Rankings of published price-earnings ratios andvalue investor attention

Jordan Moore 1

March 9, 2016

Abstract

Value investors with limited attention use fundamental metrics to identify undervaluedstocks. Price-earnings (P/E) ratios are extremely popular value proxies and are widelypublished using a common methodology. This paper tests whether rankings of publishedP/E ratios influence investor attention and cross-sectional variation in subsequent returns.In a monthly time-series test from 1974 to 2013, a long-short decile P/E attention strategyearns an average value-weighted monthly return of 101 basis points with an annual Sharperatio of 0.79. In a daily time-series test, a long-short decile P/E attention strategy earnsan average value-weighted daily return of 16.99 basis points with an annual Sharpe ratio of2.91. Strategy returns are robust to size, value, profitability, investment, price momentum,earnings momentum, short-term reversals, and relative volume. Changes to a stock’s P/Eranking predicts returns even when the stock’s P/E ratio itself does not change. The returnpremium cannot be explained by fundamental risk, clustering of attention at round numberP/E ratios, or autocorrelation in the regressors.

1Simon Business School, University of Rochester. Email: jordan.moore@simon.rochester.edu. I amgrateful to Ron Kaniel, Robert Novy-Marx, Bryce Schonberger, Bill Schwert, and Jerry Warner for extensiveguidance, and to Rob Arscott, Jozef Drienko, Maximilian Franke, Jacquelyn Gillette, Einar Kjenstad,Hongtao Li, Anisha Nyatee, Maxim Sokolov, Mihail Velikov, Hao Zou, and seminar participants at the 2015Australasian Finance and Banking Conference and 2016 Midwest Finance Association Annual Meeting forhelpful comments and suggestions.

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1. Introduction

The relation between attention and stock returns is well established. Kahneman (1973)

establishes the importance of attention as a scarce cognitive resource which influences the

decision-making process of all individual investors. Merton (1987) hypothesizes that for

any asset, a broader investor base is associated with more diversified private information,

a lower required discount rate, and a higher price. Gervais et al. (2001) and Kaniel et al.

(2012) document a positive relation between current relative volume and future returns in

equity markets. Barber and Odean (2008) relate high volumes, extreme returns, and news

coverage to net purchases by individual investors. In this paper, I propose published price-

earnings (P/E) ratios as another important attention-grabbing characteristic. If enough

value investors use published P/E ratios for screening or sorting, then rankings and changes

in rankings can influence value investor attention and subsequent returns.

Empirical results support the P/E attention hypothesis. In a monthly time-series regression

from 1974 to 2013, a long-short decile strategy earns an average value-weighted monthly

return of 101 basis points with an annual Sharpe ratio of 0.79. In a daily time-series

regression, a long-short decile strategy earns an average value-weighted daily return of

16.99 basis points with an annual Sharpe ratio of 2.91. Monthly and daily strategies

earn significant alphas in the Fama and French (2015) five-factor model which controls for

exposure to market, size, value, profitability, and investment factors. I also construct a

nine-factor model, adding factors related to four anomalies associated with changes in price

and earnings individually.2 P/E attention strategies earn economically and statistically

2Jegadeesh and Titman (1993) show that stocks with high returns in the prior two to twelve monthscontinue to outperform stocks with low returns. Jegadeesh (1990) shows that stocks with low returns in themost recent month outperform stocks with high returns. At shorter horizons, numerous studies, includingLo and MacKinlay (1990), Kaniel et al. (2008), and Nagel (2012) document these return reversals. Foster(1977) and Foster et al. (1984) show that changes in quarterly earnings from the same quarter in theprevious year positively predict subsequent returns. Bernard and Thomas (1989, 1990) document stockreturn reversals when earnings are released four quarters following an earnings surprise.

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significant value-weighted alphas controlling for exposure to the five Fama and French

(2015) factors, price momentum, monthly reversals, earnings momentum, and earnings

quality in the expiring quarter.

P/E ratios are relatively weak measures of fundamental value. Fama and French (1992)

show that P/E ratios are unable to predict cross-sectional variation in stock returns after

controlling for price-to-book (P/B) ratios. However, these asset pricing tests use fiscal-

year accounting data updated annually. Since 1970, the SEC requires US public firms to

release quarterly financial statements. Market data providers typically publish four-quarter

trailing P/E (4Q P/E) ratios, and value investors are likely to use these published P/E

ratios to aid their search for cheap stocks. Value investors must search among hundreds

or thousands of volatile stocks for the best opportunities with limited time, capital, and

attention. Investors who initially screen or sort on P/E ratios can identify promising

investments efficiently in a competitive market. P/E ratios are immensely popular and

widely available proxies for fundamental value. Figure 1 shows the relative Google search

volume for P/E ratios and P/B ratios from March 2006 to February 2016. On average, there

are 6.47 times as many searches for P/E ratios as there are searches for P/B ratios.

It is straightforward to construct a list of stocks ranked by P/E at the end of any trading

day. Major financial data providers publish 4Q P/E ratios using the current price and

the four most recent quarters of net income. Table 1 shows the output of a hypothetical

value investor screen on two dates: August 31, 2015 and November 30, 2015. The screen

outputs the 20 stocks in the S&P 400 Midcap index with the lowest positive P/E ratios,

in ascending order. In November, four stocks qualify for the screen that do not qualify

in August: CYH, CAA, TEX, and RCII. A value investor who employs this screen has a

higher probability of purchasing any of the four stocks. A value investor who considers all

S&P 400 stocks, but searches in order of increasing P/E ratio, has a higher probability of

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buying CYH, CAA, TEX, or RCII before depleting his capital. The expected aggregate

effect of this value investor behavior is a higher equilibrium price for the four stocks.

P/E rankings could proxy for fundamental risk rather than value investor attention. I

address this concern by showing that changes in P/E rankings predict subsequent returns

in a subsample of stocks where the P/E ratio itself does not change. In addition, using

the subsamples proposed by Lakonishok et al. (1994), I demonstrate that P/E attention

strategies still perform well during poor economic times. In response to the question of

whether results are driven by the attention effects of round-number P/E ratios, I show

that strategy returns are robust to excluding all observations in which stocks cross any

P/E ratio which is a multiple of 10. Some of the regressors are autocorrelated because of

overlapping formation periods. This raises the possibility that strategy return standard

errors calculated using OLS are too low. To address this, I reestimate the model using

robust standard errors and show that the nine-factor alphas remain significant.

The remainder of the paper is organized as follows. Section 2 develops the hypothesis by

reviewing prior literature on attention and stock returns. Section 3 describes the data and

the construction of important variables. Section 4 summarizes asset pricing test results

using a monthly strategy in which investors react to ex-post changes to P/E rankings.

Section 5 evaluates two strategies in which investors predict changes to P/E rankings

ex-ante using two time-series models of quarterly earnings. Section 6 incorporates daily

data to estimate the returns of higher-frequency strategies. Section 7 evaluates whether

alternative hypothesis explain the empirical results. Section 8 concludes.

2. Hypothesis Development

My hypothesis is that rankings of published P/E ratios predict stock returns because

P/E ratios influence value investor attention. I construct variables to model the rational

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behavior of value investors, including active equity mutual funds, hedge funds, proprietary

trading firms, and individuals. If the trading activity of these investors is economically

meaningful, then a measure which proxies for expected changes in value investor order flow

can predict subsequent returns.

As Grossman and Stiglitz (1980) argue, there must be some equilibrium level of mar-

ket inefficiency to justify the efforts of active investors. Value investors face attention

constraints because investment opportunities depend on stock prices and stock prices are

volatile. Peng and Xiong (2006) show that limited attention forces investors to focus on

market- and sector-specific news at the expense of firm-specific news. Hou et al (2009) find

that investor attention can lead to both insufficient responses to relevant information and

excessive responses to irrelevant information. Abel et al (2013) demonstrate that investors

apply some state-dependent rule for portfolio rebalancing when there are nontrivial fixed

costs of attention.

Many empirical studies suggest that the marginal investor faces binding attention con-

straints. Cohen and Frazzini (2008) show that investors with limited attention fail to fully

adjust the stock prices of supplier firms for changes in their customers’ future earnings

expectations. DellaVigna and Pollet (2009) show that if companies release earnings news

on Fridays, when investor attention is more limited, the stock price reaction is more de-

layed. Hirshleifer et al. (2009) show that the price response to unexpected earnings is more

delayed when investors are distracted with a large number of firms release earnings on the

same day.

The relation between proxies for investor attention and stock returns is empirically robust.

Gervais et al. (2001) identify a positive relation between relative volume and subsequent

returns for US stocks. Kaniel et al. (2012) show that this high-volume return premium

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is present in most international equity markets. Da et al. (2011) show a positive relation

between Google search frequency and future returns. Barber and Odean (2008) directly

relate three measures of investor attention to increased net purchases by individual in-

vestors: high relative volumes, extreme returns, and frequent news appearances. Attention

is also likely to influence an investor’s decision to sell stocks. Hartzmark (2015) shows

that both retail and institutional investors are substantially more likely to sell the stocks

in their portfolio with the highest and lowest returns. This finding suggests that investors

rank stocks in their portfolios on returns, and those at both extremes of the ranked list are

especially salient.

Newsworthy events and well-publicized price levels are also correlated with future returns.

Frazzini and Lamont (2007) find that stocks earn larger returns in months with expected

earnings announcements. Hartzmark and Solomon (2013) find evidence of larger returns

for firms during months with expected dividend payments. George and Huang (2004) show

that a stock’s proximity to its 52-week high predicts much of the Jegadeesh and Titman

(1993) momentum anomaly. Li and Yu (2012) show that proximity of the Dow Jones Indus-

trial Average to its 52-week high forecasts future market returns.3 The existence of binding

investor attention constraints is consistent with extensive evidence of price clustering at

round numbers and other visible figures. Appendix B lists 13 published papers document-

ing round number clustering in a variety of asset classes and other environments.

Value investors facing attention constraints must use some numerical criteria to screen or

sort for undervalued stocks. Published P/E ratios are likely candidates for screening or

sorting variables. P/E ratios are popular valuation metrics since Graham and Dodd (1934),

widely published in financial quotes, and frequently referenced in news stories. Benjamin

3On the other hand, proximity of an index of all NYSE/AMEX stocks to its 52-week high, which iseconomically more meaningful but far less visible, does not predict future market returns.

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Graham advocates using several years of earnings to calculate P/E ratios. Likewise, Camp-

bell and Shiller (1999) construct a P/E measure using a long time series and business cycle

adjustments. However, P/E ratios published in popular financial data sources such as the

Wall Street Journal, Financial Times, Bloomberg, or Google, are typically calculated using

four trailing quarters of net income.

I construct a trading strategy using a proxy for investor attention based on published

P/E rankings and show that the strategy earns economically and statistically significant

returns. However, the fact that P/E ratios proxy for value could drive the strategy returns.

Basu (1977, 1983) finds that P/E ratios predict NYSE stock returns after controlling for

size. However, Fama and French (1992) show P/E ratios are insignificant in a cross-

sectional regression which also includes P/B. The book value of equity depends on a firm’s

lifetime retained earnings, while P/E ratios capture only one year of financial performance.

Investors see new fundamentals once per quarter, while Fama and French (1992, 1993)

update fundamentals annually. Since four trailing quarters of earnings are more volatile

than the book value of equity, tests using annual updating may not accurately measure the

relative attention content of P/E and P/B.

Because earnings are in the denominator, P/E ratios are also related to profitability. Novy-

Marx (2013) and Fama and French (2015) argue that the relation between profitability and

expected stock returns is consistent with the valuation equation implied by clean surplus

accounting. Fama and French (2008) demonstrate that an earnings-to-equity profitability

measure does not reliably predict stock returns. Novy-Marx (2013) identifies gross prof-

itability, measured as the ratio of gross profits to assets, as a robust source of cross-sectional

variation in stock returns. Ball et al. (2015) construct a measure of operating profitability

which adjusts gross profits for current expenditures on sales, general, and administrative

expenses excluding research and development. It’s important to show that the profitability

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of P/E attention strategies is not due to exposure to one of these fundamental profitability

measures.

P/E attention strategies earn positive and significant alphas in a nine-factor model which

includes controls for fundamental measures of value and profitability. The Fama and French

(2015) model includes the value and profitability factors as well as controls for market excess

return, size, and investment. I augment this model with four other factors associated with

known anomalies related to changes in price or earnings individually. Price momentum

factors include the Jegadeesh and Titman (1993) prior-year return momentum in and

the Jegadeesh (1990) prior-month return reversals. Earnings momentum factors include

the Ball and Brown (1968) current quarterly earnings momentum and the Bernard and

Thomas (1989, 1990) reversal four quarters later. In addition, strategy performance in

various subsamples of the data suggest that empirical results are consistent with value

investor attention rather than fundamentals.

3. Data

Price, volume, returns, and shares outstanding data for US equities are from CRSP. All

returns are adjusted for delistings. Reporting dates and quarterly fundamentals data are

from Compustat. The sample period for data collection begins in January of 1972, when

quarterly earnings for a large number of public US firms become available. Since four

quarters of prior earnings data are necessary to calculate a trailing 4Q P/E ratio, and

eight quarters of prior earnings data are necessary to calculate SUE, the asset pricing tests

begin in January of 1974. The sample ends in December of 2013. Only common stocks

(CRSP Share Code 10 or 11) are included. I don’t exclude stocks based on liquidity reasons

or industry membership.

The trailing 4Q E/P ratio for each stock-month or stock-day observation is calculated to

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match the P/E ratio published by popular market data providers, such as the Wall Street

Journal, Financial Times, Bloomberg, or Google. E/P ratios are simply the reciprocal of

P/E ratios. Unlike P/E ratios, E/P ratios are monotonic measures of value. In practice,

when E/P≤0, no value for P/E is published. However, negative EPS values are reported,

so there is minimal cost to construct trailing 4Q E/P ratios for these stocks. The number

of shares outstanding changes between quarterly earnings releases for reasons such as share

buybacks and employee option exercises. As a result, I calculate P/E ratios using the price

and earnings measures on an aggregate basis, rather than on a per-share basis. The numer-

ator of the trailing 4Q E/P ratio is the sum of the four most recent values of Compustat

quarterly net income (NIQ). Prior earnings studies measure earnings using Compustat in-

come before extraordinary items (IBQ).4 These two measures differ in approximately 16%

of firm-quarter observations in the sample. Since IBQ excludes extraordinary items, it is

a better statistic to evaluate earnings persistence. However, my objective is to analyze

the impact of P/E ratios on investor attention. NIQ more closely reflects the US GAAP

measure of net income used to calculate earnings in published P/E ratios.

