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An Empirical Analysis of Analysts' Target Prices:

Short Term Informativeness and Long Term Dynamics

Alon Brav, Duke University

Reuven Lehavy, University of California at Berkeley

First Version: December 2000

Current Version: May 2001

Abstract

Using a large database of analysts' target prices, we examine short-term market

reactions to target price announcements and long-term co-movement of target andstock prices. We find a significant market reaction to the information contained in

analysts' target prices, both unconditional and conditional on contemporaneously

issued stock recommendations and earnings forecast revisions. For example, the

spread in average announcement day abnormal returns between positive and

negative target price revisions is as high as 7 percent. We also find that stock

recommendations and earnings forecast revisions are informative controlling for

the information in target prices. Using a cointegration approach, we explore the

long-term behavior of market and target prices and estimate the system's long-term

equilibrium. In this equilibrium a typical firm's one-year ahead target price is 22

percent higher than its current market price. Finally, while market prices react to

the information conveyed in analysts' reports, we show that any subsequentcorrections towards the long-term equilibrium are, in effect, done by analysts alone.

We provide evidence that the market understands the latter relationship and is

therefore able to anticipate, at least partially, analysts' target price revisions.

We are grateful to Jeff Abarbanell, Ravi Bansal, Tim Bollerslev, David Hsieh, Jack Hughes, Roni Michaely, and seminar

participants at University of Illinois-Champaign, University of North Carolina at Chapel Hill, University of Toronto, and

Purdue University for their comments, and thank Mark Carhart for providing the factor time-series. We also thank the

following individuals for their insights: Stan Levine from First Call, Jennifer Lyons from Lend Lease Rosen Real

Estate Securities LLC, Jim Wicklund from Dain Rauscher Inc, Ralph Goldsticker from Mellon Capital Management,

Len Yaffe from Bank of America Securities, and Peter Algert from Barclays Global Investors. We owe special thanks

to John Graham, Campbell Harvey, and Richard Willis for many invaluable insights and comments. All remaining

errors are ours. Please address correspondence to either Brav at Fuqua School of Business, Duke University, Box

90120, Durham, North Carolina 27708, phone: (919) 660-2908, email: [email protected] or Lehavy at University

of California, Berkeley, Haas School of Business, Berkeley, California 94720, phone: (510) 642-5372, email:

[email protected].


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An Empirical Analysis of Analysts' Target Prices:

Short Term Informativeness and Long Term Dynamics

Security analysts provide investors with forecasts of earnings, stock recommendations, and

target prices. These outputs convey their opinion about a firm's expected earnings performance

and price changes. Academics and practitioners alike have been interested in understanding the

value and usefulness of these signals to investors. This interest has resulted in a wide body of

academic research and numerous articles in the business press documenting that investors react

to the information contained in analysts earnings forecasts and stock recommendations.

Surprisingly, however, the properties of analysts' target prices, which presumably provide the

most concise and explicit statement on the magnitude of the firm's expected return, have

remained unexplored. While some anecdotal evidence related to announcements of price targets

is provided by the business press, academic research on what is arguably analysts' most

informative statement on firms value target prices is essentially non-existent.1

Using a large database of analysts target prices, we attempt to fill this void by

investigating two questions. We begin by examining the short-term informativeness of target

prices. Given that target prices provide investors with analysts most explicit quantitative

statement regarding firms expected return (or relative mispricing), we expect announcements of

target prices to be associated with a significant market reaction. Consistent with this prediction,

we document significant abnormal returns around target price revisions and show that the

abnormal returns are increasing in the favorableness of the target price revision. We also

examine the incremental informativeness of target prices conditional on contemporaneously

1 Bradshaw [2000] reviews a sample of 103 analysts' reports and finds that the most frequently cited explanations

given in support of a recommendation and target price are price to earnings ratios and forecasted long-term earnings

growth rates. For a subsample of 67 firms, he documents a significant correlation between target prices, stock

recommendations, and earnings based measures. Using a sample of 300 Canadian firms Bandyopadhyay, Brown and

Richardson [1995] find that forecasted earnings explain a large proportion of the variation in price forecasts.

OBrien [2001] reflects on the controversy regarding the value of price targets: price targets, at their worst, can be

used to exploit unsophisticated investorsNow that some of the dust has settled, market professionals are seeing

some marginal value in price targets, if only in interpreting the vernacular of Wall Street. Vickers and Weiss [2000]

describe that analysts are increasingly lobbing absurdly extreme calls that attract big-media attention and

encourage momentum investing.


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issued stock recommendations and earnings forecast revisions and find evidence that target price

revisions are incrementally informative even in the presence of the other two signals.

Our second question is motivated by the fact that target prices are forward looking and,

much like stock prices, linked to the underlying firm fundamental value. Therefore, using a

cointegration framework, we examine the long-term dynamics that link target and market prices.

In particular, the ratio of target price to the underlying stock price provides a natural measure of

analysts estimate of the firms annual expected return. The cointegration analysis allows us to

estimate the mean of this ratio, which we interpret as the long-term equilibrium of the two price

series, and to quantify the speed and magnitude of adjustments of the two series towards this

long-term relationship. The analysis reveals that target prices are, on average, 22 percent higher

than concurrent market prices, and that this ratio is inversely related to firm size. We also find

that once the system of prices has been shocked away from its long-run equilibrium, it is analysts

who revise their targets back to the equilibrium relationship. Market prices, in contrast, barely

contribute to this correction phase. These long-term dynamics raise the possibility that target

price revisions are partially predictable. We test for this possibility and we find evidence that

investors are able to anticipate, at least partially, analysts' target price revisions.

