Target prices, relative valuations and the compensation
for liquidity provision
Zhi Da† and Ernst Schaumburg‡,∗
October 15, 2006
Abstract
We document that S&P500 stocks experience intermittent large liquidity shocks
which are mainly idiosyncratic in nature. The liquidity events can be identified using
equity analyst target prices as instruments for changes in fundamental values. The
associated short-run reversals are economically and statistically significant and of a
magnitude not easily explained by transaction costs alone. Our findings point to a
significant premium required by investors for providing immediacy even in the market
for the most liquid stocks.
JEL Classification: G12
∗
We would like to thank Paul Gao, Kathleen Hagerty, Robert Korajczyk, Robert McDonald, Amiyatosh
Purnanandam, Avanidhar Subrahmanyam, seminar participants at Goldman Sachs Asset Management, HEC
Montreal, the July 2006 NBER Asset Pricing Workshop, University of Notre Dame, Northwestern Univer-
sity, Vanguard and especially Ravi Jagannathan for his numerous suggestions and insights. We gratefully
acknowledge financial support from the Financial Institutions and Markets Research Center at the Kellogg
School of Management.
†
zda@nd.edu, Mendoza College of Business, University of Notre Dame.
‡
e-schaumburg@northwestern.edu, Kellogg School of Management, Northwestern University.
1
1 Introduction
The significant price concessions associated with with trading large blocks of small cap stocks
has been well documented in the literature going back to Kraus and Stoll (1972) and Loeb
(1983). In most market microstructure models, the price impact can be interpreted as a
direct result of inventory costs and/or asymmetric information, both of which presumably
play a larger role for small stocks. The size and duration of the price impact associated with
uninformed trading is then a natural measure of the liquidity of an asset. Since the average
price impact is at least an order of magnitude larger for small stocks than large stocks (c.f.
Loeb (1983)), it is natural to think of large stocks as being uniformly liquid. In reality,
however, large stocks, although generally liquid, may experience episodes of illiquidity.
In this paper we ask whether it is possible to identify such episodes of illiquidity for
individual stocks and, if so, identify the reward for liquidity provision. In particular, we
focus on the S&P500 universe which on average is highly liquid although at any given
point in time a handful of stocks may experience periods of low liquidity. We propose a
novel empirical strategy for identifying such periods of low liquidity by using information
contained in equity analysts’ target prices.
Target prices can help in discerning whether recently observed returns, at least in part,
were driven by uninformed trading and therefore did not reflect changes in underlying funda-
mentals. A price concession leads to a short-run discrepancy between fundamental value and
price. Since the fundamental value itself is unobservable, the discrepancy is instead proxied
for by the spread between target price and price. We measure this spread by the “target price
implied expected return” (T P ER), defined as the ratio of consensus 12 month ahead target
price to current market price: T P ERt = T Pt /Pt − 1. While conventional liquidity measures
must disentangle information and liquidity-based trades ex-post, the T P ER instrument has
the potential to directly control for changes in fundamental values in real time. This allows
the ex-ante identification of the subset of stocks for which the cost of immediacy currently
is the highest.
For the identification to work, an unusually large large (or small) TPER should indicate
a large price concession and hence a higher degree of illiquidity. Unfortunately, the signal-
to-noise ratio of the TPER is likely to be poor for a number of reasons. First, the consensus
analyst target price is known to be noisy due to disagreement among analysts, the lack
of a commonly agreed upon absolute valuation model and the presence of analyst biases.1
Second, the target price itself is not a direct measure of fundamental value since it contains
a substantial forward-looking systematic risk component. To illustrate this, consider the
1
See e.g. Michaely and Womack (2002).
2
analyst’s target price forecast within an n-factor framework. The TPER can be decomposed
into three components:
n−1
A A
T P ER = E [α] + βM E [M kt] + βi E A [λi ]
i=1
Only the first component, the analyst’s estimated alpha, contains any signal about the
current deviation between price and fundamentals as perceived by the analysts. The second
and third terms reflects the familiar forward-looking systematic risk components consisting
of market risk and “other” risk factors. E A [·] denotes analyst’s expectations which could be
contaminated by noise due to difference of opinion, modeling error and behavioral biases.
In many cases the first term will be swamped by the other two components, which contain
no information about fundamental value. Moreover, they will contain considerable noise
when analysts have limited ability to forecast factor loadings and/or factor risk premia as
documented in Figure 1 and Figure 2. In this case, a naive sort on TPER could implicitly
be a sort on beta.
The solution we propose is to sort on TPER within groups of “similar” stocks, i.e. stocks
with “similar” risk characteristics. This will serve to eliminate much of the noise from the
systematic risk component and isolate the ‘relative value’ identified by the analyst.2 A
within-group sort on TPER is therefore more likely to produce a spread in alpha which
contains the signal about deviations from fundamental values. As a proxy for groups of
“similar” stocks we in this paper consider industry sectors.
Based on these observations, we implement a sector-neutral long-short strategy designed
to capture liquidity effects identified by the TPER instrument. The portfolio is constructed
in the following manner: at the end of every month, we consider the set of S&P500 stocks for
which at least one analyst has announced a target price during the first 25 calendar days of
the month.3 Within each sector we sort the stocks according to their T P ER and construct
an equally weighted portfolio which is long the highest T P ER stocks from each sector and
short the lowest T P ER stocks from each sector. Since the portfolio is equally weighted, it
is by construction sector neutral. Over the period 1999-2004, this strategy has yielded a
substantial abnormal return of 203bps per month.4 We interpret this alpha as a measure of
2
The latter is likely more precisely estimated given the prevalence of industry specialization among ana-
lysts and the widespread reliance on relative valuation models, as discussed further below.
3
The average 5-day lag between the portfolio formation and the beginning of the one month holding
period eliminates announcement effects as discussed below. Without this gap our results are strengthened.
4
As discussed in detail below, the choice of sampling period is dictated by the ex-ante availability of the
detailed Standard & Poors sector classification used. The abnormal return is robust to various models used
for risk adjustment.
3
the cost of immediacy.5
While the average cost of immediacy is clearly related to the notion of aggregate liquidity,
there is likely a very large idiosyncratic component to the cost of immediacy for individual
high/low TPER stocks. In fact, at the monthly frequency, we do not find any relationship
between the Pastor and Stambaugh (2003) aggregate liquidity factor and the profits of our
benchmark strategy. Instead we find a very strong relationship between the abnormal return
and individual stock liquidity characteristics.
In particular, we document that stocks entering our long-short portfolio in a given month
experience a significant increase in their bid-ask spreads, price impact measures (Breen, Ho-
drick, and Korajczyk (2002)) and Amihud illiquidity measures (Amihud (2002)). Moreover,
the abnormal return is highly correlated with these liquidity measures across time. In line
with Campbell, Grossman, and Wang (1993) and Conrad, Hameed, and Niden (1994), we
also document an increase in turnover for stocks entering our portfolio as well as a signifi-
cant change in the order imbalance between seller and buyer initiated trades. By analyzing
mutual fund holdings for a large subset of US equity mutual funds, we also find evidence
of significant imbalances in institutional buying/selling pressures for stocks with subsequent
extreme TPERs. In addition, we observe a substantial increase in the dispersion of ana-
lysts’ target price forecasts for stocks entering our portfolio, consistent with market makers
decreasing liquidity of individual stocks in response to an increased degree of information
asymmetry as in Sadka and Scherbina (2004).
Our results also indicate that, even in the case of the most liquid stocks, the price
corrections which generate the abnormal profits accrue over a period of several weeks on
average. This finding is at odds with the common presumption is that the price effects of
liquidity motivated trades tend to dissipate more quickly. Pastor and Stambaugh (2003),
for instance, in their construction of an aggregate liquidity factor, focus on liquidity effects
that play out within one day.6 It is far from clear, however, what duration in general
should be attributed to liquidity induced price movements. As has been argued in the
“limits-to-arbitrage” literature, liquidity effects, albeit temporary, could be of a considerably
longer duration as in Shleifer and Vishny (1997) and recent empirical papers by Gabaix,
Krishnamurthy, and Vigneron (2005) and Sadka and Scherbina (2004). Even in markets
5
The magnitude of the compensation for providing immediacy (134 bps for the long portfolio and 69 bps
for the short portfolio per month) documented in this paper is comparable to those documented by Keim
and Madhavan (1996) (50 to 100 bps as in Figure 1 of their paper) and by Coval and Stafford (2005) (79
bps as in Table 5 of their paper).
6
In their study of block trades Keim and Madhavan (1996) find that the price impact of a sell order on
lasts on average one day. Buy orders on the other hand tend to have a more permanent effect, much of which
accrues during the first day.
4
for liquid assets (e.g. S&P500 stocks), informational asymmetries may exist which lead to
specialization by market makers with limited capital. The resulting capital immobility can
significantly extend the duration of deviations from fundamentals, as has been argued in
Berndt, Douglas, Duffie, Ferguson, and Schranzk (2005).
We investigate a number of alternative sources of the abnormal returns on the T P ER
sorted portfolios. We conclude that the profit is not likely driven by: (1) delayed reaction to
stock recommendation (c.f. Womack (1996)); (2) reaction to target price revisions (c.f. Brav
and Lehavy (2003) and Asquith, Mikhail, and Au (2005)); (3) post-earning-announcement
drift (PEAD); or (4) pure short-term return reversal (c.f. Jegadeesh (1990) and Lehman
(1990)). Although behavioral explanations cannot be completely ruled out, we believe that
the empirical evidence in favor of liquidity events is far more compelling.
By reinterpreting the within-sector TPER sort as a “relative value” sort, our findings
contribute to the recent research on equity analyst’s target prices: Although analysts fail
to assess fundamental values themselves with any degree of precision, they on average get
relative valuations right. As in Boni and Womack (2006), this finding can be motivated by
the fact that most analysts specialize in a sector (rather than being generalists) and typically
cover about half a dozen stocks within the same industry. By analyzing the specifics of a
handful of similar firms, the analyst is well situated to rank the relative strength of each
stock going forward, although he may have significantly less insight into the forecasting of
macro factors which affect the performance of the sector as a whole. Focusing on relative
price forecasts within the same sector eliminates much of the effect of systematic risk factors
while preserving the relative strength information contained in analysts’ price targets.7
The success of our benchmark portfolio clearly demonstrates that information embedded
in the level of target prices, if properly exploited, can lead to superior investment results.
Several previous studies have examined investment strategies based on information provided
by analysts – mainly stock recommendations.8 Most of these investment strategies, however,
have produced risk-adjusted paper profits which disappear after accounting for transaction
7
Boni and Womack (2006) show that an investment strategy based on stock recommendation revisions
within the same industry improves the return significantly compared to a similar strategy without industry
control. The current paper takes a similar approach by explicitly canceling out industry effects, thereby
isolating the relative value identified by analysts. However, this paper uses target prices rather than recom-
mendations which allows for a more direct interpretation of rankings as relative valuations. The portfolios
resulting from our ‘relative value’ sort in fact look quite different. They resemble short-run reversal rather
than momentum as in Boni and Womack (2006). Finally, the focus here is on S&P500 stocks with the aim
of explicitly accounting for transaction costs.
8
Two examples are Dimson and Marsh (1984) and Barber, Lehavy, McNichols, and Trueman (2001).
Michaely and Womack (2002) provides and excellent survey of related papers.
5
costs incurred from high portfolio turnover. By contrast, our benchmark portfolio involves
only S&P 500 stocks and produces a risk-adjusted return of around 100bp per month after
accounting for direct transaction costs and a measure of price impact.9
Our main results extend beyond the S&P500 universe to the set of all stocks in the First
Call database with regular analyst coverage over the extended sample period from 1997
to 2004. In this larger sample we show that the strategy works best for small stocks and
especially value stocks. We attribute the effect of the book-to-market ratio to the fact that
analysts’ estimates for value firms (with a higher fraction of tangible assets) may be less
noisy than for growth firms, thus providing a more precise control for fundamental value.
Small stocks, on the other hand, tend to be more illiquid due to informational asymmetries.
One would therefore expect the cost of immediacy to be higher, which may explain the better
performance of our long-short strategy for small stocks. Interestingly, we also find that the
strategy performs significantly better in certain industries such as consumer discretionary
and industrials.
The remainder of the paper is structured as follows: Section 2 provides a description of
data sources. The portfolio construction and the main results for the S&P500 sample are
given in section 3. Section 4 describes the full sample results and Section 5 concludes.
2 Full Sample Data Description
The target price data for this study is provided by First Call and has the important advantage
over other data sources that it contains accurate dating of analysts’ reports.10 At the end
of each month from Dec 1996 to Dec 2004, we include only stocks for which there is at
least one (12 month ahead) target price announcement during the first 25 calendar days of
the month. It is important to note that, as a result, even our full sample includes almost
no extremely small stocks since these do not receive regular analyst coverage. We do not
“fill in the blanks” using older target prices in order to avoid introducing an upward bias
in the target prices. The bias arises because analysts are more likely to issue a target price
when they are in favor of a stock, as documented in Brav and Lehavy (2003).11 In addition,
9
The abnormal returns derive equally from the long and short side of the portfolio and it is possible to
implement a version of the strategy where the shorting of individual stocks is replaced by shorting S&P
index futures or sector ETFs.
10
See footnote 3 of Brav and Lehavy (2003) for a detailed discussion.
11
Specifically, Brav and Lehavy (2003) show that about 90% of ”buy” / ”strong buy” recommendations
are issued with target prices while only 61% of ”sell” / ”strong sell” recommendations are issued with
target prices. Furthermore, ”sell” / ”strong sell” recommendations only account for less than 5% of all
recommendations as documented in Jegadeesh et. al (2004).
