Paying Attention:

Overnight Returns and the Hidden Cost of Buying at the Open

June 2010

Henk Berkman Department of Accounting and Finance University of Auckland Business School

Auckland, New Zealand h.berkman@auckland.ac.nz

Paul D. Koch*

School of Business University of Kansas

Lawrence, KS 66045 pkoch@ku.edu

Laura Tuttle

School of Business and Management American University of Sharjah

Sharjah, UAE ltuttle@aus.edu

Ying Zhang

School of Business Missouri State University Springfield, MO 65897

YJennyZhang@MissouriState.edu

*Corresponding author. We acknowledge the helpful comments of an anonymous referee and the editor, Matthew Spiegel. We are also grateful for the input of Chris Anderson, Audra Boone, Bob DeYoung, Laura Field, Ben Jacobsen, Kelly Welch, Jide Wintoki, and seminar participants at Massey University, the University of Kansas, the New Zealand Finance Colloquium, and the national conferences of the Financial Management Association and the Eastern Finance Association. We thank Jeff Harris, Frank Hatheway, and Nasdaq-OMX for access to proprietary data. We also thank Xin Zhao for excellent research assistance. In addition, Koch acknowledges support from the University of Auckland and Massey University where he served as visitor while conducting this research. Tuttle acknowledges research support from the Commodity Futures Trading Commission where she served as a visitor.

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Paying Attention: Overnight Returns and the Hidden Cost of Buying at the Open

Abstract

Using 13 years of intraday data for U.S. stocks, we find a strong tendency for positive returns during the overnight period followed by reversals during the trading day. This behavior is driven by an opening price that is high relative to intraday prices. We find this temporary price inflation at the open is concentrated among stocks that have recently attracted the attention of retail investors, and these high attention stocks have high levels of net retail buying at the start of the trading day. In addition, we document that the sensitivity of opening prices to retail investor attention is more pronounced for stocks that are difficult to value and costly to arbitrage, and is greater during periods of high retail investor sentiment. The additional implicit transaction costs for retail traders who buy high attention stocks near the open frequently exceed the effective half spread. JEL Classification: D82, G14, G19. Key Words: market efficiency, attention, sentiment, retail investors, transaction costs, short sale restrictions, institutional ownership, opening price, overnight return.

1. Introduction Behavioral finance theories assume that individual investors are subject to sentiment that makes

them willing to trade at prices not justified by fundamentals. Moreover, because trading against

these investors can be costly and risky, sentiment-based trading can cause prices to deviate from

fundamental value for long periods of time.1 Consistent with these theories, Kumar and Lee

(2006) find that herding by retail traders helps to explain returns for stocks with high retail

concentration that are also difficult to arbitrage. Similar findings are reported in Barber, Odean,

and Zhu (2009), who show that stocks bought by retail investors underperform stocks sold by

retail investors over the following year. Further evidence that sentiment affects prices is provided

in Baker and Wurgler (2006) who document that, after periods of high (low) sentiment, stocks

that are difficult to value and costly to arbitrage earn low (high) returns.

In this paper, we focus on attention as a potential source of retail investor sentiment, and

we examine whether attention-based trading at the open can cause prices to temporarily deviate

from fundamental values. We test four hypotheses that are closely related to the finding in

Barber and Odean (2008), that individual investors are net buyers of attention-grabbing stocks.

First, we predict that high attention days for individual stocks are followed by increased net retail

buying at the start of the next trading day. Second, this retail buying pressure results in opening

prices that are high relative to prices during the rest of the trading day. Third, the sensitivity of

opening prices to retail investor attention is higher for stocks that are more difficult to value and

more costly to arbitrage. Finally, we expect that the impact of attention on opening prices is

greater during periods of high overall retail investor sentiment.

We test these predictions for the 3,000 largest U.S. stocks over the period, 1996 - 2008.

In preliminary analysis we examine quote midpoints at the open and close, and find significant 1 For example, see DeLong et al. (1990) and Shleifer and Vishny (1997).

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positive mean overnight returns of +10 basis points (bp) per day, along with negative trading day

reversals of -7 bp per day. We then explore whether these overall tendencies are due to a high

opening price, or a low closing price, or both. Consistent with the implications of attention-based

overpricing at the open, we find the opening price is high relative to subsequent intraday prices,

while there is no tendency for the closing price to decline further below intraday prices.2

These descriptive results are consistent with evidence provided in two papers that were

developed simultaneously with ours. Branch and Ma (2008) find a negative correlation between

the overnight return and the subsequent trading day return for stocks traded on the NYSE,

AMEX, and Nasdaq. They suggest that this tendency may relate to the microstructure of how

specialists and market-makers behave at the open. Cliff et al. (2008) find robust evidence that the

U.S. equity premium over the last decade is solely due to positive overnight returns. They

emphasize that evidence of systematic negative daytime reversals “present(s) a serious challenge

to traditional asset pricing models from the standpoint that these models do not predict negative

average returns.” Both studies emphasize that this behavior represents a surprising new anomaly,

and they call for further efforts to find an explanation.

We argue that attention-triggered buying by retail investors at the start of the trading day

offers a unifying explanation for this evidence of positive mean overnight returns and negative

trading day reversals. First, observe that retail investors who want to buy face a different search

problem than those who want to sell. For individuals, the decision of which stock to sell is

limited to the small set of stocks they own, because retail investors typically do not short sell.

However, when individual investors want to buy, they must select among thousands of stocks.

Odean (1999) and Barber and Odean (2008) hypothesize that individual investors manage this

problem by limiting their search to stocks that have recently attracted their attention. Consistent 2 Reliance on midquotes ensures that our results are not due to bid-ask bounce.

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with this hypothesis, they show that individual investors are net buyers on the next trading day

following days with high absolute returns, which is one of their proxies for attention.3

We extend the analysis of Barber and Odean (2008) by examining the intraday pattern of

net retail buying and prices, following high attention days. In particular, we compare prices and

order flow during the first hour of the next trading day with that during the rest of the next

trading day, following high attention days. This extension is important, because the next open is

the first opportunity since the previous close for retail investors to buy high attention stocks.4

Our analysis requires a proxy for the level of retail investor attention at the start of the

typical trading day. We use two size-adjusted market-based variables from the previous day.

First, following Barber and Odean (2008), we use the squared return yesterday as a proxy for

news that could attract the attention of retail investors today. Second, motivated by the main

result in Barber and Odean, we use actual net buying by individual investors all day yesterday as

a proxy for retail attention at the start of trading today. We obtain this second measure using

proprietary data on the intraday trading activity of retail investors, for an abridged sample of

Nasdaq stocks during the period, 1997 - 2001.5 These data also enable measurement of the

intensity of net buying by retail investors in the first hour of trading relative to that during the

rest of the trading day. For both proxies of retail attention, we find that: (i) the intensity of retail

buying of high attention stocks is significantly greater during the first hour than it is during the

rest of the trading day, and (ii) the intensity of retail buying during the first hour is significantly

greater for high attention stocks than for low attention stocks.

3 Barber and Odean (2008) also use contemporaneous daily volume as an alternative measure of retail attention. We have also used share turnover yesterday to proxy for retail investor attention at today’s open, and find robust results. 4 There is an after-hours market and a pre-open on ECNs, but high costs and other impediments to trading deter retail investors, so that professional traders dominate these markets (Barclay and Hendershott 2003, 2004). 5 We are grateful to Jeff Harris, Frank Hatheway, and Nasdaq OMX for providing these proprietary data. See Griffin et al. (2003) for details about the data.

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We next examine the implications of these intraday patterns in retail buying for price

formation at the open. We find the magnitude of overnight returns and trading day reversals is

significantly greater for high attention stocks relative to low attention stocks. In particular, for

the subsample of high attention stocks, the mean overnight return ranges from +13 to +26 basis

points (bp) per day, and the average trading day reversal ranges from -13 to -27 bp per day

(depending on the proxy for attention and the sample studied). In contrast, the average 24-hour

(close-to-close) return is close to zero. Together, these results imply that the price impact of

attention-triggered retail buying pressure at the open is only a short term phenomenon.

Behavioral finance theories emphasize that stock prices may deviate further from

fundamentals if the stock is more difficult to value and more costly to arbitrage.6 We test these

predictions in the context of our theory of attention-based retail buying at the open, by

comparing overnight and trading day returns across subsets of firms that are further stratified by

several proxies which reflect the difficulty in valuing and arbitraging stocks.

First, we consider the role of institutional ownership in concert with our proxies for retail

attention. Stocks with low institutional ownership necessarily have a high concentration of retail

investors, and are also difficult to short sell.7 For these stocks, we expect greater upward price

pressure at the open on days following news that attracts the attention of retail investors.

Consistent with this prediction, we find that the largest positive overnight returns and trading day

reversals occur in the subsample of stocks subject to both high retail attention and low

institutional ownership. For this subsample, the mean overnight return ranges from +17 to +34

bp per day, and the average trading day reversal ranges from -17 to -42 bp per day (depending on

6 For example, see Baker and Wurgler (2006) and Kumar and Lee (2006). 7 Kumar and Lee (2006) show that retail trading is negatively correlated with institutional ownership. In addition, a large body of work uses low institutional ownership to proxy for binding short sale constraints (e.g., see Almazan, 2004, Asquith et al., 2005, Berkman et al., 2009, D’Avolio, 2002, Nagel, 2005, and Ofek et al., 2004).

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the proxy for attention and the sample studied). The remaining stocks with low attention and/or

high institutional ownership also tend to have positive overnight returns and negative trading day

reversals, but these returns are smaller in magnitude and less statistically significant.

Second, we show that overnight returns and trading day reversals increase in magnitude

for finer subsamples of stocks that are progressively more difficult to value and more costly to

arbitrage. For example, when we restrict the sample to include only stocks that are hard-to-value,

with high-transaction costs, and high short interest, the mean overnight return (trading day

reversal) is very large, ranging from +43 to +61 (-45 to -70) bp per day. Note that our tests are

predictive and thus indicate that, for certain stocks, selling at the open and postponing purchases

until well after the open can result in major improvements in portfolio performance.

In an extension of our main tests, we investigate whether there is persistence across days

in retail buying pressure at the open. This analysis is motivated by the fact that there is high

persistence in retail investor sentiment, and that retail investors as a group are likely to continue

to focus on stocks with certain persistent characteristics.8 We find significant autocorrelation in

daily net retail buying during the first hour of the trading day, at the level of individual stocks.

We also find that this autocorrelation is substantially greater for stocks subject to buying pressure

than for stocks subject to selling pressure. Further tests show that, while greater persistence in

buying pressure at the open exacerbates price inflation at the open, it does not subsume the

influence of retail attention based on yesterday’s volatility or yesterday’s net retail buying.

Finally, we investigate whether the magnitude of positive overnight returns and negative

trading day reversals is exacerbated during periods with high overall investor sentiment (see

Baker and Wurgler, 2006, 2007). We consider two time series proxies for variation over time in

8 The first order autocorrelation coefficient of the monthly Baker Wurgler sentiment index is 0.95. In addition, high persistence in retail attention for certain stocks was evident during the internet bubble (Ofek and Richardson, 2004).

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the level of retail investor sentiment. Our first measure is based on the monthly sentiment index

of Baker and Wurgler, while our second measure is based on market-wide net buying activity by

retail investors during the first hour of the trading day. We find that variation over time in the

magnitude of opening price inflation for high attention stocks is significantly related to both time

series indices of market sentiment. For example, we show that mean overnight returns and

trading day reversals are more than twice as large during months with high versus low sentiment,

and this opening price inflation can be twice the magnitude of the effective half spread. An

important implication is that retail traders incur a substantial hidden transaction cost when they

buy stocks that have recently caught their attention, at inflated opening prices.

Our results are robust when we use market-adjusted returns, when we use median returns,

when we use trade prices to measure returns, and when we exclude low-price stocks. This

behavior is also ubiquitous across small and large stocks, Nasdaq and NYSE stocks, growth and

value stocks, and momentum winners and losers, although there is a larger mean overnight return

and trading day reversal for small stocks, Nasdaq stocks, growth stocks, and momentum losers.

We also find these patterns are somewhat larger in magnitude on Mondays, although they also

appear on the other days of the week. In addition, these results appear in all subperiods, although

they decline in magnitude following decimalization in 2001, and they decline somewhat more

after 2005, with the expansion of algorithmic trading.

This article proceeds as follows. Section 2 describes our sample selection and variable

construction. Section 3 reports descriptive statistics. Section 4 presents the main empirical

analysis. Section 5 analyzes persistence in retail buying pressure at the open. Section 6 examines

the time series relation between overall market sentiment and the magnitude of opening price

inflation. Section 7 provides robustness tests, and section 8 summarizes and concludes.

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2. Sample Selection and Variable Construction 2.1 Sample Selection and Daily Return Measures

Our main sample includes the 3,000 largest U.S. firms each year according to their market

capitalization on July 1, over the period 1996 - 2008. We also apply our analysis to an abridged

sample for which proprietary data on intraday retail trading were obtained from Nasdaq OMX.

These proprietary data describe each trade for Nasdaq stocks during the period, 1997- 2001, and

include the identity of market participants on each side of the trade. For this abridged sample, we

follow the procedures in Griffin et al. (2003), and classify both sides of all trades as originating

from an individual or an institution based on the market participants involved in the trade.

We calculate daily returns using quotations from TAQ.9 The opening price on day t

(opent) is the midpoint of the first valid bid and ask quotes after 9:30 a.m.10 The closing price on

day t (closet) is the midpoint of the last valid bid and ask quotes before 4:00 p.m.11 We adjust

these daily opening and closing prices for stock splits and dividends, before computing daily

returns.12 Returns are measured as the log of the price relative over each time frame considered:

24-Hour, Open-to-Open Return = otot = log(opent / opent-1); 24-Hour, Close-to-Close Return = ctct = log(closet / closet-1); Overnight, Close-to-Open Return = ctot = log(opent / closet-1); Trading Day, Open-to-Close Return = otct = log(closet / opent). 9 TAQ’s consolidated quotation file is an aggregation of quotes within each market venue. It represents a set of “top of book” records for each venue. In order to identify market-wide best prices, we calculate an inside market across all venues. For the NYSE, this calculation almost never improves upon the NYSE specialist’s price. However, in Nasdaq issues, ECNs often improve on the Nasdaq’s reported best price. 10 By “the first valid quotes” we mean the first quotes after 9:30 a.m. for which there is non-zero trade size on both the bid and the ask. For NYSE issues, selection of the open is straightforward since the opening cross is easily identified and begins the trading day. For Nasdaq issues, selection of the open is not so straightforward. Although technically the Nasdaq opens at 9:30 a.m., it is often several minutes before valid market-maker quotes appear. If the midquote precisely at 9:30 a.m. is used as the open, these quotes will often be flagged as “closed” by the market participant, or they may have zero size associated with the prices. In either case the price does not represent a firm commitment to trade. This behavior of the Nasdaq open motivates our choice of the first valid quotes after 9:30 a.m. as the opening quotes. Our results are robust when we take the midquote precisely at 9:30 a.m. as the open. 11 Occasionally, the final quotes before 4:00 p.m. have zero shares available to trade on one or both sides, or the quote is flagged as closed. For this reason, we select the last valid quote before 4:00 p.m. 12 On days when a cash dividend or a stock split becomes effective at the open, we adjust the TAQ data on opening and closing prices using CRSP data on the amount of the cash dividend or the multiple of the stock split. The adjusted opening and closing prices are then used to compute each daily return measure.