The denominator of the 4Q E/P ratio is market capitalization, calculated using the most

recent monthly or daily split-adjusted closing prices from CRSP and the most recent quar-

terly shares outstanding (CSHOQ) from Compustat. In this paper, the 4Q E/P ratio is

calculated as:

4QEPi,t =NIQi,t+NIQi,t−1+NIQi,t−2+NIQi,t−3

|PRCi,t|∗CSHOQi,t

This calculation assumes market data providers adjust quarterly earnings per share (EPS)

for changes in shares outstanding. If investors do not properly adjust the EPS time series,

the calculation of the 4Q E/P ratio is:

4For instance Basu (1977, 1983) on P/E ratios and cross-sectional stock returns, and Foster (1977),Foster et al. (1984), Bernard and Thomas (1989, 1990), and Livnat and Mendenhall (2006) on PEAD

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4QEPi,t =EPSi,t+EPSi,t−1+EPSi,t−2+EPSi,t−3

|PRCi,t|

These two calculations are identical when the shares outstanding is constant for the last

four quarters. Since the shares outstanding doesn’t typically change much, results are very

similar using the alternative calculation.

I determine the last four values of quarterly earnings using the Compustat DATAFQTR

and RDQ fields and the CRSP PERMNO link. I construct monthly and daily time series

of net income and shares outstanding using the most recent quarterly fundamentals. The

four unique values of NIQ must correspond to four consecutive fiscal quarters based on the

Compustat DATAFYEARQ and DATAFQTR fields.

Monthly asset pricing tests assume investors know quarterly earnings on the close of the

last trading day of the RDQ calendar month. This assumption may be violated for a

small percentage of firm-month observations, when earnings are released after the market

closes on the last trading day of the month. The same issue arises when Compustat

misstates RDQ and earnings are not in fact released until early the next month. On the

other hand, if RDQ has an approximately uniform distribution throughout the month, the

strategy excludes excess returns from the first 10 or 11 trading days after new earnings are

available. If earnings reports are accessible to institutional investors in real time, monthly

results may substantially understate true strategy returns.

Daily asset pricing tests assume investors know quarterly earnings on the close of the first

trading day after the reporting date, based on RDQ. If RDQ is accurate, this assumption

guards against cases when earnings are not released until after the market closes. I make

the 4Q E/P ratio unavailable on trading days when earnings are released. As a result,

stocks are not included in long-short portfolios on RDQ days. Since RDQ only includes

the earnings date, it is impossible to know whether investors have access to earnings in

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time to initiate positions by the end of the trading day.

Unfortunately, Compustat quarterly earnings are not “point in time.” The quarterly earn-

ings in the NIQ fields are the final adjusted earnings and may not match the earnings

an investor sees when the company releases quarterly financials. Livnat and Mendenhall

(2006) use a proprietary point-in-time database as well as Compustat to construct decile

PEAD strategies. The excess returns from these two strategies are very similar. Their

finding suggests that results in this paper are not sensitive to earnings restatements in

Compustat.

Table 2 summarizes changes in the cross section of 4Q E/P ratios over time by dividing

the 40 year sample into ten four-year subsamples. The number of stocks with four distinct

valid quarterly earnings from consecutive fiscal quarters increases from 2166 during the

1974-1977 subsample to a high of 5467 from 1998-2001, coinciding with the dot-com boom,

before falling to 3620 from 2010-2013. Public companies are acquired or delisted on an

ongoing basis. As a result, among firms with four consecutive quarters of valid earnings,

about 86% have eight consecutive quarters of valid earnings. The marginal stocks choosing

to go public or remain public at any given time tend to be small growth firms with volatile

earnings. As the number of public companies increase, the percentage of firms with positive

4Q E/P ratios declines and the median E/P ratio decreases. Since smaller companies have

lower E/P ratios, the median E/P ratio for individual firms understates the value-weighted

E/P ratio for the market in every subsample.

The primary variables of interest in this paper use 4Q E/P rankings and changes in rankings

to proxy for investor attention. Monthly strategies consider the attention of both “new”

investors, who screen or sort on published P/E ratios for the first time, and “returning”

investors, who evaluate stocks for the first time in three months. AttnNew is the 4QEPi,t

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percentile for stock i at the end of month t. AttnReturning is the change in 4QEPi,t

percentile for stock i from the end of month t − 3 to the end of month t. AttnTotal

is the equal-weighted average of AttnNew and AttnReturning. The daily strategies only

consider the attention of returning investors. AttnReturning(6D) is the change in 4QEPi,t

percentile for stock i from the end of day t−6 to the end of day t. AttnReturning(12D) is

the change in 4QEPi,t percentile for stock i from the end of day t− 12 to the end of day t.

In fact, actual value investor attention is unobservable. In future work, I will analyze the

Thomson-Reuters 13F institutional holdings database to try to provide empirical support

for the Merton (1987) attention hypothesis. A positive relation between values of any of

the Attn measures and future changes in the number of distinct institutional investors

would provide confirmatory evidence.

In Fama and MacBeth (1973) regressions, the dependent variables in the first stage are

monthly or daily returns of individual stocks. Returns are either CRSP monthly or daily

holding period returns or delisting returns. Lagged values of monthly returns are inde-

pendent variables in some specifications. The cumulative return from the end of month

t− 12 to the end of month t− 1 represents the Jegadeesh and Titman (1993) momentum

characteristic. The month t return proxies for the Jegadeesh (1990) short-run reversals

characteristic. In daily Fama and MacBeth regressions, I use the day t return to proxy for

returns to liquidity-providing strategies.

The log of market capitalization and log of book-to-market ratios for each stock are calcu-

lated as in Fama and French (1992). Fiscal data from December of year t− 1 are available

to investors at the end of June of year t. The Novy-Marx (2013) gross profits-to-assets ratio

and Cooper et al. (2008) asset growth ratio are calculated using the same timetable. The

Novy-Marx (2013) gross profitability measure is not calculated for financial firms, those

with SIC codes between 6000-6999. The profitability and investment characteristics for

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year t are calculated from Compustat annual data as:

(GP/AT )t = REV Tt−COGStATt

dATt = ATtATt−1

To account for PEAD, the SUE for each firm-month is calculated as in Foster (1977) and

Foster et al. (1984):

SUEt = IBQt−IBQt−4

σIBQt−1...t−8

In time-series regressions, positions are weighted by market capitalization, using the same

lag from December of year t − 1 to June of year t. Monthly factor returns for portfo-

lios controlling for market excess return (MKT), size (SMB), value (HML), profitability

(RMW), investment (CMA), momentum (UMD), and short-term reversals (STR) are from

Ken French’s website.5 The portfolio construction methodology for these factors are de-

scribed in Fama and French (1993) and in Carhart (1997). I construct portfolios to control

for SUE in the most recent quarter (SUEt) and in the expiring quarter (SUEt−3) using

the same methodology based on 2x3 independent portfolio sorts.

In daily time-series regressions, I use the daily factor returns for MKT, SMB, HML, UMD,

and STR from Ken French’s website. Since daily returns for RMW and CMA are not

available, I construct daily portfolio returns using independent 2x3 sorts on size and either

GP/AT or dAT . Likewise, I construct daily portfolio returns for SUEt and SUEt−3.

Lakonishok et al. (1994) analyze the performance of value strategies in various subsamples

to evaluate whether strategy returns are driven by mispricing or risk. Repeating their

analysis, I use data provided by the National Bureau of Economic Research (NBER) which

characterize months as expansion months or recession months.6 In the sample, the US

5Ken French’s data library is located at: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data library.html6The data on recession dates are available at: http://www.nber.org/cycles.html

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goes through seven recessions comprising about 16% of the time series.7 For the daily

strategies, recession days are those which belong to an NBER recession month. Following

Lakonishok et al. (1994), I construct subsamples based on quarterly US real GDP growth

in the next quarter, since the stock market is considered a leading indicator of the business

cycle. Business cycle data used to construct these subsamples are from the US Department

of Commerce Bureau of Economic Analysis (BEA).8

The Investment Company Fact Book (ICFB) provides data on mutual funds, ETFs, closed-

end funds, and retirement savings accounts.9 Table 20 on the ICFB website provides

annual inflows and outflows for equity mutual funds from 1984-2013. Table 34 on the

ICFB website provides data on annual purchases and sales of common stock by equity

mutual funds from 1984-2013. For each year in the sample, I calculate the total traded

dollar volume for all US common stocks in the CRSP universe, which I use as a scaling

factor. I use compounded daily excess returns for the AttnReturning(6D) strategy to

calculate a time series of annual excess returns and relate the time series to current and

lagged annual mutual fund activity.

4. Results for Ex-Post Monthly Strategies

4.1. Fama and MacBeth Regressions

Table 3 summarizes results of Fama and MacBeth (1973) monthly regressions from 1974-

2013, using only control variables. The first stage of this estimation procedure is a cross-

sectional regression for each month, where the dependent variables are the monthly per-

centage returns of each individual stock in month t. The independent variables are char-

acteristics of each stock, measured at the close of month t − 1. To reduce the influence

7Recessions in the sample: 11/73-3/75, 1/80-7/80, 7/81-11/82, 7/90-3/91, 3/01-11/01, and 12/07-6/098The BEA website is: http://www.bea.gov9The ICFB website is: http://www.icifactbook.org

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of outliers, I winsorize all independent variables at the 99% and 1% levels. In the second

stage, the time-series means of the coefficient estimates are consistent, controlling for the

effect of cross-sectional correlation.

The eight independent variables are either fundamental or mechanical. Fundamental vari-

ables control for major cross-sectional anomalies. These include the log of market equity

[log(ME)], the log of the book-to-market ratio [log(BE/ME)], the ratio of gross profits to

total assets (GP/AT), and the ratio of current assets to lagged assets (dAT). These vari-

ables control for size, value, profitability, and investment. The four mechanical variables

are those related to either price momentum or earnings momentum individually. These

include the return from the end of month t − 12 to the end of month t − 1 [R(12,1)], the

return from the end of month t − 1 to the end of month t [R(1,0)], and the standardized

unexplained earnings in both the current and expiring quarters (SUEt, SUEt−3).

Table 3 presents results from nine specifications. In the first eight specifications, the only

independent variables are an intercept and one of the controls. In the ninth specification,

independent variables include an intercept and all eight controls. Each of the first seven

variables is significant as a lone control and has the expected sign. Small stocks, value

stocks, profitable stocks, and conservative stocks earn higher returns. Stocks that have

performed well in the prior year, or poorly in the prior month, also earn higher returns.

Standardized unexplained earnings from the most recent quarter also predicts positive ex-

cess returns. Only SUEt−3 is insignificant by itself. However, in the specification which

includes all controls, SUEt−3 is negative and significant. This is probably because SUEt is

also included and earnings growth between quarter t−3 and quarter t predicts returns. Con-

sistent with the findings of Chordia and Shivakumar (2006), earnings momentum (SUEt)

subsumes price momentum [R(12,1)]. All of the other variables retain their sign and are

significant at the 5% level.

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In Table 4, I present results from four additional monthly Fama and MacBeth regressions.

These regressions include one or two measures of attention using published P/E ratios as

well as all eight controls [log(ME), log(BE/ME), GP/AT, dAT, R(12,1), R(1,0), SUEt, and

SUEt−3]. The first measure of attention, AttnNew, is calculated as the stock’s percentile

of 4QEP at the end of month t. This measure represents a stock’s current P/E ranking.

As such, it proxies for the attention a stock receives when a list of stocks, sorted by P/E,

is evaluated by a new investor. In the first specification, the coefficient on AttnNew is 0.72

basis points with a t-statistic of 3.78. Economically, a stock in the 75th percentile earns

higher returns than a stock in the 25th percentile by 36 basis points per month. The second

measure of attention, AttnReturning, is the change in a stock’s 4QEP percentile from the

end of month t − 3 to the end of month t. This measure represents a stock’s change in

P/E ranking over the last quarter. This variable proxies for the attention of an investor

who rebalances his portfolio every three months based on evaluating a list of stocks ranked

by P/E. In the second specification, the coefficient on AttnReturning is 1.3 basis points

with a t-statistic of 8.95. Economically, a one standard deviation increase in P/E ranking

between the end of month t− 1 and the end of month t is associated with 18 basis points

higher return in month t+ 1.

In the third specification of Table 4, both AttnNew and AttnReturning are included along

with the eight control variables. There is a mechanical positive correlation between the

two variables, so it is unsurprising that the coefficient on AttnNew decreases from 0.72

basis points to 0.61 basis points and the coefficient on AttnReturning decreases from 1.3

basis points to 1.0 basis points. Nevertheless, both coefficients remain economically and

statistically significant. In the fourth specification, I include a single P/E attention variable,

AttnTotal, the equal-weighted average of AttnNew and AttnReturning. This represents

the total attention of all investors, under the uninformative prior that half of the investors

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are new and half of the investors are returning. The coefficient on AttnTotal is 0.68 basis

points with a t-statistic of 5.06. In all four specifications, the signs and significance of all

eight controls are the same as in the specification including only the controls.

4.2. Time-Series Regressions

Table 5 presents results from five monthly time-series regression specifications, in which

portfolios are formed using the ex-post AttnTotal measure. In each specification, the

dependent variable is the time series of monthly returns for a portfolio which is long

every stock in the highest decile of AttnTotal and short every stock in the lowest decile

of AttnTotal. All positions are weighted by market capitalization. NYSE breakpoints

determine decile portfolio assignments. The independent variables are the corresponding

monthly returns of factor mimicking portfolios. The one-factor CAPM model includes

an intercept and the MKT factor, the excess return of a value-weighted portfolio of CRSP

common stocks above the risk-free rate. The three-factor model of Fama and French (1993)

also includes the SMB and HML factors, which proxy for the size and value premiums.

The four-factor model of Carhart (1997) augments the three-factor model with the UMD

momentum factor. The Fama and French (2015) five-factor model augments the three-

factor model with RMW and CMA, proxies for profitability and investment premiums.

Finally, I construct a nine-factor model which includes the five factors of Fama and French

(2015) as well as factors controlling for one-year price momentum (UMD), one-month price

reversals (STR), and standardized unexplained earnings (SUE) in the current (SUEt) and

expiring (SUEt−3) quarters.

This long-short decile portfolio earns an average monthly excess return of 1.01%, with

a t-statistic of 5.07, which corresponds to an annual Sharpe ratio of 0.79. As Figure

2 shows, excess returns increase monotonically across all ten individual decile portfolios.

17

The alpha is similar to the excess return after controlling for any of the fundamental factors

(MKT, SMB, HML, RMW, CMA) or price momentum (UMD). The monthly alphas for

CAPM, three-factor, four-factor, and five-factor models are 1.13%, 1.06%, 0.98%, and

0.88% respectively, with corresponding t-statistics of 5.85, 5.47, 5.00, and 4.67. Because the

AttnTotal characteristic is mechanically related to the book-to-market ratio, the long-short

portfolio has negative loadings on MKT and SMB and positive loadings on HML and RMW.