6
we only keep target price announcements during the first 25 calendar days of the month
for two reasons. First, we want to make sure that our results are not purely driven by an
immediate market reaction to target price announcements, a phenomenon considered in Brav
and Lehavy (2003) and Asquith, Mikhail, and Au (2005).12 Second, a lag of at least 5 days
makes our portfolio trading strategies easier to implement since investors are given ample
time to collect and digest target price information.
Table 1 presents a summary of the resulting full sample containing approximately 1700
stocks each month, increasing from 1095 in 1996 to 1796 in 2004. For each stock, we have on
average 2.5 target prices per month. The sample on average covers 76% of the CRSP stock
universe in terms of market capitalization, increasing from 55.5% in 1996 to 83% in 2004.
Our sample also covers most of the “representative” stocks, which are constituents of the
major equity indices. For instance, in 2004, our sample covers 496 of the S&P 500 stocks,
980 of the Russell 1000 stocks and 2780 of the Russell 3000 stocks. On average, 54% of the
stocks in our sample are listed on the NYSE, 43% are listed on NASDAQ and the remaining
3% are listed on the AMEX. The median market capitalization of stocks in our sample,
averaging over the sampling period, is 919M – much larger than that of all NASDAQ stocks
(85M ), but slightly smaller than that of all NYSE stocks (963M ).
A key variable of interest in this paper is the target price implied expected return one-
year-ahead (T P ER). T P ER is defined as the consensus target price (split adjusted) divided
by the end of month stock price minus one, or T P ERt = T Pt /Pt − 1, where the consensus
target price T Pt is the simple average of all target prices received during the first 25 calendar
days of month t.13,14 The mean T P ER during this sampling period is 40% (the median is
24%), substantially higher than one would expect for the market as a whole. This is partly
due to the fact that analysts are far more likely to issue target prices when they favor a stock.
In addition, the target price may reflect deliberate optimism on the part of the analyst as
proposed in Bradshaw and Brown (2005): The mean T P ER was as high as 64% (median
36%) in 2000 during the final stages of the NASDAQ bubble.
We break down our sample into sectors according to the first two digits of Standard
12
The fact that there is a significant market reaction to target price revisions controlling for the arrival of
other information provides evidence that investors on average consider target prices to be informative.
13
Defining the consensus target price using median does not alter the results in any significant way.
14
Bradshaw and Brown (2005) show that analysts do not appear to exhibit persistent differential abilities
in forecasting target prices. We therefore use simple averages of target prices without exploiting knowledge
of individual analyst identities.
7
and Poor’s GICS (Global Industry Classification Standard).15,16 Using IBES data, Boni and
Womack (2006) show that the GICS sector and industry definitions match well with the
areas of expertise of most analysts as defined by the set of stocks covered by each analyst.
The GICS is therefore a natural choice of sector definition although we also consider 1-digit
SIC codes and the Fama-French industry definitions below. The GICS used in this paper
are obtained from various sources: Standard and Poor’s publishes the GICS classification of
S&P500 stocks on its website. Historical GICS for some companies are available in COM-
PUSTAT starting in Dec 1994, however, all GICS classifications prior to 1999 are backfilled.
For stocks in our sample whose GICS are not available from the above two sources, we assign
the GICS according to the first three digits of its Industry Classification Code (the dnum
variable in COMPUSTAT).17 Since there are too few stocks in the Telecommunications
Services sector, we group them with the Information Technology sector to form a combined
Technology sector. The resulting 9 sectors are: Energy, Materials, Industrials, Consumer
Discretionary, Consumer Staples, Health Care, Financials, Technology and Utilities. This
classification is also consistent with the way sector ETFs are formed. Panel C of Table 1
shows the sector break down of our sample both in terms of number of stocks and in terms
of market capitalization. The three largest sectors are Consumer Discretionary, Financials
and Technology, which together account for almost 60% of the entire sample. The sector
break down of our sample is in line with that of the broad market as proxied by the S&P500
index. Across time, we observe the dominance of the Technology sector in 2000 due to the
NASDAQ bubble and the recent increase of the Energy sector due to the surge in oil prices.
The S&P500 universe which is the main focus of this paper distinguishes itself in several
respects: First, S&P500 stocks receive the most attention and coverage by analysts. On
average, analysts issue target prices for around 350 of the S&P500 stocks each month and
the average number of target prices per stock each month is 4 – significantly higher than that
of the average stock in the First Call database (2.5). Therefore, the consensus target price
15
The GICS was introduced in 1999 by Standard & Poor’s and Morgan Stanley Capital International
(MSCI) with the goal of providing a set of global sector and industry definitions more useful for investment
purposes.
16
The 4 or 6-digit GICS would, in principle, yield better sector control, but the number of stocks in each
sector would drop dramatically, making the results too noisy. For example, using the 4-digit GICS would
leave us with, on average, less than 15 stocks in each industry group per month for our benchmark S&P 500
stock sample and making it nonsensical to sort within each industry group.
17
Specifically, for stocks whose GICS are available from the first two sources, we can observe their dnums
and can infer the mapping from dnum to sector for these stocks. Making use of this mapping, we can assign
a large portion of our sample stocks into sectors. We establish the remaining 150 dnum-to-sector mappings
manually based on a detailed sector description provided by Standard and Poor’s.
8
used to compute T P ER for S&P500 stocks is less prone to outliers and presumably more
accurate. Second, S&P500 stocks are on average more liquid and cheaper to trade, which
makes it easier to bound the potential impact of transaction costs. Finally, the GICS sector
assignment of S&P500 stocks is done directly by Standard & Poor’s and does not rely on a
sometimes arbitrary mapping from SIC codes. As mentioned, the GICS sector classification
is of particular importance because it closely mirrors the way analysts are specialized. The
relative TPER within GICS sectors therefore conceptually provides a more precise signal of
deviations from fundamentals. Since the GICS (Global Industry Classification Standard)
was officially launched by Standard & Poor’s and Morgan Stanley Capital International
(MSCI) in 1999, we focus on the sample period starting in January 1999 to avoid issues with
backfilling.
Throughout the study, we obtain prices and returns from CRSP. In computing various
portfolio characteristics, we make use of data from COMPUSTAT and TAQ. Finally, we also
use stock recommendation and earning announcement data obtained from First Call.
3 The profitability of sector-neutral long-short strate-
gies using S&P500 stocks
This section describes the construction of a sector neutral long-short portfolio of S&P500
stocks which exploits temporary deviations between the prevailing market prices and funda-
mentals as measured using information contained in analyst target prices.
3.1 Excess returns and alphas
At the end of each month from December 1998 to December 2004 and within each sector, we
rank the S&P500 stocks into 9 groups according to their current month T P ERs.18 We form
9 equal weighted portfolios: Portfolio 1 consisting of the highest TPER stocks from each
sector, portfolio 2 consisting of the second highest, ... , and finally portfolio 9 consisting of
the lowest TPER stocks from each sector. For each of the resulting 9 portfolios, we compute
the first month post-formation excess returns (in excess of the risk-free rate). The results are
summarized in Panel A of Table 2. The excess returns are in general increasing in T P ER:
Portfolio 1, where analysts predict the highest 12 month return (for each stock relative to all
S&P 500 stocks within the same sector), earns the highest first month excess return (158bp)
18
In line with common practice in the empirical asset pricing literature, we exclude stocks with share prices
below five dollars in order to ensure that the results are not unduly influenced by the bid-ask bounce. This
price filter has little impact on the S&P 500 sample, eliminating less than 1% of the stocks.
9
while portfolio 9 earns the lowest first month excess return (−19bp). The return on the
spread portfolio (1 minus 9) can be regarded as the return to a portfolio of long-short sector
strategies (long stocks with the highest TPERs and short stocks with the lowest TPERs
within each sector). Forming long-short strategies within sectors has two advantages: if
analysts in fact are capable of forecasting the relative performance of stocks within the same
sector, then a sector neutral long-short strategy should directly pick up this skill. Second, to
the extent that stocks in the same sector have similar systematic risk exposures (factor risk),
sector neutrality serves to reduce the exposure to systematic risks which the analysts’ have
no comparative advantage in forecasting. The first month return to the spread portfolio 1-9
is as high as 177 bps with a t-value of 3.55.19 Panel A also shows that the excess returns to
portfolios 1 and 9 and the spread portfolio are not significantly different from zero beyond the
first month after portfolio formation. Figure 3 illustrates this point for the spread portfolio.
In fact, most of the first month return (110 bp out of 177bp) accrues during the first two
weeks post portfolio formation.
The significant first month excess returns on the spread portfolio 1-9 might of course
simply be the result of systematic risk exposures. For instance, Jegadeesh, Kim, Krische, and
Lee (2004) find some evidence that analysts chase glamor (i.e. growth) stocks and stocks with
recent strong performance. On the other hand, TPER has market price in the denominator,
so the TPER sort may capture the effect of a sort on short-run or intermediate-term reversal.
To account for these effects, we regress the monthly excess returns on the Fama-French (1993)
three factors, the Carhart (1997) momentum factor and the Fama-French short-run reversal
factor.20 The results in Panel A of Table 2 show that the risk-adjusted returns are even
higher and more significant than the average excess returns themselves: our sector neutral
long-short strategy (the spread portfolio 1-9) yields a highly significant three-factor alpha
of 203 bps (t-value of 5.06). In addition, the sector neutrality of the long-short strategy
helps in reducing (but not eliminating) the systematic risk exposures. The spread portfolio
19
About 87% of the S&P 500 stocks are listed in NYSE (NASDAQ accounts for 12% and AMEX accounts
for less than 1%). We verify that our results are not driven by the NASDAQ stocks in our S&P 500 stock
sample. Excluding NASDAQ stocks leads only to negligible changes in the results. For example, the profit
in portfolio 1-9 is 174 bp (t-value of 3.50) and the three-factor alpha is 188 bp (t-value of 3.94).
20
The three factors are: MKT, SMB and HML. MKT is the market return minus risk free rate. SMB
is the return to a zero-investment portfolio of longing small stocks and shorting big stocks. HML is the
return to a zero-investment portfolio of longing high book-to-market stocks and shorting low book-to-market
stocks. The momentum factor, UMD, is the return to a zero-investment portfolio of longing past winners and
shorting past losers. The short-term reversal factor, DMU, is constructed as the return on a zero investment
portfolio which is long last months losers and short last months winners. The time series of factor realizations
as well as detailed descriptions can be found on Ken French’s website:
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/.
10
only loads significantly on the Market and the momentum factor. The positive loading on
the MKT factor is intuitive since, ceteris paribus, high beta stocks will receive higher target
prices relative to their current market price. Interestingly, the highly significant negative
loading on the momentum factor indicates that the spread portfolio tends to load up on
intermediate-term losers and short intermediate-term winners, as we shall see. However,
relative winners and losers within S&P500 sectors do not map into the overall winners and
losers as defined in a standard short-run reversal strategy (involving a broad universe of
traded stocks). This explains why the loading on the reversal factor is insignificant.21 In the
remainder of the paper we use the five factor model as our benchmark for computing risk
adjusted returns.
If the cross sectional dispersion of TPER reflects differences in liquidity, then the prof-
itability of the spread portfolio could be due to exposure to an aggregate liquidity risk factor.
To investigate this, we add the Pastor and Stambaugh (2003) value weighted liquidity factor
as a sixth pricing factor in Panel B of Table 2. The alpha of the spread portfolio is virtually
unchanged (201bp, t-value of 4.95) and the market and momentum factors remain the only
factors with significant loadings. The implication is that, to the extent the spread portfolio
return is (partly) driven by liquidity, it is not systematic liquidity as captured by the Pastor
and Stambaugh (2003) factor.
Figure 4 summarizes our results so far. It shows the monthly time series of five-factor risk-
adjusted return to our trading strategy and the market excess return. During our sampling
period from Jan 1999 to Dec 2004, it is clear that the sector-neutral long-short strategy has
a much better risk-return trade-off than the overall market portfolio. The monthly Sharpe
ratio of the spread return and the five factor alpha are 0.41 and 0.67, respectively, and are
all clearly better than that of the market (SRM kt = 0.01) during the same period.22,23 The
time series before 1999 is shaded to highlight the fact that the GICS is backfilled and the
long-short strategy was infeasible ex-ante prior to 1999. The performance of our long-short
21
Part of the large alpha is due to the negative momentum exposure. Risk adjusting using a standard
3-factor Fama-French model yields an alpha of 196bp with a t-stat of 4.34. If we alternatively risk adjust the
spread portfolio excess return using the returns on Size and B/M sorted portfolios with similar characteristics
(along the lines of to Daniel and Titman (1997)) the alpha increases to 210 bp with a t-value of 2.72, as
shown in the last columns of Table 2B
22
The five factor-model-alpha can be thought of as the excess return of a trading strategy since factors
are also excess returns.
23
From Figure 4, it can also be seen that the average annualized alpha increases from 1999 to 2000 and
then drops off over the subsequent years until 2004. This pattern is similar to the investor sentiment factor
derived in Baker and Wurgler (2005) and may indicate that investor sentiment as partly driving the liquidity
events that we identify.
11
strategy (portfolio 1-9) is slightly reduced when including the period 1997-1999 (the average
alpha drops to 162 bps, t-stat 4.21), likely in part because of the noise introduced by the
inaccurate backfilling of the GICS in Compustat.
