II. Data

Daily market data for both stocks and ETFs are from the CRSP daily file. The stock-level data cover all U.S. listed common stocks in CRSP from January 2015 through December 2019. Intraday transaction-level data come from TAQ. The sample period is from 2015 to 2019.Footnote ³ We exclude any stocks with a prior-month closing market capitalization of less than $300 million (“micro-caps”) and exclude any stocks with a prior-month closing price per share less than $5, following Asparouhova, Bessembinder, and Kalcheva (Reference Asparouhova, Bessembinder and Kalcheva2013). After these filters, we are left with 3,309 stocks in the sample from January 2015 to December 2019.

Table 1 (Panel A) reports the summary statistics of stocks in the sample. The sample contains 3404 unique stocks and covers effectively all listed U.S. common stocks during our sample period. The definition of all variables can be found in Appendix A.

Table 1 Summary Statistics

The ETF data start from U.S. equity ETFs in the CRSP mutual funds database with a prior-month closing assets under management (AUM) of at least $100 million. We obtain daily ETF shares outstanding from Bloomberg as Ben-David et al. (Reference Ben-David, Franzoni and Moussawi2018) document that shares outstanding data from CRSP are less accurate. Daily shares owned of ETFs by Robinhood users are obtained from the website Robintrack.net. We obtain data on ETF basket weights from Markit. Historical data on index constituents and weights are from Russell Investments for Russell indexes and from S&P for S&P indexes, and they are calculated from CRSP data for CRSP indexes.

We use the benchmark index disclosed in the ETF’s prospectus for the indices whose weights are obtainable from index providers such as S&P, Russell, and CRSP. For ETFs whose benchmark index weights are not obtainable from the index providers, we impute the benchmark following Cremers and Petajisto (Reference Cremers and Petajisto2009). When we compare the imputed and true index for those ETFs where we know the true index, in every case, the imputed index is the true index. This observation bolsters confidence in our imputation.

Table 1 (Panel B) shows summary statistics for the ETFs in the sample. Consistent with other studies (Dannhauser and Pontiff (Reference Dannhauser and Pontiff2021)), ETF expense ratios are low industry-wide with a mean (median) of 19 (15) basis points per year. The tracking error, which we calculate each month as the standard deviation of the daily difference in returns between the fund and its benchmark index, is also quite low with a mean (median) of 7.8 (6.1) basis points.

Figure 1 (Graph A) shows how the total trading volume and assets under management (AUM) of U.S. equity ETFs have evolved over time. The total AUM in U.S. equity ETFs has been growing rapidly, and since 2008, ETF trading has comprised approximately one-third of all U.S. equity trading activity. The vast majority of ETF trading activity occurs in the secondary market and does not lead to AP arbitrage (Fulkerson, Jordan, and Travis (Reference Fulkerson, Jordan and Travis2022)). Figure 1 (Graph B) shows how ETF primary flows—the daily flows in and out of ETFs via creation and redemption of ETF shares—have grown over time. Compared with Figure 1 (Graph A), between 3% and 8% of quarterly ETF trading volume results in creation or redemption activity, while the rest is secondary market trading and does not result in inflows or outflows.

Figure 1 ETF Trading Volume and Primary Flows

Figure 1 (Graph A) plots quarterly total trading volume and total assets under management across U.S. equity ETFs. Graph B plots quarterly primary flows (total dollar creation and redemption activity for all funds that experienced a net creation or a net redemption, respectively) across U.S. equity ETFs.

III. ETF Mechanics and Trading Activity

This section describes exchange-traded funds (ETFs) and the features of ETFs that motivate our empirical approach. Section III.A describes the creation and redemption mechanism that ensures ETF shares track their target index closely. Section III.B describes daily net ETF fund flows (“primary flow”) and ETF index arbitrage which is how ETFs interface with underlying asset markets.

A. ETF Basket Choice

An exchange-traded fund (ETF) is an investment intermediary that tracks a basket of underlying securities. ETF shares are listed on an exchange and trade throughout the day. ETF shares track the underlying basket because of the arbitrage activity of authorized participants (APs), which are large market making firms. APs have access to the creation and redemption mechanism which allows them to exchange ETF shares for the basket of underlying securities with the ETF provider at the end of each trading day. If the ETF’s shares trade sufficiently above the basket’s net asset value, an AP sells ETF shares and buys the underlying basket of securities and vice versa. Aps, thus, provide a liquid two-sided market for the ETF’s shares, which facilitates secondary trading activity (Lettau and Madhavan (Reference Lettau and Madhavan2018), Evans et al. (Reference Evans, Moussawi, Pagano and Sedunov2019)).

The creation and redemption baskets are set daily by the ETF provider. The ETF provider has complete freedom to define the baskets, and even “heartbeat” transactions for a single index asset are common.Footnote ⁴ In setting the baskets, the basic trade-off that the ETF provider faces is to minimize expected transaction costs, which reduces the bid–ask spread that APs are willing to offer and promotes trading, and to simultaneously minimize expected tracking error against the target index.