Stocks in the long portfolio are value stocks, which are generally larger, more profitable

companies with lower market betas. Including all nine factors in the model reduces the

monthly alpha to 0.62%, with a t-statistic of 3.19. The two factors which have the largest

impact on the strategy’s alpha are SUEt and STR. A stock with positive SUEt by definition

increases its quarter t earnings above its quarter t − 4 earnings. Holding price constant,

this mechanically increases the 4QEP ratio. Likewise, a stock with low monthly returns

increases in 4QEP percentile among positive P/E stocks. Nevertheless, the strategy earns a

positive monthly nine-factor alpha which is economically and statistically significant.

The calculation of the AttnTotal characteristic assumes an equal composition of new

and returning investors. New investors only consider a stock’s P/E ranking (AttnNew).

Returning investors consider the stock’s P/E ranking relative to three months earlier

(AttnReturning). This equal-weighting assumption is consistent with an uninformative

prior over the two types of investors. Table 6 shows the results of strategies which allow

the returning investor weight (wreturning) to vary from 0 to 1 in increments of 0.1. Excess

returns of value-weighted long-short decile portfolios are positive and significant for all

values of wreturning. Five-factor alphas are also positive and significant for every strategy.

This is unsurprising, since controls for monthly reversals and SUE, the two factors which

substantially reduce portfolio alpha, are not included in the five-factor model.

When including all nine factors, the alpha estimates are positive across the entire domain

18

of wreturning, but alphas are insignificant at the extremes. The attention strategies are

insignificant for wreturning ≥ 0.9 because the excess returns are subsumed by the monthly

reversals and SUE factor returns. They are also insignificant for wreturning < 0.1 because

of monthly reversals, SUE, and HML. However, the attention strategies earn positive and

significant nine-factor alphas for 0.1 ≤ wreturning ≤ 0.8, so strategy performance is not

very sensitive to the assumption about the distribution of investor types.

Table 7 tracks the performance of ex-post monthly value-weighted long-short P/E attention

portfolios for 15 months after portfolio formation. A stock is assigned to an extreme

decile portfolios because of extreme returns in the last three months or extreme earnings

in the last fiscal quarter. Extreme earnings can influence stock returns for longer than

extreme returns. Bernard and Thomas (1989, 1990) demonstrate that seasonal differences

in quarterly earnings have a significant positive autocorrelation. Thus, strong earnings

in quarter t suggest strong earnings in quarter t + 1, which are typically released within

three months. Twelve months later, both of these earnings expire from the published

P/E ratio. Thus, it is unlikely that long-short portfolios earn significant monthly excess

returns more than 15 months after formation. Monthly ex-post P/E attention strategies

earn positive and significant excess returns in four of the first five months after portfolio

formation. Individual monthly strategy returns are insignificant for each of the next 10

months. These portfolios earn cumulative returns of 2.85% in the first five months, then

drift slightly higher to earn cumulative returns of 3.64% for the full 15 months.

In Table 8, I divide the 40-year sample into four 10-year subsamples. When portfolios

are formed using the ex-post AttnTotal measure, strategy returns are relatively similar

for the four subsamples. The strategies earn positive average monthly returns of 0.72%,

1.07%, 1.37%, and 0.81%, with corresponding t-statistics of 2.19, 3.49, 2.47, and 2.17.

Likewise, the CAPM, five-factor, and nine-factor alphas are similar across subsamples.

19

The nine-factor alphas are nearly identical for the four subsamples: 0.64%, 0.65%, 0.66%,

and 0.65%.

4.3. Double-Sorted Portfolios

Table 9 presents results from double sorts for monthly trading strategies. The top panel

summarizes results from ex-post attention strategies. At the end of each month, firms are

independently sorted into five quintiles across two dimensions using NYSE breakpoints.

The first dimension is the firm’s monthly ex-post AttnTotal measure. The second dimen-

sion is one of the eight variables used to construct monthly factor return portfolios in the

nine-factor model. Market excess return does not vary across stocks, so these eight sorting

variables include ME, BE/ME, GP/AT, dAT, R(12,1), R(1,0), SUEt, and SUEt−3. For

each quintile of each sorting variable, the dependent variable is the time series of monthly

returns for portfolios which are long stocks in quintile 5 and short stocks in quintile 1 of

AttnTotal. Positions are weighted by market capitalization and portfolio assignments use

NYSE breakpoints.

When sorting on ME, R(12,1), R(1,0), SUEt or SUEt−3, all five long-short quintile port-

folios earn positive and statistically significant excess returns. The AttnTotal strategy

performs particularly well for small stocks and for stocks with poor recent returns or poor

earnings momentum. On the other hand, the AttnTotal strategy does not add much

marginal pricing performance to stocks sorted on either BE/ME, GP/AT, or dAT. The

strategy earns positive excess returns in 14 of the 15 quintile portfolios across these three

values, but is only significant in four of them: two each of the GP/AT and dAT portfolios.

The weak performance of monthly P/E attention strategies in portfolios already sorted by

BE/ME, GP/AT, or dAT is likely due to the common accounting variables used in the

measurement of these strategies. Investors may use P/E ratios to identify promising op-

20

portunities, then evaluate BE/ME, GP/AT, or dAT before making a final trading decision.

The high-frequency P/E attention strategies still earn significant returns in portfolios first

sorted by value, profitability, or investment.

5. Results for Ex-Ante Monthly Strategies

In the first ex-ante attention model, investors predict the E/P for all stocks three months in

the future, assuming the quarterly IBQ time series follows a seasonal random walk model

with linear trend (SRW+Trend). This calculation of E[4QEPi,t+1] also assumes the best

estimate of the stock price in three months is the current price and that E(NIQi,t+1) =

E(IBQi,t+1). In other words, excess stock returns and extrordinary items for the next

quarter both have 0 mean. Using this model, dropping the i subscript, and defining the

information set (Ω) as the eight most recent values of NIQ and IBQ:

E[4QEPt+1|Ω] =3∑IBQt,t−1,t−2+4IBQt−3−3

∑IBQt−4,t−5,t−6−2IBQt−7+8NIQt+8NIQt−1+8NIQt−2

8|PRCt|∗CSHOQt

Appendix A provides details of how to derive the above equation. In the SRW+Trend

ex-ante model, AttnNew is the percentile of E[4QEPi,t+1] at the end of month t and

AttnReturning is the change in percentile of E[4QEPi,t+1] from the end of month t− 3 to

the end of month t. AttnTotal is the average of AttnNew and AttnReturning.

An even more simplistic model assumes that each stock is expected to earn the same

proportion of its market capitalization next quarter. This is essentially a flexible random

walk model where the trend term is allowed to vary by month, but not by stock. If current

stock prices are the best predictors of stock prices in three months, the E[4QEPi,t+1]

percentile is the same as the current E/P percentile, where earnings are calculated over

the previous three quarters (EP3Q). In the EP3Q model, AttnNew is the percentile of

3QEPi,t at the end of month t and AttnReturning is the change in percentile of 3QEPi,t

from the end of month t− 3 to the end of month t. AttnTotal is the average of AttnNew

21

and AttnReturning.

For the SRW+Trend and EP3QPct time-series models, Table 10 presents regression re-

sults for two Fama-MacBeth specifications. One specification includes the AttnNew and

AttnReturning individually, and the other specification includes AttnTotal. For both

specifications of both models, the coefficients on AttnNew, AttnReturning and AttnTotal

are positive and statistically significant. Each regression specification includes all eight

controls [log(ME), log(BE/ME), GP/AT, dAT, R(12,1), R(1,0), SUEt, and SUEt−3]. The

coefficients and t-statistics on the attention measures and other controls are similar across

the four specifications and similar to those using ex-post P/E percentile calculations.

Table 11 presents time-series regression results for the two ex-ante AttnTotal measures

using the full nine-factor model. The regession results are very similar for the two ex-

ante attention models. The SRW+Trend model earns an average monthly excess return of

0.99% and an average monthly nine-factor alpha of 0.40% with corresponding t-statistics of

5.72 and 2.51. The EP3QPct model earns an average monthly excess return of 0.95% and

an average monthly nine-factor alpha of 0.46% with corresponding t-statistics of 5.32 and

2.74. The SRW+Trend model earns slightly higher excess returns and slighly lower alphas

because of a more substantial weighting on the SUE and STR factors. Otherwise, both ex-

ante strategies have similar betas to risk factors. Both strategies have significant negative

loadings on MKT, and significant positive loadings on both HML and RMW because of

the types of stocks that are in the extremes of the P/E distributions. Figure 3 shows that

portfolio returns increase monotonically across deciles of the monthly ex-ante attention

measure, using the SRW+Trend model.

Other features of the ex-ante strategy results are also very similar to those of the ex-post

strategy results. The monthly persistence of returns following portfolio formation is very

22

similar for the two strategies. Ex-ante portfolios formed using the SRW+Trend model earn

positive and significant excess returns for each of the first five months following portfolio

formation. Returns in each of the next ten months are not significant. After five months,

the ex-ante strategies earn cumulative excess returns of 3.04%, drifting slightly higher to

3.59% after 15 months. Returns for the ex-post strategy are 2.85% after five months and

3.64% after 15 months. Also, ex-ante strategy returns and nine-factor alphas are relatively

stable over the four decades of the sample. Finally, the performance of double-sorted

portfolios is similar in the monthly ex-post and monthly ex-ante SRW+Trend strategies.

Small stocks and those with poor recent price and/or earnings performance earn the largest

excess returns. These strategies also have less marginal improvement in portfolios which

are first sorted on value, profitability, or investment characteristics. All fifteen of these

quintile portfolios earn positive excess returns, but only four of these portfolio returns are

statistically significant.

6. Results for High-Frequency Strategies

I construct and evaluate two benchmark short-term attention strategies using daily portfo-

lio rebalancing. Stocks report quarterly earnings four times per year, or roughly once every

62 trading days. These two short-term attention strategies employ lag lengths of 6 or 12

days. In other words, they encompass periods in which 10-20% of stocks report earnings.

Since strategy returns depend on decile sorts, the two lag lengths allow the possibility for

earnings stocks to comprise a majority of the long and short decile portfolios.

Table 12 presents estimates of Fama and MacBeth (1973) daily regressions using daily re-

turns from 1974-2013. Considering shorter windows of time, the marketplace is dominated

by returning investors. The two coefficients of interest are AttnReturning(6D), calculated

as the change in a stock’s 4QEP percentile from the close of day t− 6 to the close of day

23

t, and AttnReturning(12D), calculated as the change in a stock’s 4QEP percentile from

the close of day t − 12 to the close of day t. In the first specification, stock returns are

regressed on an intercept and AttnReturning(6D). In this specification, the coefficient

estimate of AttnReturning(6D) is 1.9 basis points with a t-statistic of 46.16. When stock

returns are regressed on an intercept and AttnReturning(12D), the coefficient estimate of

AttnReturning(12D) is 1.1 basis points with a t-statistic of 41.75.

At the daily level, the two highly-related covariates are the day t return (1DRet), which

reflects short-term changes in price, and the most recent quarterly standardized unex-

plained earnings (SUEt), which reflects short-term changes in earnings. When returns are

regressed on an intercept and the previous day’s return, the coefficient estimate on 1DRet

is -11.11 with a t-statistic of -91.88. Economically, on average 11.11% of a stock’s excess

return on day t reverses on day t + 1. When returns are regressed on an intercept and

SUEt, the coefficient on SUEt is 0.7 basis points with a t-statistic of 14.63. When a stock

releases earnings for quarter t, and the seasonal difference of that quarter’s earnings is

one standard deviation higher than the time-series mean, the stock earns positive excess

returns of 0.7 basis points per day, or about 48 basis points for the next quarter.

When either short-term P/E attention variable is regressed on an intercept and both

1DRet and SUEt, the coefficient magnitudes are substantially reduced. The coefficient

on AttnReturning(6D) drops from 1.9 basis points to 0.6 basis points and the coefficient

on AttnReturning(12D) drops from 1.1 basis points to 0.5 basis points. Nevertheless, both

variables remain statistically significant, with t-statistics of 16.82 and 19.98.

Table 13 presents results from daily time-series regression specifications using the 6-day

attention measure (AttnReturning(6D)). Portfolios are sorted into deciles daily based on

NYSE breakpoints. All positions in the long and short portfolios are weighted by market

24

capitalization. I estimate the same five models: the CAPM, Fama and French (1993) three-

factor model, Carhart (1997) four-factor model, Fama and French (2015) five-factor model,

and a nine-factor model which also controls for yearly momentum, monthly reversals, and

SUE in the current and expiring quarters. Since daily returns for the RMW and CMA

factors are not available on Ken French’s website, I construct proxies using 2x3 portfolio

sorts on market equity and the gross profitability ratio (GP/AT ) and asset growth (dAT )

characteristics respectively. I also use 2x3 portfolio sorts on market equity and SUEt and

SUEt−3 to construct the daily factor returns for these variables.

The decile long-short portfolios earn average daily returns of 16.99 basis points, with a

t-statistic of 18.87. This is consistent with an annual Sharpe ratio of 2.91. Once again,

including fundamental factors and price momentum does not substantially reduce the al-

pha. Daily alphas for the CAPM, three-factor, four-factor, and five-factor models are 16.7,

17.1, 16.6, and 17.6 respectively, with corresponding t-statistics of 18.71, 19.23, 18.69, and

19.83. Because this strategy only sorts by recent changes in P/E percentile, stocks in the

long portfolio typically have low values of 4QEP and stocks in the short portfolio have

high values of 4QEP . As a result, long-short portfolios have positive loadings on MKT

and UMD, and negative loadings on SMB, HML and GP/AT . Including all nine factors

reduces the daily alpha to 8.7 basis points with a t-statistic of 10.78. Consistent with

monthly P/E attention strategies, the two factors which greatly reduce strategy alpha are

short-term reversals (STR)10 and earnings momentum (SUEt). To demonstrate this, I

construct a two-factor model which only includes controls for STR and SUEt. The alpha,

both factor loadings, and the three corresponding t-statistics are nearly identical to the

corresponding values in the nine-factor model.

10The portfolios used to calculate daily STR returns are formed based on stock returns from the prior 20trading days, rather than stock returns from the prior calendar month.

25

Table 14 presents results from daily time-series regression specifications using the 12-day

measure. In all six model specifications, long-short portfolios earn positive alphas which

are economically and statistically significant. The portfolios earn average daily excess

returns of 15.30 basis points with a t-statistic of 17.39, which corresponds to an annual

Sharpe ratio of 2.68. The daily alphas for the CAPM, three-factor, four-factor, and five-

factor models are 14.9, 15.5, 15.1, and 16.1 basis points respectively, with corresponding

t-statistics of 17.22, 17.96, 17.48, and 18.55. Including the four additional factors directly

related to price and earnings in the nine-factor model reduces the alpha to 6.1 with a

t-statistic of 8.62. In the two-factor model which includes only STR and SUEt, alphas,

factor loadings, and t-statistics are all very similar to the corresponding values in the full

nine-factor model.