It is important to note the crucial role played by sector control. If we instead form
portfolios based on ranking the T P ER across all stocks rather than within each sector, and
compute the first month post-formation portfolio excess returns, they lose their significance,
as shown in Table 3. The long-short portfolio 1-9 (long stocks with the highest T P ER
and short stocks with the lowest T P ER) produce a spread of only 79bp (t-value of 0.86),
much smaller than the spread of 177 bp when the long-short position is constructed within
sector. In addition, without sector control, the profit becomes more volatile due to its higher
exposure to systematic risk factors, resulting in a less significant five factor alpha (t-value of
2.44 versus 5.06 with sector control). This is broadly consistent with the findings in Boni and
Womack (2006) in the context of analyst recommendations and provides further evidence
that it is the relative target prices and not the level of target prices which convey the most
information about fundamentals.24
3.2 Robustness of the benchmark portfolio specification
In order to investigate the robustness of our findings, we in Table 4 consider the effect of
various alternative portfolio formation strategies. Comparing the results in Panel A and
B it is clear that the equal weighted strategies on average do better than value weighted
strategies.25 It also emerges that dispensing with the 5 day gap, i.e. allowing target price
collection during the last 5 days of the portfolio formation month, strengthens the profitabil-
ity of the spread portfolio. This is to be expected given the well documented announcement
effect, see e.g. Brav and Lehavy (2003).
We also investigate the effect of using alternative sector specifications. The naive 1-digit
SIC sector definition does poorly (except in the no gap equal weighted scenario) while the
Fama-French 10-sector specification does much better than the 1-digit SIC but is still strictly
dominated by the 9 sector GICS. This is consistent with the ‘relative value’ interpretation
since the 9 sector GICS agruably provides the better proxy for the areas of specialization of
analysts (see e.g. Boni and Womack (2006)). Since we focus our attention to the S&P500
sample with an average of 350 observations in the cross-section each month, we do not explore
the potential beneficial effects of more precise sector control by moving to the more detailed
24
The significance of the abnormal returns stem from the significant negative loading on UMD. The Fama-
French 3-factor alpha is 127bp with a t-value of 1.65.
25
Value weighting is done separately within each sector long and short so that each sector position remain
equal weighted.
12
23 GICS industry groupings or 59 GICS industries.
Our benchmark definition of TPER is only one of many possible. In table 4 we consider
the alternative specification ATPER = average(T Pt /Pt ), i.e. the average of each analyst’s
target price divided by the market price on the announcement date, rather than the average
target price divided by the market price on the portfolio formation date. Table 4 shows that
the alternative TPER specification does significantly worse than our benchmark specification,
indicating that the price at the end of the month is more informative than a weighted average
of prices collected during the month.
Finally we check the effect of imposing a stricter requirement on the minimum number
of target prices required in a given month for a stock to be included. Requiring at least 3
target prices does not in general reduce the alpha, but the t-stat (while still significant) does
deteriorate due to the reduction in sample size. Overall, we conclude that our qualitative
results are robust to changes in the specifics of the portfolio formation strategy.
A close inspection of Figure 4 shows that a few particularly large risk adjusted returns
fall during January months, especially in 2000 and 2001. To ensure that our results are not
driven by the “January effect”, we also report the excess returns and five-factor-alpha of the
spread portfolio excluding the month of January in Table 4. After excluding January, the
return and alpha of our long-short strategy (portfolio 1-9) in the benchmark scenario drop
in magnitude to 155 bps and 183 bps, respectively with modest reductions in the levels of
significance (given a loss of 8.3% of the data). We therefore conclude that the January effect
is not a main driver of our results.
3.3 Portfolio characteristics and profit after transaction costs
Table 5 reports various portfolio characteristics. The first 12 characteristics are those studied
in Jegadeesh, Kim, Krische, and Lee (2004), which have been identified in the previous
literature as having predictive power for future stock returns. These 12 characteristics are
categorized into 5 groups. The first group contains momentum and trading volume variables
including RETP (cumulative market-adjusted return in months -6 through -1 preceding the
month of portfolio formation), RET2P (cumulative market-adjusted return in months -12
through -7 preceding the month of portfolio formation), FREV (analysts’ earnings forecast
revisions), SUE (the most recent quarter’s unexpected earnings) and TURN (average daily
volume turnover in the six months preceding the month of portfolio formation). The second
group contains valuation multiples such as EP (the earnings-to-price ratio) and BP (the
book-to-price ratio). The third group contains growth indicators such as LTG (mean analyst
forecast of expected long-term growth in earnings) and SG (the rate of growth in sales over the
13
past year). The fourth group contains a firm-size variable — SIZE — defined as the natural
log of a firm’s market capitalization. The fifth group contains fundamental indicators such
as TA (total accruals divided by total assets) and CAPEX (capital expenditures divided by
total assets).26
Apart from these 12 characteristics, we also compute three liquidity-related variables.
The first variable is a price impact measure – Pimpact – which measures the average per-
centage change in price caused by round-trip-trade of $1 million worth of the stock within
an hour. Pimpact is constructed following the technique described in Breen, Hodrick, and
Korajczyk (2002). The second variable is a bid-ask spread measure — Pspread — defined as
the average difference between current ask and bid divided by the midpoint. Both Pimpact
and Pspread are computed using intraday data from TAQ during the month of portfolio
formation (i.e. the month immediately prior to the holding period). The third variable is
liquidity measure — Amihud — discussed in Amihud (2002).27 Finally, we also report Price
(the closing price at the end of the month of portfolio formation), RET1M (the return during
the month of portfolio formation) and T P ER.
Table 5 shows that T P ER in general increases with growth indicators. If a firm has
experienced high sales growth (SG) over the past year or if its long term growth rate is
expected to be high (as captured by LTG), its stock is more likely to be associated with
a higher T P ER. This is consistent with Jegadeesh et. al. (2004)’s finding that analysts
generally prefer “glamour” stocks with higher growth potential. In addition, T P ER is
generally decreasing in past returns (RETP, RET2P and RET1M). This is not surprising
since recent losers (winners) are likely to trade at lower (higher) prices and price enters
denominator when computing T P ER. Consistent with this explanation, the average trading
price for stocks in portfolio 1 is about $32 – much lower than that of stocks in portfolio 9
which is $45. Finally, the SIZE and BP of portfolio 1 and 9 are similar, which explains why
our long-short strategy (portfolio 1-9) has small factor loadings on SMB and HML.
In general, the two extreme portfolios have higher than average transaction cost measures,
which means they are more illiquid than the average stock. The liquidity variables in Table 5
also allow us to answer a more interesting question: Can the profit of our long-short strategy
overcome the transaction costs? On one hand, we expect lower than average transaction
costs since we are trading stocks in the S&P 500 index and have excluded penny stocks.
26
Detailed descriptions of each of the 12 characteristics and their construction can be found in Jegadeesh,
Kim, Krische, and Lee (2004).
27
To compute the Amihud measure, on each trading day, we first compute the ratio between absolute daily
return and the daily dollar trading volume. This ratio is then averaged during the month to get the Amihud
liquidity measure.
14
On the other hand, our long-short strategies involve monthly portfolio rebalancing, which
potentially could amplify the transaction costs and wipe out any “paper” profits. To gauge
the magnitude of the transaction costs, we focus our attention on portfolio 1 and 9. On
average, there are 33 stocks in each of the two portfolios each month and the monthly
portfolio turnover ratio is 73.7% and 80.4% for portfolio 1 and 9 respectively. Therefore,
an estimate of transaction cost (bid-ask spread + price impact) for portfolio1 is: 73.7% ×
(48.3 + 18.3) = 49.1 bps. For portfolio 9, it is 80.4% × (37 + 14.6) = 41.5 bps.28 The
transaction costs are considerably smaller than the three-factor alphas of 93 bps and 103
bps. Altogether, the sector neutral long-short strategy (portfolio 1-9) yields a risk-adjusted
profit net of transaction costs of 105 bps (196 − 49.1 − 41.5) per month, or 12.6% per year,
which is both statistically and economically significant. In addition, the transaction cost
can be further reduced by over-weighing more liquid stocks and under-weighing less liquid
stocks as in Korajczyk and Sadka (2004).
3.4 Are the profits driven by past returns or past target price
changes alone?
The definition of TPER involves dividing by the current stock price and the question arises
whether our results are simply driven by a sort on price. To investigate this possibility, we
sort stocks into 9 portfolios according to the inverse of the stock price (1/P) at the end of
the month within each sector. This strategy produces an insignificant risk-adjusted return
of only 76bps (118bps before risk adjustment) as shown in Table 7 column 2.29 This is not
surprising because low-priced stocks tend to be small stocks so a sort on 1/P is in part a sort
on size. Controlling for the Size factor therefore eliminates much of the profit. Qualitatively
similar results hold when sorting on other price ratios, such as earnings price or sales price
ratios.
Since T P ER is defined as a ratio between target price and market price; therefore,
its current level is influenced jointly by its past return and past revisions in the target
price. Previous studies have shown that a change in market price (past return) or change
in target price alone is associated with future return. For example, Jegadeesh (1990) and
Lehman (1990) have documented significant short-run stock return reversal at horizons of 1
month or less. This is consistent with our finding as our benchmark long-short portfolio 1-9
involves long position in past losers and short position in past winners. However, short-term
28
The implicit assumption behind this calculation is that we trade 1 million dollar worth of each stock
within an hour.
29
If we exlude the momentum factor UMD, the alpha becomes only 38bps (t-value of 0.66).
15
return reversal alone does not drive our results. Table 7 reports the profits and alphas to
alternative sector-neutral long-short trading strategies based on the S&P500 stock sample.
For the purpose of comparison, the results of our long-short strategy based on T P ER are
reproduced in the first row of table 7. The third column shows the results to a long-short
strategy based on the short-term return reversal. Specifically, we form portfolios by sorting
the S&P 500 stocks within sectors based on the past 1 month return alone, and then long
the past losers and short the past winners. The loser-minus-winner return spread is 122 bps
and significant with a t-value of 2.24. However, once adjusted for risk using the five factors,
the significance disappears. The five-factor-alpha is only 62 bps with a t-value of 1.48.30
This result differs from the previous literature on reversal effects mainly because of the more
recent sample period and restricting attention to the set of S&P500 stocks receiving analyst
coverage so that no small stocks are in our sample.
Changes in target prices are known to be positively related to future returns (Brav and
Lehavy 2003, Asquith, Mikhail and Au 2005). This relationship is also evident in our S&P
500 stock sample. We examine the most recent target price change in the past-three-month
period for each stock in our 9 within-sector T P ER-sorted portfolios. If the current target
price exceeds 1.05× last target price, we classify the change as an upgrade; if the current
target price is smaller than 0.95× last target price, we classify the change as a downgrade;
otherwise, we classify it as a reiteration. If there is no target price announcement in the
3rd and 2nd month preceding the current month, we classify it as missing. We then report
the percentage of upgrade, downgrade, reiteration and missing for each portfolio in Table 8.
As one would expect, S&P 500 stocks receive frequent target price coverage: less than 1.5%
of these stocks have a target price during the current month but none during the previous
two months. The percentage of target price upgrades increases monotonically with T P ER.
In portfolio 1, which has the highest T P ER and first one month return, the recent target
price changes are dominated by upgrades (percentage of upgrade and downgrade are 55.4%
and 22.0% respectively). The reverse is true for portfolio 9 where the majority of the stocks
suffered recent downgrades (percentage of upgrade and downgrade are 19.7% and 56.7%,
respectively). However, analysts’ revision in target price alone does not drive the future
return. Defining the change in the target price DT Pt as ∆T Pt /T Pt−1 and sorting stocks
into 9 portfolios based on DT P within sectors does not yield any significant portfolio return
spread for our S&P 500 stock sample. The results are provided in column 4 of Table 7.31
30
We get comparable but weaker results by sorting on the past 3 month return. In addition, the profit
and alpha are even smaller (108 bps and 4 bps per month) if there is no sector control.
31
The computation of DT P restricts us to a subsample of our S&P500 stocks where there are target
price announcements during the preceding month. We verify that the profit to our benchmark T P ER-based
16
Finally, we examine a strategy based on both past return and target price revision.
Within each sector, we conduct a 3 by 3 independent sort based on DT P and the past one
month return. We then go long past losers with high DT P and short past winners with
low DT P . This long-short strategy now generates a significant profit of 156 bps per month
(t-value of 3.00) and a significant alpha of 126 bps per month (t-value of 2.36), (See column
5 of Table 7).
3.5 Are the profits driven by earning announcements or stock
recommendations?
Analysts provide investors with information in addition to target prices such as earning
forecast and stock recommendations, which are known to affect future returns. To ensure that
our results are not driven by pure Post-Earning Announcement Drift (PEAD), we examine
stocks in each of the within-sector T P ER-sorted portfolios of S&P 500 stocks for which
there was no earnings announcement during the portfolio formation period. The exact time
for each earning announcement is obtained from the First Call Historical Database (FCHD).
We report the excess return and the three-factor-alpha for the sub-sample with no earnings
announcements in Table 9. On average, 58% of the target price coverage occurs during a
month with no earning announcement. This percentage is quite stable across all T P ER-
sorted portfolios for our S&P 500 stock sample (although it is slightly higher for the extreme
portfolio 1 and 9). Our results do not seem to be driven by delayed reaction to earning
announcement (or post-earning announcement drift). If we focus on the subsample with
no earning-announcement during the month of portfolio formation, the profit and five-factor
alpha not only do not disappear, but become even higher (207 bps and 222 bps respectively).
To show that our results are not driven by stock recommendation alone, we construct
alternative sector-neutral long-short strategy based on the level of stock recommendations
and revisions to stock recommendations. Specifically, from December 98 to December 04,
we focus on stocks in our S&P 500 sample where there was at least one stock recommen-
dation announcement during the first 25 calendar days of the portfolio month. We con-
struct nine portfolios sorted on the level of recommendation within sectors.32 Sorting on
the level of recommendation does not seem to work; the long-high-recommendation/short-
low-recommendation strategy produces a loss (see column 6 of Table 7), consistent with the
strategy hardly changes when we move to this subsample.