The paper proceeds as follows. Section I reviews related literature and describes our

predictions. Section II describes the data. We examine the information content of target prices in

section III. Section IV describes our cointegration approach to modeling the long-term co-

movement of target and stock prices. Section V presents the cointegration results. Some of the

insights from the cointegration analysis are then used in section VI to argue that target price

revisions are partly predictable. A summary and conclusion is offered in Section VII.

I. Related Research and Empirical Predictions

Our examination of the informativeness of analysts' target prices contributes to extant

research on the information content of analysts' two other signals: stock recommendations and


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earnings forecasts. This research generally finds significant positive (negative) price reaction to

recommendation upgrades (downgrades) (e.g., Elton, Gruber, and Grossman [1986], Stickel

[1995] and Womack [1996]) and that the level of consensus analyst stock recommendations

predicts future gross abnormal returns (e.g., Barber, Lehavy, McNichols, and Trueman [2001]).

Recommendations have also been shown to contain information that is generally orthogonal to

the information in other variables known to have predictive power for stock returns (Krische and

Lee [2000]). Francis and Soffer [1997] focus on the relative informativeness of analysts' earning

forecast revisions and stock recommendations and find that each signal is informative in the

presence of the other, while Stickel [1999], Bradshaw [2000], and Markov [2001] examine the

consistency between consensus recommendations and consensus earnings forecast revisions.

We add to this research by examining the properties of analysts' target prices. We begin

our analysis with an examination of market reaction to target price announcements. Because

target prices provide investors with the analysts most explicit quantitative statement regarding

firms' expected returns, we expect to observe significant average market reaction around

announcement of such price targets. Furthermore, since greater upward (downward) revisions in

target prices are likely to represent more (less) favorable news, we expect market reactions

around target price revisions to increase in the favorableness of the revision.

Target prices, however, are issued in conjunction with stock recommendations and

earnings forecasts. We therefore extend our analysis to determine whether target price are

incrementally informative. Given the discreteness of stock recommendations we expect target

prices to be informative even in the presence of stock recommendations. Since earnings

forecasts are but one input into the target price calculation, we expect target prices to convey

information to market participants above and beyond that in the earnings revision.

While it is reasonable to expect target prices to be informative relative to stock

recommendations and earnings forecasts, the reverse is not obvious. If the target price is an

output of a valuation model that reflects the analyst's beliefs in the fundamental value of the firm,

mapping such a target price into a stock recommendation is informationally redundant. Investors


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can immediately infer the recommendation by comparing the target price to the current stock

price. Similarly, if earnings forecasts, along with other factors such as discount rates and payout

ratios, are inputs to the analyst valuation model, then the information in the earnings forecasts is

already reflected in the target price. This view suggests that both recommendations and earnings

forecast revisions should be uninformative in the presence of target price revisions.

There are, however, several reasons to expect stock recommendations and earnings

forecast revisions to be informative in the presence of target prices. First, for a given target price,

stock price movements that increase the magnitude of mispricing but, in the analyst opinion, do

not necessitate a target price revision, might lead the analyst to keep his target price but revise

his recommendation. For example, a 10 percent decrease in the price of a stock currently rated a

Buy might increase the stocks attractiveness, which can be easily conveyed to investors by an

upgrade from Buy to Strong Buy even without a target price revision. Second, for a given ratio

of target to market price, analysts argue that recommendation revisions provide additional

information on the level of confidence in that target price. For example, a target price which

exceeds current stock price by 20 percent could be perceived as more credible if it is

accompanied by a Strong Buy rather than a Buy recommendation. Put differently, a target price

might reflect the mean of the analysts posterior beliefs regarding the firm value, while a

recommendation provides additional information regarding the dispersion of these beliefs.2

Finally, earnings forecast revisions might also prove informative in the presence of target prices.

This can occur if investors consider earnings forecasts as informative but disagree with the way

the analyst incorporated the earnings information into his pricing model. We test empirically

these competing views on the information role of stock recommendations and earnings forecasts

in the presence of target prices.

2Another potential explanation, provided to us by a Goldman Sachs analyst, is that target prices convey a precise

measure of firm mispricing relative to current market price, while a recommendation may provide additional

mispricing information regarding a cross-section of similar stocks. For example, if certain investors are constrained

to hold a certain subset of the market, such as a given industry, then an analyst can employ recommendations as a

measure of intra-industry mispricing.


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The second objective of this paper is to examine the long-term comovement of stock and

target prices. Since both of these variables are linked to the underlying firm fundamental value

we model them as a cointegrated system. As we discuss in more detail below, target prices are

forward-looking, usually, one year ahead. Therefore, the ratio of the target price to the

underlying stock price provides a measure of analysts beliefs regarding the firms annual

expected return. The cointegration framework allows us to estimate the mean of this ratio and to

ask whether its magnitude is consistent with the predictions of some commonly used asset-

pricing models.

We also analyze the price systems reaction to deviations from its long-term equilibrium

ratio and quantify the speed and magnitude of adjustment of the two series towards this long-

term relationship. Our goal is to examine which price series corrects to the long-term

equilibrium once the price system has been shocked away from it. Are analysts' reacting to

deviations from the long-term equilibrium by adjusting their target prices or are market

participants responsible for most of the long-term adjustments? Under the null of market

efficiency, we predict that market prices react to the information conveyed in an analyst's report

but that any subsequent corrections to the long-term equilibrium are done by analysts alone.

