Does Program Trading Contribute to Excessive Comovement of Stock Returns?

Mingyi Lia, Xiangkang Yinb, and Jing Zhao∗

This version: 5 September, 2018

a Department of Economics and Finance, La Trobe University, Australia. Email: [email protected]. b Department of Finance, Deakin University, Australia. Email: [email protected]. * Corresponding author, Department of Economics and Finance, La Trobe University, Bundoora, VIC 3086, Australia. Tel: +61 3 9479 3120, Email: [email protected]. We are grateful to Huu Duong, Philip Gharghori, Alok Kumar, Peter Pham, Avanidhar Subrahmanyam, and participants at the 9th Financial Markets and Corporate Governance Conference and the Research Symposium on Capital Market Research for their highly valued comments. This project is supported by the Discovery Projects funding provided by the Australian Research Council (DP140100113).

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Does Program Trading Contribute to Excessive Comovement of Stock Returns?

Abstract

Daily returns of stocks with high program trading comove more with each other but less with remaining stocks. The comovement is excessive since it remains after controlling for market movements. Its excessiveness can be further demonstrated by its disconnection with news of fundamentals, and the program trading’s role in stimulating return reversal. Moreover, the excessive comovement cannot be explained by the effects of gradual information diffusion and index fund trading. Underlying this comovement is the high persistence of program trading. Our findings support the habitat investing view and demonstrate program trading creates a distinct source of excessive return comovement.

JEL Classification: G10, G12

Keywords: Program trading, Habitat investing, Excessive return comovement, Return reversal

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1. Introduction

Stock return comovement lies at the heart of modern portfolio theory and is extremely

important for investors making decisions on portfolio allocation and risk management. Following

the traditional view that stock price equates to the present value of future cash flows, comovement in stock return is perceived as the result of commonality in firm fundamentals or change in

common discount rates. However, this simple view is not supported by empirical evidence. Shiller

(1989) argues that return comovement between the U.S. and U.K. stocks is too large to be explained by their comovement in dividends. Pindyck and Rotemberg (1993) find that returns of companies conducting unrelated business comove beyond common variation in discount rates.

Contemporary literature focuses on this excessiveness, and examples for the sources of return comovement in excess to variation in common fundamentals include S&P 500 index inclusion and deletion (Barberis, Shleifer and Wurgler, 2005; hereafter BSW), overweighting of some constituents in the Nikkei 225 Index (Greenwood, 2007), change in firm headquarters location

(Pirinsky and Wang, 2006), systematic retail trading (Kumar and Lee, 2006), reclassification of index labels (Boyer, 2011), common mutual fund ownership (Anton and Polk, 2014), and stock splits (Green and Hwang, 2009).

These empirical findings are generally consistent with theories developed by Barberis and

Shleifer (2003) and BSW, which predict that correlated excessive demands drive stock returns to comove beyond their common fundamentals. However, most existing studies take an indirect approach by identifying non-fundamental characteristics of events and then examining the impacts

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of such characteristics on return comovement. 1 While such an empirical design is generally

viewed as successful in isolating non-fundamental comovement, it provides little guidance about

who these non-fundamental traders are and what the underlying channel through which excessive

demand rises is. A recent study by Chen, Singal and Whitelaw (2016) points out that some non-

fundamental events used in the literature may coincide with changes in fundamentals. Excessive

comovement among stocks following index additions and stock splits even disappear when

revisited.

This study intends to provide convincing empirical evidence of excessive comovement

caused by the trading activities of a group of non-fundamental traders—program traders. The New

York Stock Exchange (NYSE) defines program trading as: (1) simultaneous purchase or sell of 15

or more stocks as part of a coordinated trading strategy; or (2) index arbitrage.2 The fact that

program trading only trades baskets of stocks makes it unlikely to be driven by fundamentals,3

which provides an ideal and direct setting for testing excessive return comovement. However, the portfolio nature of program trading may lead one to question whether the relationship between

1 The exceptions include Kumar and Lee (2006), and Anton and Polk (2014), whose supports to the theories rely on

the amounts of individual and institutional trades, respectively.

2 We obtain proprietary data of program trading of individual stocks from the NYSE. We exclude program trading

arising from index arbitrage because there is little theoretical relevance. However, our findings remain qualitatively

similar if index arbitrage trading is included since index arbitrage is not highly active in our sample period and only

accounts for 1% of the NYSE’s trading volume.

3 The non-fundamental nature of program trading will be discussed extensively in section 2, and confirmed by the

analysis in sections 4 and 5.

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program trading and return comovement is mechanical. We focus on the excessiveness of

comovement among stocks, which is beyond this mechanical relationship. Excluding program

trading induced by index arbitrage from our analysis can further mitigate this concern.

Program trading is widely employed by institutional investors to minimize their trading costs and implement trading strategies that involve multiple stocks. It is an important investment vehicle, and its trading volume accounts for 22% of the NYSE’s trading volume over our sample period. However, the impacts of program trading on market quality are not uncontroversial. Some blame program trading for causing large price swings and such blame led the NYSE to curb program trading under certain circumstances. However, there are also academic studies showing

program trading does not destabilize stock markets or contribute to market crashes such as Black

Monday in 1987. We study program trading from a new perspective by unveiling its role in stimulating excessive comovement in stock returns, which makes the stock market less efficient.

Our study is motivated by the habitat investing view of excessive comovement proposed by BSW, which starts from the observation that many investors choose to trade only a subset of all available securities, for reasons such as transaction costs or lack of information. We support

the assertion of program traders conducting habitat investing with the evidence of very high

persistence of program trading at individual stock level. Stocks with high (low) volume of program

trading in a quarter tend to have high (low) participation of program traders in at least four

following quarters. Program traders prefer some particular stocks to others, showing typical

characteristics of habitat investing.

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To test whether habitat investing leads to excessive comovement among stocks preferred

by program traders, we adopt a two-step process similar to that of Koch, Ruenzi and Starks (2016).

In the first step, we estimate how the daily return of an individual stock comoves with the portfolio

return of high program trading stocks. Control for market returns is applied to ensure the identified

comovement is not driven by market fundamentals. In the second step, we investigate the cross- sectional relationship between the estimated comovement and the program trading of the concurrent or previous quarter. We also adopt the BSW approach to construct an alternative measurement of return comovement in the first step. This approach runs a bivariate regression of stock daily return on the portfolio returns of high program trading stocks and remaining stocks.

We find that program trading exerts a significant and positive effect on comovement measured by both approaches, and the effect remains strong after controlling for stock characteristics.

Furthermore, the bivariate regression approach indicates that stocks preferred by program traders not only comove more with each other but also comove less with the rest of the market. These findings are consistent with the predictions of BSW and Greenwood (2007), namely, that after controlling for common fundamentals, return of stock comoves more with other stocks within its habitat but less with stocks outside its habitat.

To further demonstrate that the identified return comovement is unrelated to the fundamentals, we analyze the impacts of macroeconomic and firm-specific news on the comovement. We also examine industry impact by excluding the stocks within its industry

(defined by its 2-digit SIC code) when constructing the benchmark portfolio return for each

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individual stock. Our results suggest that macroeconomic, industry, and firm-specific information

all fail to explain the excessive comovement caused by program trading.

As an alternative examination of the non-fundamental nature of program trading, we test

whether stocks with higher program trading are related to increases in their return reversals. Stock returns driven by non-fundamental trading tend to reverse in subsequent periods, while the impact of fundamental trading on stock prices tends to be permanent. Our results demonstrate that return reversal increases with program trading activities and there exists a common reversal component in stock returns induced by program trading, which supports the notion that program trading contributes to comovement among stocks that is excessive and non-fundamental.

Although program trading exhibits characteristics of habitat investing, gradual information diffusion can also generate excessive comovement in stock returns (BSW; Chordia and

Swaminathan, 2000). Since information propagation may follow a diffusion process, some stocks tend to incorporate market-wide information faster than others due to market frictions or investor base. As program traders are primarily sophisticated institutions, stocks preferred by them may incorporate market information quicker than other stocks, resulting in the identified return

comovement. An implication of this hypothesis is that stocks with high program trading should positively lead their counterparts with low program trading in returns. We test this prediction by

running a vector autoregression on daily portfolio returns of stocks with high and low program

trading, and our results do not support the hypothesis of gradual information diffusion being the

driver of program-trading-induced return comovement.

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To shed more light on the causal relationship between program trading and its return

comovement, we test their Granger causality. Program trading Granger causes return comovement

but not vice versa. This finding is consistent with our argument that program trading leads to excessive comovement, because if the relationship is driven by some omitted market-wide

economic variables, we expect the causality to be bi-directional.

Program trading is widely adopted by index fund managers (e.g. ETFs and index mutual

funds) to accommodate retail investment flows. Da and Shive (2018) show that ETF arbitrage

exacerbates return comovement with the market. Hendershott and Seasholes (2006) also discover

that after a stock is added to the S&P 500 index, its order flow from program trading starts to

comove more with program trading order flow of other S&P 500 stocks. Therefore, it is possible

for index fund trading activities to contribute to our results, especially if fund managers prefer and

dominate program trading. However, our tests demonstrate that the effect of program trading on

the identified comovement remains robust after controlling for ETF flows and index returns,

indicating program trading as a distinct driver of excessive comovement among stocks within their

habitat.

By confirming that comovement among stocks with high program trading is excessive and

non-fundamental, we characterize a risk caused by program trading. Moreover, by eliminating

alternative explanations such as the hypothesis of gradual information diffusion and so on, we

provide evidence of habitat investing explaining this excessive comovement. The rest of this paper

is organized as follows. Section 2 reviews the relevant literature on the topic. Section 3 describes

our data and variable constructions. Our baseline analysis and findings of excessive comovement

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in returns are presented in section 4, followed by an extended analysis to further demonstrate the

non-fundamental nature of comovement and to examine the effects of information diffusion and

index funds in section 5. Section 6 concludes the paper.

2. Literature Review

Program trading involves baskets of stocks and is widely considered as non-informational trading in literature. Subrahmanyam’s (1991) theoretical model predicts that portfolio trading is

less likely to be information-driven as opposed to trading individual securities, because liquidity

traders without superior information prefer to trade baskets of securities, in anticipation of lower

adverse selection costs. In their analysis of order flows derived from program trading, Hendershott and Seasholes (2009) provide empirical support for this prediction that program trading loses money on average. A similar conclusion is drawn by Boehmer and Wu (2008), who point out that in practice sell-side brokers maintain separate trading desks and charge lower commission fees for program trades, since market makers do not expect order flows from program traders to be informed. Kadan, Michaely and Moulton (2017) also argue that program trading is not being motivated by news. Furbush (2002) discusses the commonly used program trading strategies and advocates that none of them are related to fundamentals.

Despite being uninformed, program trading can still impact stock prices given its typically large trade size. This is particularly the case if order flows are correlated across program traders.

Program trading has long been blamed for causing large price swings in stock markets, see for example Grossman (1988a) and Kim and Yang (2004). Shortly after the 1987 stock market crash,

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such blame led the NYSE to impose restrictions on program trading under stressed market

conditions. 4 Nevertheless, prior academic research generally finds mixed evidence regarding

whether program trading destabilizes stock markets. For example, Grossman (1988b) documents

an insignificant relationship between daily program trading volume and index volatility. Furbush

(1989) examines program trading activities around the 1987 crash and argues they are not

responsible. By analyzing all program trades in the first quarter of 1989, Neal (1993) finds that they do not destabilize the stock market. On the other hand, Harris, Sofianos and Shapiro (1994) report a positive relationship between program trading and intraday market volatility. While there is less academic research studying the impact of program trading on return volatility using more recent data, program trading has grown substantially over the last two decades. Moreover, prior studies largely focus on the link between program trading and market volatility, yet little is known at the individual stock level. This paper concentrates on the relationship between program trading and volatility of individual stocks, and it demonstrates that program trading contributes to not only excessive volatility but also systemic volatility that is distinct from common market risk.

The habitat investing model of BSW predicts that certain groups of investors prefer to trade

only a subset of all available stocks due to various restrictions. Commonality in their order-flow

introduce excessive comovement among stocks within their preferred habitat. In accordance with

this prediction, Kumar and Lee (2006) find significant return comovement among stocks with high

retail trading. Anton and Polk (2014) study stocks with connected mutual fund ownership and

4 The restrictions are known as program trading curbs. Depending on the severity of price movements, all program

trades may be halted or only sell (buy) program trades may be permitted on upticks (downticks).

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demonstrate mutual fund flows affect return comovement. Applying principal components

analysis to electronic order flow data for a sample of NYSE-listed stocks from November 1997 to

February 1998, Corwin and Lipson (2011) find that program trades and other institutional trades

are the primary drivers of commonality in order flow and these order flow factors are related to

returns. Our finding of the high persistence of program trading complements prior studies, and

our evidence of habitat investing by program traders resulting in a distinct source of excessive

comovement among stocks directly supports the habitat investing theory of BSW.

3. Data and Variable Measurement

We obtain historical data of program trading from the NYSE, which contains information

about daily program trading volumes of all NYSE stocks from 2006Q3 to 2015Q4.5 The NYSE

separates program trading volume into two categories, index arbitrage and non-index arbitrage.

Index arbitrage typically involves exploring the price discrepancy between the futures contract of

an index and the underlying stock basket of the index. While program trading for index arbitraging has attracted substantial interests (e.g. Miller, Muthuswamy and Whaley, 1994; Stoll and Whaley,

1987; Mackinlay and Ramaswamy, 1988), we drop it from our main analysis because it has little

5 The NYSE refers to this data product as ProTrac, which is adopted by Wang and Zhang (2015) in examining the

impact of investor trading on firm valuation. Hendershott and Seasholes (2009) and Kadan, Michaely and Moulton

(2017) use a proprietary dataset of all executed trades from the NYSE, which includes program trading as a

component.

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theoretical relevance to our study.6 Index arbitrage accounts for only 1% of the NYSE’s trading volume in our sample period.7 We collect daily returns and volume data of all NYSE common

stocks (share codes 10 and 11) from CRSP, and balance sheet items from COMPUSTAT. Data of

analyst coverage and institutional ownership are collected from I/B/E/S and SEC Form 13F,

respectively.

To analyze the effects of macroeconomic and firm-specific announcements, we construct

and variables using Event Sentiment Scores from the RavenPack

𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀database. RavenPack𝐹𝐹𝐹𝐹𝐹𝐹 𝐹𝐹is𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 a leading global news database used in quantitative and algorithmic

trading. It contains comprehensive records of historical news at macroeconomic and firm levels

from leading financial news publishers including regional editions of Wall Street Journal,

Barron’s, and MarketWatch. The attractive features of the RavenPack database have made it an

ideal data source for studying information-related issues (e.g. Dai, Parwada and Zhang, 2013;

Dang, Moshirian and Zhang, 2015; Kolasinski, Reed, and Ringgenberg, 2013; Shroff, Verdi, and

6 It is quite likely that index arbitrage can affect the return comovement of stocks within the index. However, the

focus of our study is return comovement due to correlated program trading activities, which are not necessarily related

to any particular index. Nevertheless, we have extended our analysis to include program trading triggered by index

arbitrage and find no qualitative difference, therefore we do not tabulate these results.