32
Clearly T P ER and the level of stock recommendation are positively correlated. The rank correlation
between these two variables is about 0.15 for both the S&P 500 sample and the full sample. However, the
fact that the correlation is less than one indicates that target price may contain more nuanced information
than the stock recommendation alone.
17
findings in Boni and Womack (2006).
We investigate the sub-sample of stocks for which there also were stock recommendation
announcements during the 3rd or 2nd month preceding the current month. This allows us
to compute the most recent revision in recommendations during the past three month prior
to portfolio formation. We construct nine portfolios sorted on revision in recommendation
within sectors in this sub-sample. Although the long-upgrade-short-downgrade portfolio
produces a profit on average, the profit and alpha are not significant (see column 7 of table
7).33 Finally, we examine a strategy based on both past return and recommendation revision.
Within each sector, we conduct a 3 by 3 independent sort based on past one month return
and the most recent revision in recommendation. We then long past losers with upgrades and
short past winners with downgrades. This long-short strategy does not generate significant
profit and alpha either (see column 8 of Table 7).
3.6 A liquidity interpretation
Figure 5 shows the evolution of the daily median market price (Panel A) and target price
(Panel B) during the two months month prior to and one month following portfolio formation
(t = 0) for each of the two extreme within-sector T P ER-sorted portfolios of S&P 500 stocks.
The stock price at portfolio formation (t = 0) has been normalized to 1. Clearly, the market
price and target price moved in opposite directions during the months preceeding portfolio
formation. For portfolio 1, the market price drops despite an upward revision in the median
analyst’s target price, resulting in a larger gap between the target price and market price
as captured by a large T P ER. For portfolio 9, the reverse is true: the market seems
to ignore the median analyst’s downgrade in target price leading to a negative T P ER at
portfolio formation.34 In portfolio 1 and 9, the adjustment in target price during the first
month seems to be much larger than that of the market price. The magnitude of the
market price adjustment is small, consistent with the conjecture that it is a price correction
following a liquidity event. However, our results show that the correction in market price,
although relatively small in magnitude, is still significant and can be profitably exploited by
implementing the appropriate long-short strategies.
A change in market price or target price alone does not drive our results. Only when
target price and market price changes are combined in the T P ER variable can we identify
33
We again verify that the profitability of our T P ER-based strategy hardly changes when we move to
these two subsamples where we apply filters based on the availabilities of past recommendations.
34
Brav and Lehavy (2003) use cointegration analysis to show that the correction of the short-run deviation
from the long-run relation between the two is dominated by revisions to analyst’s target prices, as is also
evident from Figure 5.
18
significant future price movements. A recent change in price could be driven either by changes
in fundamentals that are likely permanent, or by investor sentiment or liquidity and therefore
likely temporary in nature. By looking at analysts’ target price revision during the same
period of time, we are able to distinguish between these two possibilities. If target price and
market price were moving in opposite directions, it is more likely that recent changes in the
market price were driven by liquidity and will be reversed in the near future. This intuition
is directly supported by the results of a double-sort based on past return and target price
revision (see column 5 of Table 7). Past losers which have experienced recent target price
upgrades have significant positive excess returns during the first month on average, while
past winners who have experienced recent target price downgrades have negative excess
returns during the first month on average. Finally, sector control refines the result because
it eliminates systematic risks that have a similar impact on all stocks within the same sector
and at the same time preserves the relative strength information contained in analyst’s price
targets. The result is less strong than for our benchmark TPER sorted portfolio which may
in part be due to the loss of observation due to the requirement of consecutive months with
target price announcements.
We can further decompose
TP TP
1 + T P ER ≡ = × (1 + Ret)−1
P−1 P−30
i.e. the target price implied expected return using the market price at the beginning of
the portfolio formation month times the (gross) return over the portfolio formation month.
Table 7 column 9 shows the result of forming a portfolio based on a 3 by 3 double sort on
past return and T¯ /P−30 . The strategy produces a significant risk adjusted profit, but again
P
not nearly as strong as for our benchmark portfolio.
In summary, a long-short strategy based on price change or target price revision alone
does not produce a significant risk-adjusted profit even after controlling systematic risk at the
sector level. To make the strategy profitable, we need to combine the information embedded
in both price and target price (e.g. Table 7 columns 1,5& 9).
Consistent with a liquidity explanation of the TPER sorted profits, the two extreme port-
folios (1 and 9) indeed display a higher than average bid-ask spread, price impact measure
and Amihud liquidity measure as seen from Table 5. However, in order to make sure this
pattern is not driven by a few illiquid stocks always appearing in portfolio 1 or 9, we compute
the average percentage changes in a stock’s bid-ask spread (Pspread), price impact measure
(Pimpact) and Amihud liquidity measure (Amihud) when the stock enters portfolio 1 or
35
portfolio 9. Panel C of Table 10 clearly shows that stocks are more illiquid during periods
35
When computing the percentage change in Pspread, we adjust for the change in price by multiplying
19
when they are in portfolio 1 or 9. In addition, Panel A of Table 10 displays the changes
in the turnover ratio (defined as trading volume divided by number of share outstanding)
across the three months (portfolio pre-formation, formation and post-formation). For both
portfolio 1 and 9, we see increases in trading volume during the portfolio formation month
(although this increase is only statistically significant for portfolio 1). This is consistent with
the liquidity-driven price-fundamental-divergence interpretation as in Campbell, Grossman,
and Wang (1993) and the empirical evidence in Conrad, Hameed, and Niden (1994). Fi-
nally, the changes in order imbalance measures from the portfolio formation month to the
subsequent month provide further supporting evidence for the liquidity-based interpretation.
We examine two order imbalance measures. OIB1 is the buyer-initiated shares purchased
less than the seller-initiated shares sold (daily). OIB2 is OIB1 scaled by the total num-
ber of shares traded. Both measures are calculated from the intraday database TAQ and
first averaged within each calendar month and then within each T P ER sorted portfolio.
The results are provided in Panel B of Table 10. Within portfolio 1, there are significant
increases in both measures, indicating more buyer-initiated trades during the month after
portfolio formation, consistent with a initial price depression during portfolio formation and
later price recovery. The reverse pattern is observed for portfolio 9, again consistent with
its price reversal pattern. Since institutional trading is associated with larger price impact,
we would expect portfolio 1 to be associated with large institutional selling and portfolio
9 to be associated with large institutional buying during the month of portfolio formation.
This is exactly what we find using US equity mutual fund holding data obtained from Morn-
ingstar. Specifically, at the end of each month from January 1999 to December 2004 and
for each stock in our S&P sample, we compute the change in holdings by mutual funds as a
group during the preceding 3 months. For the subset of mutual funds which reported their
holdings at the end of the current month and also reported 3 months earlier we compute the
changes in holdings (as a percentage of total number of shares outstanding) of each stock
and aggregate across funds as:
holdingt − holdingt−3
Mfh chg =
# of shares outstanding
12 reports the average diff and the t-value associated with diff for each of the nine TPER-
sorted portfolios. For portfolio 1, the diff is significantly negative, indicating heavy mutual
fund selling; for portfolio 9, the diff is significantly positive, indicating heavy mutual fund
buying.
The target price reflects the opinion of the analyst while the market price reflects the
opinion of the market. They differ the most in portfolio 1 and 9. It is natural to assume that
the percentage change by pt /pt−1 .
20
the degree of information asymmetry may also be higher for stocks in these two extreme
portfolios. In order to protect themselves against such information asymmetries, market
makers raise the trading cost of these stocks, making them more illiquid. Panel C of Table
10 provides additional supporting evidence for this explanation. For each stock each month,
we define its target price dispersion measure as the standard deviation of target prices re-
ceived from different analysts divided by the consensus target price, similar to the dispersion
measure used in Diether, Malloy, and Scherbina (2002).36 For a given stock, the dispersion
measure is a lot higher when it enters portfolio 1 or 9 compared to when it is in neither of
the extreme portfolios. The dispersion measure increases by 62% (with a t-value of 6.41)
when it enters portfolio 1 and by 72% (with a t-value of 8.31) when it enters portfolio 9.
If liquidity temporarily drives a wedge between price and fundamental and the near term
correction in price results in the profit and alpha of our sector-neutral long-short strategies,
we would then expect the size of the alpha to be correlated with the magnitude of illiquidity
(as measured by Pimpact, Pspread and Amihud) in the previous month. This is exactly the
case in our S&P 500 sample. Evidently, the alpha co-moves with liquidity measures across
time. The standard correlation between alpha and Pimpact is around 0.27, the correlation
between alpha and Pspread is about 0.40 and the correlation between alpha and Amihud
is about 0.29. All three correlation coefficients are statistically significant. The Spearman
Rank correlations are similar as in Table 11.
The divergence between prices and fundamentals in this case is not corrected immediately
but persists for a few weeks even for S&P500 stocks. There could be several explanations
for the delay. First, since resolving information asymmetry takes time, the associated higher
trading cost may also last for a while. Second, news that comes out during the holding period
may push the price in an unwanted direction, thus the profit to the long-short strategy is
not guaranteed. Although the profit covers the transaction cost in magnitude on average,
its significance level may be reduced after accounting for the transaction cost. There is also
downside risk. For instance, the long-short strategy produced a (risk-adjusted) loss of -6.2%
during September 2001. Third, the liquidity event may produce self-reinforcing externalities
as described in Coval and Stafford (2005) where asset fire sales by one mutual fund can
trigger subsequent fire sales by others leading to persistence and possibly deepening of the
mispricing. Finally, there may be times when the mobility of the financial capital is low, i.e.
it takes time for an investor to identify a profitable opportunity and then move capital to that
opportunity. All these considerations may prevent risk-averse arbitrageurs from promptly
correcting the price.
36
We need the stock to have at least two target prices during the first 25 calendar days in order to compute
this dispersion measure.
21
Another interesting question to ask is whether relative T P ER has any incremental pre-
dictive power once we control for other liquidity related variables. In Table 6 we consider
three alternative model specifications. In Model 1 we run a cross-sectional regression of
one-month stock returns on the book-price ratio, size, past 1 month return, TPER, and a
collection of stock liquidity characteristics. In this case only the past 1-month return appears
to have marginal predictive power and in particular TPER is insignificant. This is not too
surprising given our finding in Table 3 that TPER without sector control is uninformative.
In Model 2 we therefore include sector dummies in the regression. This has the effect of
sector demeaning all variables and will also remove any auto-correlation in sector returns.
Now TPER is the sole significant variable, although the t-stat of 2.07 is marginal. This
result is consistent with the result in Table 2 where a sort on TPER within sector produced
a significant spread in excess returns. There are at least two reasons why the result of the
cross-sectional regression may be weaker. The TPER is highly correlated with the liquidity
measures and past returns, and it is possible that these variables in combination capture
most of the pertinent information in TPER. A second reason is that the relation between
relative TPER and future returns could be non-linear. In Table 2 for instance, the profit
from going long portfolio 2 and shorting portfolio 8 is negligible. To investigate this possi-
bility further, we in Model 3 replace the continuous TPER variable by dummy indicators
indicating which portfolio a stock was assigned to in a given month. All portfolio effects can
be interpreted as relative to portfolio 1 (whose dummy is excluded). Only the coefficient
on the portfolio 9 dummy is significant (t-stat -2.88) which confirms the finding that only
extreme TPER values contain a signal about future returns. This is true, even controlling
for past returns, size, book-to-price and liquidity characteristics.
In summary, we argue that the profit to our sector-neutral long-short strategy is related
to compensation for providing immediacy during a liquidity event at the individual stock
level rather than premium for bearing the aggregate liquidity risk in the economy. The
former contains a large idiosyncratic component and is relatively short in duration, while the
latter is largely systematic in nature and has a permanent impact on expected return. The
aggregate liquidity risk has been discussed extensively in the previous literature (c.f. Pastor
and Stambaugh (2003), Acharya and Pedersen (2005), Chordia, Roll, and Subrahmanyam
(2001) and Eisfeldt (2004)) or the co-movement of liquidity among stocks (c.f. Chordia,
Roll, and Subrahmanyam (2000), Hasbrouck and Seppi (2001) and Huberman and Halka
(2001)). The six-factor model results in Panel B of Table 2 provide some direct evidence
that the profit to our sector-neutral long-short strategy is not driven by aggregate liquidity
37
risk premium. The factor loadings on an aggregate liquidity risk factor - LIQ are close to
37
LIQ is the return to a zero-investment portfolio of longing stocks with large sensitivities to the aggregate
22
zero for portfolio 1, 9 and 1-9. As a result, the alpha hardly changes after controlling for the
aggregate liquidity risk.
4 Full sample results
We extend our analysis so far to the full sample from Dec 1996 to Dec 2004 and obtain similar
results qualitatively.38 For example, the benchmark sector-neutral long-short strategies yields
an excess return of 130 bps (t-value of 3.29 ) and a five-factor alpha of 107 bps (t-value of
4.15) in the full sample (See Table 13).39
4.1 Performance in sub-samples
The most important ingredient for the success of the sector-neutral long-short strategy is
the availability of an accurate measurement of fundamental value. It is therefore natural
to conjecture that the largest profits are to be found in the subset of stocks with the most
accurate analyst forecasts. Similarly one would expect higher profits for less liquid stocks.
With this in mind, we turn to investigating the performance of this strategy within sub-
samples.
Panel A of Table 14 shows the performance for stocks listed in NYSE and NASDAQ.40
Although our sector-neutral long-short strategy produces significant profit and alphas across
both exchanges, the alpha is more significant for NYSE stocks (t-value of 4.73) than NAS-
DAQ stocks (t-value of 2.69). One possible explanation is that companies listed in NYSE
tend to be relatively more mature and exhibit more value than growth so analysts may offer
liquidity risk and shorting stocks with small sensitivities to the aggregate liquidity risk. It is proposed by
Pastor and Stambaugh (2003).