In the Supplementary Material, we present a model of the ETF provider’s problem and optimal basket weight. Underweighting a stock relative to the index reduces the expected transaction costs of trading it, at the cost of increasing tracking error. By contrast, overweighting a stock relative to the index increases both expected transaction costs and tracking error. Thus, the ETF provider strategically underweights index assets that are relatively illiquid.

Stock Liquidity and ETF Basket Inclusion

To gauge the extent of sampling, we first examine the basket weights of the ETFs in our sample relative to their benchmark index weights.

Table 2 lists the ETFs for which we obtained matched historical index weight data from the index provider. For Russell and CRSP indexes, we obtained monthly historical index weights; for the S&P indexes, we obtained yearly data. The list contains popular funds from the three largest fund providers, namely, BlackRock, State Street, and Vanguard. The sample covers four of the five largest ETFs as of 2019 and covers 37% of total AUM and 44% of total trading volume for U.S. equity ETFs over the sample period.

Table 2 ETF Sample, Benchmarks, and Statistics

We first give an example with the creation–redemption basket of VTI, the Vanguard Total U.S. Stock Market fund, relative to its benchmark index, the CRSP value-weighted U.S. stock market index. On Jan. 2, 2015, the first date in our sample, the CRSP index consisted of 3,695 stocks, while VTI’s basket consisted of 1,497 stocks. However, it is not clear from this example what fraction of ETFs actually use sampling and to what extent they use it in practice. Even if some ETFs tracking broad indexes use sampling quite heavily, the practice of sampling could be much more limited in practice, especially for large-cap ETFs that do not track such broad indexes.

To systematically examine how ETF baskets differ from their benchmark indexes, we construct a fund-stock-month panel. This panel consists of all stocks in each ETF’s benchmark index at the beginning of each month, for all ETFs in the sample for which we have historical basket and index data (Table 2). We use the stock $ i $ ’s basket weight relative to its index weight for ETF $ j $ in each month $ m $ to compute its relative weightFootnote ⁵:

$$ {\mathrm{RelWeight}}_{i,j,m}=\frac{{\mathrm{BasketWeight}}_{i,j,m}}{{\mathrm{IndexWeight}}_{i,j,m}}. $$

Table 2 displays the average relative weight for each ETF in the sample. Of the 56 ETFs in our sample, 36 have an average relative weight below 95%, and of 56, 35 have an average relative weight below 90%. Thus, for various thresholds, the majority of ETFs in our sample plausibly follow a sampling approach. We provide additional evidence supporting the prevalence of ETF sampling in the Supplementary Material.

Next, we sort all sample stocks into terciles each month based on their liquidity as measured by their prior month average effective spread. Figure 2 shows the average basket weight compared to the index weight in relative terms, for stocks in each tercile, across all ETFs in the sample. Consistent with our model’s prediction, the relative weight of an index stock in an ETF’s basket is much lower, on average, for less liquid stocks.

Figure 2 Stock Liquidity and ETF Basket Underweighting

Figure 2 displays the relative weight difference (basket weight divided by index weight) in ETF creation/redemption baskets across all the ETFs in our sample from 2015 to 2019. Sample stocks are sorted into terciles by their liquidity, measured as the prior month’s average effective spread.

Since the most illiquid stocks are most underweighted, a further prediction of our model (in Appendix B) is that the dispersion in relative weights within a given ETF should reflect the dispersion in liquidity across stocks in the index. In unreported tests, available from the authors, we check this prediction. We find that ETFs with more dispersion of liquidity across the stocks within their index have more dispersion in their relative weights as well, and this relationship holds across ETF categories as well as individual funds.

Next, we examine formal regression estimates which address a variety of potential confounders. The effect of a stock’s lagged liquidity on its $ {\mathrm{RelWeight}}_{i,j,m} $ can be interpreted as the effect on that stock’s basket weight holding its index weight fixed. We also control for stocks’ index weight in a flexible fashion, to absorb any (potentially nonlinear) effects that index weight might have on ETFs’ basket weighting decisions. To do so, we estimate the following equation:

$$ {\mathrm{RelWeight}}_{i,j,m}={\mathrm{Liquidity}}_{i,m-1}+\mathrm{Index}\;{\mathrm{Weight}\ \mathrm{Control}}_{i,j,m}+{\gamma}_{j,m}+{\unicode{x025B}}_{i,j,m}, $$

where $ {\mathrm{Liquidity}}_{i,m-1} $ is the liquidity of stock $ i $ in prior month measured by effective spread or bid–ask spread, standardized to a standard deviation of 1 for ease of interpretation. $ \mathrm{Index}\;{\mathrm{Weight}\ \mathrm{Control}}_{i,j,m} $ denotes whether the model contains the index weight (linear), weight and squared weight (square), or the weight, squared weight, and cubed weight (cubic) of stock $ i $ in the index in month $ m $ . Since the model’s prediction is based on a stock’s relative liquidity, we include fund-year-month fixed effects $ {\gamma}_{j,m} $ , which means that the variation is across stocks within each ETF’s index at each point in time.