7 This is in sharp contrast to early studies of program trading, where index arbitrage accounts for a much larger

percentage.

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Yu, 2013). To remove potentially noisy news, we focus on the most novel and relevant news

events.8

We collect data of daily ETF flows at fund level from the ETF Global database, which

contains daily net fund flows driven by the creation and redemption processes of individual ETFs.

To calculate a market-wide ETF flow, we aggregate daily net dollar flows of all U.S.-domiciled

ETFs and scale it by the total market capitalization of CRSP stocks at the end of the previous

quarter, following Koch, Ruenzi and Starks (2016).

The main explanatory variable Program Trading Participation ( ) of stock on day is

defined as the fraction of its trading volume that comes from program trad𝑃𝑃𝑃𝑃𝑃𝑃ers: 𝑖𝑖 𝑡𝑡

, , = . (1) , 𝑖𝑖 𝑡𝑡 𝑖𝑖 𝑡𝑡 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉 𝑃𝑃𝑃𝑃𝑃𝑃 𝑖𝑖 𝑡𝑡 Quarterly is defined as the daily average𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 that𝑇𝑇𝑇𝑇𝑇𝑇9𝑇𝑇 𝑇𝑇 𝑇𝑇𝑇𝑇 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉

𝑃𝑃𝑃𝑃𝑃𝑃 1 , = , , (2) 𝑑𝑑 𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖 𝑄𝑄 � 𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖 𝑡𝑡 𝑑𝑑 𝑡𝑡=1

8 There are two other variables from RevenPack relevant to our study: Event Novelty Score (ENS) and Event

Relevance Score (ERS), both ranging between 0 and 100. The ENS variable represents how new or novel a news item is. The first story reporting a categorized event is considered to be the most novel and receives a value of 100. The

ERS variable indicates how strongly the entity is related to the underlying news story, where a value of 100 is assigned to a highly relevant news item. We exclude news events with either ENS or ERS below 100.

9 We apply three time horizons in our analysis: monthly, quarterly and semi-annually. Since they lead to qualitatively similar results, we only report findings based on quarterly analysis and other results are available upon request.

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where denotes the number of trading days in quarter . For the purpose of our analysis, is more suitable𝑑𝑑 than program trading volume itself, because𝑄𝑄 it captures the relative importance𝑃𝑃𝑃𝑃𝑃𝑃 of program trading in the markets.10

Panel A of Table I reports summary statistics of quarterly , firm size ( ), stock

price ( ), book-to-market ratio ( / ), turnover ratio ( 𝑃𝑃𝑃𝑃𝑃𝑃), institutional𝑆𝑆 𝑆𝑆ownership𝑆𝑆𝑆𝑆

( ),𝑃𝑃𝑃𝑃𝑃𝑃 number of analysts following𝐵𝐵 𝑀𝑀( ), bid-ask spread𝑇𝑇𝑇𝑇𝑇𝑇 (𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 ), quarterly cumulative

stock𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 return ( ), and realized volatility 𝐴𝐴of𝐴𝐴 daily𝐴𝐴 returns ( ).𝑆𝑆𝑆𝑆 In𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 our sample period, program

trading on average𝑅𝑅𝑅𝑅𝑅𝑅 accounts for 22% of the NYSE’s trading𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 volume, with standard deviation of

7%. In Panel B, we sort all quarter-stocks into quintiles by their and report the and firm

characteristics averaged over the stocks within the quintile. 𝑃𝑃𝑃𝑃𝑃𝑃The average 𝑃𝑃𝑃𝑃𝑃𝑃of high

quintile is almost three times of that of low quintile (31% vs. 11%), which indicates𝑃𝑃𝑃𝑃𝑃𝑃 sufficient𝑃𝑃𝑃𝑃𝑃𝑃

variation of program trading volume in the𝑃𝑃𝑃𝑃𝑃𝑃 cross-section of individual stocks. has negative

relationships with firm size and turnover ratio, which are primarily driven by𝑃𝑃𝑃𝑃𝑃𝑃 the mechanical

relationship between and trading volume. Chordia and Swaminathan (2000) find that

portfolio return of high𝑃𝑃𝑃𝑃𝑃𝑃 volume stocks leads portfolio return of low volume stocks because high

volume stocks incorporate market information more quickly. Naturally, this can lead to different

return comovements between groups of high and low volume stocks. For this reason, we carefully

control firm size and turnover ratio in both nonparametric and regression analyses. The

10 Our results remain robust for alternative program trading measures such as program trading volume and the ratio of program trading volume to the number of shares outstanding.

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relationships of with stock price, number of analysts following and institutional ownership also demonstrate𝑃𝑃𝑃𝑃𝑃𝑃 a negative trend.

INSERT TABLE I HERE

4. Baseline Findings

4.1. Persistence of Program Trading Activities

The habitat investing view of BSW argues that a certain group of investors prefer to trade

only a subset of all available stocks, and hence contribute to excessive return comovement. To

verify that some stocks are indeed a more preferred habitat to program traders than others, we first examine the persistence of program trading. For every quarter in our sample period, we sort stocks into quintiles according to their s in that quarter, and then report their average s in the concurrent and four subsequent quarters𝑃𝑃𝑃𝑃𝑃𝑃 in Table II. 𝑃𝑃𝑃𝑃𝑃𝑃

INSERT TABLE II HERE

According to Table II, is a highly persistent variable in the cross-section of individual stocks. For all quintiles, 𝑃𝑃𝑃𝑃𝑃𝑃the percentages of program trading activities are quite stable over the five quarters𝑃𝑃𝑃𝑃𝑃𝑃. Taking the low quintile for example, the average varies in the narrow range of 11%-12%. In the last row of the table, we calculate the differences𝑃𝑃𝑃𝑃𝑃𝑃 of average s between stocks in the high and low quintiles. The corresponding t-statistics show that the𝑃𝑃𝑃𝑃𝑃𝑃 differences are highly significant for all𝑃𝑃𝑃𝑃𝑃𝑃 five quarters. Overall, results in this table support the view that some stocks are more preferred by program traders and program trading exhibits the characteristics of habitat investing.

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4.2. Program Trading and Excessive Return Comovement

To test the hypothesis that program traders’ habitat investing contributes to excessive

comovement in stock returns, we adopt a two-step process similar to that of Koch, Ruenzi and

Starks (2016). In the first step, we estimate the comovement between the returns of an individual

stock and a portfolio of high program trading stocks. In the second step, we test whether the

estimated return comovement is higher among stocks with a higher .

Because our study concerns the excessiveness of return comovement,𝑃𝑃𝑃𝑃𝑃𝑃 we need to extract

the effects of market movements. Thus, we run a market model over a quarter for residual returns

of stock i:

, = + , , + + , , (3)

𝑖𝑖 𝑡𝑡 𝑖𝑖 𝑚𝑚𝑚𝑚𝑚𝑚 𝑖𝑖 𝑚𝑚𝑚𝑚𝑚𝑚 𝑡𝑡 𝑖𝑖 𝑡𝑡 where , is the return𝑅𝑅𝑅𝑅𝑅𝑅 of stock𝛼𝛼 i 𝛽𝛽on day𝑅𝑅𝑅𝑅𝑅𝑅 t, 𝛿𝛿, 𝛿𝛿𝛿𝛿𝛿𝛿𝛿𝛿𝛿𝛿𝛿𝛿𝛿𝛿𝛿𝛿 the value-weighted𝑅𝑅𝑅𝑅𝑅𝑅 return of all CRSP

𝑖𝑖 𝑡𝑡 11 𝑚𝑚𝑚𝑚𝑚𝑚 𝑡𝑡 common𝑅𝑅𝑅𝑅𝑅𝑅 stocks, and , the residual return. 𝑅𝑅𝑅𝑅𝑅𝑅 Control variables ( ) include the one-

𝑖𝑖 𝑡𝑡 day lead and lag returns𝑅𝑅𝑅𝑅𝑅𝑅 of the market portfolio and the one-day lead𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 and lag returns of stock i.

The lead and lag stock returns are added to adjust autocorrelation in daily stock returns, while the lead and lag market returns are included to allow for nonsynchronous trading (Dimson, 1979;

Hutton, Marcus and Tehranian, 2009). To account for the first-order relationship between program trading and individual stock return, we also control for one-day lead, lag and contemporaneous daily of the stock.

𝑃𝑃𝑃𝑃𝑃𝑃

11 Our results are similar if we extract residual returns from the Fama-French (1993) three-factor model or using the

S&P 500 index daily returns to proxy for market return.

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We take residual return ( , ) from equation (1) and construct a daily benchmark using

𝑖𝑖 𝑡𝑡 residual returns of stocks with high𝑅𝑅𝑅𝑅𝑅𝑅 program trading volume. Specifically, we sort all sample

stocks into quintiles according to their , on day , and then compute the benchmark ,

𝑖𝑖 𝑡𝑡 12 𝐻𝐻𝐻𝐻 𝑡𝑡 by averaging , for stocks in the top𝑃𝑃𝑃𝑃 𝑃𝑃 quintile𝑡𝑡 on that day. Over a quarter, we estimate𝑅𝑅𝑅𝑅𝑅𝑅

𝑖𝑖 𝑡𝑡 the following 𝑅𝑅𝑅𝑅𝑅𝑅time-series regression model𝑃𝑃𝑃𝑃𝑃𝑃 for stock i:

, = + , , + , . (4)

𝑖𝑖 𝑡𝑡 𝑖𝑖 𝐻𝐻𝐻𝐻 𝑖𝑖 𝐻𝐻𝐻𝐻 𝑡𝑡 𝑖𝑖 𝑡𝑡 Intuitively, one can think of equation𝑅𝑅𝑅𝑅𝑅𝑅 (3) as𝛼𝛼 controlling𝛽𝛽 𝑅𝑅𝑅𝑅𝑅𝑅 for fundamental𝜖𝜖 -based return comovement

that arises from broad market movement, while , in equation (4) measures return comovement

𝐻𝐻𝐻𝐻 𝑖𝑖 that arises primarily from program trading. In𝛽𝛽 this sense, , captures comovement that is in

𝐻𝐻𝐻𝐻 𝑖𝑖 excess of common fundamentals of the market. However, we𝛽𝛽 will further demonstrate it is non-

fundamental and excessive from other perspectives in our analysis below.

In addition to the residual approach of equations (3) and (4) for the first step analysis, we also estimate return comovement by the bivariate regression approach, which is proposed by BSW and widely adopted in the literature (e.g., Greenwood, 2007; Green and Hwang, 2009; and Boyer,

2011). The regression is specified as

, = + , , + , , + , , (5) 𝐵𝐵 𝐵𝐵 𝑖𝑖 𝑡𝑡 𝑖𝑖 𝐻𝐻𝐻𝐻 𝑖𝑖 𝐻𝐻𝐻𝐻 𝑡𝑡 𝑅𝑅𝑅𝑅 𝑖𝑖 𝑅𝑅𝑅𝑅 𝑡𝑡 𝑖𝑖 𝑡𝑡 where , is the value𝑅𝑅𝑅𝑅𝑅𝑅-weighted𝛼𝛼 return𝛽𝛽 𝑅𝑅𝑅𝑅𝑅𝑅 of all stocks𝛽𝛽 in𝑅𝑅𝑅𝑅𝑅𝑅 the top 𝜀𝜀 quintile on day t and

𝑅𝑅𝑅𝑅𝑅𝑅𝐻𝐻𝐻𝐻 𝑡𝑡 𝑃𝑃𝑃𝑃𝑃𝑃 , is the value-weighted return of the remaining NYSE stocks. Thus, , in (5) measures 𝐵𝐵 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑡𝑡 𝛽𝛽𝐻𝐻𝐻𝐻 𝑖𝑖

12 The results reported in the paper are obtained by the value-weighted average of residual returns. Our results are stronger if we construct the benchmark using equal-weighted residual returns of high program trading stocks.

17

return comovement of stock related to program trading, which is the counterpart of , in (4).

𝐻𝐻𝐻𝐻 𝑖𝑖 This bivariate approach not 𝑖𝑖only considers whether high program trading stocks comove𝛽𝛽 more

with each other but also takes into account how these stocks comove with other stocks in the

market at the same time.

In the second step, we relate the measures of return comovement in a quarter, i.e., , ,

𝛽𝛽𝐻𝐻𝐻𝐻 𝑖𝑖 , and , , with of the contemporaneous and lagged quarters, respectively. If program 𝐵𝐵 𝐵𝐵 𝐻𝐻𝐻𝐻 𝑖𝑖 𝑅𝑅𝑅𝑅 𝑖𝑖 𝑖𝑖 trading𝛽𝛽 contributes𝛽𝛽 to 𝑃𝑃𝑃𝑃excessive𝑃𝑃 comovement, we expect a positive relationship between and

𝐻𝐻𝐻𝐻 . On the other hand, if stocks with high comove more with other high stocks𝛽𝛽 but less𝑃𝑃𝑃𝑃𝑃𝑃 with the rest of the market, we expect a𝑃𝑃𝑃𝑃𝑃𝑃 positive relationship between 𝑃𝑃𝑃𝑃𝑃𝑃 and but a 𝐵𝐵 𝐻𝐻𝐻𝐻 negative relationship between and . 𝛽𝛽 𝑃𝑃𝑃𝑃𝑃𝑃 𝐵𝐵 𝑅𝑅𝑅𝑅 In Panel A of Table III,𝛽𝛽 we sort 𝑃𝑃𝑃𝑃𝑃𝑃all sample stocks into quintiles by either contemporaneous

or lagged quarterly for each quarter, calculate the equal-weighted averages of , and 𝐵𝐵 𝐻𝐻𝐻𝐻 𝐻𝐻𝐻𝐻 , and report their𝑃𝑃𝑃𝑃𝑃𝑃 time-series means over the whole sample period. It can be seen𝛽𝛽 that 𝛽𝛽 and 𝐵𝐵 𝑅𝑅𝑅𝑅 𝐻𝐻𝐻𝐻 𝛽𝛽 increase monotonically in contemporaneous , which is consistent with the notion𝛽𝛽 that 𝐵𝐵 𝐻𝐻𝐻𝐻 program𝛽𝛽 trading contributes to excessive comovement.𝑃𝑃𝑃𝑃𝑃𝑃 Both and reach the maximum for 𝐵𝐵 𝐻𝐻𝐻𝐻 𝐻𝐻𝐻𝐻 stocks in the top quintile but turn to negative for stocks𝛽𝛽 in the 𝛽𝛽bottom quintile. The differences between𝑃𝑃𝑃𝑃𝑃𝑃 these two quintiles are also statistically significant at the 𝑃𝑃𝑃𝑃𝑃𝑃1% level. Turning

to the estimate, it has a monotonic negative relationship with contemporaneous , meaning 𝐵𝐵 𝑅𝑅𝑅𝑅 that after𝛽𝛽 controlling for returns of high stocks, stocks with higher program trading𝑃𝑃𝑃𝑃𝑃𝑃 comove

less with the rest of the market, as predicted𝑃𝑃𝑃𝑃𝑃𝑃 by the habitat investing model of BSW.