38
To save space, the full-sample results are included in a separate appendix available upon request.
39
We apply the same price filter to exclude stocks traded below or at $5, or about 6% of the entire
sample. We also filter out stocks whose T P ERs are in the top decile each month, which corresponds to an
average cutoff level of T P ER = 70%. The mean T P ER for such stocks is 106.3% and the median is 95%.
These stocks are also associated with the lowest analyst coverage and the highest target price dispersion
measure. Such high T P ER could be due to either data error or an extremely bullish view on the part of
the analyst, which should not be regarded as an accurate measure of “fundamental” value. We verify that
the results are qualitatively similar even if we do not apply such filter, although the profit becomes smaller
and less significant due to the noise embedded in these extremely high T P ERs. We manage to obtain sector
classification (GICS) from either S&P website or COMPUSTAT for 72% of the stocks in our sample. We
have to manually assign GICS for the remaining 28% of the stocks, which may introduce some noise in the
results.
40
There are too few AMEX-listed stocks in our sample (less than 3%) to investigate the sub-sample
performance.
23
more accurate assessments of the relative strength of companies in the same sector, result-
ing in a better performance of the long-short strategy. Another explanation is suggested by
Glosten and Milgrom (1985) and Glosten (1989), who argue that liquidity effects in the NYSE
and NASDAQ markets will differ depending on the degree of asymmetric information-based
trading. In particular, the NASDAQ’s competitive market makers result in higher liquidity
as long as asymmetric information issues are not too severe, an explanation consistent with
our strategy yielding more profits for NYSE stocks.
Panel B of Table 14 shows the performance of our sector-neutral long-short strategies
within 6 size and book-to-market doubled sorted portfolios. In general, we find the perfor-
mance much better on the value stocks (with high book-to-market ratios) than the growth
stocks (with low book-to-market ratios). We attribute the effect of the book-to-market ratio
to the fact that analysts’ estimates for value firms with a higher fraction of tangible assets
will be less noisy than for growth firms. We also find that the performance is better on the
small stocks than the large stocks. This is consistent with our liquidity explanation. Since
small stocks are more illiquid in general, the reward for providing liquidity should be higher
for small stocks. Not surprisingly, the small-value stock portfolio now produces a highly
significant profit of 236bps. In addition, this profit only loads on DMU, resulting in a large
alpha of 207bps with comparable level of significance (t-value of 4.12).
Panel C of Table 14 shows the performance across 9 sectors. In general, the alphas
are significant in the Energy, Materials, Industrials and Consumer Discretionary sectors
and not significant in the Consumer Staples, Health Care, Technology and Utilities sectors.
The relative performance across sectors is consistent with the book-to-market ratio effect
as Energy, Materials, Industrials and Consumer Discretionary sectors contain more value
stocks.41
4.2 Behavioral Interpretation
The short-term return reversal we documented is also potentially consistent with investor
overreaction as explored in various behavioral models.42 For example, De Long, Shleifer,
Summers, and Waldmann (1990), the positive feedback strategies followed by ”noise” traders
could temporarily push the price away from the fundamental value. In Daniel, Hirshleifer,
and Subrahmanyam (1998), when investors become overconfident in their private signals,
41
Arguably, Utilities sector also contains more value stocks. However, the book-to-market ratios for firms
in these sectors are difficult to interpret.
42
Barberis, Shleifer, and Vishny (1998) and Hong and Stein (1999) explain long-term return reversal.
However, in their models, price under-react to news in the short run, which is not consistent with the return
pattern we documented.
24
price can temporarily overshoot. Although we cannot completely rule out such explanations
based on investor overreaction, we think that they are less applicable for the following rea-
sons. First, the return reversals we documented occur over a relatively short horizon (most
of the price reversals happen within the first two weeks after portfolio formation), while most
of the behavioral models are designed to explain return reversal over a much longer horizon
(over a few years). Second, in overreaction stories, there has to be ”news” for investors to
overreact. Earning announcement is an important form of public news.43 However, we have
shown that the magnitudes of the return reversals are similar whether or not there are recent
earning announcements. Third, the overreaction-based explanations typically implies that
the return reversal should be higher for low book-to-market firms, again opposite to what
we have found using the full sample.
The temporary deviation between price and fundamental value may also be related to
investor’s sentiment. Baker and Stein (2004) show that investor sentiment could be related
to market liquidity especially when there are short-selling constraints. From Figure 4, it can
also be seen that the average annualized risk-adjusted return on our sector neutral long-short
strategy increases from 1999 to 2000 and then drops off over the subsequent years until 2004.
This pattern is similar to the investor annual sentiment factor derived in Baker and Wurgler
(2005). At a monthly frequency, our risk-adjusted return is also positively correlated with
another sentiment index measure — change in the Michigan Consumer Confidence Index
(correlation = 0.13). Therefore, investor sentiment could be partly driving the liquidity
events that we identify.
5 Conclusion
Large stocks are usually very liquidity. At any given point in time, however, a handful
of them could experience periods of low liquidity. In this paper we identified these stocks
using equity analysts’ target prices as a proxy for fundamental values. We exploited the
fact that news about stock fundamentals should affect both analyst target prices and the
current market prices. Price movements without corresponding movements in analyst target
prices are likely to be driven by uninformed trading and therefore reflect cost of providing
immediacy.
Although equity analysts’ target prices themselves are very noisy and often biased mea-
sures of fundamental values, we establish that much of the noise and biases in target prices
can be eliminated by focusing on the implied within-industry relative valuations. In partic-
43
For S&P 500 stock, private news or signals should be less important.
25
ular, we show that both recent losers whose target price did not decline and recent winners
whose target price did not increase (within each industry) are likely to revert in the short-run.
Our benchmark sector-neutral long-short portfolio of S&P 500 stocks earned a statistically
significant average risk adjusted profit of around 200 bps per month during the period from
1999 to 2004, much higher than most realistic transaction cost estimates.
We provide considerable evidence showing that the profits are related to a reward for
liquidity provision. Indeed, we find the profit to be highly correlated with a number of
popular cross-sectional measures of liquidity such as the bid-ask spread, price impact, the
Amihud liquidity measure and increases in turnover. Furthermore we show that changes in
institutional buying and selling pressure identified based on quarterly mutual fund filings,
are broadly consistent with a liquidity explanation of our benchmark portfolio profits.
26
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29
A Figures and Tables
40
50
Actual (%) TP Implied (%)
20
40
0
TP Implied (%)
Actual (%)
30
−20
20
−40
10
−60
01jan1999 01jan2000 01jan2001 01jan2002 01jan2003 01jan2004 01dec2004
Figure 1: Target price implied one-year-ahead expected return (TPER) versus actual
one-year return. At the end of each month from December 1998 thru December 2004, we
compute the equity analysts’ implied return forecast for the value weighted portfolio of
S&P500 stocks with analyst coverage that month (dashed line). We compare this to the ex-
post realized 12 month return of the portfolio (solid bars). The graph confirms the finding
of Bradshaw and Brown (2005) that analysts on average are unable to forecast the market
risk-premium.
1
.5
Spearman Rank Correlation
0 −.5
−1
01jan1999 01jan2000 01jan2001 01jan2002 01jan2003 01jan2004 01dec2004
Figure 2: Rank correlation between target price implied and actual sector returns
across 9 GICS (Global Industry Classification System) sectors. At the end of each
month from December 1998 thru December 2004, we create 9 value weighted GICS sector
portfolios from the set of S&P500 stocks with analyst coverage that month. We then com-
pute the 12 month return forecast for each sector implied by target prices and compute the
Spearman rank correlation with the ex-post realization of the sector returns. If analysts
were able to predict relative sector performance, then the rank correlation should be con-
sistently positive. This is clearly not the case and we conclude that analysts have no such
skill on average.
30
Profit by month
200
180
160
140
120
profit in the first
100 two weeks
bp
80
60
40
20
0
-20
1 2 3 4 5 6
Figure 3: Average monthly profit (in excess of the risk-free) to the benchmark long-
short strategy during each of the 6 months following portfolio formation. The shaded
area represents the profit accruing during the first 2 weeks.
15.00%
risk adjusted portfolio return
excess return on market portfolio
10.00%
5.00%
0.00%
-5.00%
-10.00%
-15.00%
Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Jan-04
Figure 4: Time series of the excess returns on the market portfolio and the risk
adjusted benchmark portfolio returns. The monthly (five-factor) risk adjusted returns
of the benchmark long-short strategy using S&P 500 stocks (black bars) versus the market
excess return over the risk-free (striped bars) between Feb 1997 and Dec 2004. The shaded
pre-1999 period indicates the sub-sample where the GICS classification is backfilled. This
period is excluded from the main analysis although all results remain qualitatively similar
if it is included.
31
P1 P9
1.05
1
.95
-40 -20 0 20
count
Panel A
1.6
P1 P9
1.4
1.2
1
.8
-40 -20 -5 0 20
Panel B
count
Figure 5: Evolution of the median market price and target price for the extreme
TPER-sorted portfolios. Panel A: The daily evolution of the median market price for
stocks in portfolio 1 (high TPER, dashed line) and portfolio 9 (low TPER, solid line) during
a 2 month period around the portfolio formation date. The stock price at portfolio formation
(t = 0) is normalized to 1. Panel B: The median daily target price evolution (normalized
by the market price at t=0) during the 3 month period around the portfolio formation date
(t=0). Note: the median is calculated on each day (relative to t=0). On any given day
relatively few target prices are announced for the stocks in portfolio 1 and 9, explaining the
more noisy graph in panel B.
32
Table 1: First Call target price data description. From Dec 1996 to Dec 2004, at the end of
each month, we include stocks which had at least one (1 year ahead) target price announcement
during the first 25 calendar days of the month. Panel A summarizes basic sample characteristics
Table 1: Data the coverage of the component stocks of three major
across the sampling period. Panel B presentsDescription
equity indices in US in 2004. Panel C breaks down our sample into sectors according to Standard
From Dec 1996 to Dec 2004, at the end of each month, we include stocks where there is at least one (1 year ahead) target price
and Poor’s GICS (Global Industry Classification Standard). Since there are too few stocks
announcement during the first 25 calendar days of the month. Panel A summarizes basic sample characteristics across the sampling in the
Telecommunications Services sector, we three major equity indices in Information Technology our
period. Panel B presents the coverage of the component stocks of group them with the US in 2004. Panel C breaks downsector to
sample into sectors according to Standard and Poor’s GICS (Global Industry Classification Standard). Since there are too few stocks in
form a combined “Technology” sector. This classification is consistent a combined Technology sector.
the Telecommunications Services sector, we group them with the Information Technology sector to form with the way sector ETFs
(SPDRs) consistent with the after 1999.
This classification is alsoare constructed way sector SPDRs are formed and traded.
Panel A: Basic sample characteristics
number number of % of all
of stocks target price Mean Median Median mktcap stocks in
year NYSE AMEX NASDAQ
per per stock per TPER TPER (in million $) terms of
month month mktcap
1996 1095 1.75 39.1% 23.1% 754 56.0% 3.3% 40.7% 55.5%
1997 1205 2.02 35.7% 21.5% 799 57.6% 3.5% 38.9% 58.2%
1998 1641 2.37 45.6% 28.8% 718 55.7% 3.5% 40.8% 68.6%
1999 1675 2.45 44.7% 28.6% 795 54.9% 3.1% 42.0% 73.6%
2000 1759 2.59 63.7% 36.4% 983 51.5% 2.6% 45.9% 78.5%
2001 1761 2.72 50.5% 26.4% 920 50.9% 2.3% 46.8% 80.5%
2002 1738 2.84 39.9% 23.2% 916 53.3% 2.3% 44.5% 83.1%
2003 1677 2.49 19.7% 13.4% 1,022 54.9% 2.6% 42.5% 82.8%
2004 1796 2.51 18.4% 13.2% 1,216 53.2% 2.8% 44.0% 83.0%
Panel B: Index coverage in 2004
S&P
500 Russell 1000 Russell 3000
number of stocks included 496 980 2782
percentage 99.2% 98.0% 92.7%
Panel C: Sector breakdown
Consumer Consumer
Energy Materials Industrials Health Care Financials Technology* Utilities
Discretionary Staples
in terms of number of stocks
1996 5.8% 6.3% 12.9% 19.6% 5.8% 11.9% 14.6% 20.6% 2.6%
1997 4.6% 6.6% 13.1% 19.0% 5.4% 10.3% 16.8% 20.9% 3.3%
1998 4.8% 6.0% 13.9% 18.6% 5.2% 10.2% 17.0% 20.8% 3.4%
1999 4.5% 5.7% 13.0% 18.4% 4.7% 9.4% 17.3% 23.4% 3.5%
2000 4.7% 5.5% 11.9% 17.1% 4.0% 9.6% 17.0% 27.0% 3.3%
2001 4.9% 5.1% 12.1% 16.6% 3.6% 11.5% 17.9% 25.1% 3.4%
2002 4.4% 5.1% 12.2% 17.6% 3.9% 11.2% 19.1% 23.2% 3.3%
2003 4.6% 5.3% 12.2% 17.5% 4.0% 11.1% 21.2% 20.6% 3.5%
2004 5.4% 5.5% 12.0% 17.4% 3.7% 11.3% 20.6% 20.9% 3.3%
in terms of mktcap
1996 5.5% 5.1% 11.9% 15.8% 12.1% 12.8% 13.9% 20.9% 2.0%
1997 4.4% 5.6% 12.3% 15.1% 11.6% 11.9% 14.7% 22.1% 2.3%
1998 3.4% 4.1% 12.3% 15.6% 10.2% 12.7% 15.9% 23.3% 2.6%
1999 2.9% 2.9% 10.7% 14.3% 7.6% 12.3% 15.7% 31.6% 2.0%
2000 4.4% 2.1% 8.9% 11.1% 5.1% 11.3% 15.4% 39.7% 1.9%
2001 5.6% 2.5% 10.0% 11.9% 6.4% 14.0% 20.1% 26.6% 2.8%
2002 5.7% 3.0% 9.2% 13.8% 8.2% 13.7% 21.7% 21.9% 2.7%
2003 6.8% 3.3% 9.8% 14.0% 7.0% 13.4% 22.4% 20.7% 2.6%
2004 8.1% 3.6% 9.6% 14.2% 6.9% 11.9% 22.6% 20.3% 2.9%
S&P 500 in terms of mktcap
2000 6.56% 2.29% 10.54% 10.26% 8.09% 14.33% 17.31% 26.83% 3.78%
2001 6.34% 2.61% 11.28% 13.14% 8.24% 14.35% 17.81% 23.11% 3.12%
2002 6.00% 2.83% 11.53% 13.44% 9.47% 14.93% 20.45% 18.48% 2.85%
2003 5.80% 3.04% 10.90% 11.30% 10.98% 13.31% 20.64% 21.19% 2.84%
2004 5.60% 6.40% 11.40% 17.40% 7.20% 11.00% 16.40% 18.00% 6.60%
* We combine Information Technology sector and Telecommunication Services sector to form the Technology sector, consistent with the grouping of sector ETF.