Strategy returns in this paper do not account for trading costs. High-frequency strategy

gross returns are substantially higher than monthly strategy gross returns. However, the

trading costs of implementing high-frequency strategies are also substantially higher. An-

alyzing strategy turnover, effective spreads, and other cost measures will help to estimate

the net profitability of these P/E attention strategies. At any frequency, using the P/E

attention strategy as a marginal input could improve the cost-adjusted performance of

value or profitability strategies. In future work, I will try to show that value or profitabil-

ity strategies which also consider P/E rankings earn higher gross returns and higher gross

Sharpe ratios while incurring lower trading costs. The buy-hold spread suggested in Novy-

Marx and Velikov (2016) may be an effective method to measure the practical effectiveness

of these strategies.

As Figure 4 shows, variation in excess returns for both daily attention measures is concen-

trated in the extreme deciles. This is unsurprising as the stocks near the central part of

the distribution change very little in P/E rankings during the formation period. Neverthe-

26

less, performance across deciles is nearly monotonic for the 6-day attention measure and

perfectly monotonic for the 12-day attention measure.

Table 15 presents results from daily time-series regressions in which stocks are sorted

into deciles based on change in P/E percentile over the prior N days, where N ranges

from 1 to 20. At any of these lag lengths, the long-short portfolio earns positive and

statistically signficant excess returns. The peak average daily excess return of 17.32 basis

points and t-statistic of 19.20 occur at a seven-day lag. At a one-day lag, the strategy

does not earn a significant two-factor alpha. By construction, the one-day strategy does

not include any earnings stocks. On the RDQ date, the P/E is unavailable because of

uncertainty as to whether earnings are released before the market closes. Because earnings

stocks are excluded, the only cause of substantial changes in P/E percentile is substantial

changes in price. There are not many stocks with substantial one-day changes in P/E

percentile because of price changes, so the one-day strategy is subsumed by the daily

short-term reversals strategy. However, the strategies earn significant positive two-factor

alphas for all lag lengths between 2 to 20 days. I also include performance results when

long-short decile portfolios are formed by sorting stocks on 30-day, 60-day, 90-day, and

120-day changes in P/E percentile. For each of these lags, the long-short value-weighted

decile portfolios have significant positive excess returns, but the corresponding two-factor

alphas are insignificant. Somewhere between 20 and 30 days, the performance of these

attention portfolios is explained by the performance of SUE and reversals portfolios.

Table 16 evaluates the high-frequency attention strategy performance in each of the ten-

year subsamples. For both the 6-day and 12-day strategies, the excess returns are positive

and significant in all four subsamples. However, both strategies earn substantially lower

excess returns during the fourth subsample. For the 6-day strategy, average daily excess

returns for the four subsamples are 15.9, 20.5, 20.5, and 11.7 basis points, with t-statistics of

27

11.07, 14.26, 20.5, and 11.7. Likewise, for the 12-day strategy, average daily excess returns

for the four subsamples are 18.8, 16.5, 16.5, and 8.8 basis points, with t-statistics of 12.52,

12.17, 7.68, and 4.43. There are similar declines in the CAPM alpha and five-factor alpha

in the latest subsample, however the nine-factor alpha is stable.

Consistent with monthly and daily results, earnings momentum and short-term reversals

strategies both perform poorly from 2004-2013. SUE strategy performance may suffer

during this period for legal reasons. After the passage of Regulation FD in 2000, firms

have limited ability to provide material, non-public information to favored analysts ahead

of public earnings releases. Likewise, the passage of Sarbanes-Oxley in 2002 provides serious

consequences to key executives who manipulate earnings. Short-term reversals may suffer

poor performance from 2004-2013 because technology, decimalization, and reduced trading

costs make such strategies more viable for individual investors.

Table 17 presents results from double sorts for the high-frequency attention strategies.

At the end of each day, firms are independently sorted into five quintiles across two di-

mensions using NYSE breakpoints. The first dimension is either AttnReturning(6D) or

AttnReturning(12D). The second dimension includes the eight variables (besides MKT)

used to construct daily return portfolios in the nine-factor model [ME, BE/ME, GP/AT,

dAT, R(12,1), R(1,0), SUEt, and SUEt−3]. In addition, I include a measure of relative

volume (RV), as calculated in Gervais et al. (2001). This measure compares a stock’s

share volume on day t to its time series of share volumes on days t − 50 . . . t. Stocks

whose share volumes are among the 10 highest among the previous 50 days are assigned

to quintile 5. For each quintile of each sorting variable, the dependent variable is the time

series of daily returns of portfolios which are long stocks in quintile 5 and short stocks

in quintile 1 of AttnReturning(6D) or AttnReturning(12D). Positions are weighted by

market capitalization and decile assignments use NYSE breakpoints.

28

For both AttnReturning(6D) and AttnReturning(12D), strategy returns are positive and

significant for every quintile of ME, R(12,1), R(1,0), SUEt or SUEt−3. In addition, both

strategies earn significant positive returns for all five RV quintile portfolios. The highest

returns are in RV quintile 5, which is unsurprising since volume is considered a proxy for

investor attention. Unlike the monthly strategies, the high-frequency strategies also earn

significant positive returns within each quintile of GP/AT and dAT. The daily attention

strategies have the weakest marginal performance in quintile portfolios sorted by BE/ME.

Both short-term attention strategies earn positive excess returns in all five quintile BE/ME

portfolios. However, one quintile BE/ME portfolio for the AttnReturning(6D) strategy

and three quintile BE/ME portfolios for the AttnReturning(12D) strategy are not statis-

tically significant.

7. Alternative Hypotheses

7.1. Fundamental Risk

If stocks are sorted on some measure of fundamental risk, a portfolio of the riskiest stocks

should subsequently earn the highest returns. In these attention strategies, stocks are

sorted by changes in P/E rankings. If published P/E ratios proxy for the market’s assess-

ment of fundamental risk, excess returns of these attention strategies may simply represent

a fair risk premium. I first address this concern by isolating stocks which have moved very

little in terms of P/E, but which have moved substantially in terms of P/E rankings. For

instance, a stock which has not changed in price during a 6-day period when the market

rises by 10% is likely to rise substantially in the P/E rankings.

In any given 6-day or 12-day interval, there are stocks which don’t release earnings and have

relatively small price changes. Because these stocks are likely to be in the same portion of

the unconditional AttnReturning(6D) an AttnReturning(12D) distributions at the close

29

of day t, it is not possible to form extreme decile portfolios. Instead, I calculate the

subsequent day’s cumulative abnormal return (CAR), defined as the stock’s return net of

the MKT factor return. In other words, I estimate the stock’s alpha using a CAPM model

and a beta of 1 for all stocks. From Table 13 and Table 14, it is clear that for both the 6-day

and 12-day strategies, the CAPM alpha is very close the the excess return spread, and the

loading on the MKT factor is not very large. Thus, the CAR spread should approximate

the excess return spread.

If high-frequency P/E attention strategy returns are simply a risk premium for the fun-

damental risk associated with published P/E ratios, the extreme decile CAR spread for

stocks which have moved in the P/E rankings, but not in absolute P/E, should be close to

0. In fact, Table 18 shows that the decile CAR spread for these “constant fundamentals”

stocks is economically significant, and similar in magnitude to the nine-factor alpha for the

same strategy. This evidence supports the claim that there is attention value to moving

up or down the P/E rankings that is unrelated to fundamental risk.

If P/E attention strategies earn positive alphas because of a fundamental risk premium,

they should perform very poorly during bad economic states. Table 19 splits the 6-day

attention strategy into three additional subsamples which proxy for economic conditions.

Lakonishok et al. (1994) use three proxies to evaluate whether value strategy returns

are due to risk or mispricing: market performance, ex-post recession designation, and

subsequent quarterly real GDP growth. I use the daily return of the Fama and French

MKT factor to proxy for market performance. The recession designation depends on

whether the NBER characterizes the trading day’s calendar month as a recession month.

Finally, real US GDP growth depends on the finalized quarterly figure published by the

BEA. None of these characteristics are known in advance as you form portfolios at the close

of day t, not knowing whether day t+ 1 will be a “good” or “bad” economic state.

30

The 6-day attention strategy earns positive and significant returns in each subsample. The

days are divided into quartiles of market returns. For the quartile with the highest market

returns, the strategy earns average daily returns of 29.42 basis points, versus estimates

of 11.04, 15.12, and 13.40 basis points in the remaining quartiles. However, because of

a larger conditional MKT factor loading in this subsample, the strategy actually earns

negative alphas in the CAPM, five-factor, and nine-factor models. All three models earn

positive and significant alphas in the three worst quartiles, and each alpha is highest during

the worst quartile of daily market returns.

Likewise, the 6-day attention strategy earns higher excess returns and alphas during the

16% of the sample which the NBER designates as a recession. On recession days, the

strategy earns average daily excess returns of 27.8 basis points with corresponding CAPM,

five-factor, and nine-factor alphas of 28.15, 31.28, and 17.88 basis points. Likewise, in all

three models, the strategy earns the highest daily excess returns and alphas on days with

the lowest quartile of US real GDP growth in the following fiscal quarter. These results

are consistent with Lakonishok et al. (1994), who fail to find evidence for a risk-based

explanation of value strategy performance.

7.2. Clustering of Attention at Round-Number P/E Multiples

When calculating any of the P/E attention measures, I assume that marginal attention

is uniformly distributed across the P/E rankings. This assumption is consistent with

an uninformative prior distribution of marginal attention across the aggregate investor

base. In reality, marginal attention may cluster at obvious values, such as round numbers.

In Table 20, I deconstruct the 6-day attention strategy into two subsamples. The first

subsample (RNX) contains all stocks which cross a round-number P/E ratio. Stocks in

the long (short) portfolio include those in decile 10 (1) of AttnReturning(6D) which cross

31

above (below) 0, or which cross below (above) 10, 20, 30, 40, or 50 P/E. Stocks in the long

(short) portfolios of the second subsample are in decile 10 (1) of AttnReturning(6D), but

do not cross any of the six key round number thresholds.

Stocks which cross round number P/E ratios earn average daily excess returns of 22.2

bps and nine-factor alphas of 15.3 bps, versus 17.2 bps and 9.8 bps respectively for those

which don’t cross round numbers. Although the results for the RNX subsample are larger

in magnitude, the long-short portfolios for the non-crossing subsample still earn economi-

cally and statistically significant excess returns and nine-factor alphas. Also, by construc-

tion, the RNX subsample has larger spreads in AttnReturning(6D) values. The average

AttnReturning(6D) values for stocks in the long and short portfolios in the RNX subsam-

ple are 9.9 and -13.4, versus 3.2 and -5.0 in the non-crossing subsample.

7.3. Heteroskedasticity and Autocorrelation

Table 21 presents summary time-series regression results where t-statistics are estimated

using robust standard errors. Monthly portfolios are formed based on changes in P/E

rankings over three months. Likewise, daily portfolios are formed based on changes in P/E

rankings over several days. In addition, some of the ranking variables used to construct

factor returns also overlap formation periods. Because of overlapping formation periods,

autocorrelation in the error term is a potential concern. To address this, I estimate the co-

variance matrices for the time-series regressions using the Newey and West (1987) method

and use these covariance matrices to calculate robust standard errors and t-statistics. I

select the optimal lag structure using the Newey and West (1994) method. These adjust-

ments reduce the t-statistic by between 3% and 20% depending on the model. However,

the daily and monthly P/E attention strategies still earn positive and significant alphas in

the nine-factor model.

32

7.4. Attention

For each decile of the constant fundamentals subsample, I calculate the following day’s

relative volume. Rather than a rank-based measure of relative volume, as in Gervais et

al. (2001), I construct a continuous measure. I calculate the ratio of the share volume on

day t to the average share volume for days t − 50 . . . t − 1. Figure 5 shows that stocks in

the extreme decile portfolios command greater subsequent attention in the form of higher

relative share volumes. The bars on both histograms form a U-shape. Stocks in decile 1 on

day t have higher relative volumes on day t+ 1 than stocks in deciles 2, 3, 4, or 5. Stocks

in decile 10 on day t have higher relative volumes on day t+ 1 than stocks in deciles 6, 7,

8, or 9. Stocks which move substantially in terms of P/E ranking without changing much

in terms of P/E ratio command high abnormal trading volume.

It is also noteworthy to divide the constant fundamentals subsample into positive and

negative P/E stocks. When total earnings over the trailing four quarters is negative, the

P/E ratio field is not calculated and published. Thus, even when negative P/E stocks

move substantially in the calculated P/E rankings, they do not move substantially in the

published P/E rankings. As the top two panels of Figure 6 show, the CAR is almost

monotonically increasing across deciles for positive P/E stocks. However, for negative P/E

stocks, there is not a clear trend in CAR across deciles. This supports the hypothesis that

changes in P/E rankings directly relates to investor attention.

Next, I evaluate the relation between institutional activity and strategy performance. The

Investment Company Fact Book provides aggregate data on trading activity and flows for

equity mutual funds every year from 1984-2013 (Tables 20 and 34 on the ICFB website).

I scale these measures by the total traded dollar volume for US common stocks in the

CRSP universe. I calculate the annual performance of the AttnReturning(6D) strategy

33

by compounding daily returns. Annualized strategy returns are regressed on an intercept

and current or lagged measures of equity mutual fund activity.

Table 22 presents results of this analysis. First, annualized returns are regressed on in-

dividual measures of the same year’s purchase and sale activity. The coefficient on buy

percentage is positive and statistically significant, while the coefficient on sell percentage

is negative and statistically significant. When the individual buy and sell percentages are

replaced with a net percentage, the coefficient is positive and significant. The coefficient

estimate is 0.16, so a 1% increase in scaled net fund flow corresponds to a 16% increase

in the expected annual return of the AttnReturning(6D) strategy. Likewise, annualized

returns are regressed on the same year’s inflow and outflow activity. The coefficient esti-

mate on inflow percentage is positive and the coefficient estimate on outflow percentage is

negative, though the estimates are not significant. When the returns are regressed on the

net flow percentage, the coefficient estimate is 0.13.

The next four specifications regress the annual AttnReturning(6D) returns on the same

fund activity measures calculated over the previous year. This guarantees that fund activity

precedes trading strategy returns. For instance, large changes in fund activity due to

9/11 could not possibly impact the returns to any trading strategies from January-August

of 2001. All of the signs are the same, but the estimates and t-statistics are larger in

magnitude. The coefficients on the flow measures increase by a larger proportion than the

coefficients on the trading measures, possibly because of some delay between receiving and

investing capital.

Preliminary results on fund activity suggest a positive relation between net fund flows and

subsequent returns to short-term P/E attention strategies. This is consistent with the idea

that mutual fund managers use inflows to purchase stocks with the most attractive risk-

34

adjusted returns, but satisfy redemptions by proportional portfolio reduction or sale of the

most liquid holdings. It would be possible to measure the relation between active investor

activity and P/E attention strategy returns more precisely with flow data and trade data

on US equities for active equity mutual funds.