Table 3 (Panel A) reports the results and shows that, controlling for its index weight and including fund-by-year-month fixed effects, a stock’s liquidity strongly negatively predicts its ETF basket weight. The effect is economically large and highly statistically significant. For example, in column 3, the coefficient of the stock’s relative weight on its prior month effective spread is −1.90. Put differently, a stock in the ETF’s benchmark index with a one-half standard deviation lower liquidity has approximately a 95% higher likelihood relative to the average of being omitted from the ETF basket.Footnote ⁶ Panel B reports the results within the subset of funds for which we do not need to impute the benchmark index. This sample contains more large-cap funds so that the magnitude of the relation between liquidity and basket weight is smaller, but still highly statistically significant and robust.

Table 3 Stock Liquidity and Inclusion in ETF Baskets

The Supplementary Material presents results when we compute an alternative measure of sampling behavior that accounts for the relative significance of each stock within the index. This approach reduces the disproportionate influence of stocks with minimal index weights. We find again that sampling behavior is widespread across our sample of ETFs.

Overall, the ETF basket weight data are consistent with the prediction that ETFs strategically underweight or omit illiquid index assets in their creation–redemption baskets. These results bolster our second prediction that the effects of ETF index arbitrage on underlying asset markets should be concentrated in liquid underlying assets and should be weaker or absent in illiquid underlying assets.

B. ETF Primary Flow and Index Arbitrage

1. Primary Flow

The net creation and redemption of ETF shares at the end of the day, through which assets and investor funds flow in or out of the ETF, is referred to as “primary flow.” Primary flow is how ETFs interface with underlying asset markets. The effects of ETF holdings on stocks and firms have been extensively studied (Ben-David et al. (Reference Ben-David, Franzoni and Moussawi2018), Glosten et al. (Reference Glosten, Nallareddy and Zou2021), Sağlam et al. (Reference Sağlam, Tuzun and Wermers2019)). Yet, an ETF with large and stable holdings may have a large or small (or zero) primary flow on any given day. Total trading volume in an ETF can also be misleading because most of the daily trading volume in ETFs reflects bilateral trades (Lettau and Madhavan (Reference Lettau and Madhavan2018)) that do not impact the underlying markets. By contrast, ETF primary flow directly reflects APs making use of the creation/redemption mechanism and exchanging ETF shares for index assets (Brown, Davies, and Ringgenberg (Reference Brown, Davies and Ringgenberg2021)).

We calculate each ETF $ j $ ’s primary flow on day $ t $ as the absolute change in shares outstanding on day $ t $ compared to day $ t-1 $ times the closing price on day $ t-1 $ Footnote ⁷:

$$ {\mathrm{Primary}\ \mathrm{Flow}}_{j,t}=\left({\mathrm{Shares}\ \mathrm{Outstanding}}_{j,t}-{\mathrm{Shares}\ \mathrm{Outstanding}}_{j,t-1}\right)\times {\mathrm{Price}}_{j,t}. $$

2. Index Arbitrage

We calculate the index arbitrage activity on the stock-by-day level by projecting the ETF’s primary flow onto the weight matrix of the daily ETF basket. Specifically:

$$ \mid {\mathrm{APArb}}_{i,t}\mid =\frac{\sum_j\mid {\mathrm{PrimaryFlow}}_{j,t}\mid \times {w}_{i,j,t}}{{\mathrm{MarketCap}}_{i,m-1}}, $$

where $ {w}_{i,j,t} $ is ETF $ j $ ’s basket weight in stock $ i $ on day $ t $ scaled by the market cap of the stock as of the previous month. The absolute value is taken on ETFs’ primary flow before the projection to reflect that index arbitrage occurs at an ETF-by-ETF level. For example, if a stock is a constituent of two ETFs with 1% basket weight and the two ETFs have a $100 and -$100 primary flow, respectively, the stock is subject to $2 index arbitrage activity. The assumption underlying the construction of $ \mid {\mathrm{APArb}}_{i,t}\mid $ is that primary flows are netted within each ETF-day, but that primary flows in opposite directions for different ETFs or on different days do not net with one another. In reality, netting of primary flows could occur within APs (Pan and Zeng (Reference Pan and Zeng2023)) and/or across multiple trading days (Evans et al. (Reference Evans, Moussawi, Pagano and Sedunov2019)).

3. AP Arbitrage Affects Intraday Trading Activity

To examine the effects of ETF index arbitrage on underlying markets, we first compare trading days with low AP arbitrage activity to days with high AP arbitrage activity. The prediction is that days with high AP arbitrage activity should see an increase in trading activity in underlying assets, but i) only in the most liquid assets and ii) toward the end of the trading day, when APs close out their residual positions.

Figure 3 plots the difference in intraday share turnover for U.S. equities between days on which they experience high AP arbitrage activity versus days on which they experience low AP arbitrage activity. We see that when a stock is subject to higher AP arbitrage activity, trading activity surges in the last half hour of the trading session, consistent with the idea that AP arbitrage activity is concentrated late in the day near the market close.