INSERT TABLE III HERE

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We find almost identical patterns of , and in the lower segment of Panel A, 𝐵𝐵 𝐵𝐵 𝐻𝐻𝐻𝐻 𝐻𝐻𝐻𝐻 𝑅𝑅𝑅𝑅 where stocks are sorted based on the lagged𝛽𝛽 quarterly𝛽𝛽 𝛽𝛽. It further justifies our contention:

program traders choose to trade a subset of all available𝑃𝑃𝑃𝑃𝑃𝑃 securities, and such a preferred habitat

leads to persistent participation of program trading in some stocks and contributes to excessive comovement among these stocks. To focus on the habitat view and for easier exposition, we present results based on analyzing lagged quarterly from now on, despite the fact that the results based on contemporaneous are often stronger𝑃𝑃𝑃𝑃𝑃𝑃.13

Panel B of Table III presents𝑃𝑃𝑃𝑃𝑃𝑃 average , and based on double-sorting analysis. 𝐵𝐵 𝐵𝐵 𝐻𝐻𝐻𝐻 𝐻𝐻𝐻𝐻 𝑅𝑅𝑅𝑅 Stocks are first sorted into tertiles according to𝛽𝛽 either𝛽𝛽 the previous𝛽𝛽 quarter’s firm size or turnover

ratio. Within each size or turnover tertile, stocks are further sorted into quintiles based on their

previous quarter’s . It can be seen that has a positive relationship with and but 𝐵𝐵 𝐻𝐻𝐻𝐻 𝐻𝐻𝐻𝐻 a negative one with𝑃𝑃𝑃𝑃𝑃𝑃 in all subsamples 𝑃𝑃𝑃𝑃𝑃𝑃considered. Comparing the stocks 𝛽𝛽within the𝛽𝛽 same 𝐵𝐵 𝑅𝑅𝑅𝑅 quintile rank, we find𝛽𝛽 that stocks of smaller size or with lower turnover exhibit more excessive comovement, as evidenced by the negative relationships of both firm size and turnover with

𝐻𝐻𝐻𝐻 and . The habitat view of comovement is developed in economies with limits-to-arbitrage,𝛽𝛽 𝐵𝐵 𝐻𝐻𝐻𝐻 which𝛽𝛽 predicts that stocks with more limits-to-arbitrage are more likely to exhibit excessive comovement among stocks. Since smaller and more thinly-traded stocks are expected to be associated with more limits-to-arbitrage (Shleifer and Vishny, 1994), our findings provide further evidence supporting this view.

13 These are available upon request.

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4.3. Program Trading and Excessive Return Comovement: Regression Analysis

Results in the previous subsection provide primary evidence of excessive return comovement due to program trading and its robustness against the variations in firm size and turnover ratio. However, it is still possible for program trading to be attracted by other firm characteristics that potentially affect return comovement. To address this concern, we use the

Fama-MacBeth (1973) style regressions to control for a wide range of firm characteristics, including natural logarithm of firm size ( ( )), natural logarithm of stock price ( ( )), natural logarithm of turnover ratio ( ( 𝐿𝐿𝐿𝐿 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 )), and book-to-market ratio ( / )𝐿𝐿. 𝐿𝐿 𝑃𝑃𝑃𝑃𝑃𝑃

Program traders are predomina𝐿𝐿𝐿𝐿 ntly𝑇𝑇𝑇𝑇𝑇𝑇 𝑇𝑇institutional𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 investors and prior literature𝐵𝐵 𝑀𝑀 finds that analyst coverage affects return comovement (Chan and Hameed, 2006; Hameed, Morck, Shen and

Yeung, 2015; Piotroski and Roulstone, 2004). Moreover, program traders are likely to trade a subset of stocks because of their historical return characteristics such as cumulative return and volatility. Consequently, our controls also include a percentage of 13F institutional ownership

( ), average daily bid-ask spread ( ), natural logarithm of the number of analysts following𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 plus 1 ( ( + 1)), cumulative𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 stock return ( ), and natural logarithm of realized volatility of daily𝐿𝐿 𝐿𝐿returns𝐴𝐴𝐴𝐴𝐴𝐴 ( ( )). All control variables𝑅𝑅𝑅𝑅𝑅𝑅 are lagged by one quarter in regressions. Finally, we add𝐿𝐿 𝐿𝐿an 𝑆𝑆S&P𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 500 dummy ( & 500) if the stock is a constituent of the

S&P 500 index in the concurrent quarter. This dummy𝑆𝑆 𝑃𝑃 controls for the possibility that return comovement is driven by trading activities of index funds, and we will return to this issue with more extensive tests later.

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The first two columns of Table IV present estimated slope coefficients from the regressions

of . The effect of is highly significant, indicating that program trading plays a substantial

𝐻𝐻𝐻𝐻 role𝛽𝛽 in determining excess𝑃𝑃𝑃𝑃𝑃𝑃ive comovement of stock returns. Moreover, this role is immune to the

effects of all control variables considered. Although including controls to a certain extent weakens

the positive association between and lagged quarterly , it is still highly significant at the

𝐻𝐻𝐻𝐻 1% level. In terms of economic𝛽𝛽 significance, a one-standard𝑃𝑃𝑃𝑃𝑃𝑃-deviation increase in (7%) is associated with an increase of 0.24 in , which equates to a 77% increase from its mean𝑃𝑃𝑃𝑃𝑃𝑃 of 0.30.

𝐻𝐻𝐻𝐻 Columns (3)-(4) and (5)-(6) in Table IV𝛽𝛽, respectively, report regressions of and on lagged 𝐵𝐵 𝐵𝐵 𝐻𝐻𝐻𝐻 𝑅𝑅𝑅𝑅 quarterly and controls. The results show that after controlling these𝛽𝛽 firm characteristics,𝛽𝛽

lagged quarterly𝑃𝑃𝑃𝑃𝑃𝑃 is significantly and positively related to and negatively related to . 𝐵𝐵 𝐵𝐵 𝐻𝐻𝐻𝐻 𝑅𝑅𝑅𝑅 Our findings are therefore𝑃𝑃𝑃𝑃𝑃𝑃 confirmed as being robust and not driven𝛽𝛽 by those fundamental controls.𝛽𝛽

INSERT TABLE IV HERE

Turning to the effects of control variables in columns 2 and 4, both ( ) and

( ) have significantly negative effects on and , which is consistent𝐿𝐿𝐿𝐿 𝑆𝑆 𝑆𝑆with𝑆𝑆𝑆𝑆 the 𝐵𝐵 𝐻𝐻𝐻𝐻 𝐻𝐻𝐻𝐻 𝐿𝐿findings𝐿𝐿 𝑇𝑇𝑇𝑇𝑇𝑇 𝑇𝑇from𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 our nonparametric analysis. Stock price𝛽𝛽 is found𝛽𝛽 to be an inverse proxy for

transaction costs in prior studies, while analyst coverage is often considered to be negatively

related to information asymmetry.14 As pointed out by BSW, habitat investing can arise due to transaction costs or lack of information, and therefore firms with higher transaction costs and less

14 For instance, Bhardwaj and Brooks (1992) suggest that the bid-ask spread and the brokerage commission are inversely related to stock price. Kelly and Ljungqvist (2012) use natural experiments related to analyst coverage to test asymmetric-information asset pricing models.

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information asymmetry are more likely to be preferred by habitat investors. In columns 2 and 4,

both ( ) and ( + 1) have significantly negative effects on and , consistent 𝐵𝐵 𝐻𝐻𝐻𝐻 𝐻𝐻𝐻𝐻 with 𝐿𝐿the𝐿𝐿 habitat𝑃𝑃𝑃𝑃𝑃𝑃 view.𝐿𝐿𝐿𝐿 As𝐴𝐴𝐴𝐴 program𝐴𝐴 trading is dominated by institutions, we𝛽𝛽 expect𝛽𝛽 the identified

comovement to increase with institutional ownership, which is confirmed by the significant and

positive relationships of with and in columns 2 and 4, respectively. Column 6 𝐵𝐵 𝐻𝐻𝐻𝐻 𝐻𝐻𝐻𝐻 reports the regression results𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 of , and𝛽𝛽 all estimated𝛽𝛽 coefficients on explanatory variables, except 𝐵𝐵 𝑅𝑅𝑅𝑅 for that of ( ), have a sign𝛽𝛽 opposite to the coefficients for the regression of in column 𝐵𝐵 𝐻𝐻𝐻𝐻 4. This result𝐿𝐿𝐿𝐿 is𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 intuitive because stocks with certain characteristics comove more 𝛽𝛽with stocks in

their habitat and less with the rest of the market.

5. Extended Analysis

Our analysis so far suggests a strong common return component exists among stocks with

high program trading, and such comovement is unlikely to be related to fundamentals. In this

section, we elaborate further on the non-fundamental nature of the identified comovement. We

also intend to eliminate the possibility of this comovement being the result of gradual information

diffusion or index fund trading. Because the residual and bivariate approaches lead to similar

results, we only tabulate the results obtained from the residual approach in this section and the

extended results based on the bivariate approach are available upon request.

5.1. The Effect of Information

Our first test examines the role of information in explaining program-trading-induced

return comovement. Pindyck and Rotemberg (1993) point out that the prices of different stocks

22

can move together either because of common earnings (e.g., common industry) or macroeconomic

variables that have common effects on discount rates. Thus, we test the effects of macroeconomic information and industry fundamentals by estimating the following regression model:

, = + , , , + , : × , , + , . (6)

𝑖𝑖 𝑡𝑡 𝑖𝑖 𝐻𝐻𝐻𝐻 𝑖𝑖 𝐻𝐻𝐻𝐻 𝑖𝑖 𝑡𝑡 𝐻𝐻𝐻𝐻𝐻𝐻 𝑖𝑖 𝑡𝑡−1 𝑡𝑡+1 𝐻𝐻𝐻𝐻 𝑖𝑖 𝑡𝑡 𝑖𝑖 𝑡𝑡 Here, we𝑅𝑅𝑅𝑅𝑅𝑅 re-construct𝛼𝛼 a𝛽𝛽 benchmark𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 of high𝛽𝛽 program�𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 trading for stock by𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 excluding� stocks𝜖𝜖 within

its own industry. The residual return of this benchmark is denoted by𝑖𝑖 , , , which replaces

𝐻𝐻𝐻𝐻 𝑖𝑖 𝑡𝑡 , in regression (4) and industry is defined as stocks having the same𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 2-digit SIC code. We

𝐻𝐻𝐻𝐻 𝑡𝑡 also𝑅𝑅𝑅𝑅𝑅𝑅 introduce a dummy variable : , which equals to unity if, according to

𝑡𝑡−1 𝑡𝑡+1 RavenPack, there is novel macro news𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 announced in the 3-day period surrounding day t and zero otherwise.15 If return comovement associated with program trading primarily reflects common industry information, we expect a large decline in , or even insignificant after excluding stocks

𝐻𝐻𝐻𝐻 𝑖𝑖 within the same industry in the benchmark. On the𝛽𝛽 other hand, if return comovement associated

with program trading is primarily driven by the release of macroeconomic news, we expect a

significant portion of comovement to be captured by the interaction term of macro news dummy

with , , , i.e., a significantly positive , .

𝐻𝐻𝐻𝐻 𝑖𝑖 𝑡𝑡 𝐻𝐻𝐻𝐻𝐻𝐻 𝑖𝑖 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅Table V presents the estimation results𝛽𝛽 of and for stocks sorted into quintiles

𝐻𝐻𝐻𝐻 𝐻𝐻𝐻𝐻𝐻𝐻 according to lagged only and according to both𝛽𝛽 lagged𝛽𝛽 and firm characteristics. The first row of Panel A depicts𝑃𝑃𝑃𝑃𝑃𝑃 the average within each quintile𝑃𝑃𝑃𝑃𝑃𝑃 and difference between high

𝛽𝛽𝐻𝐻𝐻𝐻 𝛽𝛽𝐻𝐻𝐻𝐻

15 We use a 3-day event window for both macro and firm-specific news to account for the possibilities of informed trading and market under-reaction or over-reaction. Our results are even stronger if using a 1-day event window.

23

and low quintiles. These figures are comparable to their counterparts reported in Panel A of

Table III,𝑃𝑃𝑃𝑃𝑃𝑃 where stocks within the same industry are not excluded from the benchmark. Moreover,

even when the sample stocks are further sorted by or , Panel A of Table V and

Panel B of Table III display remarkably similar patterns.𝑆𝑆𝑆𝑆𝑆𝑆 𝑆𝑆 These𝑇𝑇𝑇𝑇𝑇𝑇 observations𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 suggest that program- trading-induced return comovement is unlikely to be driven by program traders trading on industry information.

INSERT TABLE V HERE

Results in Panel B of Table V shows that the magnitude of is close to 0 and

𝐻𝐻𝐻𝐻𝐻𝐻 insignificant for all quintiles. 16 Therefore, macroeconomic announcement𝛽𝛽 s also fail to

explain return comovement𝑃𝑃𝑃𝑃𝑃𝑃 driven by program trading.

Patton and Verardo (2012) demonstrate that firm beta increases significantly on earnings

announcement days. They interpret their finding as investors updating their perceptions of market-

wide earnings using firm-specific information. Therefore, we also consider the effect of firm-

specific news by the following regression specification:

, = + , , + , ( , × , ) + , , (7)

𝑖𝑖 𝑡𝑡 𝑖𝑖 𝐻𝐻𝐻𝐻 𝑖𝑖 𝐻𝐻𝐻𝐻 𝑡𝑡 𝐻𝐻𝐻𝐻𝐻𝐻 𝑖𝑖 𝑖𝑖 𝑡𝑡−1 ∶𝑡𝑡+1 𝐻𝐻𝐻𝐻 𝑡𝑡 𝑖𝑖 𝑡𝑡 where 𝑅𝑅𝑅𝑅𝑅𝑅 , 𝛼𝛼 𝛽𝛽 is a𝑅𝑅𝑅𝑅𝑅𝑅 dummy variable𝛽𝛽 𝐹𝐹𝐹𝐹 that𝐹𝐹𝐹𝐹 is𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 equal to unity 𝑅𝑅𝑅𝑅𝑅𝑅if RavenPack𝜖𝜖 records any

𝑖𝑖 𝑡𝑡−1 ∶𝑡𝑡+1 novel news𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 related𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 to firm i in the 3-day period surrounding day t and zero otherwise. Regression

(7) extends baseline model (4) by including the interaction term of firm-specific news dummy with

16 In results unreported, we confirm is insignificantly different from 0 in virtually every quintile.

𝛽𝛽𝐻𝐻𝐻𝐻𝐻𝐻 𝑃𝑃𝑃𝑃𝑃𝑃

24

the residual return benchmark of high stocks. 17 If program traders buy and sell stock portfolios based on firm-specific information,𝑃𝑃𝑃𝑃𝑃𝑃 a significant portion of return comovement should

be captured by firm-specific news, reflected by a significant , . In Panel A of Table VI,

𝐻𝐻𝐻𝐻𝐻𝐻 𝑖𝑖 𝐻𝐻𝐻𝐻 exhibits patterns similar to those in Panels A and B of Table III.𝛽𝛽 More importantly, results in Panel𝛽𝛽

B of Table VI show is on average indistinguishable from 0 for all quintiles and

𝐻𝐻𝐻𝐻𝐻𝐻 subsamples stratified by𝛽𝛽 and firm characteristics of and . Thus,𝑃𝑃𝑃𝑃𝑃𝑃 firm-specific news also fails to explain𝑃𝑃𝑃𝑃𝑃𝑃 the return comovement triggered𝑆𝑆𝑆𝑆𝑆𝑆 by𝑆𝑆 program𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑇𝑇trading𝑇𝑇𝑇𝑇𝑇𝑇 .