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Note that ctct = ctot + otct. Finally, consistent with prior work, we screen the data for errors

and extreme observations.13

2.2 Variable Construction

For each stock, we estimate two proxies for the level of attention by retail investors at the start of

the trading day. Our first proxy is the square of yesterday’s close-to-close return (VOLt-1). This

measure is motivated by Barber and Odean (2008), who use the absolute return yesterday to

proxy for news that could attract the attention of retail investors, and find that increases in this

measure are associated with increases in net retail buying all day today. Our second proxy is net

shares bought by individual investors yesterday, as a percent of total share volume

(Retail_NetBuyt-1). This measure is also motivated by the results in Barber and Odean. Their

finding that individual investors are net buyers of attention-grabbing stocks suggests that stocks

with high net retail buying have (almost by definition) attracted the attention of retail investors.

For both measures, we predict that stocks which attracted the attention of retail investors

yesterday are likely to be subject to high retail investor attention at the start of trading today. In

the next section we provide evidence that substantiates this prediction.

We also use the proprietary data for Nasdaq stocks over 1997 – 2001, to compute two

measures of the intensity of net buying by retail investors during the first hour of the trading day:

NetBuy_HR1it = (Retail_NetBuy_HR1it ) / (Shares Outstandingit);

NetBuy_Diffit = (Retail_NetBuy_HR1it – (Retail_NetBuy_Restit / 5.5) / (Shares Outstandingit);

where Retail_NetBuy_HR1it = the net number of shares of stock i bought by retail investors during the first hour of trading day t;

13 Quotes are dropped from our analysis if their “mode” designation indicates that they are not normal quotes, or if the reported ask price is greater than 1.5 times the reported bid price. In addition, we omit the daily return if: (i) the bid-ask spread at the open or close is negative, or (ii) the opening or closing spread is greater than $5.00 or 30% of the midpoint quote, or (iii) the effective half spread is greater than $2.50 or 15% of the midpoint quote, or (iv) the daily open is more than 25% greater (or less) than both the previous close and the subsequent close. We also drop all daily returns for a firm if daily quotes are missing for more than 25 percent of all trading days for that firm.

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and Retail_NetBuy_Restit = the net number of shares of stock i bought by retail investors during the rest (i.e., the last 5.5 hours) of trading day t. The first variable defined above measures the rate of net retail buying during the first hour of the

trading day, as a percent of shares outstanding. The second variable captures the difference

between this rate of net retail buying during the first hour and the rate of net retail buying per

hour during the rest of the trading day.

Next, following Asquith et al. (2005), we consider two proxies for short sale constraints:

institutional ownership and relative short interest. Data on institutional holdings are from CDA

Spectrum 13F filings. Each quarter, we compute the percentage institutional ownership (INSTt)

for every firm as aggregate shares held by institutions scaled by shares outstanding. If a stock is

available in CRSP but has no information on institutional holdings, we assume that the stock has

zero institutional ownership (see Asquith et al., 2005, Gompers and Metrick, 2001, and Nagel,

2005). See Appendix A for more details. Our second proxy for short sale constraints is relative

short interest (RSIt), measured by the total number of shares sold short as a percent of shares

outstanding, using monthly data on short interest from the NYSE and the Nasdaq.

Finally, we use three measures of transaction costs: the percentage spread at the open

(SPR(open)t), at the close (SPR(close)t), and the percentage effective half spread (Spreadt).14

3. Descriptive Statistics and Intraday Price Patterns 3.1 Descriptive Statistics for Overnight and Trading Day Returns

In Panel A of Table 1, we report the mean and median values for overnight returns, trading day

returns, and 24-hour returns across all firms and days in the sample. Note that the average

14 For every trade, the percentage effective half spread is defined as the absolute difference between the trade price and the quote midpoint, as a percent of the quote midpoint. Trades are matched to quotes with a lag of one second, and then averaged to get the day’s percentage effective half spread. Our choice of a one-second lag is taken from the Nasdaq Economic Research Office, which argues this lag is optimal to match trades and quotes in its automated electronic system. Our results are not affected by this choice (see Lee and Ready, 1991, and Bessembinder, 2003).

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number of firms each day varies from 2,446 to 2,603 across the different measures of daily

returns considered. This range is less than the 3,000 largest U.S. stocks used as the initial sample,

because daily opening or closing quotes are invalid or unavailable for some of the smaller stocks

(see footnote 13 for details of our screening procedure).

Standard t-tests applied to these mean returns could be biased due to cross-correlation of

daily returns across firms on the same date (Bernard, 1987), or to autocorrelation in mean returns

across dates. In our analysis we adjust our standard errors for this possibility. Specifically, for

each of the 3,268 trading days in our 13-year sample period, we first compute the cross-sectional

mean (or median) overnight and trading day returns across all stocks in the sample. We then

compute the time series average of these cross-sectional mean (or median) returns across all

trading days in the sample period. In our portfolio analysis, the corresponding t-statistics are

based on the Newey-West adjusted standard errors of the time series mean returns.

Results on the left side of Panel A in Table 1 indicate a significant positive mean

overnight return (cto) of approximately +10 basis points (bp) per day, and a significant negative

trading day reversal (otc) of -7 bp per day, when averaged across all firms and days. As a result,

the mean return on a strategy that is long the sample stocks during the overnight period and short

the same stocks during the subsequent trading day (DIFF) would be +17 bp per day, before

deducting transaction costs. On the other hand, when we subtract the average bid-ask spread at

the daily open and close, we obtain a significant negative mean difference after transaction costs

(DIFF-TC) of -71 bp. Note that the median value of the overnight return in Panel A of Table 1

(cto) is smaller than its respective mean, while the median trading day return in Panel A (otc) is

approximately the same as the mean. Finally, the 24-hour returns (i.e., the sum of otc and cto) are

about 3 bp per day, which corresponds to around 8 percent per annum.

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3.2 Descriptive Statistics for the Main Variables

Panel B of Table 1 provides descriptive statistics for the main variables in the study. First

consider our two proxies for retail attention.. The average squared close-to-close return (VOL) is

0.127 percent, while the mean daily net retail buying (Retail_NetBuy) is not significantly

different from zero. The latter result indicates that, during the 1997 - 2001sample period, there

was no substantive shift in ownership of Nasdaq stocks between retail and institutional investors.

In contrast, our measures of the intensity of net retail buying in the first hour of the trading day

(NetBuy_HR1it and NetBuy_Diffit) reveal that, on average, retail investors tend to be significant

net buyers of stocks in the first hour of the trading day, and this hourly rate of net buying in the

first hour is significantly greater than that over the rest of the trading day.

Next consider our measures of short sale constraints and transaction costs. We find that

mean institutional ownership (INST) is 52 percent of shares outstanding. This number is higher

than the 34 percent reported in Nagel (2005), because our sample is limited to larger firms.

Relative short interest averages 3.8% of shares outstanding across all stocks and days in the

sample, similar to that reported in Asquith et al. (2005). The average spread at the open is 1.06%

of the quote midpoint, while the average spread at the close is 0.62%, and the mean effective half

spread is 0.17%. Finally, the average firm has a market capitalization of $5.21 Billion. Note that

the medians for most variables in Panel B of Table 1 are smaller than their corresponding means,

indicating some degree of positive skewness for these firm attributes, as expected.

3.3 Correlations across the Main Variables

In Panel C of Table 1 we report the average Spearman correlation across each pair of variables.15

These correlations are generally consistent with our expectations. First, note that our two proxies

15 Spearman correlations are applied to reduce the influence of outliers. Pearson correlations yield similar results.

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for retail investor attention have a significant positive correlation of 6 percent. Also, both proxies

are positively correlated with our measures of retail buying pressure in the first hour.

Second, both attention measures are positively correlated with the overnight return (cto),

and negatively correlated with the trading day return (otc). This evidence is consistent with an

upwardly biased opening price for stocks that are subject to higher attention by retail investors.

Third, consider the association between our proxies for short sale constraints and stock

returns during the overnight period versus the trading day period. The percent of institutional

ownership (INST) is significantly negatively correlated with the overnight return (cto) and

positively correlated with the trading day return (otc), while the opposite tendencies are apparent

for relative short interest (RSI). This outcome suggests that stocks subject to more binding short

sale constraints (i.e., with lower institutional ownership or higher short interest) tend to have

larger overnight returns and trading day reversals. This result is also consistent with predictions

based on our theory of attention-based overpricing at the open.

Fourth, the spread measures tend to be positively correlated with the overnight return and

negatively correlated with the trading day return, indicating a tendency for larger overnight

returns and trading day reversals for stocks with higher transaction costs. In addition, the spread

measures are negatively correlated with firm size and institutional holdings, as expected.

Finally, firm size is negatively related to overnight returns (otc), and positively related to

trading day returns (cto). This outcome suggests that smaller firms have a tendency for larger

positive overnight returns and trading day reversals. In addition, firm size is negatively

correlated with one of our attention proxies (VOL), and positively correlated with institutional

ownership and our second attention proxy (Retail_Netbuy). This evidence reinforces the need to

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control for size when we analyze the influence of institutional ownership or retail investor

attention on daily returns in our analysis (see Nagel, 2005).

3.4 The Intraday Price Pattern – All Stocks and Days

The descriptive statistics in Table 1 raise the question of whether this average positive overnight

return and negative trading day reversal are due to a high opening price or a low closing price, or

both. We address this issue by examining the pattern in prices throughout the trading day. For

each stock, we collect data on intraday midquotes at 30-minute intervals. In addition, we gather

the midquotes at 5-minute intervals during the first and last 30 minutes of the trading day. Then,

at each 5-minute or 30-minute interval (T), we construct the ratio of the midquote at that time to

the day’s closing midquote.16 We then find the average of each intraday price ratio across all

stocks every day. Finally we compute the time series mean of these cross-sectional average price

ratios for all days in the sample period. The mean sample size for this analysis is 2,528 firms per

day, for which TAQ data are available on quotes throughout the average day.

Figure 1 plots the intraday pattern in this ratio of the midquote at time T to the closing

midquote, across all stocks and days in the sample, along with the 95% confidence interval about

a ratio of one. Note that this confidence interval collapses to zero at the close, when the price

ratio equals one for all firms. This intraday price pattern reveals that, on average, the opening

price is significantly higher than the closing price by approximately 11 basis points (i.e., the

opening price ratio = 1.0011). After the open, the price declines during the first 60 minutes of

trading to within the 95% confidence interval about one, and then levels off during the middle of

the day. Then, there is a further slight decline in average prices during the afternoon, before

prices rise slightly during the last few minutes of trading. This intraday pattern is consistent with

16 We choose the closing price to scale intraday price ratios because our main analysis focuses on open-to-close and close-to-open returns. When we scale by the average midquote between 11 a.m. and 3 p.m., we find similar results.

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the implications of our attention-based explanation, indicating that prices near the open tend to

be high relative to subsequent intraday prices.

3.5 The Intraday Price Pattern for Subsamples of Stocks based on Retail Trading at the Open

The economic importance of our finding depends, in part, upon whether substantial retail trading

occurs near the open, when prices tend to be relatively high. If opening prices are high, but little

retail trading occurs at these prices, such a result would diminish the economic significance of

this intraday price behavior. On the other hand, if substantial retail trading occurs at the high

prices near the open, this evidence would enhance the economic importance of these results.

We address this issue by analyzing the intraday price pattern for quintiles of stocks each

day, partitioned by the intensity of total retail trading activity in the first hour (i.e., the sum of

shares bought and sold by retail traders during the first hour, as a percent of total daily share

volume). This analysis is applied to the abridged sample, for which we have data on retail trading

volume. Results are provided in Figure 2, and reveal that stocks with a greater intensity of retail

trading in the first hour have substantially higher opening prices during the first hour of the

trading day, which tend to decline toward the intraday average price in the middle of the day.

This evidence reinforces the economic importance of this intraday price behavior.

4. Main Empirical Tests 4.1 The Intensity of Net Retail Buying in the First Hour, and Investor Attention Our first hypothesis is that high attention days are followed by high net retail buying at the start

of the next trading day. We test this hypothesis by comparing our two measures of the intensity

of net retail buying during the first hour (NetBuy_HR1 and NetBuy_Diff), across portfolios

partitioned by our proxies for retail attention, while controlling for firm size.

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In this approach we consider each trading day as a separate event. For each day, we

control for firm size by initially sorting all firms into size terciles, based on the firm’s mean

market capitalization over the previous twenty trading days.17 Then, within each size tercile, we

form three finer portfolios by independently sorting based on each proxy for attention: VOLt-1 or

Retail_Netbuyt-1. We then compute the cross-sectional means of our two measures of the

intensity of net retail buying in the first hour (NetBuy_HR1it and NetBuy_Diffit), for each

portfolio based on low, medium, or high size-adjusted retail investor attention. Finally, we

average these cross-sectional means across all days in the sample period. The t-statistics are

based on the Newey-West adjusted standard errors of the time series means.

The first two columns in Panel A of Table 2 present these two measures of the average

intensity of net retail buying near the open, for the three attention-based portfolios, where the

level of retail investor attention is proxied by return volatility yesterday (VOLt-1). The first two

columns of Panel B present the analogous results using net retail buying yesterday

(Retail_NetBuyt-1) to proxy for attention. In both Panels A and B, each measure of the intensity

of net retail buying near the open is significantly positive for high attention stocks. Furthermore,

the difference of means for each measure of retail buying intensity at the open, across portfolios

with high versus low attention, is significantly positive at the 1% level. These results confirm our

first hypothesis, indicating that high attention days for individual stocks are followed by high net

retail buying at the start of the next trading day.

4.2 Overnight and Trading Day Returns, and Investor Attention

Our second hypothesis predicts that this attention-triggered retail buying pressure at the open

should result in opening prices that are high relative to prices during the rest of the trading day.

17 Results are robust when we do not control for size in this partitioning scheme.

16

We test this hypothesis by comparing the overnight and trading day returns across portfolios

based on low, medium, or high attention. Results appearr in the next two columns of Table 2.