Figure 3 ETF Primary Flow and Asset Turnover During the Trading Day

Figure 3 plots the difference in intraday share turnover for U.S. equities between days on which they experience high AP arbitrage activities and days on which they experience low AP arbitrage activities. Within each stock, we sort the sample days using the predicted AP arbitrage activities for the stock and calculate the average share turnovers during all intraday intervals for top decile days and those for bottom decile days. We then average them across all sample stocks for all intraday intervals. The sample consists of U.S. common stocks from 2015 to 2019.

The intraday patterns in trading volume are suggestive of how APs perform ETF index arbitrage. Specifically, APs internalize their trading in ETF shares during the day. At the end of the trading day, APs adjust their net position using the creation/redemption mechanism. Since this involves delivering or receiving a wide basket of assets, ETF index arbitrage is thus reflected in the underlying markets.

This delay and pooling of trading activity in the underlying assets suggests that ETFs have effects on asset liquidity and market quality. This finding aligns with that of Box et al. (Reference Box, Davis, Evans and Lynch2021) that price transmission between the ETF and the underlying constituents is achieved via quote adjustments rather than arbitrage trades throughout the trading day. During days when AP arbitrage is high, the delay of activity in the underlying market until the end of the trading day is likely to consume liquidity and worsen information efficiency for the underlying assets (Kyle (Reference Kyle1985), Glosten and Milgrom (Reference Glosten and Milgrom1985)). On the other hand, it is not clear how large these effects should be, since AP arbitrage activity still accounts for a small fraction (less than 1%) of total trading volume for the stocks in our sample.

Next, we examine the effects of ETF index arbitrage on underlying asset markets. In order to identify causal effects, we isolate exogenous variation in AP arbitrage activity with a novel “return-chasing” instrumental variable.

IV. Research Design

There are many market forces that affect both ETF index arbitrage and underlying asset markets, which makes causal inference challenging. We develop a novel instrumental variable to overcome the identification problem. Specifically, we instrument each ETF’s signed daily primary flow with its lagged (i.e., stale) prior-month return. Dannhauser and Pontiff (Reference Dannhauser and Pontiff2021), among others, show that uninformed investors “return-chase,” and this pattern is especially strong in ETFs relative to open-ended mutual funds. As a result, investor dollars flow into ETFs with high lagged returns and out of ETFs with low lagged returns, even though the lagged returns do not predict future returns (Broman (Reference Broman2022), Box et al. (Reference Box, Davis, Evans and Lynch2021)).

First, we estimate the predictive regression:

(1) $$ {\mathrm{PrimaryFlow}}_{j,t}=\sum \limits_{k=1}^4{\beta}_k{\mathrm{Return}}_{j,t-k}+\beta {\mathrm{Return}}_{j,t-26\to t-5}+{\gamma}_j+{\kappa}_t+{\unicode{x025B}}_{j,t}, $$

where $ j $ denotes ETF and $ t $ denotes trading day. $ {\mathrm{Return}}_{j,t-k} $ is the lagged individual daily return of ETF $ i $ for the last 4 trading days, and $ {\mathrm{Return}}_{j,t-26\to t-5} $ is the cumulative return of ETF $ j $ over the last month from $ t-5 $ to $ t-26 $ (22 trading days). $ {\gamma}_j $ is ETF fixed effects, and $ {\kappa}_t $ is day fixed effects.

We use unadjusted fund returns instead of risk-adjusted returns because the literature suggests that retail investors respond to unadjusted returns (Odean (Reference Odean1998), Ben-David and Hirshleifer (Reference Ben-David and Hirshleifer2012)). The key independent variable is the fund’s return from trading day $ t-26 $ to trading day ( $ t-5 $ i.e., the return over the prior month, lagged by 5 trading days). We lag the return by 5 trading days (at least 1 calendar week) for three reasons. First, the lag avoids the possibility of reverse causation from ETF flows (e.g., due to investors rebalancing) to ETF returns. Second, the lag rules out omitted variables such as information arrival, which could drive both investor demand for a particular ETF and that ETF’s returns. In the modern equity market where high-frequency traders operate on a time horizon of microseconds, it is safe to assume that information that was known 5 trading days ago is stale and already incorporated into prices. Third, the multiday lag allows for discretion in the funds’ operational strategy and reporting.Footnote ⁸

Table 4 (column 1) shows that a higher lagged prior-month return predicts a higher ETF primary flow. To verify that the relationship is driven by uninformed investors return-chasing, first, we examine the daily net flow of trades by retail investors in each ETF using the methodology in Boehmer, Jones, Zhang, and Zhang (Reference Boehmer, Jones, Zhang and Zhang2021). Column 2 shows that indeed, the net flow of trades by retail investors is strongly positively predicted by the lagged prior-month return. Second, we examine the daily holdings of users of Robinhood, a smartphone trading app that is popular among retail investors. Table 4 (column 3) shows that an ETF’s lagged prior-month return even more strongly predicts its popularity with Robinhood users. In sum, the results are consistent with our proposed mechanism of return-chasing by uninformed retail investors.Footnote ⁹

