TO.sub.t-1]] -0.18 *** -0.05 *** -0.04 *** t-statistic -7.64 -3.53 -3.93 Adj. [R.sup.2] 0.357 0.026 0.023 Average N 529 530 530 *** Significant at the 0.01 level. ** Significant at the 0.05 level. * Significant at the 0.10 level. Table VII. Endogeneity The quarterly sample includes S&P 500 constituents and non-S&P 500 stocks that meet the minimum requirements for size and turnover ratio from 2002 to 2013. V(s) is the pricing error of Hasbrouck (1993) estimated over a quarter, and V(s)-V(p) is the relative pricing error (scaled by standard deviation of log price, V(p), over that quarter). AC(1) is the first-order autocorrelation of daily stock return. VR(1,5) is the ratio of weekly stock return variance to five times daily stock return variance. [PO.sub.t-1] is the percentage of shares outstanding held by our passive fund sample at the end of the previous quarter, and [DELTA][PO.sub.T-1] is its change from quarters (t-2) to (t-1). [NPO.sub.t-1] is the percentage of shares outstanding held by nonpassive institutional investors at the end of the previous quarter, and [DELTA][NPO.sub.t-1] is its change from quarters (t-2) to (t-1). [Efficiency.sub.t-1] is the lagged price inefficiency measure. [MV.sub.t-1] is the stock's market value at the end of the previous quarter. SP_ADD equals 1 if the stock is added to the S&P 500 index at that quarter, and 0 otherwise. SP_DEL equals 1 if the stock is deleted from the S&P 500 index at that quarter, and 0 otherwise. Panel A repeats the cross-sectional regression in Table III but includes only pure index funds and exchange-traded funds (ETFs) in the passive fund sample. Coefficients of control variables are omitted for brevity. Panel B presents the results of a cross- sectional regression of change in PO on lagged change in price efficiency measures and other control variables. The significance level is based on the time-series variation in the quarterly regression coefficients over the sample period. The standard errors are adjusted for residual autocorrelation and heteroskedasticity based on Newey and West (1987). Panel A. Passive Fund Sample Includes Only Pure Index Funds and ETFs Dependent Ln[V(s) [absolute value [absolute value Variable /V(p)] of AC (1)] of 1 - VR (1,5)] [PO.sub.t-1] 0.06 *** 0.04 ** 0.04 ** t-statistic 3.65 2.40 2.35 [NPO.sub.t-1] -0.12 *** -0.01 0.00 t-statistic -9.44 -0.98 -0.52 Panel B. Cross-Sectional Determinants of Change in PO Measure of ALn[V(s) [DELTA [DELTA][absolute Price Inefficiency /V(p)] [absolute value of value of 1 - VR (1,5)] AC (1)] Intercept -0.02 *** -0.02 *** -0.02 *** t-statistic -4.43 -4.54 -4.51 [DELTA] -0.01 0.00 0.01 [Inefficiency.sub.t-1] t-statistic -1.03 0.15 0.81 [DELTA][PO.sub.t-1] -0.10 *** -0.10 *** -0.09 *** t-statistic -4.78 -4.76 -4.70 [DELTA]Ln[[RES.sub.t-1]] 0.00 0.00 0.00 t-statistic 0.17 0.36 0.36 [DELTA]Ln[[MV.sub.t-1]] 0.01 0.01 0.01 t-statistic 1.07 0.95 1.06 [DELTA]Ln[[TO.sub.t-1]] 0.00 0.00 0.00 t-statistic -0.20 0.18 0.21 SP_ADD 1.53 *** 1.53 *** 1.53 *** t-statistic 8.71 8.78 8.82 SP_DEL -0.96 *** -0.96 *** -0.94 *** t-statistic -3.78 -3.84 -3.67 Adj [R.sup.2] 0.127 0.124 0.124 N 503 503 503 *** Significant at the 0.01 level. ** Significant at the 0.05 level. Table VIII. Robustness Tests on Cross-Sectional Analysis The quarterly sample includes S&P 500 constituents and non-S&P 500 stocks that meet the minimum requirements for size and turnover ratio from 2002 to 2013. The same Fama-MacBeth (1973) regressions as in Table III are estimated, but coefficients of control variables are omitted for brevity. F(s) is the pricing error of Hasbrouck (1993) estimated over a quarter, and V(s)-V(p) is the relative pricing error (scaled by standard deviation of log price, V(p), over that quarter). AC(1) is the first-order autocorrelation of daily stock return. VR(1,5) is the ratio of weekly stock return variance to five times