Panels A and B of Table 2 both reveal positive mean overnight returns and negative

trading day reversals for all three portfolios, which increase in magnitude and significance as we

consider stocks subject to higher levels of attention. In both Panels, the mean difference t-test

indicates a significant difference between the mean overnight return or trading day reversal,

across portfolios subject to high versus low retail attention. In Panel A, the mean overnight

return (trading day reversal) for the high-attention portfolio is +13 bp (-13 bp) per day, across the

3,000 largest U.S. stocks over the period 1996-2008. Panel B indicates that the analogous results

are larger for the sample of Nasdaq stocks during 1997-2001, averaging +26 bp (-27 bp) per day.

It is noteworthy that the mean 24-hour close-to-close return in the last column of Table 2

is not significantly different from zero for any portfolio in Panel A or B. This result indicates that

the significant positive mean overnight return and negative trading day reversal, for stocks with

different levels of retail investor attention, represent a temporary mispricing at the open which is

corrected during the course of the typical trading day.

4.3 Overnight and Trading Day Returns, Investor Attention, and Institutional Ownership

In this section we consider institutional ownership in combination with our proxies for retail

attention. Stocks with low institutional ownership necessarily have a high concentration of retail

investors, and are also difficult to short sell. For these stocks, we therefore expect greater

upward price pressure at the open on days following news that attracts the attention of retail

investors (proxied by yesterday’s return volatility or yesterday’s net retail buying). We test this

hypothesis by applying a portfolio approach in which we compare average overnight and trading

17

day returns across portfolios of firms that are independently partitioned along two dimensions -

the level of retail investor attention and institutional ownership - while controlling for firm size.

As before, we control for firm size by initially sorting all firms into size terciles based on

the firm’s mean market capitalization over the previous twenty days. Then, within each size

tercile, we form three finer portfolios by independently sorting based on: (1) the percentage of

institutional ownership at the end of the previous quarter (INST), and (2) each proxy for retail

attention yesterday (VOLt-1 or Retail_NetBuyt-1). This procedure results in a 3 x 3 scheme of

portfolios, sorted by size-adjusted institutional ownership and each proxy for attention.

Finally, we test the implications of our attention-based theory by comparing mean

overnight and trading day returns across portfolios within each 3 x 3 scheme. If the tendency for

positive overnight returns and negative trading day reversals is not due to the bias hypothesized

in our theory of attention-triggered retail buying at the open, then we would expect no

differences in mean overnight or trading day returns across portfolios with different levels of

attention or institutional ownership. On the other hand, if this overnight return behavior is due to

net retail buying at the open triggered by attention, then we would expect greater positive

(negative) overnight (trading day) returns for portfolios with higher levels of retail attention,

combined with lower institutional ownership.

Once again, we conduct statistical tests that are not affected by potential cross-sectional

correlation in returns on the same day, or autocorrelation across days. We first average the cross-

sectional returns for each of the double-sorted portfolios, and then average across all trading days

in the sample period, relying on Newey-West adjusted standard errors of these time series means.

Consider the results in Panel A of Table 3 which uses yesterday’s squared return (VOLt-1)

to proxy for the level of retail investor attention at the open. This Panel presents three 3 x 3

18

schemes of double-sorted portfolios that provide the mean overnight returns, trading day returns,

and close-to-close returns, respectively. On average, there are 261 stocks in each of the nine

portfolios within every double-sorted partitioning scheme in Panel A.

First, consider the 3 x 3 scheme with mean overnight returns (cto) in Panel A. All nine

cells in this scheme are significantly positive. However, the largest mean overnight returns in this

scheme appear in the bottom row, for portfolios subject to high retail attention. The mean

difference t-test provided at the bottom of every column indicates that stocks with high attention

significantly outperform stocks with low attention during the overnight period. In addition, the

left column of each scheme contains the largest element in every row, indicating that stocks with

low institutional ownership tend to have larger overnight returns. Finally, the bottom left cell has

the largest mean, indicating that stocks subject to both high retail attention and low institutional

ownership have the greatest overnight returns, which average +17 bp per day.

Second, consider the mean trading day returns (otc) in the middle 3 x 3 scheme in Panel

A of Table 3. Now we find negative mean trading day reversals in all nine cells of this scheme,

whose magnitudes and significance increase with the level of retail investor attention. Once

again, the largest negative trading day returns are concentrated in the bottom row, among stocks

with high attention, and in the left column, among stocks with low institutional ownership. The

mean difference t-test at the bottom of every column shows that stocks with high retail attention

significantly underperform stocks with low attention, during the trading day. In addition, the

bottom left cell contains the largest negative mean trading day reversal, at –17 bp per day.

Third, the last 3x3 scheme in Panel A of Table 3 reinforces the result from the last

column of Table 2, showing that attention-based overpricing at the open is a short-term

phenomenon. Even for the most overpriced stocks (high volatility yesterday and low institutional

19

holdings), the significant price inflation at the open is completely reversed during the typical

trading day, so that the average close-to-close return is not significantly different from zero.

Next consider the results in Panel B of Table 3, which use net retail buying yesterday to

proxy for attention. Once again, this proxy is available only for the abridged sample of Nasdaq

stocks during the period, 1997 - 2001. The results in Panel B are consistent with those in Panel

A, although the price inflation at the open is substantially larger in magnitude. In the first 3 x 3

scheme of Panel B, the mean overnight return for stocks most prone to overpricing at the open

(i.e., the bottom left cell) is +34 bp per day. In the second 3 x 3 scheme, the mean trading day

reversal for the same cell is -42 bp. Once again, the third 3 x 3 scheme of Panel B contains mean

24-hour returns that are smaller in magnitude and not significantly different from zero. One

likely reason for the stronger intraday price pattern in Panel B is that the sample period, 1997 -

2001, represents a time of high investor sentiment (e.g., see Baker and Wurgler, 2006 and section

6 below). Furthermore, Nasdaq stocks tend to be more volatile, more difficult to value and costly

to arbitrage, and have lower institutional ownership. We further investigate these issues next.

4.4 Stocks that are Difficult to Value and Costly to Arbitrage

This section addresses our third hypothesis, by examining the relation between overpricing at the

open and variables that proxy for the difficulty in valuing a stock or the costs of arbitrage. Both

of these attributes of a stock are likely to exacerbate the extent of overpricing at the open found

in Table 3 (see Baker and Wurgler, 2006, and Kumar and Lee, 2006). To this end, Table 4

reproduces the analysis in each Panel of Table 3 three times, sequentially restricting the samples

used in Table 3 to focus on progressively finer subsamples of stocks each day that are harder to

value and more costly to arbitrage. First (1), we limit the sample to the 50% of firms each day

with the highest return volatility over the previous 20 trading days, to represent stocks that are

20

hard to value.18 Second (2), we narrow this focus by considering 50% of the hard-to-value firms

in (1) with the highest mean effective half spread over the previous 20 trading days. Third (3),

we further confine the sample each day to the 20% of the hard-to-value, high-transaction-cost

firms in (2) with the highest relative short interest in the previous month.19

Panels A, B, and C of Table 4 present the results for this sequence of progressively

greater restrictions in (1), (2), and (3) above, on the main sample, using volatility yesterday

(VOLt-1) to proxy for attention. Panels D, E, and F then present the analogous restrictions on the

abridged sample, using net retail buying yesterday (Retail_NetBuyt-1) to proxy for attention.

First consider the results in Panel A of Table 4, which limits the sample to the 50% of

firms each day with the highest recent volatility. After this restriction, there are now an average

of 129 hard-to-value stocks within every double-sorted portfolio. The resulting 3 x 3 schemes in

Panel A follow the same pattern as those in Table 3, although the positive overnight returns and

negative trading day reversals are larger in magnitude, as predicted. The bottom left cell of the

first two 3 x 3 schemes in Panel A now reveals a mean overnight return (trading day reversal) of

+26 (-24) bp per day.

Panel B of Table 4 presents the analysis after further limiting the sample of hard-to-value

firms from Panel A, to the 50% of remaining stocks with the highest effective half spread. On

average, there are now 61 stocks in every double-sorted portfolio. As expected, the mean

overnight returns and trading day reversals display similar relations with attention and

institutional ownership, but they are still larger in magnitude than the results in Panel A. In

particular, the bottom left cell of the first two 3 x 3 schemes in Panel B reveal a mean overnight

18 Baker and Wurgler (2006) argue that volatility is a good proxy for the difficulty in valuing stocks. We have also used the firm’s book-to-market ratio from the previous quarter as an alternative measure of this aspect of a stock. Results are consistent with those using return volatility over the past month, and are summarized in Table 7. 19 Asquith et al. (2005) argue that stocks with both low institutional ownership and high short interest are subject to more binding short sale constraints, and thus experience greater overpricing and subsequent price declines.

21

return (trading day reversal) of +34 (-27) bp. This result corroborates a growing body of

evidence that: (i) documents a tendency for greater overpricing among stocks with higher

transaction costs, and (ii) suggests that arbitrageurs are more sensitive to transaction costs than

are sentimental traders (in our case, attention-triggered retail buyers at the open).20

Third consider the results of our final sample restriction in Panel C of Table 4, where we

further restrict the sample used in Panel B to include only the 20% of hard-to-value, high-

transaction-cost stocks with the highest relative short interest. On average, there are now 13

stocks in every double-sorted portfolio. Again, as expected, the mean returns in Panel C are yet

larger in magnitude than the analogous results in Panels A and B, especially for the portfolio

with low institutional ownership and high retail attention. Now the bottom left cell from the first

two schemes in Panel C show a mean overnight return (trading day reversal) of +43 (-45) bp.21

Fourth, consider Panels D, E, and F of Table 4, which provide the analogous results for

subsamples based on the abridged sample of Nasdaq stocks over the period, 1997 - 2001. These

results follow the same pattern as in Panels A, B, and C, with mean overnight returns and trading

day reversals increasing in magnitude as we progress to finer subsamples based on stocks that

are harder to value, and with greater costs of arbitrage. The results in Panels D, E, and F are

substantially larger than those in Panels A, B, and C. For example, the bottom left corner cell of

the respective 3 x 3 schemes in Panels D, E, and F reveals mean overnight returns of +51, +57,

and +61 bp per day, along with average trading day reversals of -63, -67, and -70 bp per day.

For nearly every 3 x 3 scheme throughout this analysis in Table 4, the mean overnight

returns and trading day reversals increase monotonically as we move down each column to

20 For more evidence and discussion of these issues, see Sadka and Scherbina (2007). 21 Note that, when we split the sample stocks into finer groups at each stage of this analysis, the average portfolio size declines as follows. First, it falls from approximately 2,500 to 261 firms when we split into 9 groups, then down to 129 firms when we take 50% of these stocks, then to 61 when we take 50% of these, and finally to 13 when we take 20% of these. At each step we lose a few stocks due to unavailability of data on the screening variable.

22

portfolios subject to higher retail attention, and as we move left across each row to portfolios

with lower institutional ownership. In addition, the 3 x 3 schemes presenting 24-hour returns

throughout Table 4 consistently reveal close-to-close returns that are much smaller in magnitude.

Together, the results in Table 4 reinforce the view that high attention firms tend to have

positive overnight returns and trading day reversals that are larger in magnitude when they are

more difficult to value, transaction costs are higher, and short sale constraints are more binding.

This evidence provides further support for our theory of attention-based overpricing at the open.

5. Persistence in Price Inflation and Buying Pressure at the Open The previous sections show that our two market-based proxies for attention, based on yesterday’s

volatility and yesterday’s net retail buying, are effective measures of retail buying pressure at the

open today, as they predict greater overnight returns and trading day reversals. On the other

hand, retail investor attention might also be related to more persistent firm characteristics, such

as whether a stock is in a certain industry (for example, internet or biotech stocks), or whether it

is a value stock or a growth stock, or whether it had very low or high returns over the past few

months. In this section we investigate whether retail net buying at the open is persistent for

certain stocks, whether such persistence may exacerbate overnight returns and trading day

reversals, and whether the previous results still hold after controlling for such persistence.

5.1 Persistence in Retail Net Buying at the Open

First, we examine whether retail net buying at the open is persistent across days. Every day, we

distinguish between two subsets of stocks, where retail traders were either net buyers or net

sellers during the first hour of the day (i.e., where NetBuy_HR1t > 0 versus < 0). Then, for each

subset, we compute the autocorrelation between NetBuy_HR1t on that day and NetBuy_HR1t+k

for the same stock, k days later (k = 1 to 20). Next, for each subset, we average these

23

autocorrelations at every lag k, over all days in the sample period. The T-statistic for each mean

autocorrelation is constructed using the standard error of the time series mean.

These mean daily autocorrelations are presented in Table 5. Panel A reports the

autocorrelation function (ACF) for NetBuy_HR1t following days with positive NetBuy_HR1t,

and Panel B reports the analogous ACF following days with negative NetBuy_HR1t. In each

Panel, the first column presents the ACF based on the entire sample of stocks, while the next

four columns present the analogous ACF’s for subsamples of firms with different characteristics,

including value stocks and growth stocks (top and bottom quintiles by book-to-market), and

momentum winners and losers (top and bottom quintiles by past six-month return).

Panel A of Table 5 reveals large and highly significant mean daily autocorrelations for

retail net buying in the first hour, following days with net buying in the first hour (i.e., where

NetBuy_HR1t > 0). For all stocks, the mean autocorrelation at lag one day is .25 (T-statistic =

30.5), and it decays to .10 after twenty trading days (T-statistic = 16.0). Similar ACF patterns

appear in the other four columns of Panel A, indicating highly significant persistence in

NetBuy_HR1t for all subsamples.

The analogous autocorrelations in Panel B are much smaller in magnitude, following

days with net selling by retail traders in the first hour (i.e., where NetBuy_HR1t < 0). For all

stocks, the autocorrelation at lag one day is now .11 (T-statistic = 16.2), and it decays to .01 after

twenty trading days (T-statistic = 2.6). Furthermore, in Panel B the ACF’s for the four

subsamples decay rapidly toward zero following days with retail net selling in the first hour,

especially for value stocks and momentum losers.

Together, the results in Panels A and B indicate that retail net buying in the first hour is

highly persistent, particularly if retail investors were net buyers during the first hour over the past

24

month. The last four columns in Panels A and B show that persistence in retail net buying in the

first hour tends to be stronger for growth stocks versus value stocks, and for past winners versus

for losers. This evidence raises two empirical questions: (i) whether persistence in retail net

buying in the first hour might exert its own influence on the magnitude of overpricing at the

open, independent of that exerted by attention yesterday, and (ii) whether the influence of retail

attention yesterday remains after controlling for this persistence in retail buying in the first hour.