Table 4 ETF Flows and Lagged ETF Returns

We use the predicted values from regression (1) as an exogenous shifter of ETF index arbitrage. Specifically, we multiply the coefficient on $ {\mathrm{Return}}_{j,t-26\to t-5} $ from Table 4 (column 1) by each ETF’s lagged prior-month return to produce a daily predicted primary flow for each ETF on each day. We take the absolute value because a large positive or negative primary flow implies more index arbitrage activity. The first stage $ F $ -statistic is 13.5 ( $ p $ =0.0004); thus, the condition of instrument relevance is plausibly satisfied (Angrist and Kolesár (Reference Angrist and Kolesár2024)).

$$ {\displaystyle \begin{array}{c}\mid \hat{{\mathrm{PrimaryFlow}}_{j,t}}\mid =\mid {\beta}_{FirstStage}\times {\mathrm{Return}}_{j,t-26\to t-5}\mid \\ {}\\ {}\mid {\hat{\mathrm{APArb}}}_{i,t}\mid =\frac{\sum_j\mid {\hat{\mathrm{PrimaryFlow}}}_{j,t}\mid \times {w}_{i,j,m(t)-1}}{{\mathrm{MarketCap}}_{i,m(t)-1}}.\end{array}} $$

The main variable of interest $ \hat{\mid {\mathrm{PrimaryFlow}}_{i,t}\mid } $ is plausibly unrelated to information on day $ t $ and, therefore, plausibly satisfies the exclusion restriction, for two reasons. First, $ \hat{\mid {\mathrm{PrimaryFlow}}_{j,t}\mid } $ only reflects fund flows that are predicted based on each ETF’s prior-month return lagged by 5 trading days. Figure 4 plots the values of the summation of all ETFs’ actual (realized) and predicted primary flow on daily level. We see that the predicted absolute primary flow accounts for only a small fraction of the overall variation in realized primary flow. In fact, the two time series are uncorrelated with one another ( $ \rho =0.02 $ ), suggesting that any information in actual ETF primary flows is not reflected in our instrumented ETF primary flows.

Figure 4 Realized Versus Instrumented ETF Primary Flows

Figure 4 compares realized ETF primary flows daily during 2015–2019, to ETF primary flows predicted using each individual ETF’s lagged return from $ t $ – $ 26 $ to $ t $ – $ 5 $ . The sample consists of U.S. equity ETFs.

Next, we multiply the predicted ETF-level primary flows for ETF $ j $ by its basket weights as of the end of the prior month $ {w}_{i,j,m(t)-1} $ to obtain the predicted level of AP arbitrage activity in stock $ i $ on day $ t $ , scaled by the stock’s market cap as of the end of the prior month. This stock-by-day variable $ \mid {\hat{\mathrm{APArb}}}_{i,t}\mid $ resembles “flow-induced trading” in the mutual fund literature, which isolates trading activity by mutual funds due to fund flows (Coval and Stafford (Reference Coval and Stafford2007), Lou (Reference Lou2012)). Similarly, we isolate trading activity due to the (predicted) primary flows of ETFs.

In sum, our independent variable of interest $ \mid {\hat{\mathrm{APArb}}}_{i,t}\mid $ is driven by predictable variation in ETF fund flows based on stale returns. This activity is passed through to the underlying stocks depending on their prior-month basket weights. The basket weights are stable over time; the cross-sectional variation within each ETF is two orders of magnitude more than the variation in the weights over time. As a result, instrumented AP arbitrage activity is unlikely to be correlated with any stock-specific or weight-specific information on day $ t $ .Footnote ¹⁰

All these features suggest that our research design plausibly satisfies the exclusion restriction. On the other hand, the fact that, at some point in the future, ETF premiums and returns reverse is true of most financial data and trading strategies given the arrival of new information. Though we attempt to rule out alternative explanations, information or return predictability could explain part of our results. We provide additional evidence and discussion supporting the validity of the instrument in the Supplementary Material.

V. The Effects of AP Arbitrage on Underlying Assets

In this section, we examine the effects of ETF index arbitrage on underlying asset markets. We first describe the estimation strategy and investigate the effects on asset market liquidity and quality. We then examine effects on asset returns. Lastly, we contrast the instrumental variables estimates with the corresponding ordinary least squares (OLS) estimates, which shows the magnitude of the endogenous market forces that jointly affect ETF flows and asset market activity.

A. Effects on Asset Market Quality

In this section, we investigate the heterogeneous effects of ETF index arbitrage on the quality of underlying asset markets. The key prediction is that the effects will be strongest in liquid stocks and weaker or even opposite in illiquid stocks.

For each month from January 2015 through December 2019, we sort stocks into terciles based on their average effective spread over the previous month. The first tercile contains the most liquid stocks, and the third tercile contains the most illiquid stocks ex ante.