daily stock return variance. RQS is the time-weighted relative quoted spread. Amihud is the Amihud (2002) price impact measure of illiquidity. Liu is the Liu (2006) no-trade-day measure. Panel A presents results by different liquidity measures. Panel B presents results by dropping the liquidity control variable. Panel C tests several different specifications. All variables are standardized to have zero-mean and unit standard deviation in each quarter. The significance level is based on the time-series variation in the quarterly regression coefficients over the sample period. The standard errors are adjusted for residual autocorrelation and heteroskedasticity based on Newey and West (1987). Dependent Ln[V(s) [absolute value [absolute value Variable /V(p)] of AC (1)] of 1 - VR (1,5)] Panel A. Alternative Liquidity Measures [PO.sub.t-1] 0.02 * 0.03 ** 0.03 *** t-statistic 1.84 2.23 2.75 [NPO.sub.t-1] -0.12 *** -0.01 -0.01 t-statistic -9.90 -0.51 -0.57 Ln[[RQS.sub.t-1]] -0.03 -0.02 ** -0.01 t-statistic -0.65 -2.26 -1.56 [PO.sub.t-1] 0.00 0.02 * 0.03 ** t-statistic 0.10 1.70 2.45 [NPO.sub.t-1] -0.11 *** -0.01 0.00 t-statistic -9.10 -0.65 -0.53 Ln[[Amihud.sub.t-1]] -0.46 *** -0.12 *** -0.10 *** t-statistic -8.99 -4.69 -3.46 [PO.sub.t-1] 0.04 *** 0.03 *** 0.04 *** t-statistic 3.60 2.79 3.17 [NPO.sub.t-1] -0.12 *** -0.01 -0.01 t-statistic -9.23 -0.68 -0.77 Ln[[Liu.sub.t-1]] 0.57 *** 0.19 *** 0.16 *** t-statistic 6.70 2.70 3.14 Panel B. Drop Liquidity Control Variables [PO.sub.t-1] 0.03 *** 0.03 ** 0.04 *** t-statistic 2.81 2.06 2.73 [NPO.sub.t-1] -0.16 *** -0.02 * -0.02 * t-statistic -14.89 -1.73 -1.94 Panel C. Other Alternative Specifications Add S&P 500 indicator [PO.sub.t-1] 0.06 *** 0.03 ** 0.03 * t-statistic 3.01 2.24 1.76 [NPO.sub.t-1] -0.12 *** -0.01 -0.01 t-statistic -9.47 -0.54 -0.60 S&P 500 dummy -0.08 0.01 0.04 ** t-statistic -0.86 0.52 2.04 Controlling for lagged dependent variable [PO.sub.t-1] 0.03 *** 0.03 ** 0.03 *** t-statistic 3.48 2.55 2.73 [NPO.sub.t-1] -0.06 *** 0.00 -0.01 t-statistic -11.25 -0.45 -0.61 [DV.sub.t-1] 0.48 *** 0.03 *** 0.02 *** t-statistic 15.00 3.52 3.10 Use contemporaneous variables P[O.sub.t] 0.04 *** 0.03 ** 0.03 *** t-statistic 3.31 2.34 2.89 [NPO.sub.t-1] -0.12 *** -0.01 -0.01 t-statistic -8.72 -0.97 -0.80 Drop stocks with initial price < $5 [PO.sub.t-1] 0.04 *** 0.03 ** 0.03 ** t-statistic 2.72 2.49 2.68 [NPO.sub.t-1] -0.12 *** -0.01 -0.01 t-statistic -8.96 -0.73 -0.73 Retain only US common stocks [PO.sub.t-1] 0.03 ** 0.02 ** 0.03 *** t-statistic 2.12 2.23 4.13 [NPO.sub.t-1] -0.12 *** 0.00 0.00 t-statistic -10.31 -0.46 -0.24 *** Significant at the 0.01 level. ** Significant at the 0.05 level. * Significant at the 0.10 level. Table IX. Relation between Passive Ownership and Analyst Following The quarterly sample includes all S&P 500 constituents from 2002 to 2013 except for those at the bottom size decile. Natural logarithm of number of analyst following is regressed on lagged passive ownership and control variables. Following the Fama and MacBeth (1973) approach, cross-sectional regressions are estimated in each quarter and the mean coefficients are reported. [PO.sub.t-1] is the percentage of shares outstanding held by passive funds at the end of the previous quarter. [NPO.sub.t-1] is the percentage of shares outstanding held by nonpassive institutional investors at the end of the previous quarter. [ANLY.sub.t-1] is the lagged dependent variable. TO is the turnover ratio over the previous year. MV is the market value of the stock estimated by the Fama and French (1992) approach. SP500D, equals 1 if the stock is a member of the S&P 500 index in that quarter, and 0 otherwise. R1000[D.sub.t] equals 1 if the stock is a member of the Russell 1000 index in that quarter, and 0 otherwise. All variables are standardized to have zero-mean and unit standard deviation in each quarter. The significance