INSERT TABLE VI HERE

To provide a more comprehensive test on the effects of information, we include

macroeconomic, industry, and firm-specific information in one regression:

, = + , , , + , ( × , , ) (8) 𝑖𝑖 𝑡𝑡 𝑖𝑖 𝐻𝐻𝐻𝐻 𝑖𝑖 𝐻𝐻𝐻𝐻 𝑖𝑖 𝑡𝑡 𝐻𝐻𝐻𝐻𝐻𝐻 𝑖𝑖 𝑡𝑡−1 ∶𝑡𝑡+1 𝐻𝐻𝐻𝐻 𝑖𝑖 𝑡𝑡 𝑅𝑅𝑅𝑅𝑅𝑅 𝛼𝛼 𝛽𝛽+ 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅, ( 𝛽𝛽 , 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 × , , ) + ,𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅.

𝐻𝐻𝐻𝐻𝐻𝐻 𝑖𝑖 𝑖𝑖 𝑡𝑡−1 ∶𝑡𝑡+1 𝐻𝐻𝐻𝐻 𝑖𝑖 𝑡𝑡 𝑖𝑖 𝑡𝑡 After , , , and ,𝛽𝛽 are estimated𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 for stock i and𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 quarter Q, we𝜖𝜖 run a Fama-MacBeth

𝐻𝐻𝐻𝐻 𝑖𝑖 𝐻𝐻𝐻𝐻𝐻𝐻 𝑖𝑖 𝐻𝐻𝐻𝐻𝐻𝐻 𝑖𝑖 (1973)𝛽𝛽 style 𝛽𝛽regression 𝛽𝛽to investigate their cross-sectional relationships with the lagged quarterly

. According to the results reported in Table VII, the positive association between and

𝐻𝐻𝐻𝐻 lagged𝑃𝑃𝑃𝑃𝑃𝑃 is still highly significant after controlling for various sources of information.𝛽𝛽 More

importantly,𝑃𝑃𝑃𝑃𝑃𝑃 its estimated magnitudes are very close to the baseline results, where news or

17 In regression specification (7), the benchmark portfolio for a stock does not exclude stocks within its own industry, since it is more likely for investors to update their perceptions of industry earnings using firm-specific information

(Patton and Verardo, 2012). In robustness checks, we consider the benchmark portfolio with the stocks in the same industry excluded and obtain qualitatively similar results.

25

information is not explicitly considered. On the other hand, neither or exhibits a

𝐻𝐻𝐻𝐻𝐻𝐻 𝐻𝐻𝐻𝐻𝐻𝐻 significant relationship with lagged . Overall, our analysis in this 𝛽𝛽subsection𝛽𝛽 demonstrates that macroeconomic, industry, and𝑃𝑃𝑃𝑃𝑃𝑃 firm-specific information all fail to explain the return comovement associated with program trading. The lack of information’s explanatory power further supports the hypothesis that program trading contributes to excessive comovement that is not related to economic fundamentals.

INSERT TABLE VII HERE

5.2. Program Trading and Return Reversals

Although we have shown program trading is not driven by fundamentals and results in

return comovement that is not related to information, we take an alternative approach in this

subsection to further demonstrate the non-fundamental nature of program-trading-induced return

comovement. If correlated program trading activities cause stock returns to temporarily overshoot

fundamentals, the excessive return movements should be reversed in the subsequent period. On

the other hand, if the return movements driven by program trading mainly reflect common

fundamentals, the impacts of the trading on stock prices must be permanent. Therefore, the

existence of return reversal can serve as an important gauge to determine whether program trading

is driven by economic fundamentals.

We use two measures to capture the possible return reversal associated with program

trading. The first measure is simply the first-order autocorrelation of daily stock return ( ),

estimated over a quarterly horizon. Alternatively, we follow Greenwood (2007) and use daily𝐴𝐴 𝐴𝐴𝐴𝐴data

to estimate a time-series regression for stock i over a quarter:

26

, = + , , + , , + , . (9)

𝑖𝑖 𝑡𝑡 𝑖𝑖 𝑚𝑚𝑚𝑚𝑚𝑚 𝑖𝑖 𝑚𝑚𝑚𝑚𝑚𝑚 𝑡𝑡 𝐿𝐿𝐿𝐿𝐿𝐿 𝑖𝑖 𝐻𝐻𝐻𝐻 𝑡𝑡−1 𝑖𝑖 𝑡𝑡 Since the portfolio return𝑅𝑅𝑅𝑅𝑅𝑅 of 𝛼𝛼high 𝛽𝛽 stocks𝑅𝑅𝑅𝑅𝑅𝑅 in the𝛽𝛽 regressors𝑅𝑅𝑅𝑅𝑅𝑅 is lagged𝜀𝜀 by one day, ,

𝐿𝐿𝐿𝐿𝐿𝐿 𝑖𝑖 measures stock ’s return sensitivity𝑃𝑃𝑃𝑃𝑃𝑃 to the lagged return benchmark of high stocks𝛽𝛽, after controlling for contemporaneous𝑖𝑖 market return. We then run a Fama-MacBeth𝑃𝑃𝑃𝑃𝑃𝑃 (1973) style regression on or against lagged and firm characteristics. Table VIII documents a

𝐿𝐿𝐿𝐿𝐿𝐿 significantly negative𝐴𝐴𝐴𝐴𝐴𝐴 𝛽𝛽 relationship between𝑃𝑃𝑃𝑃𝑃𝑃 ACF and lagged , whether controls for firm

characteristics are included or not. This indicates that program𝑃𝑃𝑃𝑃𝑃𝑃 trading contributes to negative

autocorrelation in daily stock returns and increases return reversal. Moreover, also has a

𝐿𝐿𝐿𝐿𝐿𝐿 significantly negative relationship with lagged . Combining this result with 𝛽𝛽the observation

from Table IV that increases in lagged 𝑃𝑃𝑃𝑃𝑃𝑃, we offer support to the argument that program

𝐻𝐻𝐻𝐻 trading contemporaneously𝛽𝛽 contributes to excessive𝑃𝑃𝑃𝑃𝑃𝑃 return comovement but leads to increased

return reversal in the following trading day. Since program trading enhances return reversal

gauged by both measures, it is quite unlikely to be fundamental-driven.

INSERT TABLE VIII HERE

5.3. The Hypothesis of Gradual Information Diffusion

BSW proposes the hypothesis of gradual information diffusion as an alternative

explanation for why return of stocks may comove differently. It asserts that some stocks may

incorporate market information faster than others due to variations in market frictions or

information environment. Since program traders are predominantly sophisticated institutional

investors, one may expect their trading activities to enable stocks to more promptly incorporate

market information. If this is the case, the returns of high stocks should positively lead the

𝑃𝑃𝑃𝑃𝑃𝑃

27

returns of low stocks. We run the vector autoregression (VAR) model below to test this

relationship: 𝑃𝑃𝑃𝑃𝑃𝑃

, = + , + , + , , (10) 5 5 𝑅𝑅𝑅𝑅𝑅𝑅𝐿𝐿𝐿𝐿 𝑡𝑡 𝑎𝑎0 ∑𝑘𝑘=1 𝑎𝑎𝑘𝑘𝑅𝑅𝑅𝑅𝑅𝑅𝐿𝐿𝐿𝐿 𝑡𝑡−𝑘𝑘 ∑𝑘𝑘=1 𝑏𝑏𝑘𝑘 𝑅𝑅𝑅𝑅𝑅𝑅𝐻𝐻𝐻𝐻 𝑡𝑡−𝑘𝑘 𝑢𝑢𝐿𝐿𝐿𝐿 𝑡𝑡 , = + , + , + , . (11) 5 5 𝐻𝐻𝐻𝐻 𝑡𝑡 0 𝑘𝑘=1 𝑘𝑘 𝐿𝐿𝐿𝐿 𝑡𝑡−𝑘𝑘 𝑘𝑘=1 𝑘𝑘 𝐻𝐻𝐻𝐻 𝑡𝑡−𝑘𝑘 𝐻𝐻𝐻𝐻 𝑡𝑡 Similar to our nonparametric𝑅𝑅𝑅𝑅𝑅𝑅 𝑐𝑐 analysis,∑ 𝑐𝑐 we𝑅𝑅𝑅𝑅𝑅𝑅 sort stocks∑ into𝑑𝑑 ter𝑅𝑅𝑅𝑅𝑅𝑅tiles by their𝑢𝑢 or of

the previous quarter. Within each or tertile, we further sort𝑆𝑆 stocks𝑆𝑆𝑆𝑆𝑆𝑆 𝑇𝑇𝑇𝑇𝑇𝑇into 𝑇𝑇quintiles𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇

according to their lagged s. In𝑆𝑆𝑆𝑆 𝑆𝑆(10)𝑆𝑆 and𝑇𝑇𝑇𝑇𝑇𝑇 (11)𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇, , and , are, respectively, value-

𝐿𝐿𝐿𝐿 𝑡𝑡 𝐻𝐻𝐻𝐻 𝑡𝑡 weighted averages of day-𝑃𝑃𝑃𝑃𝑃𝑃t returns of the stocks in the𝑅𝑅𝑅𝑅𝑅𝑅 bottom and𝑅𝑅𝑅𝑅𝑅𝑅 top quintiles of the same tertile. Because of the mechanical relationship between and trading𝑃𝑃𝑃𝑃𝑃𝑃 volume, estimating the

VAR within a or tertile helps to mitigate 𝑃𝑃𝑃𝑃𝑃𝑃the impacts of firm size and turnover on the cross-autocorrelation𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝑇𝑇𝑇𝑇𝑇𝑇 of𝑇𝑇 𝑇𝑇daily𝑇𝑇𝑇𝑇𝑇𝑇 stock returns (Chordia and Swaminathan, 2000). In the VAR system, we are interested in whether lagged portfolio return of high stocks positively predicts portfolio return of low stocks; i.e., whether is significantly𝑃𝑃𝑃𝑃𝑃𝑃 greater than 0.18 5 𝑘𝑘=1 𝑘𝑘 Column “High”𝑃𝑃𝑃𝑃𝑃𝑃 in Table IX reports the sum∑ s of𝑏𝑏 regression coefficients on the five lagged

returns of the high portfolio when the dependent variable is , (i.e., ) or , 5 𝐿𝐿𝐿𝐿 𝑡𝑡 𝑘𝑘=1 𝑘𝑘 𝐻𝐻𝐻𝐻 𝑡𝑡 (i.e., ), while𝑃𝑃𝑃𝑃𝑃𝑃 Column shows the coefficients on 1-day𝑅𝑅𝑅𝑅𝑅𝑅 lagged return∑ of 𝑏𝑏the high𝑅𝑅𝑅𝑅𝑅𝑅 5 𝑘𝑘=1 𝑘𝑘 1 portfolio∑ (i.e.,𝑑𝑑 or ). Columns𝐻𝐻 “Low” and present the corresponding figures for the𝑃𝑃𝑃𝑃𝑃𝑃 low

1 1 1 portfolio. 𝑏𝑏 The 𝑑𝑑column “Granger Causality”𝐿𝐿 reports the F-statistics of Granger (1969) tests,

𝑃𝑃𝑃𝑃𝑃𝑃

18 We estimate the VAR with a maximum of 5 lags because results based on additional lags provide no material difference.

28

where XCY indicates X Granger causes Y. The table shows that although the lagged portfolio

returns of high stocks have significant power of predicting the portfolio return of low

stocks, the relation𝑃𝑃𝑃𝑃𝑃𝑃 is negative, which is in the opposite direction as predicted by the hypothesis𝑃𝑃𝑃𝑃𝑃𝑃 of

gradual information diffusion. Moreover, this two-way Granger causality also does not support

the hypothesis, which presumes information is diffused from high stocks to low stocks

but not vice versa. It, in turn, eliminates information diffusion explanation𝑃𝑃𝑃𝑃𝑃𝑃 for the excessive𝑃𝑃𝑃𝑃𝑃𝑃 return

comovement caused by program trading.

INSERT TABLE IX HERE

5.4. Causal Relationship Between Program Trading and Return Comovement

To shed further light on the issue of causality, we run a market-wide analysis to test the

Granger causality (Granger, 1969) between and with the following VAR:

𝐻𝐻𝐻𝐻 , = + 𝑃𝑃𝑃𝑃𝑃𝑃, + 𝛽𝛽 + , , (12)

𝛽𝛽𝐻𝐻𝐻𝐻 𝑄𝑄 𝑎𝑎0 𝑎𝑎1𝛽𝛽𝐻𝐻𝐻𝐻 𝑄𝑄−1 𝑏𝑏1𝑃𝑃𝑃𝑃𝑃𝑃𝑄𝑄−1 𝑢𝑢𝛽𝛽 𝑡𝑡 = + + , + , , (13)

𝑄𝑄 0 1 𝑄𝑄−1 1 𝐻𝐻𝐻𝐻 𝑄𝑄−1 𝑃𝑃𝑃𝑃𝑃𝑃 𝑡𝑡 where , is the equal-𝑃𝑃𝑃𝑃𝑃𝑃weighted𝑐𝑐 average𝑐𝑐 𝑃𝑃𝑃𝑃𝑃𝑃 of , for𝑑𝑑 𝛽𝛽all NYSE stocks𝑢𝑢 in quarter Q, and is

𝐻𝐻𝐻𝐻 𝑄𝑄 𝐻𝐻𝐻𝐻 𝑖𝑖 𝑄𝑄 equal-weighted𝛽𝛽 average for all NYSE stocks𝛽𝛽 in quarter Q. The F-statistics reported in𝑃𝑃𝑃𝑃𝑃𝑃 Panel

A of Table X show that except𝑃𝑃𝑃𝑃𝑃𝑃 for stocks within the largest tertile of firm size, the null hypothesis

that does not Granger cause is rejected. On the other hand, the insignificance of

𝐻𝐻𝐻𝐻 1 reported𝑃𝑃𝑃𝑃𝑃𝑃 in Panel B suggests that 𝛽𝛽 does not Granger cause . Overall, our VAR test𝑑𝑑s

𝐻𝐻𝐻𝐻 suggest causality runs from program𝛽𝛽 trading to its corresponding𝑃𝑃𝑃𝑃𝑃𝑃 return comovement, but not in

the opposite direction. Although different from previous analyses that focused on the cross-

29 sectional relationship, the causality test here does reveal that the identified return comovement is largely driven by the intensity of program trading activity itself.