We estimate the following equation:

(2) $$ {\displaystyle \begin{array}{l}{Y}_{i,t}=\sum \limits_{q=1}^3{\beta}^q\times \mid {\hat{\mathrm{APArb}}}_{i,t}\mid \times {\mathrm{Liquid}}_{i,t}^q\\ {}+{\mathrm{Liquid}}_{i,t}^q+{\boldsymbol{X}}_{i,m(t)-1}+{\boldsymbol{Y}}_{i,t-1}+{\gamma}_i+{\kappa}_t+{\unicode{x025B}}_{i,t}.\end{array}} $$

$ {Liquid}_{i,t}^q $ is a set of three dummy variables that equal 1 if stock $ i $ was in liquidity tercile $ q $ in the previous month. $ {\boldsymbol{X}}_{i,m-1} $ includes lagged stock-level controls—turnover, market capitalization, close price, and all market quality measures (effective spread, pricing error, volatility, and index correlation) as of the previous month. We control for lagged market quality measures to account for potential autocorrelation. Stock fixed effects, $ {\gamma}_i $ , sweep out any time-invariant stock-specific factors. The year-month fixed effects $ {\kappa}_t $ sweep out any time trends in the sample.

The key independent variable, $ \mid {\hat{\mathrm{APArb}}}_{i,t}\mid $ , is the instrumented magnitude of ETF index arbitrage in stock $ i $ on day $ t $ (Table 2). We standardize this variable to have a standard deviation of 1 over the entire sample. Thus, the coefficients $ {\beta}^1 $ , $ {\beta}^2 $ , and $ {\beta}^3 $ capture the effect of a 1-standard-deviation increase in AP arbitrage activity on the outcome variable of interest for stocks in the high-, medium-, and low-liquidity terciles, respectively.

The dependent variables $ {Y}_{i,t} $ include effective spread, pricing error, intraday volatility, and intraday correlation of stock $ i $ on day $ t $ . The effective spread is the signed distance between trade price and the midpoint of NBBO, scaled by trade price and averaged across the entire trading day weighted by the dollar value of each trade. The pricing error is calculated according to Hasbrouck (Reference Hasbrouck1993). The intraday volatility is the standard deviation of 1-minute returns over the entire trading day. The intraday correlation is the correlation between the 1-minute returns of the stock and the 1-minute returns of the SPDR S&P 500 ETF over the entire trading day.Footnote ¹¹

We begin by examining stock liquidity. On one hand, trading due to AP arbitrage is plausibly uncorrelated with information about any particular stock, and uninformed trades are liquidity improving (Kyle (Reference Kyle1985), Glosten and Milgrom (Reference Glosten and Milgrom1985)). Thus, trading due to AP arbitrage could be liquidity improving. On the other hand, our data show that ETF-driven trades appear mostly at the end of the trading day, pooling with other rebalancing activity and possibly crossing bid–ask spreads to get executed.Footnote ¹² Thus, trading driven by ETF index arbitrage could be liquidity consuming.

Table 5 (column 1) shows the differential effect of AP arbitrage activity on underlying stocks’ liquidity. We see that more AP arbitrage activity leads to wider effective spreads—reduced liquidity—in the most liquid tercile of stocks. The effect becomes weaker in the second tercile, in which stocks are mostly included in the creation/redemption basket of the ETF but are underweighted. The effect flips sign for the least liquid tercile (i.e., more AP arbitrage activities lead to slightly better liquidity in illiquid assets), perhaps because the AP arbitrage directs liquidity-consuming trading activity out of those assets. A Wald test for the high versus low liquidity terciles yields an $ F $ -statistic of 95.9, which rejects the null that the effects are the same with $ p<0.01 $ . These results suggest that APs’ index arb activity consumes liquidity in the underlying stocks, consistent with the results of Dannhauser (Reference Dannhauser2017) and Eaton, Green, Roseman, and Wu (Reference Eaton, Green, Roseman and Wu2021), and this effect is concentrated in ex ante liquid stocks.

Table 5 ETF Index Arbitrage and Asset Market Quality: IV Estimates

Table 5 (columns 2–4) shows the differential effect of AP arbitrage activity on other aspects of underlying market quality. In column 2, the outcome variable is the short-run price inefficiency (volatility of pricing error) following Hasbrouck (Reference Hasbrouck1993). We find that AP arbitrage activity leads to worse price efficiency, but again, only for stocks in the most liquid tercile. A 1-standard-deviation increase leads to a 1.9% increase in the short-run pricing error, comparable to the estimates in Israeli et al. (Reference Israeli, Lee and Sridharan2017). However, the effect is weaker in the second tercile and is insignificant in the least liquid tercile. A Wald test rejects with $ p<0.01 $ the null that the treatment effects are the same for the high-liquidity and low-liquidity tercile.

In Table 5 (column 3), the outcome variable is the intraday return volatility of the stock. Consistent with Ben-David et al. (Reference Ben-David, Franzoni and Moussawi2018), who find a positive effect of ETF ownership on monthly return volatility, we find that more AP arbitrage activity is accompanied by higher return volatility in the two most liquid terciles. A 1-standard-deviation increase leads to a 2.5% increase in liquid stocks’ volatility. The volatility-inducing effect is present in all three terciles but is monotonically smaller when liquidity is lower.

In Table 5 (column 4), the outcome variable is the correlation between the intraday returns of the individual stock and the SPDR S&P 500 ETF (SPY). Consistent with Greenwood (Reference Greenwood2007) and Da and Shive (Reference Da and Shive2018), who find a positive effect of ETF ownership on index correlation, we find that AP arbitrage activity leads to a higher intraday correlation with the market—but only in the two most liquid terciles of stocks. In the least liquid tercile of stocks, the effect is economically and mostly statistically insignificant.