3

II. Data and Variable Descriptions

A. Data Description

The target price, stock recommendation, and earnings forecast data employed in this paper

are provided by First Call. First Call has been a major supplier of analyst data to both

practitioners and academics. While the First Call data spans a shorter period than that of some of

their competitors (e.g., Zacks or I/B/E/S), First Call has always maintained that its data collection

procedures place great importance on ensuring accuracy, especially with respect to the timing of

3A related question is whether the (ex-ante) returns forecasted by analysts are unbiased and whether these

forecasted returns are more accurate relative to forecasts generated from asset pricing models such as the CAPM or

intrinsic value measures such as in Lee, Myers, and Swaminathan [1999]. Since our goal is to first understand the

dynamics that link the two price series, we examine these questions in a follow-up paper (Brav, Lehavy, and

Michaely [2001]).


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the reports. To that end, a distinguishing feature of the First Call database is that it codes the

source of each analysts report as either Real-time or Batch. Real-time refers to reports

received from live feeds such as the broker notes and are dated as the date that the report was

published. Batch reports are generated from a weekly batch file from the brokers and the

precise publication dates of the reports are unknown. With technological improvements in First

Call's data collection procedures, by 1999, the overwhelming majority of reports are coded as

Real-time. To ensure accurate dating of analysts' reports, our empirical analyses include only

observations coded as Real-time.

Table I provides descriptive statistics for the First Calls target price database (panel A),

stock recommendation database (panel B), and earnings forecast revision database (Panel C).

These statistics are provided for firms with available data on the Center for Research in Security

Prices ("CRSP"). The year 1997 is the first one with a complete target price data (coverage

begins in November 1996 with 3,862 target price reports for that year). Coverage increases over

time substantially from about 50,000 price target reports in 1997 to about 94,000 reports in 1999.

The average number of price targets per covered firm (column 3) also increases from 10 in 1997

to 18 in 1999. The target price database is quite comprehensive and includes reports for 6,544

distinct firms.4 The number of participating brokers remained fairly constant over the years, with

an increase from 123 in 1997 to 149 in 1999 (column 5), with 190 distinct brokers issuing price

target reports across all years. Each firm in the sample is covered, on average, by six brokers.

Finally, we find that these firms account for approximately 93 percent of the total market value

of all securities on CRSP and that many of the large brokers are represented in the database and

also account for a significant proportion of the observations.

Panel B of Table I provides a description of the recommendation database. In 1997, the

database includes 32,295 recommendations for 5,572 distinct firms. By 1999, the number of

recommendations reaches 42,014 for 5,929 distinct firms. The number of brokers remains fairly

4We have verified with an official at First Call that in those cases in which analysts report target price range

estimates, First Call records these as mid-point estimates.


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constant over the years with overall 325 distinct brokers included in the database. Consistent

with claims made by several analysts that certain brokerage houses which issue

recommendations have either a formal or an informal policy barring issuance of price targets, the

number of brokers issuing recommendations is higher than those issuing price targets.5

Panel C of Table I provides a description of the earnings forecast revision database. The

database includes about 124,000 earnings forecast for the period from 1997 to 1999. These

forecasts are distributed, on average, as seven forecasts per firm and pertain to 9,167 distinct

firms. These forecast revisions are issued by 282 distinct brokers with an average of seven

brokers per covered firm.

B. Variable Descriptions

We construct three alternative measures for the information content of analysts target

prices. The first, denoted TP/P, is the ratio of the announced target price to the stock price

outstanding two days prior to the announcement (all prices are converted to the same split-

adjusted basis). This ratio can be interpreted as the analysts estimate of the firms expected

return. The second measure attempts to capture whether investors react to information in target

price relative to the brokerage houses prior target price. This measure, denoted TP/P, is the

difference between the current and prior target price issued by the same brokerage house,

deflated by stock price outstanding two days prior to the announcement. The third variable is

designed to capture investor reaction to information in target price relative to the outstanding

consensus target price. Consensus target price is calculated as the average target price across all

brokerage houses. Target price outstanding for more than 90 days are excluded from the

consensus. This measure, denoted (TP-ConsTP)/P, is the difference between the brokerage

houses target price and the outstanding consensus target price immediately prior to the

5In unreported results we find that the majority of stock recommendations are issued as either Buy or Strong Buy

(68 percent), while only 29 percent are issued as a Hold and 3 percent as a Sell or Strong Sell. Also, the median

number of days between revisions is 59 days for target prices, 141 days for stock recommendations, and 92 days for

earnings forecasts. Additional description of the recommendation and target price databases is available in Appendix

A.


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announcement. This ratio is deflated by the firm's stock price two days prior to the

announcement.6

Panel A of Table II presents statistics on the three information measures as well as on the

earnings forecast revision. We winsorize these variables at the 1st and 99th percentiles to mitigate

the possible effect of extreme observations. These statistics indicate that the distributions of all

three measures are right skewed. Relative to pre-announcement stock price, target prices are

higher by 32.9 percent, are 17.5 percent higher than the brokerage houses' previously issued

target price, and 11.5 percent higher than the outstanding consensus target price.7 The right-most

column in Panel A presents descriptive statistics on the earnings forecast revision measured as

the change in the analyst forecast of earnings for the current fiscal year deflated by stock price

two days prior to the announcement. The mean (median) forecast revision is -0.41 (-0.03)

percent.

Panels B through D of Table II list the averages of the three target price information

measures conditional on the associated recommendation change. In general, changes in the target

price measures are consistent with the direction of the recommendation changes. For example,

Panel B reports that upgrades are generally associated with higher TP/P ratios than downgrades.