INSERT TABLE X HERE

5.5. Trading of Index Funds

The basket nature of program trading makes it an ideal trading platform for ETF managers to incorporate retail investment flows, and a recent study has offered evidence of ETF arbitrage contributing to excessive return comovement (Da and Shive, 2018). To address the concern that return commonality identified as driven by program trading may simply pick up the effects of index fund trading, we provide two additional tests.

First, if the identified comovement is mainly driven by ETF trading, the presence of this comovement should largely concentrate on days with large ETF inflows or outflows. Therefore we extend regression (4) to isolate the effects of ETF flows:

, = + , , + , , × (14) 𝑅𝑅𝑅𝑅𝑅𝑅𝑖𝑖 𝑡𝑡 𝛼𝛼𝑖𝑖 𝛽𝛽𝐻𝐻𝐻𝐻 𝑖𝑖𝑅𝑅𝑅𝑅𝑅𝑅𝐻𝐻𝐻𝐻 𝑡𝑡 𝛽𝛽𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑖𝑖�𝑅𝑅𝑅𝑅𝑅𝑅𝐻𝐻𝐻𝐻 𝑡𝑡 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑛𝑛𝑡𝑡� + , , × + , .

𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑖𝑖 𝐻𝐻𝐻𝐻 𝑡𝑡 𝑡𝑡 𝑖𝑖 𝑡𝑡 On each day, we aggregate market-wide𝛽𝛽 ETF �flow𝑅𝑅𝑅𝑅𝑅𝑅s and compute𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑡𝑡 a� net 𝜀𝜀dollar flow. We scale this amount by the total market capitalization of all CRSP stocks at the end of the previous quarter.

Dummy variable in regression (14) is equal to 1 if the net ETF flow on day is ranked in

𝑡𝑡 the top 25% of daily𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 net𝑛𝑛 flows in the concurrent quarter, and 0 otherwise. Similar𝑡𝑡ly,

𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑡𝑡𝑡𝑡

30

identifies days where net ETF flow is in the bottom 25%. Furthermore, we also use a more

stringent classification rule by setting the cut-off points at 10%.19

Table XI presents average , and using estimates obtained from model

𝐻𝐻𝐻𝐻 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 (14). Numbers in the square brackets𝛽𝛽 report𝛽𝛽 the percentage𝛽𝛽 of stocks whose estimated coefficients

are positively significant at the 10% level. Our first observation is that remains positive and

𝐻𝐻𝐻𝐻 highly correlated with lagged quarterly after controlling for ETF 𝛽𝛽flows. Furthermore, its magnitudes and patterns are quite similar 𝑃𝑃𝑃𝑃𝑃𝑃to its counterparts reported in Table III, where ETF flows are not considered. The magnitudes of average and on the other hand are close to

𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 0 and are generally insignificant across all 𝛽𝛽quintiles. Moreover𝛽𝛽 , we even observe a slightly negative association between and lagged𝑃𝑃𝑃𝑃𝑃𝑃 quarterly , which implies ETF inflow is likely

𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 to weaken rather than enhance𝛽𝛽 the identified excessive comovement.𝑃𝑃𝑃𝑃𝑃𝑃 Since the role of ETF flows can be reflected by coefficients and , these findings further confirm that the return

𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 comovement driven by program𝛽𝛽 trading is not𝛽𝛽 caused by ETF trading.

INSERT TABLE XI HERE

Our second test addresses the concern that the return comovement identified through our

analysis is driven by trading of index funds. Index funds trade stock portfolios and program trading

is a convenient vehicle for them. Therefore, we apply daily data to estimate the following time- series regression for stock i over all individual quarters in our sample period:

19 Our results are similar if we classify trading days based on ETF inflow and outflow distributions over the whole sample period.

31

, = + , , + , , × , + , , + , , (15)

𝑖𝑖 𝑡𝑡 𝑖𝑖 𝐼𝐼𝐼𝐼 𝑖𝑖 𝐼𝐼𝐼𝐼 𝑡𝑡 𝐼𝐼𝐼𝐼𝐼𝐼 𝑖𝑖 𝐼𝐼𝐼𝐼 𝑡𝑡 𝑖𝑖 𝑡𝑡 𝑃𝑃𝑃𝑃𝑃𝑃 𝑖𝑖 𝑖𝑖 𝑡𝑡 𝑖𝑖 𝑡𝑡 where 𝑅𝑅𝑅𝑅𝑅𝑅, is the 𝛼𝛼return𝛽𝛽 of 𝑅𝑅𝑅𝑅𝑅𝑅index on𝛽𝛽 day�𝑅𝑅𝑅𝑅𝑅𝑅 . Note that𝑃𝑃𝑃𝑃𝑃𝑃 if �we have𝛽𝛽 mis𝑃𝑃𝑃𝑃𝑃𝑃-specified𝜀𝜀 the driving

𝐼𝐼𝐼𝐼 𝑡𝑡 force for𝑅𝑅𝑅𝑅𝑅𝑅 the identified comovement,𝐼𝐼𝐼𝐼 the sensitivity𝑡𝑡 of a stock return to index return should be

partly explained by the program trading of this stock. In other words, coefficient , in

𝐼𝐼𝐼𝐼𝐼𝐼 𝑖𝑖 regression (15) should be different from zero. Table XII documents the results of the regression𝛽𝛽

for S&P 500 and Russell 2000 indexes since they are the typical targets of index funds for large-

cap and small-cap stocks, respectively. As can be seen from Table XII, estimated is mostly

𝐼𝐼𝐼𝐼𝐼𝐼 negative and insignificant in subsamples as well as for the full sample period𝛽𝛽. Thus, the relationship between and excessive comovement is not merely a consequence of program trading reflecting index𝑃𝑃𝑃𝑃𝑃𝑃-related return comovement.

INSERT TABLE XII HERE

6. Conclusion

Program trading is highly persistent and some stocks are more likely to be in the investment

habitat of program traders. The excessive return comovement in stocks preferred by program

traders is strong and evident. This excessive comovement cannot be explained by macroeconomic,

industry, and firm-specific information, which further confirms its non-fundamental nature. Thus, the evidence in this paper identifies a new and distinct source of the excessive comovement among stocks, which supports BSW’s habitat investing theory for excessive return comovment.

By examining the consequence of program trading, we find it not only introduces a strong common component in contemporaneous stock return but also leads to a common reversal

32

component in subsequent periods. This indicates that program trading adds systemic noise to daily

stock returns. The uniqueness of program-trading-induced comovement is also reflected by the fact that it cannot be explained by gradual information diffusion and ETF net flow or index fund trading, which provides additional support to the notion that habitat investing by program traders represents a distinct source of return comovement.

Findings from our study have implications for investors making decisions on risk management and asset allocation. Since return comovement associated with program trading is excessive, investors over-allocating their portfolios to high program trading stocks bear additional exposures to such risk. It is thus worthwhile to consider non-fundamental factors, for example program trading activities, when managing risk and allocating assets.

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Table I: Summary Statistics This table presents summary statistics for variables used in the study. Panel A reports statistics across all firm-quarters between 2006Q3 and 2015Q4. Panel B presents averages of and firm characteristics for each quintile. In the table, is the daily ratio of program trading volume to total trading volume, averaged over a quarter. is quarter-end market capitalization of a firm. is quarter-𝑃𝑃𝑃𝑃𝑃𝑃end stock price. / denotes a firm’s𝑃𝑃𝑃𝑃𝑃𝑃 book value of equity divided𝑃𝑃𝑃𝑃𝑃𝑃 by total market capitalization, calculated at the end of the quarter. is the daily ratio𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 of trading volume to the number of shares outstanding𝑃𝑃𝑃𝑃𝑃𝑃 , averaged over a quarter. 𝐵𝐵 𝑀𝑀 is quarter-end percentage of 13F institutional ownership. is the number of analysts following the company. 𝑇𝑇𝑇𝑇𝑇𝑇, 𝑇𝑇expressed𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 in percentage, is the average of daily spreads over a quarter, where daily spread is estimated by𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 2( )/ ( + ) using and prices of the𝐴𝐴 𝐴𝐴stock𝐴𝐴 at the end of the day. is cumulative monthly𝑆𝑆𝑆𝑆 stock𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 return over a quarter. is realized volatility estimated by daily returns over a quarter. 𝐴𝐴𝐴𝐴𝐴𝐴 − 𝐵𝐵𝐵𝐵𝐵𝐵 𝐴𝐴𝐴𝐴𝐴𝐴 𝐵𝐵𝐵𝐵𝐵𝐵 𝐵𝐵𝐵𝐵𝐵𝐵 𝐴𝐴𝐴𝐴𝐴𝐴 𝑅𝑅𝑅𝑅𝑅𝑅 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 Panel A: Full Sample Mean SD Min Max Median 22% 7% 4% 43% 21% ($Million) 8827 25257 74 140649 2111 𝑃𝑃𝑃𝑃𝑃𝑃 ($) 38.13 77.06 0.187 4509 28.46 𝑆𝑆𝑆𝑆/𝑆𝑆𝑆𝑆 0.56 1.27 0.04 2.6 0.53 𝑃𝑃𝑃𝑃𝑃𝑃 0.01 0.01 0.001 0.05 0.01 𝐵𝐵 𝑀𝑀 0.75 0.25 0.04 1.00 0.81 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 10 6.96 0.00 30 8.26 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 0.14 0.26 0.6 10.08 0.74 𝐴𝐴𝐴𝐴𝐴𝐴 0.02 0.24 -0.63 0.68 0.03 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 0.02 0.02 0.00 0.51 0.02 𝑅𝑅𝑅𝑅𝑅𝑅 Panel B: Average Firm Characteristics for Each PTP Quintile 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 High 4 3 2 Low 31% 24% 20% 17% 11% ($Million) 3840 9545 10843 9079 12031 𝑃𝑃𝑃𝑃𝑃𝑃 ($) 29.61 38.19 41.69 40.87 39.90 𝑆𝑆𝑆𝑆/𝑆𝑆𝑆𝑆 0.67 0.57 0.54 0.51 0.45 𝑃𝑃𝑃𝑃𝑃𝑃 0.56 0.78 0.99 1.30 1.77 𝐵𝐵 𝑀𝑀 0.67 0.69 0.72 0.73 0.62 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 5.6 8.99 11.04 12.33 11.33 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 0.13 0.10 0.11 0.12 0.02 𝐴𝐴𝐴𝐴𝐴𝐴 0.01 0.03 0.03 0.03 0.03 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 0.02 0.03 0.02 0.02 0.02 𝑅𝑅𝑅𝑅𝑅𝑅 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆

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Table II: Persistence of Program Trading This table demonstrates the persistence of program trading across individual stocks. For every quarter Q between 2006Q3 and 2015Q4, all NYSE stocks are sorted into quintiles according to their s in that quarter. The table reports average s of quintiles in quarter Q and the four subsequent quarters. The bottom row “High-Low” tests the differences between stocks in the top and bottom quintiles. Symbols 𝑃𝑃𝑃𝑃𝑃𝑃***, ** and * indicate statistical significance at the𝑃𝑃𝑃𝑃𝑃𝑃 1%, 5% and 10% levels, respectively. 𝑃𝑃𝑃𝑃𝑃𝑃 𝑃𝑃𝑃𝑃𝑃𝑃 Q Q+1 Q+2 Q+3 Q+4 High 31% 29% 28% 26% 25% 4 24% 23% 22% 21% 20% 3 21% 20% 20% 19% 18% 2 17% 17% 17% 16% 15% Low 12% 12% 12% 12% 11% High-Low 20%*** 17%*** 16%*** 15%*** 13%*** (24.57) (25.54) (26.44) (25.83) (25.62)

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Table III: Nonparametric Analysis of Return Comovement In Panel A, stocks are sorted into quintiles by their contemporaneous or lagged quarterly s. Equal-weighted averages of , , , and , are reported, where , ( , ) measures return comovement of stock with high program trading stocks𝐵𝐵 estimated𝐵𝐵 by the residual (bivariate)𝐵𝐵 approach, i.e., the program𝑃𝑃𝑃𝑃𝑃𝑃-trading-induced return 𝛽𝛽𝐻𝐻𝐻𝐻 𝑖𝑖 𝛽𝛽𝐻𝐻𝐻𝐻 𝑖𝑖 𝛽𝛽𝑅𝑅𝑅𝑅 𝑖𝑖 𝛽𝛽𝐻𝐻𝐻𝐻 𝑖𝑖 𝛽𝛽𝐻𝐻𝐻𝐻 𝑖𝑖 𝑖𝑖 comovement, and , measures return comovement with the rest of the market in the bivariate approach. In Panel B, stocks are first sorted𝐵𝐵 into tertiles by their firm size or turnover ratio in the previous quarter. Within each or 𝑅𝑅𝑅𝑅 𝑖𝑖 tertile, 𝛽𝛽stocks are further sorted into quintiles by their lagged quarterly s. The panel presents equal- weighted average , and for firm characteristics and subsamples. The last column “High-Low”𝑆𝑆𝑆𝑆𝑆𝑆 test𝑆𝑆 s 𝑇𝑇𝑇𝑇𝑇𝑇the difference𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 s of , 𝐵𝐵 and 𝐵𝐵 between stocks in the top and bottom quintile𝑃𝑃𝑃𝑃𝑃𝑃 s. Symbols ***, ** and * 𝐻𝐻𝐻𝐻 𝐻𝐻𝐻𝐻 𝑅𝑅𝑅𝑅 indicate statistical 𝛽𝛽significance𝛽𝛽 𝐵𝐵 at𝛽𝛽 the𝐵𝐵 1%, 5% and 10% levels, respectively.𝑃𝑃𝑃𝑃𝑃𝑃 𝐻𝐻𝐻𝐻 𝐻𝐻𝐻𝐻 𝑅𝑅𝑅𝑅 𝛽𝛽 𝛽𝛽 𝛽𝛽 𝑃𝑃𝑃𝑃𝑃𝑃 Panel A: Sorting on PTP High 4 3 2 Low High-Low Contemporaneous PTP Quintile 0.88 0.53 0.32 0.06 -0.24 1.12*** (12.02) 𝐻𝐻𝐻𝐻 𝛽𝛽 1.03 0.61 0.38 0.12 -0.16 1.18*** 𝐵𝐵 (15.99) 𝐻𝐻𝐻𝐻 𝛽𝛽 0.18 0.51 0.76 1.09 1.42 -1.24*** 𝐵𝐵 (-15.79) 𝑅𝑅𝑅𝑅 𝛽𝛽 Lagged PTP Quintile 0.83 0.52 0.31 0.08 -0.21 1.04*** (11.49) 𝐻𝐻𝐻𝐻 𝛽𝛽 0.98 0.60 0.38 0.13 -0.11 1.11*** 𝐵𝐵 (15.51) 𝐻𝐻𝐻𝐻 𝛽𝛽 0.20 0.52 0.76 1.08 1.38 -1.18*** 𝐵𝐵 (-15.87) 𝑅𝑅𝑅𝑅 𝛽𝛽