8. Conclusion

Value investors with limited attention are likely to use published P/E ratios to screen or sort

potential investments. If the trading activity associated with this attention is economically

meaningful, then published P/E rankings and changes in rankings can predict subsequent

returns. P/E attention strategy alphas are economically and statistically significant after

controlling for size, value, profitability, investment, short-term reversals, price momentum,

and earnings momentum. These strategies are consistently profitable in a wide variety of

subsamples and are not strongly related to fundamental risk.

Gervais et al. (2001) identify relative volume and Barber and Odean (2008) identify ex-

treme recent returns as characteristics which predict cross-sectional variation in stock re-

turns through investor attention. Variation in both relative volume and extreme recent

returns changes stock rankings in a number of highly visible variables. Relative volume

directly influences average volume, which is a variable considered in liquidity screens. Ex-

treme recent returns influence a number of these characteristics, including last price, market

capitalization, P/E ratio, and betas. Further study into the role of screening and sorting

in investor behavior is a promising avenue for understanding the relation between investor

attention and asset prices.

35

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40

Appendix A: Derivation of Expected P/E Ratios

Let t be the most recent publicly available quarter. Dropping the i subscript, a firm’strailing four-quarter E/P ratio is:

4QEPt =NIQt +NIQt−1 +NIQt−2 +NIQt−3

|PRCt| ∗ CSHOQt(1)

Given the available information set, Ω = NIQt...t−7, IBQt...t−7, the expected E/P ratioafter the next quarter’s earnings are announced is:

E[4QEPt+1|Ω] =E[NIQt+1] +NIQt +NIQt−1 +NIQt−2

|PRCt| ∗ CSHOQt(2)

By assumption, “Extraordinary Items” have a mean of 0 for every firm-quarter. Thus, Irewrite (2) as:

E[4QEPt+1|Ω] =E[IBQt+1] +NIQt +NIQt−1 +NIQt−2

|PRCt| ∗ CSHOQt(3)

Assume that the quarterly time series of IBQ (scaled by market capitalization) follows aseasonal random walk with linear trend:

δ = IBQt − IBQt−4 (4)

Using the previous eight quarters of net income, the estimate of the trend term, δ, is thesample average of the four seasonal differences:

δ =

∑IBQt,t−1,t−2,t−3 −

∑IBQt−4,t−5,t−6,t−7

4(5)

Given the realized values of IBQt−3, IBQt−7 and δ, the expected value of IBQt−3 is:

E[IBQt−3|IBQt−7, IBQt−3, δ] =IBQt−3 + IBQt−7 + δ

2(6)

Add δ to find E[IBQt+1]:

E[IBQt+1|IBQt−7, IBQt−3, δ] =IBQt−3 + IBQt−7 + 3δ

2(7)

41

Substitute (5) into (7):

E[IBQt+1|Ω] =3∑IBQt,t−1,t−2 + 4IBQt−3 − 3

∑IBQt−4,t−5,t−6 − 2IBQt−7

8(8)

Finally, substitute (8) into (3):

E[4QEPt+1|Ω] =3∑

IBQt,t−1,t−2 + 4IBQt−3 − 3∑

IBQt−4,t−5,t−6 − 2IBQt−7 + 8NIQt + 8NIQt−1 + 8NIQt−2

8|PRCt| ∗ CSHOQt

(9)

42

Appendix B: Evidence of Clustering at Round Number Values

Author(s) Year Asset Class or EnvironmentYule 1927 Survey data

Niederhoffer 1966 US Equities

Stevenson and Bear 1970 Commodity Futures

Harris 1991 US Equities

Christie and Schultz 1994 US Equities

Ball et al 1995 Gold

Grossman et al. 1995 London Stock Exchange Equities

Benartzi and Thaler 2001 Asset Allocation

Kandel et al. 2001 Israeli IPOs

Osler 2003 Foreign Exchange

Thomas and Morowitz 2005 Retail Prices

Baker et al. 2012 M&A target prices

Olsen 2013 Danish tax rates

43

Table 1: S&P 400 Stocks Ranked by Published P/E Ratio This table shows the 20 stocksin the S&P 400 index with the lowest positive P/E ratio, ranked in ascending order, after theclose of trading on August 31, 2015 and November 30, 2015. P/E ratios are from Bloomberg andare computed using the most recent closing price and the sum of the four most recently reportedquarterly values of earnings per share. Stocks in the S&P 400 consists of US common stocks withmarket capitalizations ranked between 100-500. These are considered “mid cap” stocks. Stockswhich are underlined in the November column are not among the 20 stocks with the lowest positiveP/E ratio at the end of August.

Ranking 31-Aug-2015 30-Nov-20151 ATW ATW2 RDC DNR3 X NE4 NE DAN5 DNR JOY6 CRC RDC7 RE TRN8 TRN TGI9 DAN CYH

10 WNR CAA11 TCO NSR12 RNR RE13 TGI WNR14 NSR TEX15 OA RCII16 JOY TCO17 ENH RNR18 AVT ENH19 CSC ARW20 ARW AVT

44

Table 2: Summary Statistics on Published P/E Ratios, 1974-2013 For all US commonstocks with four distinct quarterly values of Net Income (Compustat field NIQ) in four consecu-tive fiscal quarters, and valid CRSP monthly returns, the Trailing Four Quarter E/P (4QEP) is

calculated as: 4QEPi,t =NIQi,t+NIQi,t−1+NIQi,t−2+NIQi,t−3

|PRCi,t|∗CSHOQi,t. The full sample is divided into ten

subsamples. For each subsample, the values in the second column (N Valid 4QEP) are the aver-age monthly number of US common stocks with valid 4QEPi,t. The values in the third column(N Valid 8QEP) are the average monthly number of US common stocks with eight consecutivequarters of net income. The values in the fourth column (% Positive 4QEP) are the percentagesof valid 4QEPi,t which are positive. The values in the fifth column (Median E/P) are the time-series averages of cross-sectional median values among stocks with valid 4QEPi,t. The values in thesixth column (%1Ann/3Mo) are the percentages of observations with exactly one quarterly earningsannouncement in the previous three months.

Subsample N Valid 4QEP N Valid 8QEP % Positive 4QEP Median E/P %1Ann/3Mo1974-1977 2166 1831 91 0.140 831978-1981 2198 2073 92 0.133 851982-1985 2616 2116 84 0.085 831986-1989 3268 2649 77 0.059 811990-1993 3562 2941 73 0.049 821994-1997 4872 3817 75 0.047 831998-2001 5467 4489 67 0.038 852002-2005 4728 4468 65 0.032 862006-2009 4206 3872 68 0.035 862010-2013 3620 3458 70 0.040 88

45

Table 3: Fama and MacBeth Monthly Regressions with Controls Only, 1974-2013 Inthe cross-sectional (first-stage) regression specifications, the dependent variables are percentagemonthly returns for US common stocks. The controls for size [log(ME)], value [log(BE/ME)],profitability (GP/AT), and investment (dAT) are calculated based on calendar year t financialstatements and assumed known at the end of June in year t + 1. Controls for price momentum[R(12,1), the return from the end of month t−12 to the end of month t−1] and short-term reversals[R(1,0), the return from the end of month t− 1 to the end of month t], are assumed known at theend of month t. The control for earnings momentum is standardized unexplained earnings (SUE),

defined as SUE = IBQt−IBQt−4

σIBQt−1...t−8, where IBQ is Compustat quarterly income before extraordinary

items. Quarterly earnings needed to calculate SUE are assumed known as of the reporting date’smonth end based on Compustat field RDQ. SUEt refers to SUE in the most recent quarter, whileSUEt−3 refers to SUE in the fourth most recent quarter. All independent variables are winsorizedat the 99% and 1% levels. T-statistics are in parentheses.

Intercept 1.89 1.55 1.13 2.71 0.65 1.33 1.39 1.43 2.37(4.85) (6.14) (3.73) (9.32) (1.77) (5.11) (5.17) (5.37) (4.84)

log(ME) -0.14 -0.12(-3.10) (-2.60)

log(BE/ME) 0.45 0.30(6.12) (4.12)

GP/AT 0.76 0.66(4.93) (4.66)

dAT -1.12 -0.75(-9.10) (-7.68)

R(12,1) 0.50 0.16(2.37) (0.90)

R(1,0) -4.48 -6.13(-8.30) (-13.63)

SUEt 0.17 0.24(11.91) (20.96)

SUEt−3 -0.01 -0.03(-0.47) (-3.40)

46

Table 4: Fama and MacBeth Monthly Regressions with Ex-Post P/E Attention Vari-ables, 1974-2013 For all US common stocks with four distinct quarterly values of Net Income(Compustat field NIQ) in four consecutive fiscal quarters, and valid CRSP monthly returns, the

Trailing Four Quarter E/P (4QEP) is calculated as: 4QEPi,t =NIQi,t+NIQi,t−1+NIQi,t−2+NIQi,t−3

|PRCi,t|∗CSHOQi,t.

At the end of each month, all firms are assigned to percentiles of 4QEPi,t. AttnNew is the stock’spercentile at the end of month t. AttnReturning is the change in the stock’s percentile from the endof month t− 3 to the end of month t. AttnTotal is the average of AttnNew and AttnReturning.In the cross-sectional (first-stage) regression specifications, the dependent variables are percentagemonthly returns for US common stocks. The controls for size [log(ME)], value [log(BE/ME)],profitability (GP/AT), and investment (dAT) are calculated based on calendar year t financialstatements and assumed known at the end of June in year t + 1. Controls for price momentum[R(12,1), the return from the end of month t − 12 to the end of month t − 1] and short-termreversals [R(1,0), the return from the end of month t − 1 to the end of month t], are assumedknown at the end of month t. The control for earnings momentum is standardized unexplainedearnings (SUE), defined as SUE = IBQt−IBQt−4

σIBQt−1...t−8, where IBQ is Compustat quarterly income

before extraordinary items. Quarterly earnings needed to calculate SUE are assumed known as ofthe reporting date’s month end based on Compustat field RDQ. SUEt refers to SUE in the mostrecent quarter, while SUEt−3 refers to SUE in the fourth most recent quarter. All independentvariables are winsorized at the 99% and 1% levels. T-statistics are in parentheses.

Intercept 2.26 2.35 2.27 2.25(4.37) (4.84) (4.38) (4.43)

AttnNew 0.72 0.61(3.78) (3.00)

AttnReturning 1.3 1.0(8.95) (5.64)

AttnTotal 0.68(5.06)

log(ME) -0.14 -0.12 -0.13 -0.13(-3.35) (-2.66) (-3.29) (-3.22)

log(BE/ME) 0.21 0.30 0.22 0.22(3.27) (4.16) (3.41) (3.31)

GP/AT 0.59 0.68 0.61 0.59(4.29) (4.75) (4.46) (4.25)

dAT -0.81 -0.73 -0.79 -0.80(-8.43) (-7.31) (-8.22) (-8.19)

R(12,1) 0.12 0.18 0.14 0.15(0.70) (1.00) (0.81) (0.84)

R(1,0) -6.12 -5.92 -6.03 -5.96(-13.88) (-13.40) (-13.92) (-13.47)

SUEt 0.23 0.20 0.20 0.21(19.97) (16.85) (17.14) (17.56)

SUEt−3 -0.05 -0.03 -0.05 -0.05(-6.66) (-3.39) (-6.04) (-6.31)

47

Table 5: Monthly Portfolio Time-Series Regressions with Ex-Post P/E AttentionVariables, 1974-2013 At the end of each month, stocks are sorted into ten deciles based onAttnTotal, the average of 4QEPi,t percentile at the end of month t (AttnNew) and change in4QEPi,t percentile from the end of month t − 3 to the end of month t (AttnReturning). Decileassignments are based on NYSE breakpoints. For each monthly observation in these time-seriesregressions, the dependent variable is the percentage return of a value-weighted portfolio whichis long every stock in decile 10 and short every stock in decile 1. The independent variablesare a monthly time series of intercepts and monthly returns of one or more factor mimickingportfolios. The monthly time series for MKT, SMB, HML, UMD, RMW, CMA, and STR areall available on Ken French’s website. I construct factor mimicking portfolios for SUEt andSUEt−3 using 2x3 portfolio sorts on size and SUE analogous to HML construction in Fama

and French (1993). SUE is standardized unexplained earnings, defined as SUE = IBQt−IBQt−4

σIBQt−1...t−8,

where IBQ is Compustat quarterly income before extraordinary items. Quarterly earnings neededto calculate SUE are assumed known as of the reporting date’s month end based on Compustatfield RDQ. SUEt is a firm’s SUE in the most recent quarter, and SUEt−3 is a firm’s SUE inthe fourth most recent quarter. The CAPM model includes MKT returns as an independentvariable. The three-factor model includes MKT, SMB, and HML. The four-factor model includesMKT, SMB, HML, and UMD. The five-factor model includes MKT, SMB, HML, RMW, andCMA. The nine-factor model augments the five-factor model with UMD, STR, SUEt, and SUEt−3.