level is based on the time-series variation in the quarterly regression coefficients over the sample period. The standard errors are adjusted for residual autocorrelation and heteroskedasticity based on Newey and West (1987). (1) (2) (3) Intercept -2.31 *** -2.22 *** -0.32 *** t-statistic -7.29 -7.31 -7.72 [PO.sub.t-1] -0.16 *** -0.14 *** -0.02 *** t-statistic -3.26 -7.90 -5.10 [NPO.sub.t-1] 0.08 *** 0.07 *** 0.01 *** t-statistic 7.87 3.97 4.60 Ln[[ANLY.sub.t-1]] 0.87 *** t-statistic 57.05 Ln[TO] 0.32 *** 0.03 *** t-statistic 25.98 5.87 Ln [MV] 0.32 *** 0.04 *** t-statistic 35.30 7.23 SP500[D.sub.t] 0.58 *** 0.31 *** 0.03 *** t-statistic 15.78 8.90 4.06 R1000[D.sub.t] 1.93 *** 2.05 *** 0.31 *** t-statistic 6.29 6.34 7.27 Adj. [R.sup.2] 0.183 0.322 0.830 Average N 530 530 530 *** Significant at the 0.01 level. Table X. Effect of Passive Ownership and Trading on Price Efficiency The quarterly sample includes matched S&P 500 constituents and non- S&P 500 stocks from 2002 to 2013. The dependent variable is one of the five price inefficiency measures. F(s) is the pricing error of Hasbrouck (1993) estimated over a quarter, and V(s)-V(p) is the relative pricing error (scaled by standard deviation of log price, V(p), over that quarter). AC(1) is the first-order autocorrelation of daily stock return. VR(1,5) is the ratio of weekly stock return variance to five times daily stock return variance. [PT.sub.t] is the sum of absolute passive holding changes of a stock during the current quarter scaled by the total shares outstanding. [NPT.sub.t] is the sum of absolute nonpassive institutional holding changes of a stock during the current quarter scaled by the total shares outstanding. [PO.sub.t-1] is the percentage of shares outstanding held by the passive fund sample at the end of the previous quarter. [NPO.sub.t-1] is the percentage of shares outstanding held by nonpassive institutional investors at the end of the previous quarter. [RES.sub.t-1] is the trade-weighted relative effective spread of previous quarter. [TO.sub.t-1] is the turnover ratio over the previous quarter. MV is the market value estimated by the approach of Fama and French (1992). [PRC.sub.t-1] is stock price at the end of the previous quarter. All variables are standardized to have zero- mean and unit standard deviation in each quarter. Following the Fama and MacBeth (1973) approach, cross-sectional regressions are conducted in each quarter and the mean coefficients are reported. The significance level is based on the time-series variation in the quarterly regression coefficients over the sample period. The standard errors are adjusted for residual autocorrelation and heteroskedasticity based on Newey and West (1987). Dependent Ln[V(s) [absolute value [absolute value Variable /V(p)] of AC (1)] of 1-VR (1,5)] Intercept 0.08 *** -0.02 -0.03 t-statistic 4.15 -1.21 -1.20 [PT.sub.t] 0.02 0.00 -0.03 ** t-statistic 1.09 0.45 -2.43 [NPT.sub.t] -0.43 *** 0.12 0.14 t-statistic -4.12 1.13 1.20 [PO.sub.t-1] 0.03 * 0.03 * 0.04 *** t-statistic 1.94 2.80 3.43 [NPO.sub.t-1] -0.11 *** -0.01 -0.01 t-statistic -9.38 -0.93 -1.04 Ln[[RES.sub.t-1]] 0.09 * 0.00 -0.02 ** t-statistic 1.76 -0.14 -2.49 Ln[MV] 0.03 * -0.01 -0.02 ** t-statistic 1.71 -0.78 -2.19 Ln[[PRC.sub.t-1]] -0.54 *** -0.01 0.00 t-statistic -22.92 -0.99 -0.44 Ln[[TO.sub.t-1]] -0.17 *** -0.06 *** -0.04 *** t-statistic -8.34 -3.84 -3.89 Adj. [R.sup.2] 0.367 0.032 0.030 Average N 529 530 530 *** Significant at the 0.01 level. ** Significant at the 0.05 level. * Significant at the 0.10 level.

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Author: | Qin, Nan; Singal, Vijay |
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Publication: | Financial Management |

Article Type: | Report |

Geographic Code: | 1USA |

Date: | Dec 16, 2015 |

Words: | 16997 |

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