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Panel B: Double Sorting on Lagged Firm Characteristics and PTP PTP Quintile , Estimated by Residual Approach

𝐻𝐻𝐻𝐻 High 4 3 2 Low High-Low 𝛽𝛽 Large 0.55 0.36 0.13 -0.04 -0.26 0.81*** (10.34) 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 Median 0.78 0.46 0.23 0.09 -0.17 0.96*** (11.85) Small 1.01 0.76 0.56 0.26 -0.14 1.16*** (8.69) High 0.34 0.13 -0.03 -0.02 -0.48 0.82*** (8.47) 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 Median 0.70 0.48 0.36 0.21 0.02 0.67*** (10.23) Low 0.96 0.80 0.65 0.46 0.17 0.79*** (8.21) , Estimated by Bivariate Approach 𝐵𝐵 𝐻𝐻𝐻𝐻 High 4 3 2 Low High-Low 𝛽𝛽 Large 0.47 0.30 0.13 -0.02 -0.22 0.69*** (10.42) 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 Median 0.81 0.55 0.33 0.15 -0.06 0.91*** (12.83) Small 1.27 0.98 0.76 0.43 0.01 1.26*** (11.02) High 0.43 0.19 0.02 -0.15 -0.35 0.79*** (10.75) 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 Median 0.81 0.55 0.45 0.30 0.10 0.71*** (12.43) Low 1.15 0.93 0.72 0.49 0.25 0.90*** (10.87) , Estimated by Bivariate Approach 𝐵𝐵 𝑅𝑅𝑅𝑅 High 4 3 2 Low High-Low 𝛽𝛽 Large 0.44 0.64 0.87 1.15 1.46 -1.01*** (-14.62) 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 Median 0.20 0.57 0.85 1.08 1.38 -1.17*** (-15.44) Small 0.06 0.34 0.60 0.96 1.25 -1.19*** (-10.3) High 0.85 0.64 0.87 1.15 1.46 -1.01*** (-14.62) 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 Median 0.34 0.56 0.63 0.82 1.08 -0.74*** (-14.07) Low 0.05 0.23 0.34 0.55 0.71 -0.65*** (-8.94)

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Table IV: Regression Analysis of Return Comovement We regress , , , and , on a set of explanatory variables, respectively, using the Fama-MacBeth (1973) 𝐵𝐵 𝐵𝐵 method, where𝐻𝐻𝐻𝐻 𝑖𝑖 ,𝐻𝐻𝐻𝐻 ( 𝑖𝑖 , ) measures𝑅𝑅𝑅𝑅 𝑖𝑖 return comovement of stock with high program trading stocks estimated by 𝛽𝛽 𝛽𝛽 𝐵𝐵 𝛽𝛽 the residual (bivariate)𝐻𝐻𝐻𝐻 𝑖𝑖 𝐻𝐻𝐻𝐻approach𝑖𝑖 and , measures return comovement with the rest of the market in the bivariate approach. 𝛽𝛽 is the𝛽𝛽 daily program trading𝐵𝐵 participation ratio of stock𝑖𝑖 averaged over a quarter. Control variables 𝑅𝑅𝑅𝑅 𝑖𝑖 include natural logarithm of firm size 𝛽𝛽( ( )), natural logarithm of stock price ( ( )), book-to-market ratio 𝑖𝑖 ( / ), natur𝑃𝑃𝑃𝑃al𝑃𝑃 logarithm of average daily turnover ratio ( ( )𝑖𝑖), percentage of 13F institutional ownership ( ), bid-ask spread in percentage𝐿𝐿 𝐿𝐿( 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 ), natural logarithm of the number𝐿𝐿𝐿𝐿 of𝑃𝑃𝑃𝑃𝑃𝑃 analysts following plus 1 (𝐵𝐵 𝑀𝑀( + 1)), quarterly cumulative stock return ( 𝐿𝐿),𝐿𝐿 and𝑇𝑇𝑇𝑇𝑇𝑇 natur𝑇𝑇𝑇𝑇𝑇𝑇al𝑇𝑇𝑇𝑇 logarithm of daily realized return volatility (𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼( )). Dummy variable & 500𝑆𝑆𝑆𝑆 is 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆equal to 1 if the stock is a constituent of S&P 500 index in the quarter. Except𝐿𝐿𝐿𝐿 𝐴𝐴𝐴𝐴 for𝐴𝐴 & 500 dummy which is calculated in the 𝑅𝑅𝑅𝑅𝑅𝑅current quarter, all other explanatory variables take their values either𝐿𝐿𝐿𝐿 𝑆𝑆 at𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 the end or of the average𝑆𝑆 over𝑃𝑃 the previous quarter. Symbols ***, ** and * indicate statistical significance at the 1%, 5%𝑆𝑆 and𝑃𝑃 10% levels, respectively.

Residual Approach Bivariate 𝐵𝐵Approach Bivariate 𝐵𝐵Approach 𝐻𝐻𝐻𝐻 𝐻𝐻𝐻𝐻 𝑅𝑅𝑅𝑅 (1) 𝛽𝛽 (2) (3) 𝛽𝛽 (4) (5) 𝛽𝛽 (6) 0.055*** 0.036*** 0.054*** 0.034*** -0.061*** -0.024*** (9.69) (9.10) (11.64) (9.95) (-11.26) (-8.06) 𝑃𝑃𝑃𝑃𝑃𝑃( ) -0.052* -0.118*** 0.127*** (-0.94) (-6.45) (6.33) 𝐿𝐿𝐿𝐿(𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆) -0.065** -0.075*** 0.045* (-2.26) (-2.73) (1.67) 𝐿𝐿𝐿𝐿/ 𝑃𝑃𝑃𝑃𝑃𝑃 0.072** -0.005 0.034 (2.53) (-0.18) (1.29) 𝐵𝐵 𝑀𝑀( ) -0.186*** -0.197*** 0.279*** (-5.82) (-5.44) (8.29) 𝐿𝐿𝐿𝐿 𝑇𝑇𝑇𝑇𝑇𝑇 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 0.001*** 0.001*** -0.001*** (2.82) (4.12) (-3.38) 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 -0.671*** -1.012*** 0.457*** (-3.85) (-6.41) (2.73) 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆( + 1) -0.089*** -0.102*** 0.086*** (-4.46) (-4.93) (4.89) 𝐿𝐿𝐿𝐿 𝐴𝐴𝐴𝐴𝐴𝐴 -0.432*** -0.248 0.367*** (-3.39) (-1.59) (4.06) 𝑅𝑅𝑅𝑅𝑅𝑅( ) -0.026 0.053 0.208*** (-0.38) (0.87) (4.06) 𝐿𝐿𝐿𝐿& 𝑆𝑆500𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 -0.009 -0.031 0.004*** (-0.52) (0.87) (4.06) 𝑆𝑆 𝑃𝑃

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Table V: Effect of Macroeconomic News , and , are estimated for individual stock i by the following regression specification for each quarter: , = + , , , + , : × , , + , , 𝛽𝛽𝐻𝐻𝐻𝐻 𝑖𝑖 𝛽𝛽𝐻𝐻𝐻𝐻𝐻𝐻 𝑖𝑖 where , is residual𝑖𝑖 𝑡𝑡 return𝑖𝑖 of stock𝐻𝐻𝐻𝐻 𝑖𝑖 i on𝐻𝐻𝐻𝐻 day𝑖𝑖 𝑡𝑡 t obtained𝐻𝐻𝐻𝐻𝐻𝐻 𝑖𝑖 from a regression𝑡𝑡−1 𝑡𝑡 +on1 market𝐻𝐻𝐻𝐻 return𝑖𝑖 𝑡𝑡 , 𝑖𝑖 𝑡𝑡 , , is the value- weighted average 𝑅𝑅𝑅𝑅𝑅𝑅of residual𝛼𝛼 return𝛽𝛽 s of𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 stocks that𝛽𝛽 are in �the𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 top quintile but𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 not in the� same𝜖𝜖 industry as stock i 𝑖𝑖 𝑡𝑡 𝐻𝐻𝐻𝐻 𝑖𝑖 𝑡𝑡 (defined𝑅𝑅𝑅𝑅𝑅𝑅 by its 2-digit SIC code) on day t, : is a dummy variable that equals 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅to 1 if day t is in the 3- day period surrounding a macroeconomic news events. , measures𝑃𝑃𝑃𝑃𝑃𝑃 program-trading-induced return comovement, 𝑡𝑡−1 𝑡𝑡+1 while measures additional comovement𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 associated with macroeconomic news. The table first reports average , 𝐻𝐻𝐻𝐻 𝑖𝑖 and for quintiles sorted based on the previous𝛽𝛽 quarter’s . It then reports average and for 𝐻𝐻𝐻𝐻𝐻𝐻 𝑖𝑖 subsamples𝛽𝛽 formed by double sorting: stocks are first sorted into tertiles by their firm size or turnover ratio of the 𝐻𝐻𝐻𝐻 𝐻𝐻𝐻𝐻𝐻𝐻 𝐻𝐻𝐻𝐻 𝐻𝐻𝐻𝐻𝐻𝐻 previous𝛽𝛽 𝛽𝛽quarter; and then sorted into quintiles according to lagged quarterly𝑃𝑃𝑃𝑃𝑃𝑃 . The last column 𝛽𝛽“High-Low”𝛽𝛽 tests the difference of or between stocks in the top and bottom quintiles. Symbols ***, ** and * indicate statistical significance at the 1%, 5% and 10% levels, respectively. 𝑃𝑃𝑃𝑃𝑃𝑃 𝐻𝐻𝐻𝐻 𝐻𝐻𝐻𝐻𝐻𝐻 𝛽𝛽 𝛽𝛽 𝑃𝑃𝑃𝑃𝑃𝑃 Panel A: Estimated PTP Quintile 𝛽𝛽𝐻𝐻𝐻𝐻 High 4 3 2 Low High-Low All Stocks 0.71 0.41 0.22 -0.01 -0.31 1.03*** (10.4) Large 0.36 0.23 0.03 -0.15 -0.42 0.78*** (9.11) 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 Median 0.62 0.37 0.14 0.01 -0.29 0.92*** (11.85) Small 0.94 0.68 0.47 0.22 -0.17 1.12*** (7.55) High 0.24 0.05 -0.12 -0.3 -0.61 0.86*** (8.95) 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 Median 0.57 0.37 0.27 0.13 -0.04 0.62*** (8.66) Low 0.84 0.68 0.53 0.35 0.09 0.75*** (8.21) Panel B: Estimated PTP Quintile 𝛽𝛽𝐻𝐻𝐻𝐻𝐻𝐻 High 4 3 2 Low High-Low All Stocks 0.08 0.05 -0.01 0.03 0.09 -0.01 (-0.06) Large -0.07 -0.08 -0.08 0.01 0.13 -0.20 (-1.64) 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 Median 0.01 -0.01 0.11 0.02 -0.03 -0.11 (0.64) Small 0.08 0.19 0.37 -0.03 -0.03 0.11 (0.48) High 0.04 -0.07 0.04 0.09 0.20 -0.16 (-1.04) 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 Median 0.03 -0.01 0.05 0.00 -0.01 0.05 (0.4) Low 0.05 0.14 0.07 0.08 0.02 0.03 (0.18)

42

Table VI: Effect of Firm-Specific News , and , in the table are estimated for individual stock i by the following regression specification for each quarter: 𝛽𝛽𝐻𝐻𝐻𝐻 𝑖𝑖 𝛽𝛽𝐻𝐻𝐻𝐻𝐻𝐻 𝑖𝑖 , = + , , + , , : × , + , ,

where , is residual return𝑖𝑖 𝑡𝑡 of𝑖𝑖 stock𝐻𝐻𝐻𝐻 𝑖𝑖i on 𝐻𝐻𝐻𝐻day𝑡𝑡 t obtained𝐻𝐻𝐻𝐻𝐻𝐻 𝑖𝑖 from a regression𝑖𝑖 𝑡𝑡−1 𝑡𝑡+1 on market𝐻𝐻𝐻𝐻 𝑡𝑡 return,𝑖𝑖 𝑡𝑡 , is the value- weighted average of 𝑅𝑅𝑅𝑅𝑅𝑅residual 𝛼𝛼return𝛽𝛽s of𝑅𝑅𝑅𝑅𝑅𝑅 stocks that𝛽𝛽 are �in𝐹𝐹𝐹𝐹 𝐹𝐹the𝐹𝐹 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹top quintile𝑅𝑅𝑅𝑅𝑅𝑅 on day� t, 𝜖𝜖 is a 𝑖𝑖 𝑡𝑡 𝐻𝐻𝐻𝐻 𝑡𝑡 , : dummy𝑅𝑅𝑅𝑅𝑅𝑅 variable that equals to 1 if day t is in the 3-day period surrounding a firm-specific news release.𝑅𝑅𝑅𝑅𝑅𝑅 measures 𝑖𝑖 𝑡𝑡,−1 𝑡𝑡+1 program-trading-induced return comovement, while measures𝑃𝑃𝑃𝑃𝑃𝑃 additional comovement𝐹𝐹𝐹𝐹 𝐹𝐹associated𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 with firm- , 𝐻𝐻𝐻𝐻 𝑖𝑖 specific news. The table first reports average and for quintiles sorted based on the previous 𝛽𝛽quarter’s . 𝐻𝐻𝐻𝐻𝐻𝐻 𝑖𝑖 It then reports average and for subsamples 𝛽𝛽formed by double sorting: stocks are first sorted into tertiles by 𝐻𝐻𝐻𝐻 𝐻𝐻𝐻𝐻𝐻𝐻 their firm size or turnover ratio of the previous𝛽𝛽 quarter;𝛽𝛽 and then sorted into quintiles according to lagged quarterly𝑃𝑃𝑃𝑃𝑃𝑃 𝐻𝐻𝐻𝐻 𝐻𝐻𝐻𝐻𝐻𝐻 . The last column𝛽𝛽 “High-Low”𝛽𝛽 tests the difference of or between stocks in the top and bottom quintiles. Symbols ***, ** and * indicate statistical significance at the 1%, 5% and 10% levels, respectively. 𝐻𝐻𝐻𝐻 𝐻𝐻𝐻𝐻𝐻𝐻 𝑃𝑃𝑃𝑃𝑃𝑃 𝛽𝛽 𝛽𝛽 𝑃𝑃𝑃𝑃𝑃𝑃 Panel A: Estimated PTP Quintile 𝛽𝛽𝐻𝐻𝐻𝐻 High 4 3 2 Low High-Low All Stocks 0.83 0.54 0.31 0.08 -0.07 0.90*** (6.11) Large 0.56 0.41 0.15 -0.33 0.15 0.14* (1.66) 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 Median 0.79 0.45 0.25 0.08 -0.17 0.96*** (11.12) Small 1.01 0.78 0.53 0.30 -0.17 1.18*** (9.52) High 0.36 0.13 -0.01 -0.18 -0.06 0.42 (1.06) 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 Median 0.72 0.50 0.37 0.22 0.04 0.69*** (11.28) Low 0.95 0.81 0.68 0.44 0.15 0.80*** (8.78) Panel B: Estimated PTP Quintile 𝛽𝛽𝐻𝐻𝐻𝐻𝐻𝐻 High 4 3 2 Low High-Low All-Stocks -0.17 -0.13 0.05 0.02 -0.17 0.003 (0.01) Large -0.02 -0.04 -0.07 -0.14 -0.47 0.44 (1.13) 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 Median 0.01 -0.1 0.07 0.08 -0.14 0.15 (0.96) Small -0.40 -0.34 0.30 0.08 0.21 -0.60 (-1.37) High -0.36 0.06 0.15 -0.14 0.40 0.04 (0.09) 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 Median -0.32 0.06 0.02 0.14 -0.06 -0.26 (-0.96) Low -0.13 -0.2 -0.26 0.28 0.08 -0.21 (-0.64)