Model CAPM Fama-French 3F Carhart 4F Fama-French 5F 9FLong-Short Return 1.01 1.01 1.01 1.01 1.01

(5.07) (5.07) (5.07) (5.07) (5.07)Sharpe Ratio 0.79 0.79 0.79 0.79 0.79Alpha 1.13 1.06 0.98 0.88 0.63

(5.85) (5.47) (5.00) (4.67) (3.33)MKT -0.24 -0.16 -0.15 -0.15 -0.19

(-5.77) (-3.66) (-3.24) (-3.40) (-4.52)SMB -0.21 -0.21 -0.01 0.01

(-3.34) (-3.34) (-0.02) (0.22)HML 0.19 0.21 0.28 0.45

(2.80) (3.12) (3.31) (5.22)UMD 0.08 -0.02

(1.79) (-0.47)RMW 0.68 0.40

(7.54) (4.18)CMA -0.25 -0.30

(-1.91) (-2.29)STR 0.16

(3.00)SUEt 0.48

(3.95)SUEt−3 0.36

(2.76)

48

Table 6: Sensitivity Analysis, Monthly Portfolio Time-Series Regressions withEx-Post P/E Attention Variables, 1974-2013 At the end of each month, stocks are sortedinto ten deciles based on the weighted average of 4QEPi,t percentile at the end of month t(wnew) and change in 4QEPi,t percentile from the end of month t − 3 to the end of month t(wreturning = 1 − wnew). Decile assignments are based on NYSE breakpoints. For each monthlyobservation in these time-series regressions, the dependent variable is the percentage return of avalue-weighted portfolio which is long every stock in decile 10 and short every stock in decile 1. Theindependent variables are a monthly time series of intercepts and monthly returns of one or morefactor mimicking portfolios. The monthly time series for MKT, SMB, HML, UMD, RMW, CMA,and STR are all available on Ken French’s website. I construct factor mimicking portfolios for SUEtand SUEt−3 using 2x3 portfolio sorts on size and SUE analogous to HML construction in Fama

and French (1993). SUE is standardized unexplained earnings, defined as SUE = IBQt−IBQt−4

σIBQt−1...t−8,

where IBQ is Compustat quarterly income before extraordinary items. Quarterly earnings neededto calculate SUE are assumed known as of the reporting date’s month end based on Compustatfield RDQ. SUEt is a firm’s SUE in the most recent quarter, and SUEt−3 is a firm’s SUE inthe fourth most recent quarter. The five-factor model includes MKT, SMB, HML, RMW, andCMA. The nine-factor model augments the five-factor model with UMD, STR, SUEt, and SUEt−3.

wreturning Long-Short Return 5F Alpha 9F Alpha0 0.82 0.52 0.32

(3.22) (2.38) (1.48)0.1 0.94 0.64 0.44

(3.84) (3.00) (2.09)0.2 0.99 0.76 0.60

(4.31) (3.78) (2.97)0.3 0.97 0.74 0.57

(4.45) (3.89) (2.98)0.4 1.08 0.90 0.72

(5.25) (4.81) (3.84)0.5 1.01 0.88 0.63

(5.07) (4.67) (3.33)0.6 0.86 0.75 0.40

(4.67) (4.15) (2.30)0.7 0.82 0.75 0.42

(4.80) (4.23) (2.48)0.8 0.84 0.74 0.39

(5.23) (4.36) (2.53)0.9 0.71 0.60 0.22

(4.57) (3.67) (1.51)1 0.58 0.53 0.12

(3.57) (3.11) (0.77)

49

Table 7: Persistence of Monthly Ex-Post P/E Attention Portfolio Returns 1974-2013At the end of each month, stocks are sorted into ten deciles based on the average of 4QEPi,tpercentile at the end of month t and change in 4QEPi,t percentile from the end of month t − 3to the end of month t. Decile assignments are based on NYSE breakpoints. This table presentsmonthly and cumulative percent returns for value-weighted portfolios which are long every stockin decile 10 and short every stock in decile 1 for the first 15 months following portfolio formation.T-statistics for monthly returns are in parentheses.

Monthly CumulativeMonth Return t Return1 1.01 (5.07) 1.012 0.61 (3.20) 1.633 0.30 (1.67) 1.934 0.46 (2.47) 2.405 0.44 (2.25) 2.856 0.26 (1.35) 3.127 0.18 (0.94) 3.308 0.17 (0.89) 3.489 0.02 (0.08) 3.5010 0.09 (0.48) 3.5911 0.05 (0.23) 3.6412 -0.08 (-0.43) 3.5613 -0.08 (-0.39) 3.4814 -0.01 (-0.04) 3.4715 0.17 (0.90) 3.64

50

Table 8: Subsample Analysis by Date, Monthly Ex-Post Portfolio Time-SeriesRegressions, 1974-2013 At the end of each month, stocks are sorted into ten deciles based onthe average of 4QEPi,t percentile at the end of month t and change in 4QEPi,t percentile from theend of month t− 3 to the end of month t. Decile assignments are based on NYSE breakpoints. Foreach monthly observation in these time series regressions, the dependent variable is the percentagereturn of a value-weighted portfolio which is long every stock in decile 10 and short every stock indecile 1. The independent variables are a monthly time series of intercepts and monthly returns ofone or more factor mimicking portfolios. The monthly time series for MKT, SMB, HML, UMD,RMW, CMA, and STR are all available on Ken French’s website. I construct factor mimickingportfolios for SUEt and SUEt−3 using 2x3 portfolio sorts on size and SUE analogous to HMLconstruction in Fama and French (1993). SUE is standardized unexplained earnings, defined as

SUE = IBQt−IBQt−4

σIBQt−1...t−8, where IBQ is Compustat quarterly income before extraordinary items.

Quarterly earnings needed to calculate SUE are assumed known as of the reporting date’s monthend based on Compustat field RDQ. SUEt is a firm’s SUE in the most recent quarter, and SUEt−3is a firm’s SUE in the fourth most recent quarter. The CAPM alpha controls for MKT. Thefive-factor alpha controls for MKT, SMB, HML, RMW, and CMA. Finally, the nine-factor alphaalso controls for UMD, STR, SUEt and SUEt−3.

Time Period Long-Short Return CAPM Alpha Five-Factor Alpha Nine-Factor Alpha1974-2013 1.01 1.13 0.88 0.63

(5.07) (5.85) (4.67) (3.33)1974-1983 0.72 0.82 0.96 0.64

(2.19) (2.65) (2.73) (1.97)1984-1993 1.07 1.06 1.06 0.65

(3.50) (3.41) (3.22) (1.38)1994-2003 1.37 1.68 0.95 0.66

(2.47) (3.30) (2.03) (1.38)2004-2013 0.82 0.99 0.81 0.65

(2.17) (2.73) (2.11) (1.67)

51

Table 9: Monthly Portfolio Time-Series Regressions: Double Sorts, 1974-2013Firm-month observations are assigned to five quintiles based on the most recent available value ofeach sorting variable. Independently, firm-month observations are assigned to five quintiles basedon the average of 4QEPi,t percentile at the end of month t and change in 4QEPi,t percentilefrom the end of month t − 3 to the end of month t. All quintile assignments are based on NYSEbreakpoints. Within each quintile of each sorting variable, this table reports average monthlyreturns of value-weighted portfolios which are long every stock in quintile 5 and short every stockin quintile 1. T-statistics are in parentheses.

1 2 3 4 5ME 1.22 1.11 0.91 0.80 0.74

(6.66) (5.11) (4.28) (3.75) (3.59)BE/ME 0.41 0.14 -0.05 0.24 0.25

(1.86) (0.67) (-0.25) (1.10) (1.27)GP/AT 0.24 0.17 0.40 0.65 0.53

(1.00) (0.85) (1.67) (2.53) (2.20)dAT 0.22 0.31 0.43 0.28 0.71

(1.03) (1.46) (2.00) (1.27) (3.12)R(12,1) 1.35 1.08 0.83 0.72 0.47

(5.99) (5.54) (4.00) (3.56) (2.08)R(1,0) 1.15 0.66 0.85 0.68 0.60

(4.65) (3.19) (3.78) (3.21) (2.61)SUEt 0.91 0.71 0.65 0.66 0.39

(4.21) (3.02) (2.45) (2.30) (1.45)SUEt−3 1.02 1.10 0.76 0.83 0.60

(4.39) (4.78) (2.90) (3.16) (2.51)

52

Table 10: Fama and MacBeth Monthly Regressions with Ex-Ante P/E AttentionVariables, 1974-2013 In the SRW+Trend specification, the expected trailing four quarter E/P(E[4QEPi,t+1]) is calculated by modeling the quarterly IBQ time series as a seasonal random walkwith trend (See Appendix A for details). In the EP3QPct specification, E[4QEPi,t+1] is calculatedbased on the assumption that every stock has the same expected net income as a proportionof its market capitalization. At the end of each month, all firms are assigned to percentiles ofE[4QEPi,t+1]. AttnNew is the stock’s percentile at the end of month t. AttnReturning is thechange in the stock’s percentile from the end of month t − 3 to the end of month t. AttnTotalis the average of AttnNew and AttnReturning. In the cross-sectional (first-stage) regressionspecifications, the dependent variables are percentage monthly returns for US common stocks.The controls for size [log(ME)], value [log(BE/ME)], profitability (GP/AT), and investment (dAT)are calculated based on calendar year t financial statements and assumed known at the end ofJune in year t + 1. Controls for price momentum [R(12,1), the return from the end of montht − 12 to the end of month t − 1] and short-term reversals [R(1,0), the return from the end ofmonth t − 1 to the end of month t], are assumed known at the end of month t. The control for

earnings momentum is standardized unexplained earnings (SUE), defined as SUE = IBQt−IBQt−4

σIBQt−1...t−8,

where IBQ is Compustat quarterly income before extraordinary items. Quarterly earnings neededto calculate SUE are assumed known as of the reporting date’s month end based on Compustatfield RDQ. SUEt refers to SUE in the most recent quarter, while SUEt−3 refers to SUE in thefourth most recent quarter. All independent variables are winsorized at the 99% and 1% levels.T-statistics are in parentheses.

Model SRW+Trend SRW+Trend EP3QPct EP3QPctIntercept 2.24 2.22 2.25 2.24

(4.33) (4.42) (4.35) (4.47)AttnNew 0.73 0.74

(4.18) (3.70)AttnReturning 0.77 0.75

(5.42) (5.40)AttnTotal 0.75 0.75

(7.92) (6.86)log(ME) -0.13 -0.14 -0.14 -0.14

(-3.20) (-3.14) (-3.36) (-3.28)log(BE/ME) 0.23 0.24 0.22 0.23

(3.47) (3.46) (3.35) (3.31)GP/AT 0.61 0.60 0.60 0.59

(4.42) (4.24) (4.35) (4.17)dAT -0.77 -0.76 -0.79 -0.79

(-8.09) (-7.89) (-8.27) (-8.10)R(12,1) 0.09 0.11 0.12 0.13

(0.51) (0.62) (0.68) (0.77)R(1,0) -6.13 -6.04 -6.08 -5.97

(-13.98) (-13.60) (-13.97) (-13.50)SUEt 0.18 0.18 0.20 0.20

(15.81) (15.57) (17.52) (16.92)SUEt−3 -0.04 -0.04 -0.03 -0.03

(-5.20) (-4.99) (-3.63) (-3.39)

53

Table 11: Monthly Portfolio Time-Series Regressions with Ex-Ante P/E AttentionVariables, 1974-2013 At the end of each month, stocks are sorted into ten deciles basedon the average of E[4QEPi,t+1] percentile at the end of month t and change in E[4QEPi,t+1]percentile from the end of month t − 3 to the end of month t. In the SRW+Trend specification,the expected trailing four quarter E/P (E[4QEPi,t+1]) is calculated by modeling the quarterlyIBQ time series as a seasonal random walk with trend (See Appendix A for details). In theEP3QPct specification, E[4QEPi,t+1] is calculated based on the assumption that every stock hasthe same expected net income as a proportion of its market capitalization. For each monthlyobservation in these time series regressions, the dependent variable is the percentage return of avalue-weighted portfolio which is long every stock in decile 10 and short every stock in decile 1.Decile assignments are based on NYSE breakpoints. The independent variables are a monthlytime series of intercepts and monthly returns of one or more factor mimicking portfolios. Themonthly time series for MKT, SMB, HML, UMD, RMW, CMA, and STR are all available onKen French’s website. I construct factor mimicking portfolios for SUEt and SUEt−3 using 2x3portfolio sorts on size and SUE analogous to HML construction in Fama and French (1993). SUE

is standardized unexplained earnings, defined as SUE = IBQt−IBQt−4

σIBQt−1...t−8, where IBQ is Compustat

quarterly income before extraordinary items. Quarterly earnings needed to calculate SUE areassumed known as of the reporting date’s month end based on Compustat field RDQ. SUEt is afirm’s SUE in the most recent quarter, and SUEt−3 is a firm’s SUE in the fourth most recent quarter.

Model SRW+Trend EP3QPctLong-Short Return 0.99 0.95

(5.72) (5.32)Sharpe Ratio 0.89 0.849F Alpha 0.40 0.46

(2.51) (2.74)MKT -0.11 -0.14

(-3.24) (-3.72)SMB 0.03 0.01

(0.51) (0.25)HML 0.36 0.47

(4.92) (6.07)UMD 0.07 0.10

(1.53) (2.12)RMW 0.19 0.24

(2.36) (2.80)CMA -0.11 -0.22

(-1.01) (-1.85)STR 0.20 0.14

(4.25) (2.83)SUEt 0.68 0.45

(6.64) (4.16)SUEt−3 0.27 0.28

(2.49) (2.37)

54

Table 12: Fama and MacBeth Daily Regressions, 1974-2013 For all US common stockswith four distinct quarterly values of Net Income (Compustat field NIQ) in four consecutive fiscalquarters, and valid CRSP monthly returns, the trailing four quarter E/P (4QEP) is calculated

as: 4QEPi,t =NIQi,t+NIQi,t−1+NIQi,t−2+NIQi,t−3

|PRCi,t|∗CSHOQi,t. At the end of each trading day, firms are

assigned to percentiles of 4QEPi,t. Because of uncertainty about what time of day earnings arereleased, 4QEPi,t is considered unavailable on the trading day of the quarterly reporting date,based on Compustat field RDQ. In the cross-sectional (first-stage) regression specifications, thedependent variables are daily returns in basis points for US common stocks. AttnReturning(6D)(AttnReturning(12D)) is the change in percentile from the close of day t− 6 (t− 12) to the closeof day t. Other controls are the most recent daily stock return (1DRet), and the most recent

quarterly standardized unexplained earnings (SUEt), defined as SUEt = IBQt−IBQt−4

σIBQt−1...t−8, where

IBQ is Compustat quarterly income before extraordinary items. Quarterly earnings needed tocalculate SUE are assumed known as of the close of the first trading day following the quarterlyearnings release, based on Compustat field RDQ. 1DRet and SUEt are winsorized at the 99% and1% levels. T-statistics are in parentheses.

Intercept 8.8 8.8 7.9 8.7 8.3 8.2(9.32) (9.30) (9.07) (9.24) (8.87) (8.85)

AttnReturning(6D) 1.85 0.60(46.16) (16.82)

AttnReturning(12D) 1.05 0.45(41.75) (19.98)

1DRet -11.11 -13.57 -13.60(-91.88) (-128.08) (-128.49)

SUEt 0.69 0.74 0.68(14.63) (15.54) (14.35)

55

Table 13: Daily Portfolio Time-Series Regressions, Decile Sorts on AttnReturning(6D),1974-2013 At the end of each day, stocks are sorted into ten deciles based on the change in 4QEPi,tpercentile from the end of day t−6 to the end of day t. For each daily observation in these time seriesregressions, the dependent variable is the return in basis points of a value-weighted portfolio whichis long every stock in decile 10 and short every stock in decile 1. Decile assignments are based onNYSE breakpoints. Because of uncertainty about what time of day earnings are released, 4QEPi,tis considered unavailable on the trading day of the quarterly reporting date, based on Compustatfield RDQ. The independent variables are a daily time series of intercepts and daily returns of oneor more factor mimicking portfolios. The daily time series for MKT, SMB, HML, UMD, and STRare all available on Ken French’s website. I construct factor mimicking portfolios for GP/AT , dAT ,SUEt and SUEt−3 using 2x3 portfolio sorts on size and GP/AT , dAT , or SUE analogous to HMLconstruction in Fama and French (1993). Gross profitability (GP/AT ) and asset growth (dAT ) arecalculated based on calendar year t financial statements and assumed known at the end of June inyear t+ 1. SUE is standardized unexplained earnings, defined as SUE = IBQt−IBQt−4

σIBQt−1...t−8, where IBQ

is Compustat quarterly income before extraordinary items. Quarterly earnings needed to calculateSUE are assumed known as of the end of the first trading day following the earnings release datebased on Compustat field RDQ. SUEt is a firm’s SUE in the most recent quarter, and SUEt−3 isa firm’s SUE in the fourth most recent quarter.