In Panels C and D we also find that the mean TP/P and (TP-ConsTP)/P are consistently positive

for upgrades and negative for downgrades. For example, an upgrade from a Buy to a Strong Buy

recommendation is associated with a mean upward revision in TP/P of 26.7 percent whereas a

downgrade from Buy to a Hold recommendation is associated with a mean downward revision of

10.2 percent. Similarly, an upgrade from a Hold to a Strong Buy recommendation is associated

with a mean revision in target price relative to consensus target price of 20 percent while a

6We have also explored a further refinement of the three information measures by scaling each of these measures by

the prior price standard deviation measured over the 90 days preceding the event. We find qualitatively similar

results in Section III with these scaled information measures.7

Inunreported results we find that, consistent with the common wisdom that analysts prefer dropping rather than

downgrading stocks with unfavorable prospects (e.g., McNichols and O'Brien [1997]), the frequency of target price

downgrades is fairly small. Only about 5 percent of target price reports are issued below concurrent stock price,

about 25 percent of target price reports reflect downward revision from brokerage houses prior report, and about 43

percent reflect a downward revision from the outstanding consensus target price.


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downgrade from a Strong Buy to a Hold recommendation entails a revision of 9.9 percent in the

target price. Finally, consistent with the notion that recommendation reiterations contain less

information than recommendation upgrades or downgrades, such reiterations are associated with

relatively smaller target price revisions.

We have also calculated statistics, as in Panels B through D, for the variation in earnings

revisions by stock recommendation revisions (unreported). Similar to the results in these panels,

we find that earnings revisions are monotonically related to the favorableness of the

recommendation change. The fact that revisions in target prices, recommendations, and earnings

forecasts are generally in the same direction suggests that, at least partially, these signals share

the same information content. In Section III we explore whether the information in each of these

signals subsumes the information in the other.

III. Market Reaction to Target Price Announcements

A. Unconditional Informativeness of Target Prices

In this section we examine whether the information content of target prices announcements

is associated with abnormal returns around those announcements. Specifically, we compute the

abnormal return around each announcement and present the average abnormal return for

portfolios ranked on the basis of the magnitude of the relevant information content measure.

Abnormal return is computed as the difference between the firm buy and hold return and the buy

and hold return on the NYSE/AMEX/NASDAQ value weight market index over the period

beginning two days prior to and ending two days subsequent to the target price announcement. 8

These results are reported in Figure I and Table III.

The visual evidence in Figure I and the reported results in Table III indicate that average

abnormal return around target price revisions is statistically significant and, in general,

8Results for the period of 1 to +1 days around the announcement are qualitatively similar. Also, to avoid possible

cross-correlation problem due to identical return observations, we delete all but one of identical return observations

within each portfolio.


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monotonically increasing in the favorableness of the revision. For example, the average

abnormal return for portfolios ranked on the basis of the change in the target price relative to the

outstanding consensus target price, (TP-ConsTP)/P, range from an average of 2.164 percent for

the least favorable revision to 2.608 percent for the most favorable one. The largest spread in

abnormal returns is in portfolios ranked on the basis of the change in the individual brokerage

house target price with average returns ranging from 3.956 percent to 3.208 percent for the least

and most favorable revisions, respectively.9

Combining these findings with those in extant literature of a significant positive (negative)

price reaction to favorable (unfavorable) stock recommendation (e.g., Womack [1996] and

Stickel [1995]) and earnings forecast revisions (Givoly and Lakonishok [1979], Elton, Gruber,

and Gultekin [1981], Lys and Sohn [1990], and Francis and Soffer [1997]) raises an interesting

question regarding the incremental information content of target prices in the presence of these

two other signals. We therefore extend our analysis, in Section III.B below, to distinguish

whether target price revisions are incrementally informative.

B. Informativeness of Target Prices Conditional on Stock Recommendations and Earnings

Forecast Revisions

Table IV provides regression results relating event-day abnormal returns to

recommendation levels, recommendation changes, earnings forecast revisions, and the target

price revision measure TP/P.10

9In unreported results we performed three additional robustness tests. In the first we examined whether earnings

announcements drive the documented average returns around target price announcements. To this end we excluded

from the abnormal return calculation observations that fell within a five-day window of an earnings announcement.

The results are qualitatively the same. Second, to account for the possibility that the documented abnormal return is

due to other firm specific events immediately prior to the target price announcement, we calculated abnormal returns

starting at day zero through day +2. Our results remain unchanged. Finally, we extended the post-event window

through sixty days after the target price announcement. We found no abnormal return for positive revisions and

some evidence of negative drift (-4 percent) for negative target price revisions. We leave for future research a

detailed examination of the predictive ability of target prices.10

This information proxy is the scaled change in the individual brokerage house target price. We present results

using this proxy to ensure comparability with the earnings forecast and recommendation revisions that are also

based on the individual brokerage house's revision. Analysis using the other two measures yields similar results.


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We begin, in panel A, by regressing event-day abnormal returns, AR, on three

recommendation levels, the earnings forecast revision, F/P, and the target prices revision

TP/P.11 Our goal is to determine whether target price revisions are informative in the presence

of earnings revisions and the level of the stock recommendation. In particular, we the regression

takes the following form:

+

+

+++=

P

TP

P

FSBBUYHOLDAR 321

where the indicator variables take the value 1 if the stated recommendation level is met and zero

otherwise.