5.2 Persistence in Price Inflation, Retail Net Buying, and Overpricing at the Open

We investigate both empirical issues by introducing two stock-specific measures of the

persistence in retail net buying at the open, measured over the previous month. The first measure

is the sum of NetBuy_HR1t over the past 20 trading days, and reflects aggregate accumulated net

shares bought by retail investors during the first hour of all trading days over the past month, as a

percent of shares outstanding. We also introduce an indirect measure of persistence in net retail

buying at the open, which represents the recurring tendency for a stock to have inflated opening

prices over the past month. This measure is defined as the percent of the previous 20 trading days

with positive overnight returns (cto > 0) and negative trading day reversals (otc < 0).

In Table 6 we re-apply the analysis of Table 3, to construct the 3 x 3 schemes based on

our proxies for retail investor attention yesterday and institutional ownership. However, we now

limit the analysis to the top tercile of stocks each day with the highest persistence in price

inflation or net retail buying in the first hour, over the past month. In Panel A of Table 6 we

analyze the main sample over the period, 1996 - 2008. Data on net retail buying are unavailable

for much of this period. Thus, we use the percent of the past 20 days with cto > 0 and otc < 0 as

our measure of persistence in price inflation at the open, while we rely on return volatility lagged

one day as our measure of retail attention yesterday. In Panel B we apply the same analysis to the

25

abridged sample of Nasdaq stocks over the period, 1997 - 2001, using the same measure of

persistence in price inflation at the open, but we now rely on retail net buying lagged one day as

our measure of retail attention yesterday. Finally, in Panel C we again analyze the abridged

sample, but we now use our alternative measure of aggregate accumulated net retail buying in

the first hour over the previous 20 days, to proxy for persistence in retail buying at the open,

while again using retail net buying lagged one day as our measure of retail attention yesterday.

All three Panels of Table 6 reveal mean overnight (cto) and trading day (otc) returns that

are substantially larger than the analogous results in Table 3. The magnitude of these results is on

a par with the analysis in Panels B and E of Table 4, applied to the subsamples of hard-to-value

stocks with high transaction costs. Furthermore, as we move down the rows of the 3 x 3 schemes

for cto and otc in Table 6, we continue to find overnight returns and trading day reversals that

increase significantly for portfolios subject to higher levels of retail attention yesterday.

Together, this evidence indicates that: (i) persistence in retail net buying in the first hour does

exert its own influence on the magnitude of overpricing at the open, (ii) but the influence of retail

attention yesterday remains after controlling for persistence in retail buying at the open.

6. Variation over Time in Overpricing at the Open: the Role of Sentiment The previous sections establish that, for a large group of stocks subject to high attention and low

institutional holdings, the opening price tends to be very high relative to intraday prices. In this

section we examine how the magnitude of this opening price inflation changes through time, and

whether any such time-variation in this overpricing is related to changes in investor sentiment.

This analysis requires a time series measure that tracks the level of retail investor

sentiment over time. We examine two alternative proxies. Our first measure is the sentiment

index in Baker and Wurgler (2006, 2007). This sentiment measure is a composite index based on

26

the first principal component of six different sentiment proxies, orthogonalized with respect to

several macroeconomic conditions. The Baker-Wurgler sentiment index is available on a

monthly basis from the start of our sample period to the end of 2007.22

Our second measure is the actual net buying activity of retail investors during the first

hour of the trading day, as a percent of shares outstanding, averaged across all stocks and all

days during the period. This measure is motivated by the results in Table 2, which indicate that

net retail buying in the first hour is an effective proxy for cross-sectional differences in retail

investor sentiment based on attention. We refer to this measure as our retail sentiment index. The

available data on net retail buying enable measurement of this sentiment index for trading in

Nasdaq stocks over period, 1997 - 2001.

Our tests in this section are designed to establish whether monthly variation in these two

proxies for retail investor sentiment can explain variation through time in the extent to which

opening prices are pushed above ‘fundamental’ values (i.e., values during the rest of the trading

day). We first calculate daily overnight and trading day returns for groups of stocks classified

using the same procedures as before. That is, we compute the mean overnight and trading day

returns for the 3 x 3 scheme of portfolios sorted along two dimensions: size-adjusted

institutional ownership and retail investor attention yesterday. Next, for each month, we calculate

the mean daily overnight and trading day returns to measure the average daily performance of

each portfolio during the overnight and trading day periods, respectively, throughout that month.

Thus our monthly overnight (trading day) return measure for each portfolio, CTOm (OTCm),

contains the mean of daily overnight (trading day) returns during each month (m).

22 For details see Baker and Wurgler (2006). Their monthly sentiment index can be downloaded from Jeffrey Wurgler’s website at www.stern.nyu.edu/~jwurgler.

27

We then examine the monthly performance of a portfolio that is long the stocks that are

most subject to inflation of opening prices (i.e., the bottom left corner portfolio in the 3 x 3

scheme), and short the stocks that are least subject to inflation of opening prices (i.e., the top

right corner portfolio in the scheme). That is, we construct a zero-cost hedge portfolio that is

long stocks with low institutional holdings and high attention (bottom left corner), and short

stocks with high institutional ownership and low attention (top right corner).

Figure 3 presents the evolution over the period, 1996 - 2007, of several variables that

measure retail investor sentiment, the extent of overpricing at the open, and transaction costs.

First, we plot in Figure 3 quarterly movements in the Baker-Wurgler sentiment index over this

period. Second, we also plot the average return on the hedge portfolio during the overnight and

trading day periods, respectively, using yesterday’s return squared as the attention proxy. Finally,

for each quarter, we plot the average effective half spread for stocks that are most sensitive to

price inflation at the open (i.e., stocks with high attention and low institutional ownership).23

Figure 4 presents the analogous information using our retail sentiment index, for the

abridged sample of Nasdaq stocks over the period, 1997 - 2001. In this figure we compile the

returns on the hedge portfolio, using yesterday’s net retail buying as our proxy for attention. For

comparison, we also plot in Figure 4 the Baker-Wurgler sentiment index and the mean effective

half spread for the portfolio of stocks that are most likely subject to opening price inflation.24

First consider the information in Figure 3. This plot reveals that overnight returns on the

hedge portfolio are positively related to the Baker-Wurgler sentiment index (correlation is .30, p-

value is .001), while trading day returns are negatively related to this index (correlation is -.33, p-

value is .001). Similarly, Figure 4 shows that overnight returns on the hedge portfolio are

23 For clarity, we divide the Baker Wurgler sentiment index by 2 and report quarterly averages of all variables. 24 Here we divide the Baker Wurgler sentiment index by 2, multiply the retail sentiment index with 10, and report quarterly averages of the variables.

28

positively related to the retail sentiment index, while trading day returns are negatively related to

this index. Consistent with this picture, we find that overnight hedge portfolio returns and the

retail sentiment index have a correlation of .47 (p-value is .001), while trading day returns and

the retail sentiment index have a correlation of -.51 (p-value is .001). Furthermore, in Figure 4

the Baker-Wurgler index is highly correlated with the retail sentiment index. Based on the 60

months for which we have data on both indices, we find a correlation of .77 (p-value is .001).25

Figures 3 and 4 also plot the average effective half spread for the subsample of stocks

most prone to price inflation at the open (i.e., those subject to high attention and low institutional

ownership). For comparison purposes, the negative value of this measure of transaction costs is

plotted alongside the trading day (open-to-close) return of the hedge portfolio, which we regard

as a measure of the implicit cost of buying at the open for stocks prone to opening price inflation.

Both Figures show that this implicit cost of buying at the open is similar in magnitude to the

effective half spread, for much of the sample period. Moreover, in times of high sentiment, this

mean open-to-close reversal can be more than twice the size of the effective half spread.

There are two practical implications of this result. First, in periods of high sentiment, a

trader who sells overpriced stocks at the open and buys them back later in the day could earn a

positive return even after accounting for transaction costs. The second implication is more

general and also applies during periods of low investor sentiment. Because of their inclination to

buy stocks that have recently caught their attention, at inflated opening prices, retail traders

effectively incur a substantial hidden transaction cost. The plots reveal that this implicit

transaction cost is similar in magnitude to the effective half spread, averaging 14 bp per day.

25 Note that the positive overnight returns on the hedge portfolio in Figures 3 and 4 become very large just prior to the technology sector crash in March of 2001 and they remain positive throughout 2001. In comparison, the negative trading day reversals on the hedge portfolio become even larger during the crash. Apparently, the bulk of the 2001 correction in stocks most subject to opening price inflation occurred during the trading day (see Cliff et al. 2008).

29

7. Extensions and Robustness Tests In Table 7 we apply the main analysis from our portfolio approach of Table 3, but we base this

analysis on alternative return measures, or various subsamples of stocks, or different time

periods. For each test, the four columns on the left side of Table 7 report results based on the

main sample of 3,000 largest U.S. stocks over the period, 1996 - 2008, where the level of retail

investor attention is proxied by return volatility yesterday (VOLt-1). The right four columns

present the analogous results based on the abridged sample of Nasdaq stocks over the period,

1997 - 2001, using retail net buying yesterday (Retail_NetBuyt-1) to proxy for attention.

For brevity, in all of these robustness tests we only present the mean returns for the two

extreme corner portfolios of every 3 x 3 scheme, for stocks with low institutional holdings and

high attention (bottom left corner) and for stocks with high institutional holdings and low

attention (top right corner). The base-case provided at the top of Table 7 reproduces the results

for these two corner portfolios from Table 3. In every subsequent robustness test (row) of Table

7, we change only one aspect of the analysis to facilitate comparison with the base case.

7.1 Using Market-Adjusted Returns, Trade Prices, Median Returns, and No Low-Price Stocks

The results of our first robustness test appear just below the base case in Table 7. In this test we

analyze market-adjusted abnormal returns. Market-adjusted overnight or trading day returns are

obtained by subtracting the market return over the same time frame, where the market return

over each time frame is the value-weighted average return across all stocks in the sample. This

test reveals that, using market-adjusted returns, we still find significant evidence of price

inflation at the open, although the mean overnight abnormal returns are somewhat smaller than

the actual returns in the base case. Since these abnormal returns are based on value-weighted

30

market returns, these results imply that small stocks tend to have greater price inflation at the

open than large stocks (we present more evidence on this issue below).

Our second robustness test in Table 7 uses the first and last trade prices of the day to

compute overnight and trading day returns, rather than the opening and closing midquotes.

Results are virtually identical to the base case using midquote returns. Together, the evidence in

the base case and this robustness test indicate that our results reflect the behavior of both trade

prices and midquotes, and are not attributable to bid-ask bounce.

The third test in Table 7 uses the median return across stocks in each subsample every

day, rather than the mean, before computing the time series average of these median returns

across all days in the sample period. Results are again similar to the base case, although the

median overnight return is somewhat lower than the base case. One implication is that our mean

results are not attributable to outliers. Another implication is that half of the sample stocks have

overnight returns and trading day reversals that exceed the medians provided in this test.

Our fourth robustness test excludes stocks each day whose average daily closing price

during the previous three months is below $5. This exclusion yields hedge portfolio returns that

are again similar to the base case, indicating that our results are not due to low-price stocks.

7.2 NASD versus NYSE Stocks

The fifth and sixth tests provided in Table 7 reproduce the analysis in Table 3 for the subsamples

of Nasdaq and NYSE stocks, respectively. There are reasons to expect potentially divergent

behavior across Nasdaq and NYSE stocks at the day’s open and close. The NYSE specialist

system is substantively different from the Nasdaq trading regime based on market makers. These

two markets have important structural differences in opening and closing mechanisms, order

routing, and linkages that reduce fragmented trading. In addition, during our thirteen-year sample

31

period, the Nasdaq market evolves from a telephone-mediated market to a fully automated

electronic limit order book in several jarring transformations. These factors can create frictions in

opening and closing prices. Finally, the bulk of Nasdaq stocks are smaller firms with higher

transaction costs and greater information asymmetries. These divergent features of Nasdaq

versus NYSE stocks lead us to expect greater mispricing at the open, and thus larger overnight

returns and trading day reversals, for Nasdaq stocks.26

These expectations are born out in Table 7. While we find significant positive overnight

returns and negative trading day reversals for stocks with high attention and low institutional

ownership, for both NYSE and Nasdaq stocks, these returns are substantially larger in magnitude

for Nasdaq stocks. On the other hand, this evidence reveals that this overnight return behavior is

not limited to Nasdaq stocks, but also characterizes NYSE stocks, albeit in smaller magnitudes.

7.3 Small versus Large Stocks

The seventh and eighth tests of Table 7 pursue a similar line of inquiry by examining subsamples

of stocks in the smallest and largest quintiles each day, by mean market capitalization over the

previous 20 trading days. This analysis reveals that opening price inflation for high attention

stocks is larger in magnitude for small firms than for large firms. However it is noteworthy that,

while this evidence documents a strong size effect in overnight returns and trading day reversals,

firm size is not the sole cause of our results in Tables 2 – 4. In all these analyses we examine

how overnight returns and trading day reversals are related to attention, institutional ownership,

and transaction costs, after first controlling for size. Thus, while small stocks tend to experience

larger overnight returns and trading day reversals, this behavior is not limited to small stocks.

7.4 Growth versus Value Stocks and Winners versus Losers 26 These issues also emphasize the importance of proper identification of opening and closing prices (see Gerety and Mulherin, 1994, Harris, 1989, Rogalski, 1984, Smirlock and Starks, 1986, and our footnotes 9-13 above).

32

Our ninth and tenth tests in Table 7 split the sample stocks each day into the bottom and top

quintiles based on the firm’s book-to-market ratio at the end of the previous quarter. For both the

main sample and the abridged sample, we find evidence that growth stocks have larger overnight

returns and trading day reversals. For example, focusing on the stocks in the main sample that

have high attention and low institutional ownership, we find the average overnight return

(trading day reversal) is +20 (-23) bp for growth stocks versus +13 (-9) bp for value stocks.

Our eleventh and twelfth tests in Table 7 partition the sample stocks each day into the

bottom and top quintiles based on the stock return over the previous six months. For both the

main sample and the abridged sample, we find strong evidence that momentum losers have

larger overnight returns and trading day reversals than momentum winners. In particular, for the

main sample, the mean overnight return (trading day reversal) equals +32 (-31) for momentum

losers versus +14 (-13) for momentum winners.27

7.5 Overnight and Trading Day Returns on Mondays versus Other days of the Week

Cliff et al. (2008) find that the recent behavior of overnight and trading day returns between

Friday’s close and Monday’s close has reversed from that prevailing before the mid-1990’s, so

that now the opening price on Monday tends to be greater than the closing price on Friday.28 We

examine whether the results in the previous sections are mainly due to high opening prices on

Mondays, by analyzing overnight and trading day returns for the 3 x 3 scheme of portfolios on

Mondays versus other days of the week.