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Table VII: Program-Trading-Induced Return Comovement and Information , , , and , in the table are estimated for individual stock i by the following regression specification for each quarter: 𝐻𝐻𝐻𝐻 𝑖𝑖 𝐻𝐻𝐻𝐻𝐻𝐻 𝑖𝑖 𝐻𝐻𝐻𝐻𝐻𝐻 𝑖𝑖 𝛽𝛽 𝛽𝛽 , = 𝛽𝛽+ , , , + , ( × , , ) + , ( , × ) + . 𝑖𝑖 𝑡𝑡 𝑖𝑖 𝐻𝐻𝐻𝐻 𝑖𝑖 𝐻𝐻𝐻𝐻 𝑖𝑖,𝑡𝑡, 𝐻𝐻𝐻𝐻𝐻𝐻, 𝑖𝑖 𝑡𝑡−1 ∶𝑡𝑡+1 𝐻𝐻𝐻𝐻 𝑖𝑖 𝑡𝑡 𝐻𝐻𝐻𝐻𝐻𝐻 𝑖𝑖 𝑖𝑖 𝑡𝑡−1 ∶𝑡𝑡+1 where𝑅𝑅𝑅𝑅𝑅𝑅 is 𝛼𝛼residual𝛽𝛽 return𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 of stock𝛽𝛽 i on day𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 t obtained𝑤𝑤 𝑠𝑠from a regression𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 on market𝛽𝛽 return,𝐹𝐹𝐹𝐹𝐹𝐹 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 is the value- , 𝐻𝐻𝐻𝐻 𝑖𝑖 𝑡𝑡 𝑖𝑖 𝑡𝑡 , , weighted average of residual𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 returns of stocks𝜖𝜖 that are in the top quintile but not in the same industry as stock i 𝑖𝑖 𝑡𝑡 𝐻𝐻𝐻𝐻 𝑖𝑖 𝑡𝑡 (defined𝑅𝑅𝑅𝑅𝑅𝑅 by its 2-digit SIC code) on day t, ( , : ) is a dummy𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 variable that equals to 1 if day t is in the 3-day period surrounding a macroeconomic (firm𝑃𝑃𝑃𝑃𝑃𝑃-specific) news event. measures program- 𝑡𝑡−1 ∶𝑡𝑡+1 𝑖𝑖 𝑡𝑡−1 𝑡𝑡+1 , trading-induced return comovement, while𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 ( ) measures𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 additional comovement associated with , , 𝐻𝐻𝐻𝐻 𝑖𝑖 macroeconomic (firm-specific) news. The table reports regressions of , and 𝛽𝛽 , respectively, on a set 𝐻𝐻𝐻𝐻𝐻𝐻 𝑖𝑖 𝐻𝐻𝐻𝐻𝐻𝐻 𝑖𝑖 , , , of explanatory variables using the Fama-MacBeth𝛽𝛽 (1973)𝛽𝛽 method. is daily program trading participation ratio 𝐻𝐻𝐻𝐻 𝑖𝑖 𝐻𝐻𝐻𝐻𝐻𝐻 𝑖𝑖 𝐻𝐻𝐻𝐻𝐻𝐻 𝑖𝑖 averaged over a quarter. Control variables include natural logarithm of𝛽𝛽 firm𝛽𝛽 size ( (𝛽𝛽 )), natural algorithm of stock price ( ( )), book-to-market ratio ( / ), natural𝑃𝑃𝑃𝑃𝑃𝑃 logarithm of average daily turnover ratio ( ( )), percentage of 13F institutional ownership ( ), bid-ask spread 𝐿𝐿in𝐿𝐿 percentage𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 ( ), natural logarithm of the𝐿𝐿 number𝐿𝐿 𝑃𝑃𝑃𝑃𝑃𝑃 of analysts following plus 1 ( 𝐵𝐵 (𝑀𝑀 + 1)), quarterly cumulative stock return ( ), natural logarithm𝐿𝐿𝐿𝐿 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 of𝑇𝑇𝑇𝑇 𝑇𝑇𝑇𝑇daily realized return volatility ( ( )). Dummy𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 variable & 500 is equal to 1𝑆𝑆𝑆𝑆 if 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆the stock is a constituent of S&P 500 index in the quarter. Except for𝐿𝐿𝐿𝐿 &𝐴𝐴𝐴𝐴500𝐴𝐴 dummy which is calculated in the concurrent𝑅𝑅𝑅𝑅𝑅𝑅 quarter, all other explanatory variables take their values𝐿𝐿𝐿𝐿 either𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 at the end or of the average𝑆𝑆 𝑃𝑃over the previous quarter. Symbols ***, ** and * indicate statistical significance at the 1%,𝑆𝑆 5%𝑃𝑃 and 10% levels, respectively.

(1) 𝐻𝐻𝐻𝐻 (2) (3) 𝐻𝐻𝐻𝐻𝑀𝑀 (4) (5) 𝐻𝐻𝐻𝐻𝐻𝐻 (6) 0.058*** 𝛽𝛽 0.034*** -0.027 𝛽𝛽 -0.017 0.004𝛽𝛽 -0.256 (9.19) (7.03) (-1.44) (-0.97) (0.02) (-1.08) 𝑃𝑃𝑃𝑃𝑃𝑃( ) -0.089*** -0.018 -0.384 (-3.32) (-0.41) (-0.53) 𝐿𝐿𝐿𝐿(𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆) -0.086** 0.186 -1.262 (-2.10) (1.49) (-0.41) 𝐿𝐿𝐿𝐿/ 𝑃𝑃𝑃𝑃𝑃𝑃 0.032 0.256* -1.73 (1.15) (1.80) (-1.25) 𝐵𝐵 𝑀𝑀( ) -0.235 -0.131 0.06 (-7.89) (-0.56) (0.03) 𝐿𝐿𝐿𝐿 𝑇𝑇𝑇𝑇𝑇𝑇 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 0.001*** -0.003 -0.06 (3.83) (-0.74) (-1.02) 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 -0.701*** -0.713 -28.69 (-3.90) (-1.17) (-0.95) 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆( + 1) -0.069*** -0.119 -1.981 (-3.43) (-0.55) (-0.89) 𝐿𝐿𝐿𝐿 𝐴𝐴𝐴𝐴𝐴𝐴 -0.475*** -0.416 -13.64 (-3.53) (-1.55) (1.09) 𝑅𝑅𝑅𝑅𝑅𝑅( ) -0.054 0.791* -0.59 (-0.79) (1.92) (-0.16) 𝐿𝐿𝐿𝐿& 𝑆𝑆500𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 0.002 -0.008 0.01 (0.15) (-0.07) (0.00) 𝑆𝑆 𝑃𝑃

44

Table VIII: Evidence of Return Reversals This table reports the outcomes of Fama-MacBeth (1973) style regressions on measures of return reversals at individual stock level. Dependent variable in specifications (1) and (2) is the first-order autocorrelation of daily stock return estimated over a quarter. In specifications (3) and (4), dependent variable , is estimated by applying daily data over a quarter to the following model: 𝐿𝐿𝐿𝐿𝐿𝐿 𝑖𝑖 , = + , , + , , +𝛽𝛽 , , where is value-weighted return of all CRSP stocks on day and is the value-weighted return of all , 𝑖𝑖 𝑡𝑡 𝑚𝑚𝑚𝑚𝑚𝑚 𝑖𝑖 𝑚𝑚𝑚𝑚𝑚𝑚 𝑡𝑡 𝐿𝐿𝐿𝐿𝐿𝐿 𝑖𝑖 𝐻𝐻𝐻𝐻 𝑡𝑡−1 , 𝑖𝑖 𝑡𝑡 stocks in the top quintile 𝑅𝑅𝑅𝑅𝑅𝑅on day 𝛼𝛼 1𝛽𝛽. Among𝑅𝑅𝑅𝑅𝑅𝑅 independent𝛽𝛽 𝑅𝑅𝑅𝑅𝑅𝑅 variables, 𝜀𝜀 is the daily program trading 𝑚𝑚𝑚𝑚𝑚𝑚 𝑡𝑡 𝐻𝐻𝐻𝐻 𝑡𝑡−1 participation𝑅𝑅𝑅𝑅𝑅𝑅 ratio averaged over a quarter. Control variables include𝑡𝑡 natural𝑅𝑅𝑅𝑅𝑅𝑅 logarithm of firm size ( ( )), natural algorithm of𝑃𝑃𝑃𝑃𝑃𝑃 stock price ( ( 𝑡𝑡)),− book-to-market ratio ( / ), natural logarithm𝑃𝑃𝑃𝑃𝑃𝑃 of average daily turnover ratio ( ( )), percentage of 13F institutional ownership ( ), bid-ask spread in percentage𝐿𝐿 (𝐿𝐿 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 ), natural logarithm of the number of𝐿𝐿 𝐿𝐿analysts𝑃𝑃𝑃𝑃𝑃𝑃 following plus 1 ( ( 𝐵𝐵 𝑀𝑀+ 1)), quarterly cumulative stock return ( ), natural𝐿𝐿 logarithm𝐿𝐿 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑇𝑇of𝑇𝑇𝑇𝑇 daily realized return volatility ( ( )). Dummy𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 variable & 500 is equal to 1 if 𝑆𝑆𝑆𝑆the𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 stock is a constituent of S&P 500 index in the quarter. Except for𝐿𝐿 𝐿𝐿&𝐴𝐴𝐴𝐴500𝐴𝐴 dummy which is calculated in the concurrent𝑅𝑅𝑅𝑅𝑅𝑅 quarter, all other explanatory variables take their values𝐿𝐿𝐿𝐿 𝑆𝑆either𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 at the end or of the average𝑆𝑆 𝑃𝑃 over the previous quarter. Symbols ***, ** and * indicate statistical significance at the 1%,𝑆𝑆 𝑃𝑃 5% and 10% levels, respectively.

Return Autocorrelation ( )

(1) (2) (3) 𝐿𝐿𝐿𝐿𝐿𝐿 (4) -0.002*** -0.003𝐴𝐴***𝐴𝐴𝐴𝐴 -0.01*** 𝛽𝛽 -0.008*** (-6.63) (-8.00) (-9.51) (-8.93) 𝑃𝑃𝑃𝑃𝑃𝑃( ) -0.004** -0.001 (-2.22) (-0.16) 𝐿𝐿𝐿𝐿(𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆) 0.001 0.003 (0.95) (0.47) 𝐿𝐿𝐿𝐿/ 𝑃𝑃𝑃𝑃𝑃𝑃 -0.002 0.012 (-0.97) (1.13) 𝐵𝐵 𝑀𝑀( ) 0.004 0.029*** (1.13) (2.87) 𝐿𝐿𝐿𝐿 𝑇𝑇𝑇𝑇𝑇𝑇 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 0.001 0.001 (1.42) (1.02) 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 -0.052*** 0.073 (-4.36) (1.58) 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆( + 1) -0.001 -0.004 (-0.57) (-0.75) 𝐿𝐿𝐿𝐿 𝐴𝐴 𝐴𝐴𝐴𝐴 -0.045*** -0.096*** (-5.60) (-2.58) 𝑅𝑅𝑅𝑅𝑅𝑅( ) -0.009 -0.003 (-1.20) (-0.24) 𝐿𝐿𝐿𝐿& 𝑆𝑆500𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 0.002** 0.003 (2.05) (0.81) 𝑆𝑆 𝑃𝑃

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Table IX: Gradual Diffusion of Information This table presents slope coefficients estimated for the following VAR: , = + , + , + , , = + 5 + 5 + . 𝐿𝐿𝐿𝐿 ,𝑡𝑡 0 𝑘𝑘=1 𝑘𝑘 𝐿𝐿𝐿𝐿, 𝑡𝑡−𝑘𝑘 𝑘𝑘=1 𝑘𝑘 𝐻𝐻𝐻𝐻, 𝑡𝑡−𝑘𝑘 𝐿𝐿𝐿𝐿,𝑡𝑡 Sample stocks are sorted into te𝑟𝑟rtiles by𝑎𝑎 their∑5 size𝑎𝑎 or𝑟𝑟 turnover∑ 5ratio𝑏𝑏 at𝑟𝑟 the end of𝑢𝑢 the previous quarter. Within each 𝐻𝐻𝐻𝐻 𝑡𝑡 0 𝑘𝑘=1 𝑘𝑘 𝐿𝐿𝐿𝐿 𝑡𝑡−𝑘𝑘 𝑘𝑘=1 𝑘𝑘 𝐻𝐻𝐻𝐻 𝑡𝑡−𝑘𝑘 𝐻𝐻𝐻𝐻 𝑡𝑡 firm size or turnover tertile, stocks𝑟𝑟 are further𝑐𝑐 ∑ sorted𝑐𝑐 𝑟𝑟 into quintiles∑ according𝑑𝑑 𝑟𝑟 to their𝑢𝑢 lagged quarterly . Variable and are daily portfolio returns of stocks in the bottom and top PTP quintiles within a or tertile. “Low” column reports or and “High” column reports or , while column𝑃𝑃𝑃𝑃𝑃𝑃 reports 𝐿𝐿𝐿𝐿 𝐻𝐻𝐻𝐻 𝑟𝑟 or 𝑟𝑟and column reports5 or5 . Their statistical significance level5 s are estimated5 𝑆𝑆under𝑆𝑆𝑆𝑆𝑆𝑆 the𝑇𝑇𝑇𝑇𝑇𝑇 null𝑇𝑇𝑇𝑇 𝑇𝑇hypothesis𝑇𝑇𝑇𝑇 𝑘𝑘=1 𝑘𝑘 𝑘𝑘=1 𝑘𝑘 𝑘𝑘=1 𝑘𝑘 𝑘𝑘=1 𝑘𝑘 1 that (summed) slope coefficient∑ 𝑎𝑎 (s)∑ of corresponding𝑐𝑐 lagged portfolio∑ return𝑏𝑏(s) is∑ equal𝑑𝑑 to 0. C𝐿𝐿olumn “Granger 1 1 1 1 1 𝑎𝑎Causality”𝑐𝑐 reports𝐻𝐻 the F-statistics𝑏𝑏 under𝑑𝑑 the null hypothesis that the portfolio return of high (low) stocks does not Granger cause the portfolio return of low (high) stocks, denoted by HCL (LCH). Symbols ***, ** and * indicate statistical significance at the 1%, 5% and 10% levels, respectively. 𝑃𝑃𝑃𝑃𝑃𝑃 𝑃𝑃𝑃𝑃𝑃𝑃 Panel A: Size Tertiles Low High Granger Causality Large 0.04 0.06 -0.08 -0.40*** HCL 3.77*** 𝐿𝐿1 𝐻𝐻1 𝐿𝐿𝐿𝐿 0.02 0.05 -0.13*** -0.33*** LCH 2.00* Median 𝑟𝑟 0.12*** 0.22*** -0.16*** -0.53*** HCL 7.34*** 𝐻𝐻𝐻𝐻 𝑟𝑟 0.03 0.11** -0.17*** -0.42*** LCH 4.34*** 𝐿𝐿𝐿𝐿 Small 𝑟𝑟 0.09*** 0.08 -0.04 -0.01 HCL 2.58** 𝐻𝐻𝐻𝐻 𝑟𝑟 -0.02 -0.03 -0.12*** -0.16* LCH 4.7*** 𝑟𝑟𝐿𝐿𝐿𝐿 Panel B: Turnover𝐻𝐻𝐻𝐻 Tertiles 𝑟𝑟 Low High Granger Causality