33
Table 2: Returns on within-sector TPER-sorted portfolios of S&P 500 stocks. At the end of
each month from November 1998 to December 2004 and within each sector, we rank S&P 500 stocks
in our sample into 9 portfolios according to the current month TPERs and label them from 1 to 9 (1
with the highest TPER and 9 with the lowest TPER). For each stock, we compute the first month
post-formation market adjusted excess returns (in excess of the risk free rate). Finally, we equally-
weigh the excess returns of all stocks in the same portfolio. Panel A reports the average excess returns
during each of the first six months after portfolio formation and risk-adjusted alphas using a Five-factor
model. The five factors are the three Fama-French factors, a momentum factor (UMD) and a reversal
factor (DMU). Panel B reports the alphas from a Six-factor model which includes the Pastor-Stambaugh
value-weighted aggregate liquidity factor(LIQ). Panel B also reports the Characteristics-adjusted returns
where the benchmark characteristics portfolios are either the 5 by 5 Book-to-market and Size double-
sorted portfolios or the 3 by 3 by 3 Book-to-market, Size and Momentum triple-sorted portfolios. All
Table 2
returns and alphas are monthly.
Panel A: Excess returns and five-factor alphas of TPER-sorted portfolios
First Five-factor model Future excess return
mth
excess month month month month month
alpha MKT SMB HML UMD DMU
return 2 3 4 5 6
1 1.58% 1.34% 1.367 0.039 0.470 -0.334 0.027 1.19% 0.68% 1.13% 0.53% 1.00%
1.77 3.47 14.04 0.43 4.37 -5.75 0.40 1.34 0.78 1.28 0.60 1.06
2 0.91% 0.58% 1.232 0.057 0.445 -0.267 0.105 0.54% 0.64% 0.79% 0.57% 0.49%
1.17 2.10 17.72 0.89 5.79 -6.42 2.18 0.72 0.88 1.06 0.80 0.64
3 0.60% 0.35% 1.057 -0.014 0.439 -0.207 0.037 0.20% 0.42% 0.55% 0.44% 0.64%
0.90 1.13 13.59 -0.20 5.12 -4.45 0.69 0.34 0.59 0.81 0.64 0.96
4 0.95% 0.72% 1.082 -0.014 0.401 -0.128 -0.059 0.67% 0.89% 0.47% 0.56% 0.37%
1.56 3.01 17.78 -0.24 5.96 -3.52 -1.41 1.13 1.50 0.71 0.89 0.60
5 0.77% 0.57% 1.000 -0.078 0.412 -0.095 -0.043 0.40% 0.68% 0.43% 0.69% 1.01%
1.36 2.12 14.77 -1.25 5.51 -2.34 -0.92 0.67 1.08 0.68 1.16 1.61
6 0.57% 0.37% 0.954 -0.012 0.426 -0.132 -0.107 0.52% 0.82% 0.88% 0.63% 0.15%
1.06 1.74 17.80 -0.23 7.20 -4.14 -2.88 0.92 1.58 1.55 1.04 0.23
7 0.48% 0.38% 0.955 -0.107 0.300 -0.076 -0.064 0.69% 0.60% 0.68% 0.52% 0.83%
0.92 1.88 18.66 -2.28 5.30 -2.49 -1.79 1.33 1.09 1.25 0.87 1.47
8 0.46% 0.32% 0.980 -0.075 0.290 -0.078 -0.041 0.44% 0.84% 0.90% 0.42% 0.53%
0.83 1.33 16.27 -1.35 4.37 -2.16 -0.98 0.80 1.43 1.54 0.72 0.92
9 -0.19% -0.69% 1.084 0.154 0.583 -0.092 -0.083 0.55% 0.38% 0.33% 0.56% 0.88%
-0.33 -3.00 18.49 2.85 9.00 -2.63 -2.05 0.85 0.64 0.51 0.86 1.31
1-9 1.77% 2.03% 0.283 -0.115 -0.113 -0.242 0.110 0.63% 0.30% 0.79% -0.03% 0.12%
3.55 5.06 2.79 -1.23 -1.00 -3.99 1.57 1.37 0.58 1.73 -0.07 0.27
34
Panel B: Six-factor alphas and characteristic-adjusted returns of TPER-sorted portfolios
Six-factor model Char. adj. excess return
BM /Size / Mom
alpha MKT SMB HML UMD DMU LIQ BM / Size 5x5
3x3x3
1 1.29% 1.407 0.106 0.462 -0.283 0.026 -0.092 1.64% 1.36%
3.33 13.69 1.00 4.30 -3.92 0.39 -1.18 1.13 3.54
2 0.52% 1.279 0.136 0.435 -0.207 0.104 -0.108 1.13% 0.83%
1.92 17.75 1.84 5.78 -4.09 2.21 -1.98 0.87 2.74
3 0.30% 1.097 0.053 0.431 -0.155 0.037 -0.092 0.64% 0.31%
0.97 13.44 0.63 5.06 -2.71 0.69 -1.49 0.56 1.12
4 0.72% 1.087 -0.006 0.400 -0.123 -0.059 -0.010 1.02% 0.76%
2.95 16.73 -0.09 5.90 -2.69 -1.40 -0.20 0.94 3.56
5 0.56% 1.009 -0.062 0.410 -0.083 -0.043 -0.022 1.16% 0.56%
2.05 14.00 -0.83 5.44 -1.63 -0.92 -0.40 1.05 2.27
6 0.34% 0.980 0.032 0.421 -0.099 -0.108 -0.060 0.84% 0.40%
1.60 17.40 0.56 7.15 -2.51 -2.92 -1.41 0.75 1.70
7 0.41% 0.936 -0.140 0.304 -0.101 -0.063 0.045 0.27% 0.41%
1.99 17.29 -2.52 5.37 -2.66 -1.79 1.10 0.26 2.02
8 0.33% 0.969 -0.093 0.292 -0.091 -0.041 0.025 0.11% 0.09%
1.37 15.11 -1.41 4.36 -2.02 -0.97 0.51 0.10 0.42
9 -0.72% 1.107 0.192 0.578 -0.063 -0.084 -0.052 -0.46% -0.37%
-3.11 17.86 3.01 8.93 -1.45 -2.06 -1.12 -0.40 -1.39
1-9 2.01% 0.300 -0.086 -0.116 -0.220 0.110 -0.040 2.10% 1.74%
4.95 2.77 -0.77 -1.03 -2.90 1.55 -0.48 2.72 4.20
Table 3: Returns on TPER-sorted portfolios of S&P 500 stocks without sector control. At
the end of each month from December 1998 to December 2004, we rank all S&P 500 stocks in our
sample into 9 portfolios according to the current month TPERs and label them from 1 to 9 (1
with the highest TPER and 9 with the lowest TPER). For each stock, we compute the first month
post-formation excess returns (in excess of the risk free rate). Finally, we equally-weigh the excess
returns of all stocks in the same portfolio. We report the average excess returns and risk-adjusted
Table 3
alphas (using the Five-factor model). All returns and alphas are monthly.
First mth Five-factor model
TPER
excess return alpha MKT SMB HML UMD DMU
1 0.86% 0.95% 1.414 0.079 0.016 -0.572 0.216 71.4%
0.74 2.03 11.99 0.73 0.12 -8.13 2.64
2 0.71% 0.52% 1.185 -0.069 0.346 -0.252 0.148 36.1%
0.91 1.63 14.75 -0.94 3.90 -5.25 2.67
3 1.22% 0.83% 1.101 0.005 0.460 -0.169 0.157 27.6%
1.79 2.85 14.98 0.07 5.66 -3.85 3.09
4 0.62% 0.40% 1.066 -0.046 0.445 -0.181 -0.008 22.3%
0.98 1.51 15.74 -0.74 5.95 -4.49 -0.16
5 1.00% 0.67% 1.063 -0.035 0.519 -0.020 -0.125 17.9%
1.82 2.77 17.27 -0.61 7.63 -0.54 -2.93
6 0.92% 0.70% 0.962 -0.097 0.438 -0.017 -0.118 13.8%
1.87 3.66 19.77 -2.16 8.15 -0.58 -3.49
7 0.49% 0.19% 0.890 0.005 0.464 -0.061 -0.081 9.7%
1.03 0.91 16.99 0.10 8.02 -1.96 -2.23
8 0.27% 0.08% 0.938 -0.029 0.465 -0.074 -0.194 4.7%
0.52 0.28 13.66 -0.46 6.14 -1.81 -4.08
9 0.07% -0.34% 1.054 0.135 0.585 -0.052 -0.236 -10.0%
0.14 -1.57 19.08 2.66 9.60 -1.57 -6.16
1-9 0.79% 1.29% 0.360 -0.056 -0.569 -0.520 0.451 81.4%
0.86 2.44 2.69 -0.46 -3.86 -6.52 4.88
35
Table 4: Robustness to alternative portfolio formation strategies. We examine the robustness of the average excess and Five-factor
risk-adjusted returns to changes in the benchmark portfolio formation strategy described in Section 3.1. All returns and alphas are
monthly averages over the period January 1999 - January 2005 (72 months). Panel A: Equal weighted portfolios with and without
a 5 day gap between the target price collection period and the portfolio formation date. The ‘GICS’, ‘SIC’ and ‘FF sectors’ columns
correspond to three different choices of sector classification schemes: the GICS (our benchmark, numbers in bold), 1-digit SIC codes and
the Fama-French sector definitions respectively. The column ‘≥3 TP/mth’ results from using the GICS sector specification but requiring
that stocks have at least three target price announcements during the portfolio formation period. The column ‘Ex-Jan’ displays the
result obtained by using the GICS sector classification but excluding January months from the sample. Finally, the column ‘ATPER’
displays the result of using as an alternative definition of TPER: the average of announced target prices divided by the respective market
price on the day of the announcement (rather than the average of announced target prices divided by the market price on the portfolio
formation date). Panel B: Value weighted portfolio results.
Panel A: Excess returns and 5-factor alphas for equal weighted portfolios
5 day gap no gap
GICS SIC FF Sectors ≥3 TP/mth Ex-Jan ATPER GICS SIC FF Sectors ≥3 TP/mth Ex-Jan ATPER
Portf 1 (α) 0.0134 0.0102 0.0103 0.0186 0.0125 0.0095 0.0141 0.0114 0.0106 0.0161 0.0131 0.0095
t-stat 3.47 2.59 2.65 3.21 3.06 2.98 3.65 2.72 2.73 3.32 3.23 2.92
Portf 9 (α) -0.0069 -0.0024 -0.0043 -0.0006 -0.0058 -0.0005 -0.0075 -0.0038 -0.0050 -0.0005 -0.0063 -0.0018
t-stat -3.00 -1.03 -1.92 -0.14 -2.41 -0.22 -3.01 -1.59 -2.04 -0.13 -2.43 -0.73
36
1-9 (excess ret) 0.0177 0.0094 0.0140 0.0164 0.0155 0.0077 0.0189 0.0123 0.0150 0.0152 0.0164 0.0105
t-stat 3.55 1.30 2.53 2.28 3.07 1.68 3.55 1.72 2.66 2.32 3.06 2.25
1-9 (α) 0.0203 0.0126 0.0146 0.0192 0.0183 0.0101 0.0215 0.0152 0.0156 0.0165 0.0194 0.0114
t-stat 5.06 2.93 3.47 3.00 4.43 2.82 5.08 3.45 3.77 2.91 4.52 3.10
Panel B: Excess returns and 5-factor alphas for value weighted portfolios
5 day gap no gap
GICS SIC FF Sectors ≥3 TP/mth Ex-Jan ATPER GICS SIC FF Sectors ≥3 TP/mth Ex-Jan ATPER
Portf 1 (α) 0.0069 0.0064 0.0048 0.0166 0.0068 0.0045 0.0079 0.0078 0.0054 0.0120 0.0076 0.0046
t-stat 1.84 1.79 1.24 3.04 1.73 1.28 2.11 2.06 1.38 2.60 1.96 1.32
Portf 9 (α) -0.0089 -0.0054 -0.0037 -0.0025 -0.0082 0.0000 -0.0084 -0.0052 -0.0049 -0.0030 -0.0075 -0.0016
t-stat -3.29 -2.30 -1.45 -0.60 -3.03 0.00 -2.94 -2.00 -1.75 -0.76 -2.59 -0.54
1-9 (excess ret) 0.0132 0.0076 0.0055 0.0165 0.0114 0.0019 0.0136 0.0091 0.0064 0.0131 0.0113 0.0050
t-stat 2.56 1.14 0.99 2.35 2.22 0.41 2.49 1.35 1.06 1.99 2.08 1.02
1-9 (α) 0.0158 0.0118 0.0085 0.0191 0.0149 0.0045 0.0163 0.0131 0.0103 0.0150 0.0151 0.0062
t-stat 3.56 2.61 1.78 3.04 3.41 0.98 3.58 2.90 2.14 2.65 3.40 1.39
Table 5: Characteristics of TPER-sorted portfolios using S&P 500 stocks. Panel A: We
report various accounting and return based characteristics of TPER-sorted portfolios using S&P
500 stocks. RETP is the cumulative market-adjusted return in months -6 through -1 preceding
the month of portfolio formation; RET2P is the cumulative market-adjusted return in months -12
through -7 preceding the month of portfolio formation); FREV is the analyst earnings forecast
revision; SUE is the most recent quarter’s unexpected earnings; TURN is the average daily volume
turnover in the six months preceding the month of portfolio formation; EP is the earnings-to-price
ratio; BP is the book-to-price ratio; LTG is the mean analyst forecast of expected long-term growth
in earnings; SG is the rate of growth in sales over the past year; SIZE is defined as the natural log
of a firm’s market capitalization; TA is total accruals divided by total assets; CAPEX is the capital
expenditures divided by total assets. Panel B: We report the liquidity related characteristics of the
TPER sorted portfolios. Pimpact is the percentage change in price caused by a $1 million trading
volume within half an hour, calculated as in Breen, Hodrick, and Korajczyk (2002); Pspread is the
percentage bid-ask spread calculated using tick by tick data; Amihud is the liquidity measure of
Amihud (2002) (calculated using daily data and multiplied by 107 ); Price is the closing price at
the end of the month of portfolio formation; RET1M is the return during the month of portfolio
Table 5: formation. Pimpact, Pspread and Amihud are all averages over the month of portfolio formation.