Our thirteenth and fourteenth tests in Table 7 present the results. For both the main

sample and the abridged sample, we find significant positive overnight returns and trading day

27 It is interesting to note that momentum losers reveal larger mean overnight returns and trading day reversals than winners, despite the somewhat lower persistence in net retail buying at the open for losers revealed in Table 5. 28 For other related work on the weekend effect, see Harris (1986), Jain and Joh (1988), Kamara (1997), Rogalski (1984), Schwert (2003), Smirlock and Starks (1986), and Wang et al. (1997).

33

reversals on Mondays, as well as the other days of the week, although the opening price inflation

is somewhat greater on Mondays. For example, for the main sample we find the mean overnight

(trading day) return on Mondays is +20 (-35) bp, for stocks with low institutional ownership and

high attention, whereas the analogous results on other days of the week are +16 (-12) bp.29

7.6 Overnight and Trading Day Returns over Different Subperiods

Our last three tests in Table 7 investigate the stability of overnight and trading day returns over

time, by analyzing three subperiods covering 1996 - 2000, 2001 - 2004, and 2005 - 2008.

Results reveal significant positive overnight returns and negative trading day reversals for the

overpriced portfolio, in all three subperiods. On the other hand, the late 1990’s experienced the

largest mean overnight returns and trading day reversals for stocks with high attention and low

institutional ownership. The magnitude of this opening price inflation then diminished somewhat

after decimalization in 2000, and it declined somewhat further after 2005, with the expansion of

ECN’s and algorithmic trading in recent years. Still, although the results are somewhat weaker

over the most recent four-year period, clear evidence remains that high attention stocks continue

to have significant overnight returns and trading day reversals. This evidence reinforces our

results in Figures 3 and 4, which show that this opening price inflation occurs throughout the

sample period, but is larger in magnitude during periods of high investor sentiment.

8. Summary and Conclusions This paper investigates the role of attention as a potential source of retail investor sentiment, and

examines whether attention-based trading can cause prices to temporarily deviate from

fundamental values at the open of the typical trading day. We show that high attention days for

29 Note that the mean overnight and trading day returns tend to offset one another for other weekdays, while the positive mean overnight return on Mondays is dominated by the larger negative mean trading day reversal, for both corner portfolios. This evidence indicates that the negative average weekend performance over the sample period, from Friday’s close to Monday’s close, tends to occur during the trading day on Monday.

34

individual stocks are followed by high net retail buying at the start of the next trading day.

Moreover, this increased retail buying pressure results in opening prices that tend to be high

relative to prices during the rest of the trading day.Furthermore, we find that these predictable

intraday price patterns are more pronounced for stocks that are difficult to value and costly to

arbitrage, and they are larger in magnitude during periods of high investor sentiment.

This study is the first to investigate intraday patterns in retail trading activity and price

formation in relation to investor sentiment, proxied by retail investor attention. By investigating

our theory of attention-based overpricing at the open, we uncover and help to resolve a here-to-

fore unexplained intraday price anomaly: stocks that have recently attracted the attention of

retail investors have a strong tendency for net retail buying at the open, which leads to high

opening prices and positive returns during the overnight period followed by reversals during the

subsequent trading day.

Our results should be of interest to both investors and regulators alike. During periods of

high investor sentiment, a strategy of selling high attention stocks at the open and postponing

purchases until well after the open can result in significant improvements to portfolio

performance. More importantly, this evidence shows that some retail investors bear substantive

hidden costs, through their penchant for buying stocks at inflated prices during the first hour of

next trading following high attention days. For example, during periods of high investor

sentiment, the implicit transaction costs for buying high attention stocks during the first hour can

be as high as twice the effective half spread. The first step towards reducing this hidden cost of

buying high attention stocks at the open is to enhance awareness among retail traders of the

potentially detrimental price impact of such trading activity.

35

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Almazan, Andres, Keith C. Brown, Murray Carlson and David A. Chapman. "Why Constrain Your Mutual Fund Manager?" Journal of Financial Economics, 2004, Vol. 73, No. 2, 289-321. Asquith, Paul, Parag Pathak, and Jay Ritter, “Short Interest, Institutional Ownership, and Stock Returns,” Journal of Financial Economics, 2005, Vol. 78, No. 2, 243-276. Baker, M. and J. Wurgler. “Investor sentiment and the cross-section of stock returns,” Journal of Finance, 2006, Vol. 61, No. 4, 1645-1680. Baker, M. and J. Wurgler. “Investor sentiment in the stock market,”Journal of Economic Perspectives, 2007, Vol. 21, No. 2, 129-152. Barber, Brad, Terrence Odean “All that Glitters: The Effect of Attention and News on the Buying Behavior of Individual and Institutional Investors,” Review of Financial Studies, 2008, Vol. 21, No. 2, 785-818. Barber, Brad, Terrence Odean and Ning Zhu “Do Retail Trades Move Markets?” Review of Financial Studies, 2009, Vol. 22, No. 1, 151-186. Berkman, Henk, Valentine Dimitrov, Prem Jain, Paul Koch, and Sheri Tice, “Sell on the News: Differences of Opinion, Short Sale Constraints, and Returns around Earnings Announcements,” Journal of Financial Economics, 2009, Vol. 92, 376-399. Barclay, Michael J., and Terrence Hendershott, “Price Discovery and Trading After Hours,” Review of Financial Studies, 2003, Vol. 16, No. 4, 1041-1073. __________, “Liquidity Externalities and Adverse Selection: Evidence from Trading After Hours,” Journal of Finance, 2004, Vol. 59 (No. 2), 681-710. Bernard, Victor, “Cross-sectional dependence and problems in inference in market-based accounting research,” Journal of Accounting Research, 1987, Vol. 25, l-48. Bessembinder, H., “Issues in Assessing Trade Execution Costs,” Journal of Financial Markets, 2003, Vol. 6, 233-257. Branch, Ben, and Aixin Ma, “The Overnight Return, One More Anomaly,” University of Massachusetts Working Paper, 2008, http://ssrn.com/abstract=937997. Cliff, Michael, Michael Cooper, and Huseyin Gulen, “Return Differences between Trading and Non-trading Hours: Like Night and Day,” Working Paper, 2008, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1004081#PaperDownload. D’Avolio, Gene., “The Market for Borrowing Stock,” Journal of Financial Economics, 2002, Vol. 66 (Nos. 2-3), 271-306.

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De Long, J. Bradford, Andrei Shleifer, Lawrence H. Summers, and Robert J. Waldmann, “Noise trader risk in financial markets,” Journal of Political Economy, 1990, Vol. 98: 4, 703-738. Gerety, Mason S., and Harold Mulherin, “Price Formation on Stock Exchanges: The Evolution of Trading Within the Day,” Review of Financial Studies, 1994, Vol. 7, 609-629. Gompers, P., and Metrick, A., “Institutional investors and equity prices,” Quarterly Journal of Economics, 2001, Vol. 116, 229–259. Griffin, John M., Jeffrey H. Harris, and Selim Topaloglu, “The dynamics of institutional and individual trading,” Journal of Finance, 2003, Vol. 58, 2285-2320. Harris, Lawrence, “A Transaction Data Study of Weekly and Intradaily Patterns in Stock Returns,” Journal of Financial Economics, 1986, Vol. 16, 99-117. __________. “A Day-end Transaction Price Anomaly,” Journal of Financial and Quantitative Analysis, 1989, Vol. 24, 29-45. Jain, P., and G. Joh, “The Dependence between Hourly Prices and Trading Volume,” Journal of Financial and Quantitative Analysis, 1988, Vol. 23, 269-283. Kamara, A., “New Evidence on the Monday Seasonal in Stock Returns,” Journal of Business, 1997, Vol. 70, 63-84. Kumar, Alok and Lee, Charles M. C., “Retail Investor Sentiment and Return Comovements,” Journal of Finance, 2006, Vol. 61:5, 2451-2486. Lee, C. M. C., and M. J. Ready, “Inferring Trade Direction from Intraday Data,” Journal of Finance, 1991, Vol. 46, 733-746. Nagel, Stefan, “Short Sales, Institutional Investors and the cross-section of stock returns, Journal of Financial Economics, 2005, Vol. 78, No. 2, 277-309. Odean, T., “Do Investors Trade Too Much?” American Economic Review, 1999, Vol. 89, No. 5, 1279-1298. Ofek, E., M. Richardson, and R. Whitelaw, “Limited Arbitrage and Short Sales Restrictions: Evidence from the Options Markets,” Journal of Financial Economics, 2004, Vol. 74, 305-342. Rogalski, Richard, “New Findings Regarding Day-of-the-week Returns Over Trading and Non-trading Periods: A Note,” Journal of Finance, 1984, Vol. 35, 1603-1614. Sadka, Ronnie, and Anna Scherbina, “Analyst Disagreement, Mispricing, and Liquidity,” Journal of Finance, 2007, Vol. 62, 2367-2403. Schwert, G. William, “Anomalies and Market Efficiency,” 2003, University of Rochester.

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Shleifer, Andrei, and Robert Vishny, “The limits of arbitrage”, Journal of Finance, 1997, Vol. 52, 35-55. Smirlock, Michael, and Laura Starks, “Day-of-the-week and Intraday Effects in Stock Returns,” Journal of Finance, 1986, Vol. 35, 197-210. Wang, K., Y. Li, and J. Erickson, “A New Look at the Monday Effect,” Journal of Finance, 1997, Vol. 52, 2171-2186.

38

Appendix A: Data Collection for Institutional Holdings

We use low institutional ownership to proxy for short sale constraints, because it embodies both

direct and indirect costs of short selling (Nagel, 2005). First, direct costs include fees to borrow

stock, which can be high when the supply of loanable shares is scarce. Since institutions are the

main suppliers of stock loans, low institutional ownership often reflects low supply and high

direct costs of short selling. On the other hand, over the short time frames analyzed in this study,

these direct costs are likely to be small compared to other direct trading costs (i.e., the spread,

commission, and price impact).30 Thus a second, more plausible reason why low institutional

ownership is important in our study rests with the indirect costs of short selling. Indirect costs

involve institutional and cultural constraints that effectively prevent short selling by institutional

investors. Due to these constraints, most professional investors simply never sell short, and thus

cannot trade against overpriced stocks they do not own (Almazan et al., 2004). Given these

indirect short sale constraints, efficient pricing depends on individual investors who own the

stock. However, individual stock owners may not recognize or act on any overpricing, especially

over such short time frames. Consequently, stocks with low institutional ownership could

experience the recurring and persistent overpricing behavior we hypothesize overnight.31

Quarterly data on institutional holdings are taken from CDA Spectrum 13F filings. All

institutional investors that manage portfolios of $100 Million or more must file quarterly 13F

reports with the SEC. These institutions include banks, insurance companies, brokerage firms,

pension funds, etc. Institutions are required to report all equity holdings greater than 10,000

shares or $200,000 in value, at the end of each quarter. Consistent with prior research, we refer

to institutional ownership as the equity holdings of managers that submit quarterly 13F Filings.

30 See Asquith et al. (2005), D’Avolio (2002), and Ofek et al (2004). 31 Since institutions can always buy underpriced stocks, there are no such impediments to arbitrage on the buy side.

39

Following other research, we address problems and inconsistencies in the quarterly 13F

filings data from Thomson Financial Institutional Holdings (see Asquith et al., 2005, Gompers

and Metrick, 2001, and Nagel, 2005). For example, one problem arises due to occasional missing

or inaccurate data in the 13F filings on the number of shares outstanding at the end of the filing

quarter. We resolve this problem by replacing the end-of-quarter shares outstanding from the

Thomson Financial Institutional Holdings database with the analogous variable from CRSP.

Another potential problem has to do with stock splits, which can cause inaccuracies in the

institutional holdings data. For example, an institution may submit a late 13F filing after the

SEC’s 45-day deadline following the end of a quarter, when a split occurred during this 45-day

grace period. In this situation, CDA Spectrum adjusted the holdings record even though it should

not have been adjusted for the record date. In such cases there are inaccuracies due to the failure

of CDA Spectrum to properly synchronize the holdings data with the split-adjustment.

We find the magnitude of these problems is small for our sample. We use CRSP data to

document all firm-quarters when a stock split occurred in the dataset on 13F filings (this includes

all quarters that experience changes in shares outstanding due to stock splits or stock dividends).

We find that 2.5 percent of all firm-quarters in our dataset are during quarters with stock splits.

This evidence suggests that the potential problem associated with stock splits and late

13F filings is likely to have a minimal impact on our results. Still, we have followed several

procedures to investigate the impact of this potential problem. First, we have omitted from our

analysis all observations during firm-quarters when a stock split or stock dividend occurs.

Second, we have replaced all daily observations on institutional ownership during a quarter with

a stock split with the previous quarter’s value of the percent of institutional ownership for that

firm. All these procedures lead to robust results consistent with those presented in this study.

1.0004

1.0006

1.0008

1.001

1.0012

atio

Figure 1. Intraday Price PatternRatio of Midquote at Intraday Time (T) to the Closing Midquote

across All U.S. Stocks and Days

Intraday Price Ratios

Upper 95% Conf Interval

Lower 95% Conf Interval

This intraday price pattern traces out the ratio of the midquote at different times (T) during the trading day, to the closing midquote. These intraday price ratios are computed for each stock at 5-minute intervals over the first and last 30-minutes of the trading day, and at 30-minute intervals over the rest of the trading day. First, for each day we average this price ratio at every intraday time (T) across all stocks in the sample. Second, we compute the time series mean of these daily cross-sectional averages across all days in the sample period. The 95 percent confidence interval about a ratio of 1.0 is constructed using the standard error of the time series mean across all days, at each time (T).

40

0.9994

0.9996

0.9998

1

1.0002

0 1 2 3 4 5 6 7

Pric

e R

a

Time (T): Hour of the Trading Day

1.002

1.003

1.004

1.005

1.006

Rat

io

Figure 2. Intraday Price PatternsRatio of Midquote at Intraday Time (T) to Closing Midquote for Quintiles of Stocks

based on Total Retail Trading during the First Hour of the Day as a Percent of Daily Volume

Quintile 1

Quintile 2

Quintile 3

Quintile 4

Quintile 5

These intraday price patterns trace out the ratio of the midquote at intraday time (T) to the closing midquote. These price ratios are provided at 5-minute intervals over the first and last 30-minutes of the trading day, and at 30-minute intervals over the rest of the trading day. First, for each day we average this price ratio at every time (T), across all stocks in each quintile based on total share volume by retail investors during the first hour of the day, as a percent of total daily volume. Next, for each quintile we compute the time series average of these daily cross-sectional mean price ratios across all days in the sample period. The 95 percent confidence interval about a ratio of 1.0 is constructed using the standard error of the time series mean at each time (T), using only the top quintile of stocks each day with high retail trading in the first hour. This quintile has the largest standard errors, and thus the widest confidence interval. Thus, comparison of the intraday pattern for other quintiles with this confidence interval represents a conservative approach to determine the statistical significance of these intraday price patterns.