Fama-French Carhart Fama-FrenchModel CAPM 3F 4F 5F 9F 2FLong-Short Return 16.99 16.99 16.99 16.99 16.99 16.99

(18.87) (18.87) (18.87) (18.87) (18.87) (18.87)Sharpe Ratio 2.91 2.91 2.91 2.91 2.91 2.91Alpha 16.7 17.1 16.6 17.6 9.3 9.2

(18.71) (19.23) (18.69) (19.83) (11.68) (11.72)MKT 0.12 0.09 0.11 0.08 -0.01

(14.27) (10.35) (12.25) (8.72) (-0.91)SMB -0.09 -0.09 -0.10 -0.10

(-5.07) (-5.18) (-5.92) (-6.76)HML -0.15 -0.11 -0.20 0.03

(-8.41) (-5.55) (-9.69) (1.40)UMD 0.12 0.08

(9.64) (6.33)GP/AT -0.13 -0.01

(-4.83) (-0.29)dAT -0.01 -0.03

(-0.11) (-1.46)STR 0.63 0.62

(56.25) (59.87)SUEt 0.29 0.38

(10.92) (18.87)SUEt−3 0.02

(0.74)

56

Table 14: Daily Portfolio Time-Series Regressions, Decile Sorts on AttnReturn-ing(12D), 1974-2013 At the end of each day, stocks are sorted into ten deciles based on thechange in 4QEPi,t percentile from the end of day t − 12 to the end of day t. For each daily ob-servation in these time series regressions, the dependent variable is the return in basis points of avalue-weighted portfolio which is long every stock in decile 10 and short every stock in decile 1.Decile assignments are based on NYSE breakpoints. Because of uncertainty about what time ofday earnings are released, 4QEPi,t is considered unavailable on the trading day of the quarterlyreporting date, based on Compustat field RDQ. The independent variables are a daily time seriesof intercepts and daily returns of one or more factor mimicking portfolios. The daily time seriesfor MKT, SMB, HML, UMD, and STR are all available on Ken French’s website. I constructfactor mimicking portfolios for GP/AT , dAT , SUEt and SUEt−3 using 2x3 portfolio sorts on sizeand GP/AT , dAT , or SUE analogous to HML construction in Fama and French (1993). Grossprofitability (GP/AT ) and asset growth (dAT ) are calculated based on calendar year t financialstatements and assumed known at the end of June in year t+ 1. SUE is standardized unexplainedearnings, defined as SUE = IBQt−IBQt−4

σIBQt−1...t−8, where IBQ is Compustat quarterly income before ex-

traordinary items. Quarterly earnings needed to calculate SUE are assumed known as of the endof the first trading day following the earnings release date based on Compustat field RDQ. SUEtis a firm’s SUE in the most recent quarter, and SUEt−3 is a firm’s SUE in the fourth most recentquarter.

Model CAPM Fama-French 3F Carhart 4F Fama-French 5F 9F 2FExcess Return 15.30 15.30 15.30 15.30 15.30 15.30

(17.39) (17.39) (17.39) (17.39) (17.39) (17.39)Sharpe Ratio 2.68 2.68 2.68 2.68 2.68 2.68Alpha 14.9 15.5 15.1 16.1 6.1 6.1

(17.22) (17.96) (17.48) (18.55) (8.62) (8.73)MKT 0.14 0.11 0.13 0.09 -0.02

(17.56) (12.76) (14.29) (10.45) (-2.41)SMB -0.05 -0.05 -0.07 -0.07

(-3.09) (-3.17) (-3.90) (-5.09)HML -0.22 -0.18 -0.27 -0.02

(-12.44) (-9.81) (-13.27) (-1.00)UMD 0.10 0.07

(8.24) (5.70)GP/AT -0.15 0.02

(-6.04) (1.00)dAT 0.04 -0.02

(1.68) (-0.95)STR 0.76 0.75

(76.83) (81.82)SUEt 0.31 0.39

(13.31) (21.86)SUEt−3 -0.01

(-0.42)

57

Table 15: Daily Portfolio Time-Series Regressions with Varying Formation Periods,Decile Sorts, 1974-2013 At the end of each day, stocks are sorted into ten deciles based on thechange in 4QEPi,t percentile from the end of day t − N to the end of day t. Decile assignmentsare based on NYSE breakpoints. Because of uncertainty about what time of day earnings arereleased, 4QEPi,t is considered unavailable on the trading day of the quarterly reporting date,based on Compustat field RDQ. For each daily observation in these time-series regressions, thedependent variable is the return in basis points of a value-weighted portfolio which is long everystock in decile 10 and short every stock in decile 1. The independent variables are a daily timeseries of intercepts and daily returns of two factor-mimicking portfolios. The daily time seriesfor STR is available on Ken French’s website and represents returns to a short-term (20-day)reversals strategy. I construct the factor-mimicking portfolio for SUEt using 2x3 portfolio sorts onsize and SUE analogous to HML construction in Fama and French (1993). SUE is standardized

unexplained earnings, defined as SUE = IBQt−IBQt−4

σIBQt−1...t−8, where IBQ is Compustat quarterly income

before extraordinary items. Quarterly earnings needed to calculate SUE are assumed known asof the end of the first trading day following the earnings release date based on Compustat field RDQ.

Formation Period (N) Excess Return T-Statistic 2F Alpha T-Statistic1 3.55 3.41 0.19 0.182 8.18 9.02 3.31 3.803 13.03 14.77 7.44 9.034 14.99 16.48 8.50 10.245 16.15 17.65 8.73 10.766 16.99 18.87 9.17 11.727 17.32 19.20 8.81 11.538 17.00 19.02 8.45 11.399 16.50 18.64 7.72 10.5710 16.07 17.98 6.76 9.3211 16.07 17.93 6.69 9.4612 15.30 17.39 6.07 8.7313 14.66 16.64 4.88 7.2414 13.71 15.61 3.74 5.6115 12.91 14.85 3.33 5.0216 12.81 14.79 3.02 4.6417 12.60 14.63 2.75 4.3118 12.46 14.35 2.46 3.8719 12.23 14.11 2.08 3.2920 12.07 13.94 1.80 2.8630 9.34 11.20 0.29 0.4460 7.66 9.79 0.24 0.3490 6.05 7.81 -0.64 -0.90120 5.87 7.61 -0.07 -0.09

58

Table 16: Subsample Analysis by Date, Daily Portfolio Time-Series Regressions, 1974-2013 At the end of each day, stocks are sorted into ten deciles based on the change in 4QEPi,tpercentile from the end of day t−6 to the end of day t (AttnReturning(6D)). Independently, at theend of each day, stocks are sorted into ten deciles based on the change in 4QEPi,t percentile fromthe end of day t− 12 to the end of day t (AttnReturning(12D)). Decile assignments are based onNYSE breakpoints. Because of uncertainty about what time of day earnings are released, 4QEPi,tis considered unavailable on the trading day of the quarterly reporting date, based on Compustatfield RDQ. For each daily observation in these time series regressions, the dependent variable isthe return in basis points of a value-weighted portfolio which is long every stock in decile 10 andshort every stock in decile 1. The independent variables are a daily time series of intercepts anddaily returns of one or more factor-mimicking portfolios. The daily time series for MKT, SMB,HML, UMD, and STR are all available on Ken French’s website. I construct factor-mimickingportfolios for GP/AT , dAT , SUEt and SUEt−3 using 2x3 portfolio sorts on size and GP/AT ,dAT , or SUE analogous to HML construction in Fama and French (1993). Gross profitability(GP/AT ) and asset growth (dAT ) are calculated based on calendar year t financial statements andassumed known at the end of June in year t+1. SUE is standardized unexplained earnings, definedas SUE = IBQt−IBQt−4

σIBQt−1...t−8, where IBQ is Compustat quarterly income before extraordinary items.

Quarterly earnings needed to calculate SUE are assumed known as of the end of the first tradingday following the earnings release date based on Compustat field RDQ. SUEt is a firm’s SUE in themost recent quarter, and SUEt−3 is a firm’s SUE in the fourth most recent quarter. The CAPMmodel only controls for MKT. The five-factor model includes MKT, SMB, HML, GP/AT , and dAT .The nine-factor model augments the five-factor model with UMD, STR, SUEt and SUEt−3.

Time Period Excess Return CAPM Alpha Five-Factor Alpha Nine-Factor AlphaAttnReturning(6D)1974-2013 17.0 16.7 17.6 9.3

(18.87) (18.71) (19.83) (11.68)1974-1983 15.9 15.8 16.5 7.7

(11.07) (11.03) (11.39) (5.97)1984-1993 20.5 19.9 20.4 7.6

(14.26) (14.21) (14.46) (6.23)1994-2003 20.5 20.0 19.7 9.9

(9.19) (9.09) (8.83) (4.79)2004-2013 11.7 11.4 13.1 9.1

(5.85) (5.74) (6.74) (5.41)AttnReturning(12D)1974-2013 15.3 14.9 16.1 6.1

(17.39) (17.22) (18.55) (8.62)1974-1983 18.8 18.6 19.6 9.5

(12.52) (12.49) (13.04) (7.60)1984-1993 16.5 15.8 16.4 3.8

(12.17) (12.10) (12.59) (3.54)1994-2003 16.5 15.9 16.4 3.5

(7.68) (7.56) (7.69) (2.00)2004-2013 8.8 8.5 10.1 4.9

(4.43) (4.30) (5.24) (3.28)

59

Table 17: Daily Portfolio Time-Series Regressions: Double Sorts, 1974-2013 Firm-dayobservations are assigned to five quintiles based on the most recent available value of each sorting variable.RV is relative volume, as determined in Gervais et al. (2001). For example, stocks in RV quintile 5have share volumes which rank among the 10 highest of the previous 50 days. Independently, firm-dayobservations are assigned to five quintiles based on both the change in 4QEPi,t percentile from the end ofday t− 6 to the end of day t (AttnReturning(6D)) and the change in 4QEPi,t percentile from the end ofday t− 12 to the end of day t (AttnReturning(12D)). Quintile portfolio assignments are based on NYSEbreakpoints. Within each quintile of each sorting variable, this table reports time-series monthly returnsof value-weighted portfolios which are long every stock in quintile 5 and short every stock in quintile 1 ofthe 6DChg or 12DChg measure. T-statistics are in parentheses.

AttnReturning(6D)

1 2 3 4 5

ME 46 49 31 15 9.1(29.32) (56.41) (48.12) (26.46) (12.41)

BE/ME 3.2 6.4 5.7 6.6 11(0.94) (2.48) (2.24) (2.19) (2.88)

GP/AT 7.4 8.5 9.9 13 14(5.59) (9.44) (10.51) (14.01) (13.90)

dAT 8.8 9.9 10 11 12(5.86) (11.14) (12.43) (12.72) (11.71)

R(12,1) 11 12 13 12 11(7.03) (12.68) (14.89) (15.05) (10.74)

R(1,0) 10 9.2 9.9 9.8 14(7.00) (9.71) (8.06) (12.01) (13.88)

SUEt 10 9.8 12 12 10(9.75) (10.33) (12.77) (13.60) (10.69)

SUEt−3 11 11 11 12 10(10.20) (11.16) (11.82) (12.73) (10.93)

RV 9.5 9.1 10.0 11 14(10.13) (10.44) (11.09) (11.46) (13.56)

AttnReturning(12D)

1 2 3 4 5

ME 38 39 26 15 9.0(26.26) (48.52) (42.97) (27.46) (12.67)

BE/ME 7.4 5.6 4.7 3.5 6.1(2.12) (2.30) (1.85) (1.10) (1.60)

GP/AT 7.1 7.7 11 13 14(5.62) (8.98) (11.84) (13.77) (13.44)

dAT 7.8 10 9.5 11 12(5.65) (11.85) (11.98) (12.65) (12.44)

R(12,1) 11 11 12 11 11(7.83) (12.09) (14.69) (14.30) (11.38)

R(1,0) 10 8.4 9.5 9.7 16(7.80) (9.73) (8.15) (11.57) (15.45)

SUEt 8.9 11 11 12 10(8.70) (11.65) (12.82) (14.10) (11.12)

SUEt−3 11 10 9.8 11 10(9.62) (10.69) (11.36) (12.11) (10.65)

RV 8.5 6.3 8.8 9.9 15(9.76) (7.13) (10.07) (10.81) (15.33)

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Table 18: Subsample Analysis by Constant Fundamentals Unconditionally, firms areassigned at the end of each month or day to decile portfolios based on one of four attentionmeasures determined by recent changes in P/E rankings. Decile assignments are based on NYSEbreakpoints. All data points are removed if the absolute value of the change in 4QEPi,t during theappropriate formation period is above some threshold. For the remaining subsample, I calculatethe next period’s cumulative adjusted return (CAR), defined as CARi,t = reti,t − MKTi,t.Security returns are CRSP holding period returns or delisted returns, and market returns arevalue-weighted monthly or daily returns of all US common stocks on CRSP, available on KenFrench’s website. The monthly nine-factor model includes MKT, SMB, HML, RMW, CMA, UMD,STR, SUEt, and SUEt−3. The daily nine-factor model includes MKT, SMB, HML, GP/AT , dAT ,UMD, STR, SUEt, and SUEt−3.