The regression results clearly indicate that target price revisions are positively and

significantly related to event-day abnormal returns controlling for the information in the level of

the associated stock recommendation and the earnings forecast revision (=4.312 with t

statistic=46.5). Economically, a one standard deviation in TP/P contributes to a

0.424*4.312=1.83 percent average event day abnormal return. Moreover, the estimates of the

coefficients 1, 2, and 3 and their ordering ( 321


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where the indicator variables take the value 1if the stated recommendation revision is met and

zero otherwise. Much like the results in the previous panel, we find that target price revisions

are incrementally informative. The estimated coefficient is significant both statistically and

economically. We also find that both revisions in earnings forecasts and stock recommendations

are informative as well. The coefficients 1, 2, and 3 and their expected ordering

( 321


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+

+

++++

+++

++=

P

TP

P

FHOLDtoHOLDBUYtoBUYSBtoSB

BUYtoHOLDSBtoBUYSBtoHOLD

HOLDtoBUYBUYtoSBHOLDtoSBAR

987

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321

where the indicator variables take the value 1 if the stated recommendation revision is met and

zero otherwise. To ensure a meaningful interpretation of the incremental role of the relative

recommendation revision, we focus on recommendations that were either revisedfrom or revised

to the same recommendation. The relevant comparison are (i) upgrades to Strong Buy from

either Buy or Hold (i.e., a test of1=2), (ii) upgrades from Hold to either Strong Buy or Buy

(i.e., a test of1=3), (iii) downgrades from Strong Buy to either Hold or Buy (i.e., a test of4=5), and (iv) downgrades to Hold from either Strong Buy or Buy (i.e., a test of4=6).13

The regression results are consistent with the prediction that larger revisions in stock

recommendations are more informative. For example, the coefficient estimate associated with

upgrades to Strong Buy from Hold (3.276) is significantly different (p-value of 0.024) from the

one associated with upgrades to Strong Buy from Buy (2.246). Similarly, the coefficient

estimate associated with downgrades from Strong Buy to Hold (-4.485) is significantly different

(p-value of 0.008) from the one associated with downgrades from Strong Buy to Buy (-3.109).

Results are somewhat weaker for revisions either from or to Hold. For example, the p-value

13Because First Call converts the specific language of the recommendation into Strong Buy, Buy, Hold, Sell or

Strong Sell, some of the information contained in the recommendations is lost. For example, while a

recommendation of Market Performer, Natural, Maintain or Hold may convey a different message to investors, all

these recommendations are all being coded as Hold on the First Call database. In terms of our empirical analysis,

this lowers our ability to find results in support of our prediction.


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associated with the test of difference in the coefficient of downgrades from Strong Buy to Hold

relative to a revision form a Buy to Hold is 0.056.14

In sum, the evidence in Tables III and IV indicates that target prices are informative

controlling for the information in stock recommendations and earnings forecast revisions.

Furthermore, we document a role for the degree of the recommendation change which is

consistent with the prediction that analysts use the degree of the recommendation revision as a

signal of their confidence in their target price (e.g., variability in posterior beliefs).

IV. Modeling Long Term Equilibrium between Market Prices and

Target Prices

The analysis in Section III suggests that market participants perceive analysts' target

prices as an informative signal regarding firm value. That analysis, however, cannot address the

second issue discussed above, regarding the joint movement of stock and target prices. Since

both of these price series are linked to the underlying firm fundamental value, we study the

dynamics of their long-term co-movement. Because both sets of prices are nonstationary, we

employ a cointegration framework and estimate the linear combination of the price series that is

stationary. This linear combination is termed as the system's long-term equilibrium and is

parameterized as the ratio of target and market prices. Cointegration also implies that any price

deviations from this long-term equilibrium ratio are stationary as well. That is, if on a given date

the system is in equilibrium, a shock to any of the variables will lead to a price path that will

14 In additional (untabulated) tests, we allow the slope coefficient on the target price and earnings forecast revisions

to differ across recommendation levels (strong buy, buy, and hold) and changes (upgrades, downgrades, and

reiterations). Specifically, we estimated three separate regressions of event-day abnormal return on an intercept,

TP/P, and F/P by the level of the recommendation (i.e., Strong Buy, Buy, and Hold), and three similar regressionsby the change in the recommendation (upgrades, downgrades, and reiterations). We then test for the equality of the

three respective slope coefficients for each set of regressions. The null hypothesis of equality of the coefficient

estimates on the target price revision is rejected for both the set of the Strong Buy, Buy, and Hold regressions and

the upgrades, downgrades, and reiterations regressions. The coefficients on target price revisions are inversely

related to the favorableness of the recommendation. Consistent with the prediction in Francis and Soffer [1997], we

find that the coefficient on earning forecast revision is increasing in the favorableness of the recommendation.


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settle back to the long-term equilibrium.15 We analyze the price systems reaction to deviations

from this long-term equilibrium ratio by examining which price series corrects to the long-term

equilibrium once the system has been shocked away. That is, are analysts the ones reacting to

deviation from the long-term equilibrium by adjusting their target prices or are market

participants responsible for most of the adjustment? Moreover, how long is required for the

system to converge back to its long-term equilibrium?

Our empirical analysis is conducted on time series of individual firms weekly consensus

stock and target prices. Consensus target price is calculated as the average target price across all

brokerage houses. Target price outstanding for more than 90 days were excluded from the

consensus. We choose a weekly interval to avoid microstructure problems associated with daily

data. Given the long-term nature of the cointegration analysis, we require each firm to have a

minimum of 500 trading days (approximately 104 consecutive weeks) with continuous stock and

target price data. The final sample consists of 900 firms. While the choice of a two-year

minimum reduces the number of firms that we can study, it is a necessary requirement as we are

interested in studying the long-term dynamics of target and market prices.16

To set the stage for our methodological approach and to build intuition for the full sample

analysis, we begin by examining the joint price behavior of a single firm, IBM. We present the

full-scale analysis in Section V.