High -0.011 -0.13 0.051 0.12 HCL 2.23* -0.04𝐿𝐿 -0.21*** -0.06𝐻𝐻 0.17 LCH 4.05*** 𝐿𝐿𝐿𝐿 Median 𝑟𝑟 -0.04 0.05 0.03 -0.14 HCL 0.68 𝐻𝐻𝐻𝐻 𝑟𝑟 -0.06 -0.06 -0.03 -0.11 LCH 2.53* 𝐿𝐿𝐿𝐿 Low 𝑟𝑟 0.02 0.11 -0.01 -0.12 HCL 0.13 𝐻𝐻𝐻𝐻 𝑟𝑟 -0.02 -0.04 -0.15*** -0.24*** LCH 1.48 𝑟𝑟𝐿𝐿𝐿𝐿 𝐻𝐻𝐻𝐻 𝑟𝑟

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Table X: Granger Causality Test on Return Comovement This table presents summary statistics estimated from the following VAR: , = + , + + , , = + + + . 𝐻𝐻𝐻𝐻 𝑄𝑄 0 1 𝐻𝐻𝐻𝐻 𝑄𝑄−1 1 , 𝑄𝑄−1 𝛽𝛽 𝑡𝑡. Sample stocks are sorted into tertiles𝛽𝛽 by their𝑎𝑎 size or𝑎𝑎 𝛽𝛽turnover ratio𝑏𝑏 𝑃𝑃𝑃𝑃𝑃𝑃 at the end 𝑢𝑢of the previous quarter. For each stock, 𝑄𝑄 0 1 𝑄𝑄−1 1 𝐻𝐻𝐻𝐻 𝑄𝑄−1 𝑃𝑃𝑃𝑃𝑃𝑃 𝑡𝑡 , measures program-induced return𝑃𝑃𝑃𝑃𝑃𝑃 comovement𝑐𝑐 𝑐𝑐 𝑃𝑃𝑃𝑃𝑃𝑃 of stock𝑑𝑑 𝛽𝛽 in quarter𝑢𝑢 , estimated by the residual approach. ( ) is equal-weighted average of ( ) for stocks in each size/turnover tertile in quarter Q. Column 𝐻𝐻𝐻𝐻,𝑖𝑖 , “All𝛽𝛽 Stocks” reports summary statistics for VARs estimated among𝑖𝑖 the whole𝑄𝑄 sample stocks without being stratified 𝐻𝐻𝐻𝐻 𝑄𝑄 𝑄𝑄 𝐻𝐻𝐻𝐻 𝑖𝑖 𝑖𝑖 according𝛽𝛽 𝑃𝑃𝑃𝑃𝑃𝑃 to firm size or turnover ratio. F-statistic𝛽𝛽 𝑃𝑃𝑃𝑃 reports𝑃𝑃 statistics for the Granger causality test. Symbols ***, ** and * indicate statistical significance at the 1%, 5% and 10% levels, respectively.

Panel A: Summary Statistics of Estimated Parameters in , = + , + + F-statistic : = 0 𝛽𝛽𝐻𝐻𝐻𝐻 𝑄𝑄 𝑎𝑎0 𝑎𝑎1𝛽𝛽𝐻𝐻𝐻𝐻 𝑄𝑄−1 𝑏𝑏1𝑃𝑃𝑃𝑃𝑃𝑃𝑄𝑄−1 𝑢𝑢𝑡𝑡 All Stocks 𝐻𝐻0 𝑏𝑏1 Large Median Small High Median Low 0.03 -𝑆𝑆0.17𝑆𝑆𝑆𝑆𝑆𝑆 -0.36 -0.59*** 𝑇𝑇𝑇𝑇𝑇𝑇-𝑇𝑇0.11𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 -0.02 -0.17 (0.47) (-1.48) (-1.61) (-3.16) (-1.25) (-0.12) (-1.50) 0 𝑎𝑎 0.07 0.28* 0.54*** 0.05 0.31* 0.60*** 0.38** (0.41) (1.68) (3.81) (0.29) (1.84) (4.02) (2.38) 1 𝑎𝑎 0.52 1.72*** 2.62** 3.28*** 1.71*** 1.09* 1.73*** (1.23) (2.85) (2.39) (3.14) (3.18) (1.71) (2.74) 1 F𝑏𝑏-Statistic 1.63 8.14*** 5.71** 9.82*** 10.1*** 2.94* 7.51*** Adj. 0.01 0.40 0.51 0.27 0.49 0.42 0.45 Panel 2B: Summary Statistics of Estimated Parameters in = + + + 𝑅𝑅 , F-statistic : = 0 𝑃𝑃𝑃𝑃𝑃𝑃𝑄𝑄 𝑐𝑐0 𝑐𝑐1𝑃𝑃𝑃𝑃𝑃𝑃𝑄𝑄−1 𝑑𝑑1𝛽𝛽𝐻𝐻𝐻𝐻 𝑄𝑄−1 𝑢𝑢𝑡𝑡 All stocks 𝐻𝐻0 𝑑𝑑1 Large Median Small High Median Low 0.01** 0.01*𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 0.01 0.01 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇0.01𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 0.01 0.01* (2.07) (1.71) (1.37) (1.82) (1.48) (1.13) (1.69) 0 𝑐𝑐 0.87*** 0.88*** 0.89*** 0.88*** 0.91*** 0.88*** 0.88*** (21.49) (19.69) (14.56) (22.32) (18.14) (15.40) (17.71) 1 𝑐𝑐 0.01 0.01 0.00 0.00 -0.01 0.01 0.01 (1.01) (0.81) (0.28) (0.18) (-0.153) (0.89) (0.57) 1 F𝑑𝑑-Statistic 1.02 0.64 0.75 0.03 0.02 0.11 0.57 Adj. 0.94 0.95 0.89 0.95 0.94 0.89 0.93 2 𝑅𝑅

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Table XI: Effect of ETF Flows , , , and , in the table are estimated for individual stock i by the following regression specification for each quarter: 𝛽𝛽𝐻𝐻𝐻𝐻 𝑖𝑖 𝛽𝛽𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑖𝑖 𝛽𝛽𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑖𝑖 , = + , , + , , × + , , × + , ,

where , 𝑖𝑖is𝑡𝑡 residual𝑖𝑖 return𝐻𝐻𝐻𝐻 𝑖𝑖 of𝐻𝐻𝐻𝐻 stock𝑡𝑡 i 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸on 𝐸𝐸day𝑖𝑖 t obtained𝐻𝐻𝐻𝐻 𝑡𝑡 from a𝑡𝑡 regression𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 on𝑖𝑖 market𝐻𝐻𝐻𝐻 𝑡𝑡 return, 𝑡𝑡 , is𝑖𝑖 𝑡𝑡the value- weighted 𝑅𝑅𝑅𝑅𝑅𝑅average 𝛼𝛼of residual𝛽𝛽 𝑅𝑅𝑅𝑅𝑅𝑅 returns of𝛽𝛽 stocks�𝑅𝑅𝑅𝑅𝑅𝑅 that are in𝐸𝐸 𝐸𝐸𝐸𝐸𝐸𝐸the 𝑛𝑛top� 𝛽𝛽 quintile�𝑅𝑅𝑅𝑅𝑅𝑅. measures𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑡𝑡 program� 𝜀𝜀 -trading- 𝑖𝑖 𝑡𝑡 , 𝐻𝐻𝐻𝐻 𝑡𝑡 induced𝑅𝑅𝑅𝑅𝑅𝑅 return comovement, while ( ) measures additional comovement on days with𝑅𝑅𝑅𝑅𝑅𝑅 high ETF inflow , , 𝐻𝐻𝐻𝐻 𝑖𝑖 (outflow). In Panel A, is equal to 1 if the net ETF flow on day𝑃𝑃𝑃𝑃𝑃𝑃 is ranked in the𝛽𝛽 top 25% flow of the concurrent 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑖𝑖 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑖𝑖 quarter and 0 otherwise, and 𝛽𝛽 identifies𝛽𝛽 days whose daily net ETF is in the bottom 25%. In Panel B, the cut- 𝑡𝑡 off is 10%. In each quarter,𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑛𝑛 all stocks are sorted into quintiles by their𝑡𝑡 lagged quarter . The table reports the 𝑡𝑡 equal-weighted average ,𝐸𝐸 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑡𝑡, and . Numbers in the square brackets report the percentage of stocks with estimated coefficient positively significant at the 10% confidence level. Column𝑃𝑃𝑃𝑃𝑃𝑃 “High-Low” tests the 𝐻𝐻𝐻𝐻 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 differences of , 𝛽𝛽 and𝛽𝛽 between𝛽𝛽 stocks in the top and bottom quintile. Symbols ***, ** and * indicate statistical significance at the 1%, 5% and 10% levels, respectively. 𝐻𝐻𝐻𝐻 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝛽𝛽 𝛽𝛽 𝛽𝛽 𝑃𝑃𝑃𝑃𝑃𝑃 Panel A: Cut-off at Top 25% and Bottom 25% for ETF Net Flow PTP Quintile High 4 3 2 Low High-Low 0.84 0.51 0.31 0.07 -0.28 1.13*** [48%] [34%] [25%] [19%] [13%] (9.58) 𝐻𝐻𝐻𝐻 𝛽𝛽 -0.20 -0.05 -0.04 -0.01 0.06 -0.27* [11%] [12%] [12%] [12%] [11%] (-1.90) 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝛽𝛽 0.04 0.04 -0.01 -0.01 0.03 0.01 [13%] [11%] [11%] [11%] [11%] (0.08) 𝛽𝛽𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 Panel B: Cut-off at Top 10% and Bottom 10% for ETF Net Flow PTP Quintile High 4 3 2 Low High-Low 0.84 0.51 0.31 0.09 -0.20 1.04** [49%] [31%] [27%] [16%] [14%] (11.33) 𝐻𝐻𝐻𝐻 𝛽𝛽 0.00 0.00 0.01 0.01 0.01 -0.01* [10%] [11%] [10%] [12%] [11%] (-1.84) 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝛽𝛽 -0.01 0.03 -0.04 -0.09 -0.07 -0.05 [11%] [10%] [10%] [10%] [9%] (-0.43) 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝛽𝛽

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Table XII: Program Trading and Return Comovement with Major Equity Index , , , and , are estimated for individual stock i by the following time-series regressions over a quarter: = + + × + + , 𝐼𝐼𝐼𝐼 𝑖𝑖 𝐼𝐼𝐼𝐼𝐼𝐼 𝑖𝑖 𝑃𝑃𝑃𝑃𝑃𝑃 𝑖𝑖 , , , , , , , , , 𝛽𝛽 𝛽𝛽 𝛽𝛽 where , and , 𝑖𝑖denote𝑡𝑡 𝑖𝑖 returns𝐼𝐼𝐼𝐼 𝑖𝑖 of 𝐼𝐼𝐼𝐼stock𝑡𝑡 i 𝐼𝐼𝐼𝐼and𝐼𝐼 𝑖𝑖 index𝐼𝐼𝐼𝐼 𝑡𝑡ID, respectively,𝑖𝑖 𝑡𝑡 𝑃𝑃𝑃𝑃 𝑃𝑃on𝑖𝑖 day𝑖𝑖 𝑡𝑡 t and𝑖𝑖 𝑡𝑡 , is the ratio of program trading participation𝑅𝑅𝑅𝑅𝑅𝑅 𝛼𝛼of stock𝛽𝛽 i 𝑅𝑅𝑅𝑅𝑅𝑅on day t. 𝛽𝛽 � 𝑅𝑅𝑅𝑅𝑅𝑅measures 𝑃𝑃𝑃𝑃𝑃𝑃index-�related𝛽𝛽 return𝑃𝑃𝑃𝑃𝑃𝑃 comovement𝜀𝜀 associated with 𝑖𝑖 𝑡𝑡 𝐼𝐼𝐼𝐼 𝑡𝑡 , 𝑖𝑖 𝑡𝑡 program𝑅𝑅𝑅𝑅𝑅𝑅 trading. 𝑅𝑅𝑅𝑅𝑅𝑅 The table considers S&P 500 and Russell 2000 indexes and reports the sample𝑃𝑃𝑃𝑃𝑃𝑃 means of the 𝐼𝐼𝐼𝐼𝐼𝐼 𝑖𝑖 estimated parameters in the full sample or subsamples𝛽𝛽 divided by years, while numbers in the square brackets report the percentage of stocks with estimated coefficient significant at the 10% level.

& & Mean % positive Mean % positive Mean % positive 𝛽𝛽𝑆𝑆 𝑃𝑃500 𝛽𝛽𝑆𝑆 𝑃𝑃500𝑃𝑃 𝛽𝛽𝑃𝑃𝑃𝑃𝑃𝑃 2006-2007 0.992 [80%] 0.160 [20%] -0.004 [7%] 2008-2009 1.199 [95%] -0.249 [22%] -0.004 [6%] 2010-2011 1.240 [96%] -0.011 [22%] -0.005 [7%] 2012-2013 1.192 [92%] -0.232 [14%] -0.001 [11%] 2014-2015 1.060 [94%] -0.415 [9%] 0.000 [11%] Full Sample 1.112 [92%] -0.192 [25%] -0.002 [7%]

Mean𝑅𝑅 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅2000% positive Mean 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅2000% positive𝑃𝑃 Mean 𝑃𝑃𝑃𝑃𝑃𝑃% positive 2006-2007 0.831𝛽𝛽 [79%] 0.019𝛽𝛽 [20%] -0.003 𝛽𝛽 [8%] 2008-2009 1.049 [95%] -0.130 [26%] -0.005 [6%] 2010-2011 0.958 [95%] 0.152 [28%] -0.006 [7%] 2012-2013 0.952 [91%] -0.190 [18%] -0.005 [7%] 2014-2015 0.906 [92%] -0.178 [17%] 0.000 [11%] Full Sample 0.967 [93%] -0.141 [30%] -0.002 [6%]

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