41

0.998

0.999

1

1.001

0 1 2 3 4 5 6 7

Pric

e R

Intraday Time (T): Hour of the Trading Day

U95 - Q5

L95 - Q5

Figure 1

0.6

1.1

Baker‐Wurgler Sentiment index

Overnight Returns

Figure 3. Retail Investor Sentiment, Overnight Returns, and Transaction Costs: 1996 - 2008This Figure presents the evolution over the period, 1996 ‐ 2007, of several variables that measure retail investor sentiment, the extent of overpricing at the open, and transaction costs.  First, we report quarterly averages of the monthly Baker‐Wurgler sentiment index.  Next, for each quarter, “Overnight Returns” plots the average daily overnight (close‐to‐open) return of a zero‐cost hedge portfolio that is long stocks with low institutional holdings and high attention (i.e., the bottom left corner of the 3 x 3 scheme in Table 3), and short stocks with high institutional ownership and low attention (i.e., top right corner of the scheme).  “Trading Day Returns” plots the average trading day (open‐to‐close) return on the same hedge portfolio. We also plot the average daily effective half spread for the subsample of stocks that are most sensitive to price inflation at the open (i.e., stocks in the bottom left corner of the scheme, with high attention and low institutional ownership). 

42

‐1.4

‐0.9

‐0.4

0.1

1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Effective Half Spread Trading Day Returns

Figure 4. Retail Investor Sentiment, Overnight Returns, and Transaction Costs: 1997 - 2001This Figure presents the evolution over the period, 1997 ‐ 2001, of several variables that measure retail investor sentiment, the extent of overpricing at the open, and transaction costs. We report quarterly averages of the monthly Baker‐Wurgler sentiment index, and the quartely average of the Retail Investor Sentiment Index (defined as the actual net buying activity by retail investors during the first hour of the trading d f h di d ll k d ll d d i h ) F h “O i h R ”day, as a percent of shares outstanding, averaged across all stocks and all days during the quarter).  For each quarter, “Overnight Return” plots the average daily overnight (close‐to‐open) return of a zero‐cost hedge portfolio that is long stocks with low institutional holdings and high attention (bottom left corner of the 3 x 3 scheme), and short stocks with high institutional ownership and low attention (top right corner of the scheme).  “Trading Day Return” plots the average trading day (open‐to‐close) return on the same hedge portfolio. We also plot the average daily effective half spread, for the subsample of stocks that are most sensitive to price inflation at the open (i.e., stocks in the bottom left corner of the scheme with high attention and low institutional ownership)

1.25Retail Investor Sentiment Index

left corner of the scheme, with high attention and low institutional ownership). 

0.75

Baker‐Wurgler Sentiment Index

Overnight Returns

0.25

1997 1997.5 1998 1998.5 1999 1999.5 2000 2000.5 2001 2001.5 2002

0 75

‐0.251997 1997.5 1998 1998.5 1999 1999.5 2000 2000.5 2001 2001.5 2002

Effective Half Spread

‐1.25

‐0.75

Trading Day Returns

43

Table 1. Descriptive Statistics and Correlations across Variables

We apply our analysis to two major samples. Our main analysis is applied to the subsample of the 3,000 largest U.S. stocks each year with nonmissing TAQ data on quotes, over the 13-year period 1996 - 2008. We also analyze an abridged sample of all Nasdaq firms over the period, 1997 - 2001, for which data on intraday retail trading activity are available. The focus of this study is on percentage overnight and trading day returns, measured as 100 times the log of the price relative using quote midpoints at the open and the close: cto = close-to-open (overnight) return, and otc = open-to-close (trading day) return. We also analyze the difference between overnight and trading day returns (DIFF = cto - otc), as well as this same difference after deducting transaction costs measured as the average spread at the day's open and close: DIFF-TC = DIFF - [SPR(open)+SPR(close)] / 2. In addition, we examine daily returns measured over the 24-hour periods from close-to-close and from open-to-open: ctc, and oto.

We consider two alternative proxies for retail investor attention: (i) VOLt-1 = the squared 24-hour (close-to-close) return yesterday, and (ii) Retail_NetBuyt-1 = the net number of shares bought by retail investors yesterday, as a percent of total share volume. In addition, we compute two measures of the intensity of net retail buying in the first hour of the trading day, relative to the rest of the trading day: (i) NetBuy_HR1t = the net number of shares bought by retail investors during the first hour of the trading day, as a percent of shares outstanding, and (ii) NetBuy_DIFFt = the difference between the net number of shares bought by retail investors during the first hour, and the hourly rate of net buying by retail investors during the rest of the trading day, as a percent of shares outstanding.

Next, we consider two proxies for short sale constraints and three measures of transaction costs. Our two proxies for short sale constraints are: (i) the percent of institutional ownership (INST) computed from quarterly 13F Filings using aggregate shares held by institutions as a percent of shares outstanding, and (ii) relative short interest (RSI) measured as the number of shares sold short each month divided by shares outstanding. Our three measures of daily transaction costs include: (i) the bid-ask spread as a percent of the quote midpoint at the open (SPR(open)), (ii) the analogous percent spread at the close (SPR(close)), and (iii) the daily effective half spread (Spread). Finally, firm size (SIZE) is proxied by daily market capitalization.

The descriptive statistics in Panels A and B are calculated by first computing the cross-sectional mean (or median) each day, and then averaging these means (or medians) across all days in the sample period. The standard deviation of the time series average across daily means is then used to construct the t-test for each statistic in Panels A and B. Similarly, the Spearman correlations in Panel C are calculated by first computing the cross-sectional correlation each day, and then averaging these correlations across all days in the sample. Once again, the standard deviation of the time series average correlation is used to construct the t-test for each average correlation in Panel C.

44

cto otc DIFF ctc oto

.098 -.066 .165 -.707 .031 .029

.045 -.061 .108 -.618 -.016 .-.027 5.2 ** -3.3 ** 6.1 ** -24.8 ** 1.1 1.2

2446 2459 2446 2384 2446 2603

* indicates significance at the .05 level; and ** indicates significance at the .01 level.

24-Hour Returns

DIFF - TC

Overnight & Trading Day Returns

Mean (%) Median (%) T (H0: Mean = 0)

Panel A: Descriptive Statistics for Overnight (Close-to-Open) Returns, Trading Day (Open-to-Close) Returns, and 24-Hour Returns

Avg # of Firms per Day

44

Table 1, continued

INST RSI

Mean (%) .127 -.003 .039 .025 .520 .038 1.06 .62 .17 5,210,406 Median (%) .059 .144 .004 .004 .532 .022 .72 .41 .12 1,109,234

31.2 ** -.1 24.8 ** 26.2 ** 214.6 ** 101.1 ** 83.6 ** 68.3 ** 81.1 ** 175.8 **Avg # Firms/Day 2601 402 400 400 2680 2680 2615 2618 2462 2533

Panel C: Spearman Correlations

VOL 1.00Retail_NetBuy .061 ** 1.00

NetBuy_HR1 .051 ** .436 ** 1.00NetBuy_DIFF .027 ** .011 ** .785 ** 1.00

T (H0: Mean=0)

Panel B: Descriptive Statistics for Measures of Retail Investor Attention, Short Sale Constraints, Transaction Costs, and Firm Size

Short Sale Constraints Transaction Costs

SPR(close)NetBuy_HR1

Firm SizeProxies for Attention Retail Buying in 1st Hour

Spread SIZE ($000)SPR(open)Retail_NetBuyVOL NetBuy_DIFF

45

INST .083 ** .005 ** .023 ** .025 ** 1.00RSI .358 ** .045 ** .050 ** .034 ** .390 ** 1.00

SPR(open) .172 ** -.031 ** -.053 ** -.043 ** -.136 ** -.073 ** 1.00SPR(close) .159 ** -.027 ** -.048 ** -.044 ** -.189 ** -.126 ** .465 ** 1.00Spread .333 ** -.023 ** -.055 ** -.052 ** -.283 ** -.084 ** .569 ** .570 ** 1.00SIZE -.222 ** .030 ** .060 ** .051 ** .163 ** .008 -.563 ** -.531 ** -.705 ** 1.00

cto .055 ** .042 ** .034 ** .016 ** -.011 ** .020 ** .021 ** .006 ** .020 ** -.017 **otc -.043 ** -.114 ** -.031 ** .051 ** .009 ** -.023 ** -.005 ** -.018 ** -.024 ** .029 **DIFF .056 ** .113 ** .034 ** -.045 ** -.011 ** .027 ** .009 ** .017 ** .025 ** -.028 **DIFF - TC .000 .113 ** .038 ** -.040 ** .040 ** .061 ** -.203 ** -.166 ** -.134 ** .119 **

* indicates significance at the .05 level; and ** indicates significance at the .01 level.

45

Panel A. Using Return Volatility Yesterday (VOLt-1) to Proxy for Retail Investor Attention: 3,000 Largest U.S. Stocks, 1996 - 2008

Low .020 ** .014 .03 ** -.03 .00 Medium .032 ** .021 .04 ** -.05 * .00

High .072 ** .045 ** .13 ** -.13 ** .01

High - Low .052 .031 .11 -.10 .01T-stat 11.7 ** 10.9 ** 7.7 ** -3.1 ** 0.1

Table 2. Net Retail Buying During the First Hour of the Trading Day, Overnight Returns, Trading Day Returns, and 24-Hour Returns,

Overnight Return (cto%)NetBuy_DiffaNetBuy_HR1aAttention

Across Portfolios Sorted by Proxies for Retail Investor Attention

24-Hour Return (ctc%)Trading Day Return (otc%)

This table reports the hourly rate of net buying by retail investors during the first hour of trading, as well as the difference between this rate and the analogous hourly rate during the rest of the trading day, along with the overnight return, trading day return, and 24-hour return. The first two measures are defined as follows :

(1) NetBuy_HR1 = (Retail_NetBuy_HR1) / (shares outstanding).(2) NetBuy_Diff = [(Retail_NetBuy_HR1) - (Retail_NetBuy_Rest / 5.5)] / (shares outstanding).

These measures are computed using proprietary data from Nasdaq OMX on intraday trading activity by retail investors, for Nasdaq stocks during 1997 - 2001.We report these measures for a 3 x 1 scheme of portfolios where stocks are partitioned each day into terciles by the level of retail investor attention. We use two

alternative proxies for retail investor attention: (i) in Panel A we consider stock return volatility lagged one day, measured as the square of yesterday's close-to-close return; (ii) in Panel B we use the net number of shares bought by retail investors all day yesterday, as a percent of total share volume.

For every portfolio, we first compute the mean value of each measure across firms every day, and then average these cross-sectional means across all days in the sample period. The Newey-West adjusted standard error is used to obtain the statistical significance for the average behavior of each portfolio. At the bottom of each column, we provide the mean-difference T-test across portfolios with high versus low retail investor attention.

46

Panel B. Using Retail Net Buying Yesterday (Retail_NetBuyt-1) to Proxy for Retail Investor Attention: Nasdaq Stocks, 1997 - 2001

Low -.021 ** -.004 ** .04 * -.12 * -.08 Medium .028 ** .020 ** .16 ** -.16 ** .00

High .110 ** .060 ** .26 ** -.27 ** .00

High - Low .131 .064 .22 -.15 .07T-stat 29.5 ** 24.3 ** 6.8 ** -2.1 * 0.7

* indicates statistical significance at the .05 level; ** at the .01 level.

Overnight Return (cto%)a

Attention NetBuy_DiffaNetBuy_HR1a

a These figures are computed for the subsample of Nasdaq Stocks over the period, 1997 - 2001, for which data are available from Nasdaq OMX on net retail buying.

Trading Day Return (otc%)a 24-Hour Return (ctc%)a

46

Table 3. Overnight Returns, Trading Day Returns, and 24-Hour Returns across Portfolios Double-Sorted by Proxies for Retail Investor Attention Yesterday, and Institutional Ownership

This table reports mean overnight returns (close-to-open or cto), trading day returns (open-to-close or otc), and 24-hour returns (close-to-close or ctc), for a 3 x 3 scheme of portfolios partitioned each day into terciles along two dimensions. The portfolios in each row are sorted according to a low, medium, or high level of retail investor attention yesterday; the columns are sorted by institutional ownership in the previous quarter.

We examine two alternative proxies for the level of retail investor attention yesterday. In Panel A we use stock return volatility lagged one day, measured as the square of yesterday's close-to-close return. This analysis is applied to the subsample of the 3,000 largest U.S. firms each year for which TAQ data are available, over the 13-year period 1996 - 2008. In Panel B we use the net number of shares bought by retail investors all day yesterday, as a percent of total share volume. This proxy is obtained using proprietary data on intraday trading activity by retail investors. These data were made available by Nasdaq OMX, for an abridged sample of all Nasdaq stocks over the period 1997 - 2001.

In each 3 x 3 scheme of Panel A, we independently double-sort the sample stocks every day into terciles, based on the firm's size-adjusted: (1) stock return volatility lagged one day, and (2) institutional ownership the previous quarter. We size-adjust these proxies by first sorting the sample firms each day into terciles by the firm's market capitalization, and then within each size tercile, we sort firms into finer terciles by (1) or (2). In each 3 x 3 scheme of Panel B, we apply the same procedure using our second proxy for retail investor attention yesterday: the net number of shares bought by retail investors lagged one day, as a percent of total share volume.

For every portfolio in each 3 x 3 scheme, we first compute the mean return across firms every day, and then average these cross-sectional means across all days in the sample period. The Newey-West adjusted standard error is then used to obtain the statistical significance for each portfolio's average daily return. At the bottom of each column in every 3 x 3 scheme, we provide the mean-difference T-test across portfolios with high versus low retail investor attention yesterday, conditional on institutional ownership.

4747

Table 3, continued

Panel A. Using Stock Return Volatility Yesterday to Proxy for Retail Investor Attention: 3,000 Largest U.S. Stocks, 1996-2008

Retail Investor Attention Stock Return Volatility Yesterday Low High Low High Low High

Low .03 ** .02 ** .02 ** -.03 * -.03 -.03 .00 .00 .00 Medium .05 ** .04 ** .04 ** -.06 ** -.04 -.04 -.01 .01 .00

High .17 ** .13 ** .10 ** -.17 ** -.12 ** -.09 ** .00 .01 .01

High - Low .13 .11 .08 -.13 -.09 -.07 .00 .02 .01T-stat 8.9 ** 7.7 ** 5.8 ** -4.0 ** -2.7 ** -2.0 * 0.0 0.4 0.3

Panel B. Using Net Retail Buying Yesterday to Proxy for Retail Investor Attention: Nasdaq Stocks, 1997-2001

Retail Investor AttentionNet Retail Buying

Overnight Return (cto%) Trading Day Return (otc%)Institutional Ownership Institutional Ownership

Medium Medium

24-Hour Return (ctc%)

Medium

Institutional Ownership

a On average, there are 261 firms in the portfolio for each cell of these 3 x 3 partitioning schemes. * indicates statistical significance at the .05 level; ** at the .01 level.