Panel A: 12 characteristics studied in Jegadeesh et.al. (2004)
Valuation Firm Fundamental
Momentum and trading volume Growth Indicators
Multipliers Size Indicators
RETP RET2P FREV (bp) SUE TURN EP BP LTG SG SIZE CAPEX TA
mean
1 -3.39% 4.00% -12.30 0.39 0.74 0.013 0.45 15.27 1.156 16.30 3.87% -2.31%
2 0.80% 4.33% 7.68 0.57 0.70 0.036 0.40 15.21 1.151 16.37 4.24% -2.05%
3 2.76% 4.45% 14.71 0.57 0.68 0.033 0.39 14.95 1.141 16.41 4.04% -1.97%
4 4.65% 5.29% 15.19 0.61 0.68 0.040 0.38 14.28 1.130 16.37 4.12% -1.90%
5 5.68% 4.94% 12.17 0.60 0.67 0.037 0.38 14.63 1.119 16.38 4.04% -1.59%
6 7.02% 4.81% 19.83 0.63 0.66 0.037 0.38 13.94 1.127 16.32 4.09% -2.13%
7 6.61% 5.26% 7.29 0.65 0.66 0.040 0.38 13.37 1.111 16.30 3.93% -1.86%
8 7.59% 5.22% 5.46 0.66 0.66 0.033 0.39 13.50 1.107 16.24 3.94% -2.25%
9 6.60% 4.44% -6.69 0.46 0.69 0.037 0.43 13.03 1.096 16.19 4.00% -1.60%
median
1 -6.57% -0.3% 18.98 0.24 0.77 0.039 0.38 13.63 1.087 16.30 2.77% -2.03%
2 -1.87% 1.6% 21.39 0.29 0.72 0.043 0.34 13.54 1.080 16.29 3.10% -1.82%
3 -0.18% 1.6% 24.00 0.35 0.70 0.044 0.34 13.19 1.077 16.37 3.00% -1.97%
4 1.46% 1.8% 22.26 0.34 0.69 0.045 0.33 12.56 1.074 16.29 3.02% -1.81%
5 3.74% 2.4% 19.83 0.34 0.67 0.046 0.33 12.65 1.066 16.28 3.13% -1.53%
6 4.54% 1.9% 21.38 0.33 0.67 0.046 0.34 12.48 1.073 16.21 3.09% -1.94%
7 5.31% 2.6% 15.28 0.32 0.67 0.046 0.32 12.08 1.068 16.15 2.97% -1.86%
8 5.15% 2.2% 15.52 0.33 0.67 0.045 0.33 11.94 1.063 16.13 3.02% -2.03%
9 4.23% 0.2% 9.14 0.29 0.72 0.046 0.36 11.24 1.060 16.04 3.05% -1.73%
37
Panel B: Other characteristics
Liquidity Others
Pimpact Pspread
(in bp) (in bp) Amihud Price RET1M TPER
mean
1 18.3 48.3 8.02 31.8 -5.31% 67.9%
2 14.4 42.0 6.34 37.2 -3.22% 36.4%
3 12.9 39.1 5.52 39.5 -1.13% 28.4%
4 12.4 38.4 5.33 42.8 -0.03% 23.0%
5 12.2 36.5 5.29 44.9 1.62% 18.8%
6 12.0 35.6 5.04 45.2 2.79% 14.8%
7 12.6 34.9 5.34 46.8 3.97% 10.7%
8 12.8 35.5 5.50 46.5 5.22% 5.1%
9 14.6 37.0 6.18 45.1 6.04% -9.0%
median
1 10.4 44.0 4.12 28.2 -4.52% 53.0%
2 8.6 38.1 3.59 34.2 -3.36% 34.1%
3 8.2 35.3 3.22 36.8 -1.22% 27.1%
4 7.7 34.7 3.20 40.2 -0.01% 22.4%
5 7.7 32.7 3.09 41.8 1.07% 18.4%
6 7.6 32.0 3.13 42.2 2.30% 14.4%
7 7.8 31.2 3.18 43.0 3.34% 10.3%
8 8.4 31.9 3.37 42.6 4.27% 5.3%
9 9.0 32.5 3.68 40.3 4.77% -5.1%
38
Table 6: Cross sectional regressions with S&P500 stock sample. Each month from
December 1998 to December 2004, we run cross-sectional regressions of 1 month returns
on three sets of explanatory variables. These include: lagged 1 month return (ret), tar-
get price implied expected return (TPER), TPER based portfolio assignment dummies
(Port 2,...,Port 9), log market cap (SIZE), book to price ratio (BP) as well as a number
of liquidity characteristics calculated for each stock each month using daily and intra day
data. These include trading volume as percentage of outstanding shares (Turnover), the
Breen, Hodrick, and Korajczyk (2002) dollar volume price impact measure (Pimpact), the
average percentage bid-ask spread (Pspread), the change in order imbalance from the pre-
vious month (Oib chg), and a measure of the aggregate change in mutual fund holdings
(Mfh chg). In addition, Models 2 and 3 include sector dummies for the 9 GICS sectors. All
variables are standardized so that the regression slope coefficient can be interpreted as the
impact on return of a one standard deviation change. The reported slope coefficients are
averaged across time and the robust t value is computed using Newey-West autocorrelation
adjusted standard error with 6 lags (we consider 6 lags appropriate since the construction
of BP may utilize data up to 6 month old). There are, on average 239 S&P500 stocks in
each cross-section with the complete set of characteristics. The average R-squared of the
cross-sectional regressions is given in the final row.
Model 1: Model 2: Model 3:
TPER w/o Sector TPER w. Sector TPER Portid w.
Dummies Dummies Sector Dummies
Coef. t-value Coef. t-value Coef. t-value
Intercept 0.0231 0.49 0.0394 1.06 0.0506 1.59
BP 0.0041 0.38 -0.0017 -0.18 -0.0034 -0.36
SIZE -0.0021 -0.28 -0.0010 -0.18 -0.0012 -0.21
Pimpact 0.6801 0.54 1.1843 0.89 1.0652 0.78
Pspread 0.5729 0.79 0.5495 0.90 0.6160 0.97
Oib_chg -0.0038 -0.40 -0.0157 -1.23 -0.0187 -1.50
Mfh_chg 0.0005 1.82 0.0006 1.97 0.0005 1.87
Turnover 3.9377 1.36 2.4039 1.28 2.2800 1.22
Log_Amihud -0.0006 -0.10 0.0009 0.20 0.0010 0.22
RET1M -0.0303 -2.08 -0.0094 -0.62 -0.0053 -0.37
TPER 0.0056 1.01 0.0128 2.07
Port_2 -0.0058 -1.22
Port_3 -0.0072 -1.44
Port_4 -0.0056 -1.09
Port_5 -0.0070 -1.38
Port_6 -0.0048 -0.96
Port_7 -0.0065 -1.34
Port_8 -0.0089 -1.57
Port_9 -0.0153 -2.88
Avg R-sq 16.5% 26.3% 26.1%
39
Table 7: Profits to alternative sector-neutral long-short strategies in the S&P sample. At the
end of each month from December 1998 to December 2004, we construct various sector-neutral long-
short strategies using S&P 500 stocks in our sample. For each strategy, we report the equally-weighted
first-month excess return (in excess of the risk-free rate) for the long and short portfolio, the profit
to the overall long-short strategy and its associated Five-factor alpha. All returns and alphas are
monthly.
TPER: Within each sector, we sort stocks into 9 portfolios according to the current month TPERs,
then long stocks with the highest TPER and short stocks with the lowest TPER.
1/P: Within each sector, we sort stocks into 9 portfolios according to the inverse of the stock price
(1/P) at the end of the month, then long stocks with the lowest 1/P and short stocks with the highest
1/P.
Ret: Within each sector, we sort stocks into 9 portfolios according to the current month returns, then
long past losers and short past winners.
DTP: Within each sector, we sort stocks into 9 portfolios according to the current month DTP (change
in target price), defined as ∆TPt /TPt−1 , then long stocks with the highest DTP and short stocks with
the lowest DTP.
DTP×Ret: Within each sector, we conduct a 3 by 3 independent sort based on DTP and Ret, then
long past losers with high DTP and short past winners with low DTP.
Rec: We take the sub-sample of stocks with at least one recommendation announced during the first
25 calendar days of the current month. Within each sector, we sort stocks into 9 portfolios according
to the current month average level of analyst stock recommendation (Rec), then long stocks with the
highest recommendations and short stocks with the lowest recommendations.
∆Rec: We take the sub-sample of stocks with at least one recommendation announced during the
first 25 calendar days of the portfolio formation month which also had a recommendation during either
of the preceding two month. We compute the most recent revision in recommendations (∆Rec) and
within each sector, we sort stocks into 9 portfolios according to ∆Rec, then long stocks with the
highest ∆Rec and short stocks with the lowest ∆Rec.
∆Rec ×Ret: Within each sector, we conduct a 3 by 3 independent sort based on ∆Rec and Ret,
then long past losers with high ∆Rec and short past winners with low ∆Rec.
TP
ret× P−30 : Within each sector, we conduct a 3 by 3 independent sort based on Ret and average
target price divided by the market price at the beginning of the portfolio formation month. We
then long past losers with high TP/P−30 and short past winners with low TP/P−30 .
Table 7:
TPER 1/P Ret DTP DTP×Ret Rec ∆Rec ∆Rec×Ret Ret×TP/P-30
Long excess ret 1.58% 1.52% 1.36% 0.76% 1.41% 0.41% 0.92% 0.83% 1.78%
1.77 1.73 1.63 1.15 1.83 0.62 1.38 1.11 1.82
Short excess ret -0.19% 0.34% 0.15% 0.80% -0.15% 1.07% 0.43% 0.41% 0.14%
-0.33 0.66 0.24 1.08 -0.24 1.41 0.64 0.68 0.22
L-S excess ret 1.77% 1.18% 1.22% -0.04% 1.56% -0.66% 0.49% 0.42% 1.64%
3.55 1.84 2.24 -0.09 3.00 -1.55 1.37 0.94 2.53
L-S alpha 2.03% 0.76% 0.62% 0.15% 1.26% -0.61% 0.32% 0.20% 1.46%
5.06 1.80 1.48 0.38 2.36 -1.32 0.87 0.45 2.57
40
Table 8: Change in Target Price for within-sector TPER-sorted portfolios for S&P 500
stocks. We examine the most recent target price change in the past three months for each stock
in the Change in Target Price for within-sector TPER-sorted portfolios for S&P 500 stocks
Table 7: within-sector TPER-sorted portfolios. If the current target price exceeds 1.05 × last target
price, we classify the change as an upgrade; if the current target price is smaller than 0.95 × last
target price change in change as a months for otherwise, we classify it as reiteration. If
We examine the most recentprice, we classify the the past three downgrade; each stock in the within-sectoraTPER-sorted portfolios. If
target
he current target price exceeds 1.05 × last target price, we classify the change as an upgrade; if the current target price is smaller than 0.95
there is no target price announcement in the 3rd and 2nd month preceding the current month,
× last target price, we classify the change as a downgrade; otherwise, we classify it as a reiteration. If there is no target price
3rd and 2nd it as missing. We current month, percentage as missing. downgrade, reiteration and
announcement in thewe classify month preceding thethen report the we classify it of upgrade,We then report the percentage of upgrade,
missing for each each portfolio.
downgrade, reiteration and missing forportfolio.