Long-ShortStrategy Period Threshold CAR (bp) 9F AlphaAttnTotal 1M 1% 48 63(Ex-Post)AttnTotal 1M 2% 60 63(Ex-Post)AttnTotal 1M 1% 41 40(Ex-Ante: SRW+Trend)AttnTotal 1M 2% 48 40(Ex-Ante: SRW+Trend)AttnReturning 6D 0.5% 7.6 9.3(6D)AttnReturning 6D 1% 10.8 9.3(6D)AttnReturning 12D 0.5% 5.1 6.1(12D)AttnReturning 12D 1% 8.1 6.1(12D)

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Table 19: Subsample Analysis by Economic State, Daily Portfolio Time-Series Regressions,1974-2013 At the end of each day, stocks are sorted into ten deciles based on the change in 4QEPi,tpercentile from the end of day t− 6 to the end of day t (AttnReturning(6D)). For each daily observationin these time-series regressions, the dependent variable is the return in basis points of a value-weightedportfolio which is long every stock in decile 10 and short every stock in decile 1. Decile assignmentsare based on NYSE breakpoints. Because of uncertainty about what time of day earnings are released,4QEPi,t is considered unavailable on the trading day of the quarterly reporting date, based on Compustatfield RDQ. The independent variables are a daily time series of intercepts and daily returns of oneor more factor mimicking portfolios. The daily time series for MKT, SMB, HML, UMD, and STRare all available on Ken French’s website. I construct factor mimicking portfolios for GP/AT , dAT ,SUEt and SUEt−3 using 2x3 portfolio sorts on size and GP/AT , dAT , or SUE analogous to HMLconstruction in Fama and French (1993). Gross profitability (GP/AT ) and asset growth (dAT ) arecalculated based on calendar year t financial statements and assumed known at the end of June inyear t + 1. SUE is standardized unexplained earnings, defined as SUE =

IBQt−IBQt−4

σIBQt−1...t−8, where IBQ is

Compustat quarterly income before extraordinary items. Quarterly earnings needed to calculate SUEare assumed known as of the end of the first trading day following the earnings release date basedon Compustat field RDQ. SUEt is a firm’s SUE in the most recent quarter, and SUEt−3 is a firm’sSUE in the fourth most recent quarter. The CAPM model includes MKT returns as an independentvariable. The five-factor model includes MKT, SMB, HML, GP/AT , and dAT . The nine-factor modelaugments the five-factor model with UMD, STR, SUEt, and SUEt−3. The full sample is subdividedinto quartiles of daily MKT performance (top panel), NBER designation of expansion or recession (sec-ond panel), and quartiles of the next quarter’s US real GDP growth, calculated by the BEA (bottom panel).

Subsample Excess Return CAPM Alpha Five-Factor Alpha Nine-Factor Alpha

MKT Quartile

Highest 29.42 -24.86 -27.31 -6.98(12.63) (-6.17) (-6.63) (-1.89)

3rd 11.04 13.41 15.11 8.62(8.78) (4.73) (5.33) (3.32)

2nd 15.12 15.06 15.75 8.11(11.61) (7.21) (7.48) (4.29)

Lowest 13.40 24.13 27.52 9.95(6.51) (7.01) (7.85) (3.08)

NBER Designation

Expansion 15.24 14.74 14.91 8.04(18.12) (17.73) (17.80) (10.47)

Recession 27.80 28.15 31.28 17.88(7.95) (8.09) (9.19) (6.06)

∆ Next Q Real GDP

Highest 15.40 14.90 14.89 7.22(10.10) (9.88) (9.74) (5.17)

3rd 16.11 15.83 16.69 9.88(11.58) (11.32) (11.86) (7.63)

2nd 14.86 14.65 14.68 6.92(8.39) (8.36) (8.45) (4.50)

Lowest 22.61 23.13 24.69 12.03(9.55) (9.90) (10.67) (5.90)

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Table 20: Subsample Analysis by Round Number Crossings, Daily Portfolio Time-Series Regressions, 1974-2013 At the end of each day, stocks are sorted into ten deciles based onthe change in 4QEPi,t percentile from the end of day t−6 to the end of day t (AttnReturning(6D)).Because of uncertainty about what time of day earnings are released, 4QEPi,t is considered un-available on the trading day of the quarterly reporting date, based on Compustat field RDQ. Foreach daily observation in these time series regressions, the dependent variable is the return in basispoints of a value-weighted portfolio which is long every stock in decile 10 and short every stockin decile 1. Decile assignments are based on NYSE breakpoints. The independent variables are adaily time series of intercepts and daily returns of one or more factor mimicking portfolios. Thedaily time series for MKT, SMB, HML, UMD, and STR are all available on Ken French’s website.I construct factor mimicking portfolios for GP/AT , dAT , SUEt and SUEt−3 using 2x3 portfoliosorts on size and GP/AT , dAT , or SUE analogous to HML construction in Fama and French(1993). Gross profitability (GP/AT ) and asset growth (dAT ) are calculated based on calendar yeart financial statements and assumed known at the end of June in year t + 1. SUE is standardizedunexplained earnings, defined as SUE = IBQt−IBQt−4

σIBQt−1...t−8, where IBQ is Compustat quarterly income

before extraordinary items. Quarterly earnings needed to calculate SUE are assumed known as ofthe end of the first trading day following the earnings release date based on Compustat field RDQ.SUEt is a firm’s SUE in the most recent quarter, and SUEt−3 is a firm’s SUE in the fourth mostrecent quarter. The CAPM model includes MKT returns as an independent variable. The five-factor model includes MKT, SMB, HML, GP/AT , and dAT . The nine-factor model augments thefive-factor model with UMD, STR, SUEt, and SUEt−3. The full sample is subdivided into stockscrossing round number P/E thresholds (RNX) and all others. Stocks in the long (short) portfolioof RNX must be in decile 10 (1) of AttnReturning(6D) and must have crossed above (below) 0 orbelow (above) 10, 20, 30, 40, or 50 P/E from the end of day t− 6 to the end of day t.

Performance Excess Return CAPM Alpha Five-Factor Alpha Nine-Factor AlphaAttnReturning(6D)All 17.0 16.7 17.6 9.3

(18.87) (18.71) (19.83) (11.68)RNX 22.2 21.9 23.4 15.3

(14.18) (14.02) (14.95) (9.84)Others 17.2 16.9 17.7 9.8

(18.74) (18.57) (19.47) (11.80)Characteristics N Long N Short Avg Score Long Avg Score ShortAll 525 266 4.1 -6.8RNX 73 57 9.9 -13.4Others 452 209 3.2 -5.0

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Table 21: Time-Series Regressions with Heteroskedasticity and AutocorrelationRobust Standard Errors, 1974-2013 The covariance matrices are reestimated for five monthlyex-post time-series models described in Table 5, five monthly ex-ante (SRW+Trend) time-seriesmodels described in Table 11, and five daily (AttnReturning(6D)) time-series models describedin Table 13. These new estimates use Newey and West (1987) standard errors to control forheteroskedasticity and autocorrelation. This method uses an automatic selection of optimal lags,described in Newey and West (1994). The dependent variable in the ex-post monthly models is thereturn of a value weighted portfolio, which is long every stock in the highest decile of AttnTotaland short every stock in the lowest decile. AttnTotal is the average of 4QEPi,t percentile at theend of month t (AttnNew) and change in 4QEPi,t percentile from the end of month t − 3 to theend of month t (AttnReturning). The dependent variable in the ex-ante monthly models is ananalogous monthly time series of value-weighted portfolio returns, where AttnTotal is calculatedusing E[4QEPi,t+1] based on modeling the time series of quarterly net income as a seasonalrandom walk with trend (see Appendix A for details). The dependent variable in the daily modelsis the return of a value weighted portfolio, which is long every stock in the highest decile ofAttnReturning6D and short every stock in the lowest decile. AttnReturning6D is the change in4QEPi,t percentile from the end of day t − 6 to the end of day t. The independent variables area monthly or daily time series of intercepts and monthly or daily returns of one or more factormimicking portfolios. Details of portfolio construction for each model are described in Tables 5,11, and 13. All decile assignments are based on NYSE breakpoints. The standard errors impliedby the covariance matrices are used to calculate heteroskedasticity and autocorrelation robustt-statistics.

Monthly Model Monthly Alpha (%) OLS T-Stat. HAC Robust T-StatEx-PostCAPM 1.13 5.85 5.50Three-Factor 1.06 5.47 5.17Four-Factor 0.98 5.00 4.39Five-Factor 0.88 4.67 4.20Nine-Factor 0.63 3.33 2.78Ex-Ante(SRW+Trend)CAPM 1.07 6.28 6.14Three-Factor 1.03 5.97 5.72Four-Factor 0.84 4.88 4.47Five-Factor 0.83 4.83 4.56Nine-Factor 0.40 2.51 2.19Daily Model Daily Alpha (bp) OLS T-Stat. HAC Robust T-Stat(AttnReturning(6D))CAPM 16.7 18.71 18.09Three-Factor 17.1 19.23 18.14Four-Factor 16.6 18.69 17.59Five-Factor 17.6 19.83 18.20Nine-Factor 9.3 11.68 9.38

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Table 22: Mutual Fund Activity and 6D Attention Strategy Performance, 1984-2013For each year from 1984-2013, annual returns for the AttnReturning6D strategy are calculatedby compounding daily returns. At the end of each day, stocks are sorted into ten deciles basedon the change in 4QEPi,t percentile from the end of day t− 6 to the end of day t. For each dailyobservation in these time-series regressions, the dependent variable is the return in basis points ofa value-weighted portfolio which is long every stock in decile 10 and short every stock in decile1. Decile assignments are based on NYSE breakpoints. Because of uncertainty about what timeof day earnings are released, 4QEPi,t is considered unavailable on the trading day of the quarterlyreporting date, based on Compustat field RDQ. The time series of annual returns are regressedon an annual time series of intercepts and one or more measures of mutual fund activity. Tradeactivity (BuyPctt, SellPctt) and flow activity (InflowPctt, OutflowPctt) data are for all equitymutual funds, based on Investment Company Fact Book Tables 20 and 34. All trade and flow dataare scaled by the same year’s total traded dollar volume for all US common stocks in the CRSPuniverse. T-statistics are in parentheses.

Intercept 0.66 0.44 0.34 0.46 0.83 0.43 0.52 0.45(2.54) (5.41) (1.20) (6.10) (3.37) (5.30) (1.90) (6.00)

BuyPctt 0.19(2.67)

SellPctt -0.22(-2.41)

NetBSPctt 0.16(2.56)

InflowPctt 0.12(2.11)

OutflowPctt -0.09(-0.98)

NetIOPctt 0.13(2.46)

BuyPctt−1 0.23(3.34)

SellPctt−1 -0.29(-3.21)

NetBSPctt−1 0.18(2.77)

InflowPctt−1 0.16(2.77)

OutflowPctt−1 -0.17(-1.84)

NetIOPctt−1 0.15(2.91)

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Figure 1: Relative Google Search Volume, 2006-2016 This figure shows the relativeGoogle Search Volume of price-earnings (P/E) ratio and price-book (P/B) ratio from March 1,2006 to February 29, 2016. Data are from Google Trends (https://www.google.com/trends).Search volumes include all Google web searches which Google attributes to the P/E and P/Btopics. Common search terms which Google attributes to the P/E topic include p/e, pe ratio,p/e ratio, price earnings, price earnings ratio, and price to earnings. Common search termswhich Google attributes to the P/B topic include p/b, pb ratio, p/b ratio, price book, bookto price, price book ratio, price book value, market book ratio, and market to book. Volumesare normalized so the topic-week observation with the most searches is assigned a volume of100. This observation corresponds to the number of searches for the P/E ratio topic dur-ing the week from October 5, 2008 to October 11, 2008. The weekly ratio of the volume ofsearches for P/E to the volume of searches for P/B ranges from 3.55 to 10.40 with an average of 6.47.

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Figure 2: Monthly Ex-Post P/E Attention Strategy Performance by Decile, 1974-2013Each bar in this figure represents the average monthly excess return of a value-weighted portfolio.The figure presents average excess returns for monthly “ex-post” attention portfolios. At the endof each month, US common stocks are sorted by AttnTotal, the average of 4QEPi,t percentile atthe end of month t (AttnNew) and change in 4QEPi,t percentile from the end of month t − 3 tothe end of month t (AttnReturning). Excess returns are portfolio returns net of the one-monthtreasury bill rate. Monthly T-bill rates are from Ken French’s data library. Decile assignments arebased on NYSE breakpoints.

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Figure 3: Monthly Ex-Ante P/E Attention Strategy Performance by Decile, 1974-2013Each bar in this figure represents the average monthly excess return of a value-weighted portfolio.The figure presents average excess returns for monthly “ex-ante” attention portfolios. At the endof each month, US common stocks are sorted by AttnTotal, the average of E[4QEPi,t+1] percentileat the end of month t (AttnNew) and change in E[4QEPi,t+1] percentile from the end of montht − 3 to the end of month t (AttnReturning). E[4QEPi,t+1] is calculated based on modelingthe time series of quarterly earnings as a seasonal random walk with trend (see Appendix A fordetails). Excess returns are portfolio returns net of the one-month treasury bill rate. MonthlyT-bill rates are from Ken French’s data library. Decile assignments are based on NYSE breakpoints.

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Figure 4: Daily Performance by Decile, 1974-2013 Each bar in these figures representsthe average daily excess return of a value-weighted portfolio. The top figure presents returnsto 6-day P/E attention portfolios. At the end of each day, US common stocks are sorted byAttnReturning6D, the change in 4QEPi,t percentile from the end of day t − 6 to the end of dayt. The bottom figure presents returns to 12-day P/E attention portfolios. At the end of each day,US common stocks are sorted by AttnReturning12D, the change in 4QEPi,t percentile from theend of day t − 12 to the end of day t. Because of uncertainty about what time of day earningsare released, 4QEPi,t is considered unavailable on the trading day of the quarterly reporting date,based on Compustat field RDQ. Excess returns are portfolio returns net of the daily return of theone-month treasury bill. Daily T-bill rates are from Ken French’s data library. Decile assignmentsare based on NYSE breakpoints.

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Figure 5: Relative Volume by Decile, 1974-2013 Each bar in these figures representsthe average daily relative volume of a decile P/E attention portfolio. The top figure presentsrelative volumes of 6-day P/E attention portfolios. At the end of each day, US common stocksare sorted by AttnReturning6D, the change in 4QEPi,t percentile from the end of day t − 6 tothe end of day t. The bottom figure presents relative volumes of 12-day P/E attention portfolios.At the end of each day, US common stocks are sorted by AttnReturning12D, the change in4QEPi,t percentile from the end of day t − 12 to the end of day t. Because of uncertainty aboutwhat time of day earnings are released, 4QEPi,t is considered unavailable on the trading day ofthe quarterly reporting date, based on Compustat field RDQ. Decile assignments are based on

NYSE breakpoints. Relative volume is calculated asRVi,t =|PRCi,t|∗V OLi,t

0.02∗∑50N=1 |PRCi,t−N |∗V OLi,t−N

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Figure 6: CAR by Decile for Positive and Negative P/E Stocks, Constant Fundamen-tals Subsample, 1974-2013 Each bar in these figures represents the average daily excess returnof a value-weighted portfolio. Firms are assigned at the end of each day to decile portfolios basedon AttnReturning12D, the change in 4QEPi,t percentile from the end of day t− 12 to the end ofday t. Because of uncertainty about what time of day earnings are released, 4QEPi,t is consideredunavailable on the trading day of the quarterly reporting date, based on Compustat field RDQ.Decile assignments are based on NYSE breakpoints. All data points are removed if the absolutevalue of the change in 4QEPi,t from the end of day t − 12 to the end of day t is larger than 1%.For the remaining subsample, I calculate the next period’s cumulative adjusted return (CAR),defined as CARi,t = reti,t−MKTi,t. Security returns are CRSP holding period returns or delistedreturns, and market returns are value-weighted monthly or daily returns of all US common stockson CRSP, available on Ken French’s website.

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