24-Hour Return (ctc%)Institutional Ownership

Trading Day Return (otc%)Institutional Ownership

Overnight Return (cto%)Institutional Ownership

48

Net Retail Buying Yesterday Low High Low High Low High

Low .09 ** .06 * .02 -.19 ** -.15 ** -.09 -.09 -.09 -.07 Medium .23 ** .18 ** .13 ** -.28 ** -.21 ** -.10 -.06 -.03 .02

High .34 ** .31 ** .24 ** -.42 ** -.30 ** -.22 ** -.08 .01 .02

High - Low .24 .25 .22 -.23 -.15 -.13 .01 .10 .09T-stat 6.4 ** 7.1 ** 6.5 ** -2.9 ** -2.0 * -1.7 0.1 1.1 1.0

a On average, there are 90 firms in the portfolio for each cell of these 3 x 3 partitioning schemes. * indicates statistical significance at the .05 level; ** at the .01 level.

Medium MediumInstitutional Ownership Institutional Ownership

MediumInstitutional Ownership

48

Panel A. Using Volatility Yesterday to Proxy for Retail Attention, 1. for Hard-to-Value Stocks: 1. Top 50% of 3,000 Largest U.S. Stocks Each Day over the Period, 1996-2008, with Highest Return Volatility over Past 20 Days.a Retail Investor Attention Stock Return Volatility Yesterday Low High Low High Low High Low .07 ** .06 ** .05 ** -.13 ** -.09 ** -.07 * -.06 -.03 -.02 Medium .12 ** .09 ** .08 ** -.16 ** -.11 ** -.10 ** -.05 -.02 -.03

High .26 ** .20 ** .15 ** -.24 ** -.19 ** -.16 ** .01 .01 .00High - Low .18 .14 .11 -.11 -.09 -.09 .07 .04 .02

T-stat 8.6 ** 7.2 ** 6.1 ** -2.4 * -2.2 * -2.1 * 1.4 0.9 0.4

Panel B. Using Volatility Yesterday to Proxy for Retail Attention, 1. for Hard-to-Value Stocks, 2. with High Transaction Costs:

2 T 50% f th St k E h D ith Hi h t Eff ti H lf S d a

Medium Medium

a On average, there are 129 firms in the portfolio for each cell of these 3 x 3 partitioning schemes. * indicates statistical significance at the .05 level; ** at the .01 level.

Medium

1. Top 50% of 3,000 Largest U.S. Stocks Each Day over the Period, 1996-2008, with Highest Return Volatility over Past 20 Days;

Table 4. Overnight Returns, Trading Day Returns, and 24-Hour Returns Across Double-Sorted Portfolios,

24-Hour Return (ctc%)Institutional Ownership

Trading Day Return (otc%)Institutional Ownership

Overnight Return (cto%)Institutional Ownership

for Subsamples of Stocks Each Day: (1) that are Hard to Value, (2) with High Transaction Costs, and (3) with High Short Interest

This Table follows the same format as Table 3. Panels A, B, and C use yesterday's return volatility to proxy for retail investor attention, in order to analyze stocks: 1. that are Hard-to-Value (i.e., the 50% of stocks each day with the highest return volatility over the past 20 days), 2. with High Transaction Costs (i.e., the 50% of stocks in 1 with the highest effective half spread), and 3. with High Short Interest (i.e., the 20% of stocks in 2 with the highest relative short interest). Panels D, E, and F provide analogous results using yesterday's net retail buying to proxy for retail attention.

49

2. Top 50% of these Stocks Each Day with Highest Effective Half Spread. a Retail Investor Attention Stock Return Volatility Yesterday Low High Low High Low High Low .09 ** .07 ** .07 ** -.17 ** -.15 ** -.11 ** -.08 * -.08 * -.04 Medium .15 ** .13 ** .11 ** -.19 ** -.18 ** -.13 ** -.05 -.05 -.02

High .34 ** .28 ** .23 ** -.27 ** -.24 ** -.20 ** .07 .05 .03 High - Low .25 .21 .16 -.10 -.09 -.09 .15 .12 .07

T-stat 11.1 ** 9.6 ** 8.1 ** -2.1 * -1.8 -1.9 2.7 ** 2.3 * 1.4 a On average, there are 61 firms in the portfolio for each cell of these 3 x 3 partitioning schemes. * indicates statistical significance at the .05 level; ** at the .01 level.

Institutional Ownership Institutional OwnershipTrading Day Return (otc%) 24-Hour Return (ctc%)

Institutional OwnershipMedium Medium Medium

Overnight Return (cto%)

49

Table 4, continued

Panel C. Using Volatility to Proxy for Attention, 1. for Hard-to-Value Stocks, 2. with High Transaction Costs, 3. and High Short Interest:

2. Top 50% of these Stocks Each Day with Highest Effective Half Spread; 3. Top 20% of these Stocks Each Day with Highest Relative Short Interest.a

Retail Investor Attention Stock Return Volatility Yesterday Low High Low High Low High

Low .15 ** .07 .12 ** -.33 ** -.27 ** -.18 ** -.19 ** -.20 ** -.07 Medium .22 ** .19 ** .14 ** -.35 ** -.24 ** -.19 ** -.13 ** -.06 -.05

High .43 ** .39 ** .29 ** -.45 ** -.35 ** -.30 ** -.02 .04 -.01 High - Low .28 .32 .18 -.12 -.08 -.12 .16 .24 .06

T-stat 8.6 ** 6.4 ** 6.0 ** -1.8 -1.1 -1.8 2.2 * 2.7 ** 0.8

Panel D. Using Net Retail Buying Yesterday to Proxy for Retail Attention, 1. for Hard-to-Value Stocks: 1. Top 50% of Nasdaq Stocks Each Day over the Period, 1997-2001, with Highest Return Volatility over Past 20 Days.a

MediumInstitutional Ownership

1. Top 50% of 3,000 Largest U.S. Stocks Each Day over the Period, 1996-2008, with Highest Return Volatility over Past 20 Days;

Overnight Return (cto%) Trading Day Return (otc%) 24-Hour Return (ctc%)Institutional Ownership Institutional Ownership

Medium Medium

a On average, there are 13 firms in the portfolio for each cell of these 3 x 3 partitioning schemes. * indicates statistical significance at the .05 level; ** at the .01 level.

50

p % q y , , g y y Retail Investor Attention

Net Retail Buying Yesterday Low High Low High Low High

Low .19 ** .13 ** .06 ** -.35 ** -.31 ** -.20 ** -.16 -.18 * -.13 Medium .35 ** .30 ** .22 ** -.48 ** -.38 ** -.21 ** -.13 -.08 .00

High .51 ** .47 ** .35 ** -.63 ** -.49 ** -.35 ** -.12 -.02 -.01

High - Low .32 .33 .29 -.28 -.18 -.16 .04 .15 .13T-stat 6.1 ** 6.6 ** 6.3 ** -2.6 ** -1.7 -1.6 0.3 1.2 1.1

Medium Medium

Trading Day Return (otc%)

a On average, there are 49 firms in the portfolio for each cell of these 3 x 3 partitioning schemes. * indicates statistical significance at the .05 level; ** at the .01 level.

Institutional OwnershipInstitutional Ownership24-Hour Return (ctc%)Institutional Ownership

Medium

Overnight Return (cto%)

50

Table 4, continued

Panel E. Using Net Retail Buying Yesterday to Proxy for Retail Attention, 1. for Hard-to-Value Stocks, 2. with High Transaction Costs: 1. Top 50% of Nasdaq Stocks Each Day over the Period, 1997-2001, with Highest Return Volatility Over Past 20 Days; 2. Top 50% of these Stocks Each Day with Highest Effective Half Spread. a

Retail Investor Attention Net Retail Buying Yesterday Low High Low High Low High

Low .23 ** .20 ** .08 ** -.36 ** -.28 ** -.24 ** -.13 -.08 -.15 Medium .42 ** .37 ** .26 ** -.49 ** -.43 ** -.26 ** -.07 -.06 .00

High .57 ** .55 ** .47 ** -.67 ** -.56 ** -.43 ** -.10 -.01 .03

High - Low .34 .35 .39 -.30 -.28 -.20 .03 .07 .19T-stat 6.3 ** 6.6 ** 8.0 ** -2.7 ** -2.5 * -1.9 0.3 0.5 1.6

Panel F. Using Retail Buying to Proxy Attention, 1. for Hard-to-Value Stocks, 2. with High Transaction Costs, 3. and High Short Interest: 1. Top 50% of Nasdaq Stocks Each Day over the Period, 1997-2001, with Highest Return Volatility Over Past 20 Days; 2. Top 50% of these Stocks Each Day with Highest Effective Half Spread; 3. Top 20% of these Stocks Each Day with Highest Relative Short Interest.a

a On average, there are 23 firms in the portfolio for each cell of these 3 x 3 partitioning schemes. * indicates statistical significance at the .05 level; ** at the .01 level.

Medium Medium Medium

Overnight Return (cto%) Trading Day Return (otc%) 24-Hour Return (ctc%)Institutional Ownership Institutional Ownership Institutional Ownership

51

Retail Investor Attention Net Retail Buying Yesterday Low High Low High Low High

Low .35 ** .27 ** .10 -.43 ** -.47 ** -.24 * -.08 -.20 -.14 Medium .47 ** .46 ** .27 ** -.71 ** -.61 ** -.43 ** -.24 -.15 -.15

High .61 ** .65 ** .49 ** -.70 ** -.67 ** -.52 ** -.09 -.02 -.03

High - Low .26 .38 .39 -.27 -.20 -.28 -.01 .18 .11T-stat 3.3 ** 4.8 ** 5.0 ** -1.8 -1.2 -1.9 -0.1 1.0 0.7

a On average, there are 5 firms in the portfolio for each cell of these 3 x 3 partitioning schemes. * indicates statistical significance at the .05 level; ** at the .01 level.

Medium

24-Hour Return (ctc%)Institutional Ownership Institutional Ownership Institutional Ownership

Overnight Return (cto%) Trading Day Return (otc%)

Medium Medium

51

Table 5. Autocorrelation Function for Retail Net Buying Near the Open, following Days with Net Buying versus Net Selling Near the Open

Lag k Daysin future ACF(k) ACF(k) ACF(k) ACF(k) ACF(k)

1 .25 30.5 ** .16 14.2 ** .28 27.6 ** .21 24.6 ** .24 22.8 **2 .19 25.8 ** .11 9.9 ** .23 24.1 ** .15 20.3 ** .21 22.1 **3 .17 23.6 ** .11 10.6 ** .21 23.5 ** .13 19.5 ** .19 20.3 **4 .16 22.8 ** .10 9.9 ** .19 21.7 ** .13 18.3 ** .18 20.2 **5 .15 22.7 ** .09 9.0 ** .20 22.9 ** .12 17.7 ** .17 18.9 **6 .14 20.0 ** .09 9.0 ** .18 19.7 ** .11 16.2 ** .16 17.3 **7 .13 19.3 ** .09 8.5 ** .18 20.2 ** .10 15.7 ** .15 18.1 **8 .13 18.7 ** .09 8.6 ** .18 20.2 ** .10 15.3 ** .15 17.5 **9 .13 19.4 ** .08 8.2 ** .17 19.6 ** .11 16.7 ** .15 17.5 **

10 .12 18.3 ** .08 8.2 ** .17 19.6 ** .11 16.5 ** .15 17.3 **11 .12 19.0 ** .08 8.2 ** .16 18.6 ** .10 15.7 ** .15 16.8 **

Growth StocksAll Stocks

Panel A. Autocorrelation Function for NetBuy_HR1, following Days with Retail Net Buying in the First hour (i.e., NetBuy_HR1 > 0)

LosersT-Stat

WinnersT-StatT-Stat T-Stat T-Stat

Value Stocks

In this Table we present the mean daily autocorrelation function (ACF) for net retail buying in the first hour of the trading day, as a percent of shares outstanding (NetBuy_HR1). In Panel A we construct this ACF following all days with net buying in the first hour, while in Panel B we use only days with net selling in the first hour. For each day with NetBuy_HR1 > 0 for Panel A (or with NetBuy_HR1 < 0 for Panel B), we first compute the Pearson autocorrelation coefficient at future lags, k = 1 -20 days later, across all stocks in the sample studied. Second, we average these daily autocorrelations across all days in the sample period. The T-statistic associated with each mean autocorrelation is constructed using the standard error of the time series mean. In the second column we provide this mean ACF across all stocks each day. In the subsequent columns, we provide the analogous mean ACF's for subsets of stocks each day, including only value stocks or growth stocks (i.e., the top or bottom quintiles by book-to-market), and including only momentum losers or winners (i.e., the bottom or top quintiles by the past six-month return).

52

11 .12 19.0 .08 8.2 .16 18.6 .10 15.7 .15 16.812 .12 18.6 ** .10 10.0 ** .16 18.8 ** .09 13.9 ** .15 17.6 **13 .12 18.1 ** .07 6.5 ** .17 19.6 ** .10 15.3 ** .15 17.8 **14 .12 18.4 ** .07 7.1 ** .16 19.5 ** .09 15.0 ** .14 16.9 **15 .12 18.0 ** .07 7.1 ** .16 19.7 ** .09 13.3 ** .15 17.5 **16 .12 18.5 ** .07 7.2 ** .16 20.2 ** .09 14.4 ** .14 16.7 **17 .11 17.0 ** .07 7.8 ** .15 17.8 ** .09 13.6 ** .13 15.7 **18 .11 16.9 ** .07 6.5 ** .15 18.3 ** .08 13.0 ** .12 14.6 **19 .12 18.4 ** .08 7.7 ** .15 19.2 ** .09 15.0 ** .14 16.6 **20 .10 16.0 ** .07 7.2 ** .16 19.5 ** .09 14.3 ** .13 16.2 **

* represents statistical significance at the .05 level; and ** at the .01 level.