% of missing % of upgrade % of downgrade % of reiteration
1 2.03% 55.35% 21.96% 20.7%
2 1.34% 46.18% 22.35% 30.1%
3 1.10% 39.46% 26.55% 32.9%
4 1.25% 38.90% 25.57% 34.3%
5 1.32% 36.90% 25.36% 36.4%
6 0.96% 34.13% 28.21% 36.7%
7 1.56% 30.93% 32.00% 35.5%
8 1.56% 25.52% 39.93% 33.0%
9 1.87% 19.74% 56.73% 21.7%
Table 9: Effect of earning announcement on the S&P 500 sample. From Jan 99 to Dec
04, we focus on stocks in 9 within-sector TPER-sorted portfolios of S&P 500 where there was
no earning announcement during the month of portfolio formation. We then compute the excess
e 9: returns and the associated Five-factor alphas for both full sample and the sub-sample with no
earning announcement. All returns and alphas are monthly.
% of obs Sub-sample without earn_anno
Port without
earn_anno excess return Five-factor alpha
High TPER 61.8% 1.71% 1.63%
1.82 2.86
2 59.0% 1.26% 0.79%
1.44 1.96
3 57.8% 0.95% 1.00%
1.19 1.98
4 57.1% 0.98% 0.94%
1.28 1.82
5 55.7% 0.69% 0.44%
1.08 0.99
6 56.0% 0.98% 0.76%
1.37 1.37
7 57.0% 0.74% 0.45%
1.26 1.18
8 56.3% 0.25% 0.03%
0.40 0.09
Low TPER 59.2% -0.35% -0.59%
-0.54 -1.65
1-9 2.07% 2.22%
3.15 3.30
41
Table 10: Liquidity related characteristics of TPER-sorted portfolios in the S&P 500 sam-
ple. Panel A reports the turnover during the month before (t-1), during (t) and after (t+1) the
portfolio formation for our nine within-sector TPER-sorted portfolios using S&P 500 stock sample
from Jan 99 to Dec 04. The turnover is defined as total monthly trading volume divided by the
number of share outstanding. Panel B reports two average order imbalance measures during both
portfolio formation month (t) and during the month after (t+1): OIB1is the buyer-initiated shares
purchased less than the seller-initiated shares sold (daily). OIB2 is OIB1 scaled by the total num-
ber of shares traded. Panel C reports the average percentage change in bid-ask spread (Pspread) ,
price impact measure (Pimpact), Amihud liquidity measure (Amihud) and dispersion in analyst’s
target price forecast (Dispersion) when a stock is in portfolio 1 or portfolio 9 as compared to when
it is not. When computing the percentage change in Pspread, we adjust for the change in price by
multiplying the percentage change by pt /pt−1 .
Table 10:
Panel A: Turnover before, during and after portfolio formation
Turnover Turnover change from t-1 t-value of the
Portfolio Turnover (t+1)
(t-1) (t) to t change
1 18.73% 19.76% 19.53% 1.02% 2.69
2 16.30% 16.79% 16.47% 0.50% 1.61
3 15.29% 15.60% 15.51% 0.30% 1.07
4 14.52% 14.87% 14.68% 0.35% 1.20
5 14.29% 14.59% 14.37% 0.30% 1.00
6 14.14% 14.27% 14.09% 0.13% 0.50
7 13.92% 14.03% 13.81% 0.11% 0.37
8 14.95% 15.21% 14.70% 0.27% 0.78
9 15.75% 16.13% 15.85% 0.38% 1.10
Panel B: Order imbalance measures during and after portfolio formation
OIB1 during
OIB1 one OIB2 at OIB2 one
formation
port month later (2)-(1) t-value formation month later (4)-(3) t-value
month
(2) (3) (4)
(1)
1 88830.5 156595.1 67764.6 5.19 0.0393 0.0549 0.0155 6.23
2 117721.3 134149.1 16427.8 1.71 0.0453 0.0548 0.0096 4.01
3 137495.0 146562.8 9067.8 0.61 0.0497 0.0559 0.0062 2.74
4 139808.3 139294.6 -513.7 -0.05 0.0571 0.0603 0.0032 1.46
5 153430.8 147019.8 -6411.0 -0.70 0.0634 0.0623 -0.0011 -0.55
6 161499.7 147136.1 -14363.6 -1.70 0.0680 0.0643 -0.0037 -1.81
7 173850.1 157260.6 -16589.5 -1.79 0.0725 0.0642 -0.0083 -4.00
8 174748.0 148157.9 -26590.1 -2.76 0.0742 0.0643 -0.0099 -4.46
9 193638.6 160568.1 -33070.5 -3.11 0.0769 0.0639 -0.0130 -5.75
Panel C: Changes in liquidity related characteristics when stock moves into the extreme portfolios (1 or 9)
When stock enters portfolio 1 When stock enters portfolio 9
pspread pimpact Amihud Dispersion pspread pimpact Amihud Dispersion
Percentage change 6.5% 11.4% 9.9% 61.9% 7.0% 9.7% 7.5% 72.3%
t-value 3.42 3.36 3.71 6.41 3.96 3.31 3.50 8.31
42
Table 11: Correlation between alpha and liquidity characteristics. We compute the cor-
relations among price impact measure (Pimpact), bid-ask-spread (Pspread), the Amihud liquidity
measure and the Five-factor-alpha next month of our Sector-neutral Long-short strategy using S&P
500 stocks from December 1998 to December 2004. The standard correlation coefficients and p-
values are reported in the lower triangle and the spearman rank correlation coefficients are reported
Table 11 in the upper triangle.
Correlation P-value
alpha Pimpact Pspread Amihud alpha Pimpact Pspread Amihud
alpha 0.261 0.443 0.297 alpha 0.027 0.000 0.012
Pimpact 0.266 0.703 0.866 Pimpact 0.024 0.000 0.000
Pspread 0.396 0.676 0.812 Pspread 0.001 0.000 0.000
Amihud 0.294 0.858 0.817 Amihud 0.012 0.000 0.000
Table ?: Mutual fund holding change across TPER-sorted portfolios
Table 12: Trading pattern of US equity mutual funds across TPER sorted portfolios. At the
end of month from 1/1999 to 12/2004 and for each stock in for S&P sample, we
For eacheach month from December 1998 to December 2004 and our each stock in our S&P sample,
we compute the amount holdings by mutual funds as amount brought (Tot_buy) 3 months. For
compute the total change insold (Tot_sell) and the total a group during the preceding by
the subset of mutual by comparing the mutual fund holdings immediately prior to the
mutual funds as groupfunds which reported their holdings at the end of the current month and also
reported the holdings immediately after changes in holdings (as a percentage of total number of
month and 3 months earlier we compute the the month and a trading imbalance measure
shares outstanding) ofbuy −stock and aggregate across funds as:
Tot _ each Tot _ sell
(diff) as diff = . We then report the average Tot_sell, Tot_buy,
(Tot _ buy + Tot _ sell ) / 2 holding − holding
t t−3
Mfh chg = .
diff and the t-value associated with diff for each of the nine TPER-sorted portfolios (1
#shares outstanding
being the highest TPER and 9 being the lowest TPER). The mutual fund holding data are
We then report the average
obtained from Morning Star. diff and the t-value associated with diff for each of the nine TPER-
sorted portfolios (1 being the highest TPER and 9 being the lowest TPER). diff is winsorized at
1st and 99th percentiles.
TPER-sorted
diff ( ×104 ) t-value
Portfolio
1 -14.70 -5.15
2 -6.15 -1.99
3 -1.38 -0.45
4 -1.75 -0.49
5 6.98 2.67
6 5.51 1.60
7 9.98 3.13
8 8.54 2.73
9 12.48 3.56
43
Table 13: Returns on within-sector TPER-sorted portfolios for the full sample. At the end
of each month from Dec 1996 to Dec 2004 and within each sector, we rank stocks into 9 groups
according to the current month TPERs and label them from 0 to 9 (0 with the highest TPER and
9 with the lowest TPER). For each stock, we compute its future excess returns (in excess of the
risk free rate). Finally, we equally-weigh the excess returns of all stocks within the same portfolio.
We report the average excess returns and risk-adjusted alphas (using the Five-factor model). All
returns and alphas are monthly.
Table 13:
First mth excess Five-factor model TPER
Port return alpha MKT SMB HML UMD DMU mean median
1 0.29% 0.14% 0.129 0.163 -0.089 -0.076 0.186 56.4% 54.5%
1.24 0.91 3.57 4.62 -1.97 -3.16 6.29
2 -0.06% -0.16% 0.098 0.046 0.003 -0.077 0.123 42.0% 40.5%
-0.35 -1.08 2.80 1.34 0.08 -3.27 4.31
3 0.14% 0.12% 0.019 0.007 0.001 -0.040 0.065 33.4% 32.4%
1.38 1.15 0.79 0.31 0.04 -2.44 3.27
4 -0.14% -0.18% 0.006 -0.055 0.040 0.021 0.026 27.1% 26.2%
-1.22 -1.53 0.23 -2.02 1.14 1.12 1.12
5 -0.30% -0.25% -0.043 -0.105 0.026 0.032 -0.041 21.8% 21.3%
-2.41 -2.26 -1.60 -4.00 0.79 1.77 -1.88
6 -0.35% -0.29% -0.088 -0.101 -0.012 0.096 -0.079 17.0% 16.6%
-2.19 -2.27 -2.86 -3.41 -0.32 4.70 -3.18
7 -0.67% -0.46% -0.152 -0.130 0.001 0.045 -0.169 12.1% 11.8%
-3.34 -3.37 -4.66 -4.09 0.01 2.07 -6.33
8 -0.92% -0.71% -0.157 -0.056 -0.024 0.050 -0.176 6.2% 6.1%
-4.61 -4.86 -4.41 -1.62 -0.54 2.12 -6.06
9 -1.01% -0.93% -0.040 -0.033 0.028 0.098 -0.192 -7.4% -5.3%
-4.87 -5.56 -0.98 -0.84 0.55 3.65 -5.82
1-9 1.30% 1.07% 0.169 0.196 -0.116 -0.175 0.378
3.28 4.15 2.72 3.24 -1.51 -4.22 7.46
44
Table 14: Performance of sector-neutral long-short strategies in various sub-samples.
Panel A reports the results for NYSE and NASDAQ stocks separately. Panel B reports the
results across size and book-to-market double sorted groups. Panel C reports the results
within each of our nine sectors. The sampling period is from Jan 1997 to Dec 2004. All
and
returns14: alphas are monthly.
Table
Panel A: NYSE vs. NASDAQ
Exchange excess ret. alpha MKT SMB HML UMD DMU
NYSE 1.28% 1.13% 0.218 0.040 0.073 -0.186 0.195
4.07 4.73 3.76 0.71 1.02 -4.82 4.13
NASDAQ 1.45% 1.15% 0.071 0.290 -0.150 -0.213 0.542
2.61 2.69 0.69 2.87 -1.16 -3.08 6.40
Panel B: Size and book-to-market sorted sub-samples
excess
Group Size B/M alpha MKT SMB HML UMD DMU
return
Small value 272,647 0.84 2.36% 2.07% 0.104 0.142 0.033 0.041 0.193
4.92 4.12 0.86 1.22 0.22 0.52 1.99
Small Growth 322,905 0.30 1.12% 1.15% 0.080 0.023 -0.325 -0.315 0.515
1.33 1.48 0.43 0.13 -1.41 -2.57 3.45
Medium value 1,263,608 0.68 1.02% 0.95% 0.222 -0.065 0.095 -0.168 0.169
2.02 1.91 1.87 -0.56 0.65 -2.13 1.76
Medium
1,285,998 0.24
growth 0.62% 0.56% 0.412 0.081 -0.171 -0.271 0.283
0.83 0.85 2.61 0.53 -0.87 -2.59 2.22
Large value 10,844,724 0.55 0.88% 0.84% 0.109 -0.163 -0.117 -0.139 0.323
1.92 2.08 1.13 -1.74 -0.97 -2.17 4.14
Large growth 25,703,362 0.18 0.65% 0.23% 0.085 0.095 -0.270 -0.132 0.811
0.84 0.37 0.57 0.66 -1.46 -1.34 6.76
Panel C: Different sectors
GICS Sector excess ret. alpha MKT SMB HML UMD DMU
10 Energy 1.87% 1.45% 0.479 0.258 0.199 -0.341 0.378
2.42 2.09 2.86 1.59 0.96 -3.07 2.77
15 Materials 1.53% 1.57% 0.109 0.287 -0.197 -0.199 0.093
2.50 2.57 0.74 2.00 -1.08 -2.02 0.78
20 Industrials 1.82% 1.96% 0.375 0.086 -0.035 -0.281 -0.117
3.47 4.06 3.21 0.76 -0.24 -3.62 -1.23
25 Consumer Discr. 2.36% 2.42% -0.031 0.125 -0.147 -0.179 0.175
5.85 6.11 -0.32 1.34 -1.23 -2.79 2.23
30 Consumer Staples 1.21% 0.92% 0.221 0.316 -0.046 -0.131 0.267
1.59 1.18 1.17 1.72 -0.20 -1.04 1.73
35 Health Care -0.29% -0.33% 0.081 0.164 -0.461 -0.315 0.582
-0.30 -0.36 0.37 0.77 -1.71 -2.17 3.27
40 Financials 1.13% 0.69% 0.312 -0.032 0.258 0.077 0.128
3.12 1.89 3.56 -0.38 2.37 1.31 1.79
45 & 50 Technology 1.11% 0.49% 0.174 0.347 -0.351 -0.134 0.909
1.29 0.73 1.08 2.23 -1.76 -1.26 6.96
55 Utilities 0.86% 0.77% 0.148 0.223 0.131 -0.296 0.170
1.29 1.13 0.90 1.39 0.64 -2.69 1.26
45