Our simple model and mechanism predict that excluded stocks should see zero treatment effects. Instead, for the least liquid stocks, we see treatment effects that are near-zero and mostly statistically insignificant. This may be because our model does not capture many other aspects of market behavior such as substitutability between stocks, other holdings of the ETF sponsor (Pan and Zeng (Reference Pan and Zeng2023)), and effects on noise trader behavior (Foucault, Sraer, and Thesmar (Reference Foucault, Sraer and Thesmar2011)).

To sum up, we find that ETF index arbitrage has negative effects on liquidity and price efficiency and positive effects on volatility and return correlation. The unconditional effects we find are close to the magnitudes documented in the existing literature. For example, Ben-David et al. (Reference Ben-David, Franzoni and Moussawi2018) find a 1-standard-deviation increase in ETF ownership is associated with a 0.16 standard deviation higher daily stock volatility; we find that a 1-standard-deviation increase in ETF index arbitrage is followed by a 0.75/9.42 = 0.08 standard deviation change. Our unconditional estimates for price efficiency and comovement are also similar to those of Glosten et al. (Reference Glosten, Nallareddy and Zou2021) and Greenwood (Reference Greenwood2007). Since our research design and sample are different from these prior studies, our findings represent out-of-sample confirmation of their results.

More importantly, we find that these effects are all present for the tercile of liquid stocks only and are weak, absent, or even opposite in illiquid stocks. This finding is consistent with our main prediction. The mechanism driving this prediction is that ETFs on average systematically tilt their baskets in the same direction, namely, toward liquid assets and away from illiquid assets. Put differently, the treatment effects of ETFs on asset markets that prior research has documented are confined to a minority of liquid underlying assets.

This heterogeneity also means that unconditional estimates of average treatment effects, which are implicitly equal-weighted across all sample stocks, will tend to understate the effects of ETFs on asset markets. The bottom row of Table 5 reports the average treatment effects (i.e., without splitting stocks into liquidity terciles). We see that all of the estimates are significantly smaller than the treatment effect within the most liquid tercile; the understatement varies from −35% for volatility to −71% for pricing error. Thus, the fact that the treatment effects vary systematically across assets based on those assets’ liquidity is of first-order importance for understanding the effects that ETFs have on asset markets.

B. Price Impact and Information Content

Since AP arbitrage have impacts on trading activity and market quality, a natural question is whether they impact asset returns. First, if the trading activity of APs has significant price impact, we would expect to see an effect on closing prices and returns on day $ t $ . Second, if our instrumented AP arbitrage activity does contain information about future fund flows or asset values, violating the exclusion restriction, then we would expect to see an effect on returns on days $ t+1 $ , $ t+2 $ , and so on. Thus, looking for effects of our instrument on future stock returns represents a test of the exclusion restriction.

Table 6 presents estimates with daily stock returns as the outcome variable. In column 3, we see that AP arbitrage activity in stock $ i $ has no significant relationship with its contemporaneous return. The lack of statistical and economic significance suggests that contemporaneous AP arbitrage activities have limited price impact.

Table 6 ETF Index Arbitrage and Stock Returns: IV Estimates

AP arbitrage activity also has an economically insignificant relation with returns on future trading days and with no differential effect between liquid and illiquid terciles. A Wald test fails to reject equality with an F-stat of less than 2. The lack of predictive power for future returns leads us to conclude that our instrument is not confounded by market-relevant information. Instead, it reflects flow-driven, nondiscretionary trading activity driven by the preannounced ETF basket weights. We conduct additional robustness checks in Section VI which also cut against the possibility that instrumented AP arbitrage activity could potentially contain market-relevant information.

We observe that instrumented AP arbitrage activity is slightly positively associated with the stock’s return over the 2 prior trading days leading up to day $ t $ . The magnitude of the differential relations with prior-day returns is quite small—3–4 basis points per standard deviation of AP arbitrage activity. This observation is consistent with APs potentially taking time to smooth out their execution over multiple days (Evans et al. (Reference Evans, Moussawi, Pagano and Sedunov2019)), and it motivates our lagging the stale monthly return instrument by several trading days.

In sum, the relation of instrumented ETF index arbitrage with returns on day $ t $ suggests no significant price impact, and its relation with returns on days $ t+1 $ and $ t+2 $ suggests no meaningful information content.Footnote ¹³ The latter findings are consistent with the findings of other studies of ETF market impact which use different research designs (Dannhauser and Pontiff (Reference Dannhauser and Pontiff2021), Box et al. (Reference Box, Davis, Evans and Lynch2021)).

VI. Alternative Explanations

One concern with our findings is that market dynamics are changing over time and could drive both AP arbitrage activity and also stock turnover and liquidity. First, market structure evolves over time, and time-varying factors such as high-frequency trading activity and market fragmentation are known to impact market quality (Weller (Reference Weller2018), Haslag and Ringgenberg (Reference Haslag and Ringgenberg2023)). Second, the arrival of market-relevant information could drive increased AP arbitrage activity and at the same time cause market makers and participants to alter their trading activity in individual stocks. This section examines these three alternative explanations for our findings—high-frequency trading (HFT), market fragmentation, and market-moving news.