52

Table 5, continued

Lag k Daysin future ACF(k) ACF(k) ACF(k) ACF(k) ACF(k)

1 .11 16.2 ** .06 5.4 ** .11 12.7 ** .08 10.8 ** .12 15.3 **2 .07 11.0 ** .04 3.6 ** .08 9.3 ** .03 4.4 ** .09 12.6 **3 .05 9.8 ** .02 1.9 .06 7.6 ** .01 2.3 * .08 11.6 **4 .05 8.8 ** .03 2.6 * .05 6.1 ** .01 1.9 .07 9.4 **5 .04 6.3 ** .01 1.2 .05 6.0 ** .01 1.9 .06 8.5 **6 .03 6.2 ** .02 2.2 * .05 6.0 ** .00 0.4 .05 7.5 **7 .03 6.7 ** .02 2.3 * .04 5.5 ** .01 1.8 .05 7.8 **8 .03 5.3 ** .01 1.1 .03 4.3 ** .00 0.1 .04 6.6 **9 .02 3.9 ** .02 1.9 .04 4.8 ** .00 0.7 .04 6.6 **

10 .02 3.2 ** .01 1.4 .04 4.8 ** .00 0.3 .04 5.4 **11 .02 4.3 ** .01 0.6 .03 4.6 ** .00 -0.8 .04 5.7 **12 .02 3.3 ** .02 2.0 * .03 4.7 ** .00 -1.0 .04 5.8 **13 .01 2.7 ** -.01 -0.7 .03 3.8 ** .00 -0.8 .04 5.9 **14 .01 2.8 ** -.01 -1.1 .03 3.8 ** -.01 -1.2 .04 7.0 **15 .02 3.6 ** -.01 -0.6 .03 4.2 ** -.01 -1.2 .03 5.1 **16 .02 3.4 ** .00 -0.2 .03 4.1 ** -.01 -2.6 * .03 5.5 **17 .01 3.1 ** -.02 -2.4 * .03 4.2 ** -.01 -1.7 .03 5.0 **18 .01 2.8 ** -.01 -0.9 .03 3.4 ** -.01 -0.3 .02 3.9 **

T-StatT-Stat T-Stat T-Stat T-Stat

Panel B. Autocorrelation Function for NetBuy_HR1, following Days with Retail Net Selling in the First hour (i.e., NetBuy_HR1 < 0)

All Stocks Value Stocks Growth Stocks Losers Winners

53

18 .01 2.8 .01 -0.9 .03 3.4 .01 -0.3 .02 3.919 .02 4.9 ** .00 0.1 .02 2.6 ** .00 -0.2 .03 4.2 **20 .01 2.6 * .00 0.4 .02 2.7 ** -.01 -1.5 .03 4.0 **

* represents statistical significance at the .05 level; and ** at the .01 level.

53

Panel A. Top 33% of 3,000 Largest U.S. Stocks Each Day over Period, 1996-2008, with Greatest Persistence in High Opening Prices, Measured as the Percent of the Past 20 Trading Days with cto > 0 and otc < 0.

Overnight Return (cto%)Retail Attention Yesterday

for Subsamples of Stocks Each Day with High Persistence in Price Inflation or Retail Buying at the Open, over the Past MonthTable 6. Overnight Returns, Trading Day Returns, and 24-Hour Returns Across Double-Sorted Portfolios,

Trading Day Return (otc%) 24 Hour Return (ctc%)

In this Table we return to our previous analysis of Table 3, to analyze the 3 x 3 scheme of portfolios double-sorted by the level of retail investor attention yesterday, and institutional ownership. In this Table, we limit the analysis to the top 33% of stocks in our sample each day, with high persistence in price inflation or retail investor buying at the open, during the previous month.

We follow the analysis in Table 3, to examine two alternative proxies for the level of retail investor attention yesterday: (i) stock return volatility lagged one day, and (ii) net retail buying yesterday as a percent of total volume. We now introduce two alternative proxies for persistence in price inflation or retail investor buying at the open, over the past month: (i) the percent of the past 20 days with cto > 0 and otc < 0, and (ii) accumulated net retail buying in the first hour over the past month, as a percent of shares outstanding.

In Panel A we analyze the main sample including the 3,000 largest U.S. stocks over the period, 1996 - 2008. Here we measure retail attention yesterday as the square of the close-to-close return lagged one day, and we limit the analysis to the top 33% of sample stocks each day with the highest percent of the previous 20 trading days with cto > 0 and otc < 0. In Panel B, we analyze the abridged sample of Nasdaq stocks over the period, 1997 - 2001. Here we measure retail attention yesterday as net retail buying lagged one day as a percent of total volume, and we limit the analysis to the top 33% of sample stocks each day with the highest percent of the previous 20 days with cto > 0 and otc < 0. Finally, in Panel C, we also analyze the abridged sample, but we consider only the top 33% of sample stocks each day according to our alternative proxy for persistence in retail investor buying at the open: the accumulated net number of shares bought by retail investors during the first hour of the day over the past month, as a percent of shares outstanding.

54

Stock Return Volatility Lagged One Day Low High Low High Low High

Low .13 ** .11 ** .09 ** -.14 ** -.12 ** -.09 ** -.01 -.02 .00 Medium .17 ** .14 ** .12 ** -.20 ** -.14 ** -.11 ** -.03 .00 .01

High .33 ** .27 ** .21 ** -.32 ** -.24 ** -.18 ** .01 .03 .03

High - Low .20 .16 .12 -.18 -.12 -.09 .02 .04 .03T-stat 10.4 ** 9.3 ** 7.5 ** -4.4 ** -3.0 ** -2.4 * 0.3 0.9 0.7

Overnight Return (cto%)

a On average, there are 89 firms in the portfolio for each cell of these 3 x 3 partitioning schemes. * indicates statistical significance at the .05 level; ** at the .01 level.

Retail Attention Yesterday

Institutional Ownership

Trading Day Return (otc%) 24-Hour Return (ctc%)

Institutional OwnershipMedium Medium Medium

Institutional Ownership

54

Table 6, continued

Panel B. Top 33% of Nasdaq Stocks Each Day over the Period, 1997-2001, with Greatest Persistence in High Opening Prices, Measured as the Percent of the Past 20 Trading Days with cto > 0 and otc < 0.

Net Retail Buying Lagged One Day Low High Low High Low High

Low .31 ** .24 ** .17 ** -.39 ** -.35 ** -.18 ** -.08 -.11 -.01 Medium .43 ** .39 ** .31 ** -.53 ** -.40 ** -.26 ** -.10 -.01 .06

High .56 ** .50 ** .42 ** -.65 ** -.51 ** -.41 ** -.09 -.01 .01

High - Low .24 .25 .25 -.26 -.16 -.23 -.01 .10 .02T-stat 5.1 ** 5.6 ** 6.1 ** -2.6 ** -1.7 -2.5 * -0.1 0.9 0.3

Panel C. Top 33% of Nasdaq Stocks Each Day over the Period, 1997-2001, with Highest Persistence in Retail Buying at the Open, Measured as the Sum of Net Shares Bought by Retail Investors during the First Hour of the Trading Day, Aggregated over the Past 20 Trading Days, as a Percent of Shares Outstanding.

a On average, there are 37 firms in the portfolio for each cell of these 3 x 3 partitioning schemes. * indicates statistical significance at the .05 level; ** at the .01 level.

Retail Attention Yesterday

Retail Attention Yesterday

Institutional Ownership Institutional Ownership Institutional OwnershipMedium Medium Medium

Overnight Return (cto%) Trading Day Return (otc%) 24 Hour Return (ctc%)

Overnight Return (cto%) Trading Day Return (otc%) 24-Hour Return (ctc%)

55

Net Retail Buying Lagged One Day Low High Low High Low High

Low .16 ** .13 ** .10 ** -.33 ** -.24 ** -.16 * -.17 * -.11 -.07 Medium .34 ** .27 ** .22 ** -.44 ** -.26 ** -.18 ** -.10 .00 .04

High .44 ** .38 ** .32 ** -.57 ** -.41 ** -.28 ** -.13 -.03 .03 High - Low .28 .25 .22 -.24 -.16 -.12 .04 .08 .10

T-stat 5.2 ** 5.2 ** 5.0 ** -2.3 * -1.7 -1.3 0.4 0.7 0.9

Medium Medium

Retail Attention Yesterday

MediumInstitutional Ownership Institutional Ownership

Overnight Return (cto%)Institutional Ownership

Trading Day Return (otc%) 24-Hour Return (ctc%)

a On average, there are 37 firms in the portfolio for each cell of these 3 x 3 partitioning schemes. * indicates statistical significance at the .05 level; ** at the .01 level.

55

Table 7. Robustness Tests Based on Alternative Return Measures and Subsamples

Sample:Attention Proxy:

Return Measure:

Left Left Left Left

Base Case (Table 3) .17 .02 -.17 -.03 .34 .02 -.42 -.09Newey-West t-ratio 11.9 ** 3.5 ** -5.6 ** -1.3 11.3 ** 1.0 -6.8 ** -1.8

1. Using Market-Adjusted .12 -.03 -.18 -.03 .24 -.07 -.42 -.09 Abnormal Returns 14.1 ** -4.2 ** -10.1 ** -3.5 ** 12.3 ** -5.6 ** -9.8 ** -3.0 **

2. Using Trade Pricesa .17 .02 -.17 -.01 .33 .00 -.41 -.08 to Measure Returns 10.1 ** 2.7 ** -4.8 ** -.3 11.0 ** .2 -6.8 ** -1.4

3. Using Median Return .09 .02 -.16 -.04 .20 .01 -.42 -.11

VOLt-1 Retail_NetBuyt-1

RightBottom

RightTop Bottom TopCell in 3x3 Matrix :

Bottom Left and Top Right Corner Cells in Each 3x3 Matrix

cto(%) otc(%)

3,000 U.S. Stocks, 1996-2008 Nasdaq Stocks, 1997-2001

cto(%) otc(%)

Bottom Top Bottom TopRight Right

This Table presents a set of robustness tests. In every test, we reproduce the portfolio approach from Table 3, but we change some aspect of the analysis. For brevity, we present only the two cells in each 3 x 3 scheme that are subject to the greatest and least forces behind overpricing at the open: the bottom left corner cell for firms with high attention and low institutional ownership, and the top right corner cell for firms with low attention and high institutional ownership. The base-case reproduces these two corner cells from the 3 x 3 schemes in Table 3. In each subsequent test (row), we change only one aspect of the analysis to facilitate comparison with the base case. The tests using volatility yesterday (VOLt-1) to proxy for retail attention are applied to the main sample of 3,000 largest U.S. stocks over the period, 1996-2008. The tests using net retail buying yesterday (Retail_NetBuyt-1) are applied to the abridged sample of Nasdaq stocks over the period, 1997-2001.

56

3. Using Median Return .09 .02 .16 .04 .20 .01 .42 .11 across Stocks Each Day 9.2 ** 3.4 ** -6.5 ** -2.5 * 9.5 ** .8 -8.7 ** -2.5 *

4. No Low-Price Stocks .13 .02 -.13 -.02 .30 .02 -.37 -.09 (with Price < $5) 9.4 ** 2.9 ** -4.5 ** -1.1 10.0 ** .8 -6.0 ** -1.7

.28 .03 -.27 -.07 .34 .02 -.42 -.0913.9 ** 3.6 ** -7.1 ** -2.5 * 11.3 ** 1.0 -6.8 ** -1.8 .09 .01 -.07 -.01 −   −   −   −  6.0 ** .8 -3.1 ** -.7 −   −   −   −  

.29 .07 -.19 -.05 .45 .07 -.39 -.0818.3 ** 8.6 ** -5.3 ** -2.1 * 13.8 ** 3.3 ** -5.9 ** -1.4 .09 .01 -.11 .00 .32 .07 -.37 -.215.1 ** 1.5 -3.9 ** .2 6.8 ** 1.9 -4.2 ** -2.9 **

9. Growth Stocks .20 .03 -.23 -.04 .37 .04 -.46 -.14 (Low Quintile, B / M)c 9.8 ** 3.4 ** -6.0 ** -1.5 8.6 ** 1.2 -5.5 ** -1.9 10. Value Stocks .13 .04 -.09 -.03 .23 -.01 -.24 -.01 (High Quintile, B / M)c 9.5 ** 4.7 ** -3.0 ** -1.5 6.2 ** -.3 -3.5 ** -.2

* indicates statistical significance at the .05 level, and ** indicates significance at the .01 level.a Results based on trade prices using VOLt-1 are computed over the sample period, 1996 - 2004.b For the Nasdaq stocks in the right four columns, cutoffs of market capitalization for small and large stock quintiles are based on the stratification each day using the 3,000 largest U.S. stocks.c For the Nasdaq stocks in the right four columns, cutoffs of B / M for growth and value stock quintiles are based on the stratification each day using the 3,000 largest U.S. stocks.

8. Large Stock Quintileb

5. Nasdaq Stocks

6. NYSE Stocks

7. Small Stock Quintileb

56

Table 7, continued

Sample:

Attention Proxy:

Return Measure:

Left Left Left Left

Base Case (Table 3) .17 .02 -.17 -.03 .34 .02 -.42 -.09Newey-West t-ratio 11.9 ** 3.5 ** -5.6 ** -1.3 11.3 ** 1.0 -6.8 ** -1.8

11. Momentum Losers .32 .06 -.31 -.08 .48 .09 -.61 -.17(Low Quintile, 6-mo Return) 14.7 ** 6.2 ** -8.0 ** -3.0 ** 12.5 ** 3.2 ** -7.9 ** -2.7 ** 12. Momentum Winners .14 .03 -.13 -.04 .26 .02 -.25 -.12(High Quintile, 6-mo Return) 9.0 ** 3.4 ** -4.0 ** -1.7 8.5 ** 1.3 -3.8 ** -1.9

.20 .04 -.35 -.11 .37 .05 -.66 -.305.8 ** 3.0 ** -5.4 ** -2.6 ** 5.4 ** 1.0 -4.8 ** -2.7 **

.16 .02 -.12 -.01 .33 .02 -.36 -.0410.3 ** 2.5 * -3.8 ** -.2 9.9 ** .7 -5.6 ** -.8

.25 .04 -.24 -.03 .37 .05 -.46 -.1210.2 ** 4.1 ** -5.0 ** -1.4 11.4 ** 2.2 * -6.9 ** -2.2 *

3,000 U.S. Stocks, 1996-2008 Nasdaq Stocks, 1997-2001

13. Mondays

14. Other WeekDays

15. 1996 - 2000d

cto(%) otc(%)

Cell in 3x3 Matrix : Bottom Top BottomRight

Bottom Left and Top Right Corner Cells in Each 3x3 Matrix

VOLt-1 Retail_NetBuyt-1

Right Right Right

cto(%) otc(%)

Top Bottom Top Bottom Top

57

.16 .00 -.22 .01 .17 -.11 -.21 .036.4 ** .3 -4.1 ** .5 2.5 * -2.2 * -1.4 .3

.13 .03 -.16 -.07 −   −   −   −  5.2 ** 2.0 * -2.7 ** -1.5 −   −   −   −  

* indicates statistical significance at the .05 level, and ** indicates significance at the .01 level.d Data on Retail_NetBuyt-1 are unavailable before 1997, so the entries in this row for this proxy are for 1997-2000.e Data on Retail_NetBuyt-1 are unavailable after 2001, so the entries in this row using this proxy are for 2001 only.

16. 2001 - 2004e

17. 2005 - 2008

57