15We follow the cointegration literature (Engle and Granger [1987]) by using the term equilibrium in reference to

the relation that ties together the two price series over the long-run. The main motivation for the use of this term is

the idea that when two cointegrated economic variables drift apart then economic forces (market mechanism, for

example) tend to drive them back together. Lee, Myers, and Swaminathan [1999] employ this intuition in modeling

the long-term relation between price and intrinsic value on the Dow 30 stocks. As Campbell and Shiller [1988]

have argued, however, such an "equilibrium" can occur simply because one variable is a rational expectation of the

future of another variable which follows an integrated process. Campbell and Shiller's interpretation is important

since target prices are, by definition, analysts' forecasts of future prices.16

We have replicated the cointegration analysis using a minimum of 250 trading days and obtained similar results.

In addition, the analysis was also conducted on size-sorted portfolios containing all firms in our database. Again, our

conclusions regarding the dynamics of market and target prices remain unchanged.


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A. Basic Setup and Application to IBM's price Behavior

Figure II depicts the time-series of weekly market prices for IBM over our sample period,

January 1997 through December 1999, taken from CRSP. We also plot the weekly consensus

target price and the ratio of target prices to market prices, denoted TP/P. Inspection of this figure

provides a key insight. While both price series are non-stationary,17 it is evident that market and

target prices share a long-run common relationship. This association is captured by our third

variable, TP/P. It can be seen that target prices, which are forward looking, are consistently

higher than current market prices but the ratio of the two price series fluctuates about a common

value at approximately 1.2 (see the right-hand-side vertical axis). When either price series

deviates from this ratio, the system tends to revert back to it over time.

Using a cointegration approach (Engle and Granger [1987]) we provide direct evidence

regarding both the long-term relationship and the manner with which these prices correct

towards this long-term equilibrium. To do that, we assume that annual expected return, and

therefore the mean of the TP/P ratio, is constant over our sample period.18 We estimate both the

magnitude of this ratio and the dynamics that force the two sets of prices to converge to the long-

run equilibrium. We have already established that the market reacts to the information conveyed

in the analyst's report. Any remaining departure from the long-term relationship should therefore

be eliminated by analysts and/or market participants revising their prices. Our goal is to quantify

these price dynamics.

Since we want to retain the flexibility of modeling different beliefs regarding the

association between market and target prices and allow for parameter uncertainty, we adopt a

Bayesian approach to cointegration (see Bauwens and Lubrano [1996] and Bauwens and Giot

[1997]). Within the Bayesian framework, we begin with subjective prior beliefs regarding the

model parameters. Posterior beliefs are then generated using sample information via Bayes

theorem. These beliefs summarize our knowledge about the parameters of interest conditional on

17We are unable to reject the null of non-stationarity with an augmented Dickey-Fuller test.

18Over 90 percent of the price target reports used to construct the consensus estimate are one-year ahead prices.


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both the model and the data. An important feature of the Bayesian framework is that it enables

us to formally incorporate subjective prior beliefs regarding the parameters of interest. For

example, prior beliefs which indicate that IBM is risky (in a CAPM sense, for example) should

lead to a higher expected return and therefore to prior beliefs that the mean of the TP/P ratio is

high. Alternatively, prior beliefs that indicate that the firm is overvalued should lead to a lower

expected return and therefore that the mean of the TP/P ratio is low. Finally, Bayesian posterior

beliefs explicitly reflect our uncertainty about the firms parameters known as estimation risk

(e.g., Barry (1974), Jorion (1991), and Klein and Bawa (1976)). We now describe the

methodology as applied to IBM.

We denote the time t target price by tpt and market prices pt. Let xt denote a (2 x 1) vector

with elements tpt and pt. Both variables are assumed integrated of order one, that is, stationary

after first differencing. Cointegration of the two price series means that there is a (2 x 1) vector

such that the linear relationship 'xt=0. For example, if, on average, analysts forecast that target

prices are twenty percent higher than current market prices then [ ]2.11= .

We begin by writing the price system in an error correction form:

,,,1,11 Ttxxxtt

p

iitit

K

=++= = (1)where

itx is a (2 x 1) vector of first differences lagged i periods and ( ),0~ Nt , assumed

independent over time. The matricesi and are both (2 x 2) and the latter is assumed positive

definite. is the (2 x 2) long-run impact matrix which contains the cointegrating vector.

Inclusion of this term in this Vector Autoregressive Regression ("VAR") follows from the

Granger Representation Theorem. 's rank is equal to the number of cointegrating relationship

which in our simple case is just one.

Following earlier literature we parameterize as follows:

,'= (2)

where both and are (2 x 1) vectors. contains the cointegrating coefficients and is the

vector of weights in the VAR regression. The vector can be interpreted as a vector of


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"adjustment coefficients", that is, the elements in allow us to quantify how target prices and

market prices react to past dis-equilibrium errors. By obtaining posterior beliefs on the elements

in we can quantify the way in which the two time-series contribute to the correction of the

system back to the long-term equilibrium.

Given this parameterization, Equation (1) can be re-written as follows,

,'~

' EWBEZXEZXY +=++=++= (3)

where Y is a (T x 2) matrix containing the time tfirst differences of the two vectors, tx . X is a

(T x k) matrix in which the rows are simply ( )' 1'

1 ,, + ptt xx K so ( )12 = pk . In the empirical

implementation below we set p=3 as we find no qualitative differences in the results for longer

lags. Z is a (T x 2) matrix with the tth row 1'

tx . E is a (T x 2) matrix of stacked residuals'

t .

is a (k x 2) matrix obtained by stacking the 'i matrices. The parameter matrix ( )

''=B is a

((k+1) x 2) matrix. ( )ZXW ~~ = is a (T x (k+1)) matrix, and ZZ=~ can be interpreted as

capturing the time-series of deviations from the long-run equilibrium.