First, it could be that the increase in HFT activity over our sample period differentially affected stocks’ liquidity. This is because high-frequency traders potentially improve stock liquidity but endogenously choose to trade stocks that are inherently liquid (Brogaard, Hendershott, and Riordan (Reference Brogaard, Hendershott and Riordan2014)). Greater HFT activity or competition also plausibly affects how APs carry out ETF index arbitrage. To capture HFT activity in each stock over time, we construct the trade-to-order ratio using the SEC MIDAS data following the same procedure in Weller (Reference Weller2018). For each stock, we sum the trade volume and the order volume over the month and calculate the ratio of the two:

$$ {TOR}_{i,m}=\frac{\sum_{t\in m}{\mathrm{Trading}\ \mathrm{Volume}}_{i,t}}{\sum_{t\in m}{\mathrm{Order}\ \mathrm{Volume}}_{i,t}}, $$

where $ i $ denotes stock and $ m $ denotes month.Footnote ¹⁴ This yields a measure, TOR, that is highly associated with HFT activity as demonstrated by Weller (Reference Weller2018).Footnote ¹⁵

We then rerun our main estimates on measures of market quality, adding the contemporaneous stock-by-month values of TOR. We interact TOR with the liquidity terciles so that we capture and control for differential effects of HFT activity. Table 7 shows the results. HFT activity, as measured by TOR, has strong differential effects on market quality. For example, higher HFT activity is associated with significantly improved liquidity for all stocks, with the effect being strongest in the most liquid tercile of stocks (Table 7, column 1). Columns 2–4 show HFT’s differential effects on the other measures of market quality as well.

Table 7 ETF Index Arbitrage and Asset Market Quality: Controlling for HFT

Despite the differential effects of HFT trading on market quality, the differential effects of AP arbitrage survive almost unchanged. Compared to Table 5, the coefficients and significance levels for the most and least liquid terciles and the difference between them remain similar in all cases. Thus, variation in high-frequency trading activity during our sample does not explain the effects that we find.

Second, it could be that the increase in market fragmentation over our sample period affected stocks’ liquidity and also ETF index arbitrage activity. To examine this possibility, we construct a stock-by-month Herfindahl–Hirschman Index (HHI) of trading volumes across market venues:

$$ {HHI}_{i,m}=\sum \limits_{j,t\in m}{\left(\frac{{\mathrm{Trading}\ \mathrm{Volume}}_{i,j,t}}{\sum_j{\mathrm{Trading}\ \mathrm{Volume}}_{i,j,t}}\right)}^2, $$

where $ i $ denotes stock, $ j $ denotes market venue, and $ m $ denotes month.Footnote ¹⁶ This measure captures the degree of realized market fragmentation, for each stock in each month individually.

We then rerun our main estimates on measures of market quality, adding the contemporaneous stock-by-month controls for market fragmentation (HHI). Table 8 shows the results. Market fragmentation has strong differential effects on market quality. For example, greater market fragmentation is associated with significantly worse liquidity for the most liquid tercile of stocks, but with significantly improved liquidity for the least liquid tercile (Table 8, column 1). Columns 2–4 show strong differential effects on the other measures of market quality as well.

Table 8 ETF Index Arbitrage and Asset Market Quality: Controlling for Market Structure

However, despite the differential effects of market fragmentation on market quality, the differential effects of AP arbitrage survive almost unchanged. Compared to Table 5, the coefficients and significance levels for the most and least liquid terciles and the difference between them remain similar in all cases. Thus, variation in market fragmentation does not explain the effects that we find.

Third, it could be that when there is market-moving news (or the risk of market-moving news arriving), market makers and participants change their trading behavior differentially in liquid versus illiquid assets, at the same time affecting ETF index arbitrage activity. To examine this possibility, we add the magnitude (absolute value) of the CRSP value-weighted U.S. market index on each day as an additional explanatory variable, interacted with each stock’s liquidity tercile.

Table 9 shows the results. The magnitude of the market return has its own differential effects on market quality. However, the differential effects of AP arbitrage again survive and are again similar compared to the estimates in Table 5. Compared to Table 5, the coefficients and significance levels for the most and least liquid terciles and the difference between them remain similar in most cases, albeit the statistical significance of the differential effect is weaker for correlation.

Table 9 ETF Index Arbitrage and Asset Market Quality: Controlling for Market News

In untabulated tests, we restrict our sample to days on which the CRSP value-weighted U.S. market index return was within the range (−1%, 1%). This robustness check drops days on which the market moved significantly, likely when some significant event or news occurred. Restricted to “quiet market days,” our estimates are again similar to those in Table 5. This is an additional robustness check against the possibility that our instrument might carry market-relevant information that it could bias our inference. Taken together, we conclude that market-moving news does not explain the differential effects that we find.

Thus, for the three major market forces that we examine—high-frequency trading, market fragmentation, and market-moving news—we conclude that our estimates are not driven by these alternative explanations.