The likelihood function is therefore,

( ) ( ) ( ) .~~5.0exp,, '12/ BWYBWYtrBl T (4)

We specify a diffuse prior on all the model parameters accept for . As Bauwens andLubrano [1996] point out, an informative prior on and the added identification of the first

element in ( )b,1= , guarantee that the marginal posterior for the cointegrating coefficient will

have finite moments. The latter informative prior is denoted ( )bp0 and we assume it is a Normal

distribution with meanb and standard deviation b . Setting b equal to 1.2 means that the

investor believes that the one-year-ahead target price should be twenty percent higher than

current market price. Obviously, the strength of such beliefs is governed by the magnitude of b

with highly informative beliefs captured by small values forb . Section IV.B below provides

the detailed construction of ( )bp0 . Prior beliefs are therefore given by

( ) ( ) .,, 021

0 bpBbpn+

(5)


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The joint posterior distribution is proportional to the product of the prior distribution in

equation (5) and the likelihood in equation (4). Our main goal is to obtain the marginal posterior

distributions of our parameters of interest, and b, as well as any functions of these parameters.

These marginal distributions are derived in Appendix C.

B. Specification of Prior Beliefs

The specification of prior beliefs in equation (5) necessitates a construction of the prior

distribution ( )0p . As described above, the identification of the first element in , ( )b,1= ,

implies that we need to form the prior on b, which captures analysts' beliefs regarding the firm's

expected annual return. For example, setting the mean of these beliefs equal to 1.2 indicates that

we believe that IBM's annual return is expected to be twenty percent.

Recall that our price data begins in January 1997. Hence, our efforts in generating the

investor's prior beliefs necessarily center on the period preceding this month. In particular, we

use the five-year period form January 1992 through the end of 1996 to form the posterior beliefs

of a Bayesian investor regarding IBM's expected annual return. These beliefs serve as prior

beliefs for the cointegration analysis. The formation of investor beliefs requires that we take a

stand on an asset-pricing model and then derive the investor's posterior beliefs conditional on the

chosen model.

We assume that asset returns are generated by the Fama-French [1993] three-factor

model. The first factor is the excess return on the value weighted market portfolio (RMRF). The

second factor is the return of a factor-mimicking portfolio, SMB, which is the return on a zero

investment portfolio formed by subtracting the return on a large firm portfolio from the return on a

small firm portfolio. Similarly, the third factor is the return of another mimicking portfolio, HML,


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defined as the return on a portfolio of high book-to-market stocks less the return on a portfolio of

low book-to-market stocks.19

tttttftibm HMLSMBRMRFrr ++++= 3210,, (6)

Let [ ]'3210 ,,, denote the (4x1) vector including the intercept and factor loadings

and a (3x1) vector of factor premiums. Given this asset-pricing model, we write IBM's monthly

expected excess return, , as follows,

= '1 . (7)

We derive 's posterior moments following Pastor and Stambaugh [1999]. Their approach is

adopted for two reasons. First, it is fully Bayesian and therefore allows us to account for

uncertainty in both the factor loadings, , and factor premiums, . Second, Pastor and

Stambaugh's approach provides an elegant way with which we can allow for model mispricing.

That is, we can incorporate a belief in the falsehood of the asset-pricing model and allow for

analyst's beliefs in the mispricing of the firm's equity. For example, prior beliefs that IBM's

expected return is higher by one percent per month relative to the model's prediction are easily

captured by centering prior beliefs on0 accordingly.

Appendix B provides the detailed construction of beliefs regarding IBM's monthly

expected excess return, , which are then used to derive beliefs for the firm's annual expected

return. The latter beliefs, which we capture by a Normal distribution, serve as priorbeliefs for

the cointegration analysis below. We present the cointegration results in Section Cbelow and

highlight the sensitivity of our conclusions to differing prior beliefs.

19The breakpoints for small and large are determined by NYSE firms alone, but the portfolios contain all firms traded on

NYSE, AMEX, and NASDAQ. The breakpoints for the high book-to-market portfolio represents the top 30 percent of

all firms on COMPUSTAT while the low book-to-market portfolio contains firms in the lowest 30 percent of the

COMPUSTAT universe of firms. We have also replicated the analysis in this section using both the CAPM and a

four-factor model as in Carhart [1997]. The conclusions drawn in this section are robust to these alternative asset-

pricing models.


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C. Cointegration Results for IBM

We present the cointegration results in Table V. We focus our attention on posterior

moments for b, the parameter capturing the long-run ratio of target prices relative to market

prices, and the vector of response coefficients , the 2x1 vector capturing the response

coefficients of each price variable to deviations from the long-run equilibrium. The table

contains two panels that reflect the investor's prior beliefs in model mispricing (see the

discussion in Section IV.B and derivation in the Appendix). Panel A corresponds to prior beliefs

that ignore any mispricing and impose dogmatic beliefs in the exact pricing ability of the three-

factor model. Panel B allows for mispricing. We do so by setting0

, the parameter governing

the standard deviation of prior mispricing, to one percent and center the prior mean of

mispricing,b , at zero.

The message from both panels is similar. Beginning with Panel A, posterior beliefs

regarding b, the long-run ratio of target prices to market prices, are centered at 1.204 with

standard deviation equal to 1.7 percent. Panel B, in which we allow for mispricing, results in

posterior beliefs regarding the long-run ratio that are centered at 1.215. While prior beliefs were

centered at 1.117 and 1.177, the differences in prior beliefs regarding mispricing have a

relatively minor effect on b's posterior distribution. This is a direct result of the fact that the

prior's standard deviations in both panels are high and relatively uninformative relative to the

large sample information.

The posterior moments of the vector of response coefficients , in either panel, provide

interesting evidence on the manner with which target and market prices adjust to the long-term

equilibrium. The target price response, tp, is large and positive with a relatively low posterior

standard deviation while the market price response, market, is close to zero with relatively high

posterior uncertainty. This means that once the system of prices has been shocked away from its

long-term equilibrium, it is analysts, rather than market participants, who tend to revise their

target prices towards the long-run equilibrium. For example, a one-dollar shock in either target

or stock price that causes the system to deviate from its long-run equilibrium ratio of 1.204, will


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be corrected by analysts adjusting target prices downward by 21.9 cents each week while market

prices adjust by a negligible 3.3 cents.

Combining IBMs cointegration results with the event analysis above provides

preliminary evidence that market prices, in effect, only respond to the information conveyed in

the announcement of target prices, but otherwise do not react to temporary deviations from the

long-term relationship with target prices.

V. Full Sample Implementation of the Cointegration Analysis

In this section we implement the cointegration analysis for the full sample of 900 firms

and derive, for each firm, posterior beliefs regarding the parameters of interest. These

parameters capture the long-run ratio of target prices relative to market prices, b, and the 2x1

vector of response coefficients, , that captures how each price variable responds to deviations

from the long-run equilibrium. Unless noted otherwise, we begin by estimating these parameters

using prior beliefs which impose dogmatic beliefs in the Fama and French three-factor model.

Since the regression analysis results in 900 posterior distributions, we report statistics on the

means and standard deviations of these posterior distributions.

We report the results in Table VI. Panel A contains information regarding posterior

means for the parameters of interest b and , while Panel B provides information regarding

posterior standard deviations for the same parameters. In each panel we report full sample

results in the first row. In the next five rows we report the same statistics for sub-samples of

firms sorted by market capitalization ("size").20 To the extent that size differences are associated

with cross-sectional differences in information asymmetry or risk, our analysis sheds light on the

dynamics of target prices as they relate to this firm characteristic. We discuss results related to

the posterior distributions of the long-run ratio of target to market prices, b, in Section V.A. The

20Size quintiles are formed on the basis of NYSE capitalization cutoffs and are adjusted quarterly. Each Amex and

NASDAQ firm is placed in the appropriate NYSE size quintile based on the market value of its equity at the end of

the quarter.


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discussion regarding the posterior distributions of the vector of response coefficients is given

in Section V.B.

A. Posterior Beliefs Regarding the Long-Run Ratio of Target to Market Prices, b.

Consider first the full sample results given in the first row of Panel A. The fifth and sixth

columns indicated that the grand-average of the 900 posterior means equals 1.22 with a 0.07

standard deviation. That is, conditional on at least two years of continuous consensus coverage,

we find that the average firm in this sample is expected to earn 22 percent annually. 21 Note that

the third and fourth columns present, for comparison purposes, the grand average of the prior

means which equal 1.15 with a standard deviation of 0.04. It can be seen that if analysts form

their beliefs using data preceding our sample period, then there is, on average, 22-15=7 percent

discrepancy in the expected annual return.

Further information regarding the parameter b is given in first row of Panel B. Across

the 900 firms, the grand-average of the posterior standard deviations is 3.5 percent and the

standard deviation of this second moment is 1.8 percent. These figures tell us that the average

firm bs posterior distribution is centered at 22 percent with a standard deviation equal to 3.5

percent. Last, as in Panel A, the third and fourth columns present, for comparison purposes, the

grand average of thepriorstandard deviations, which equal 5.8 percent with a standard deviation

1.5 percent.

The remaining rows in both panels of Table VI provide results for firms sorted into size

quintiles. Beginning with firms in the smallest quintile, the grand-average ofb's posterior means

is 1.27 and it declines monotonically to 1.19 for the firms in the largest quintile. From Panel B

we can see that posterior standard deviations also decline monotonically from 5.4 percent to 2.6

percent as we move from the smallest to the largest quintile. This pattern indicates that,

21The geometric average annual market return over our sample period is 19.9 percent.


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conditional on being followed, analysts expect a higher annual price appreciation for small

stocks.

As can be seen from the third column, which provides the prior means, part of the cross-

sectional difference in analysts' expected annual return is indeed driven by differences in three-

factor risk exposures. Risk, however, cannot explain all of these differences. First, it can be seen

that the three-factor model generates 18-13=5 percent spread in expected annual returns between

the large and small stocks whereas the sample spread is 8 percent. Furthermore, as we noted

earlier, the asset pricing models that we entertain here generates prior beliefs that are lower by an

average of 7 percent across the size quintiles.

The preceding evidence on the discrepancies between b's prior and posterior means can

be explained in two ways. First, analysts might employ an asset-pricing model which predicts

systematically higher expected returns than the three-factor model. To explore this possibility,

we replicate our analysis with other asset pricing models such as the CAPM and Carhart's (1997)

four-factor model which also controls for differences in average returns due to momentum

effects. We find, however, similar results. Next, we examine whether allowing for mispricing

uncertainty about the Fama and French three-factor model, as in Pastor and Stambaugh [1999],

can explain the above discrepancy. To this end, we repeat the estimation with prior beliefs which

allow for possible mispricing (prior mean of regression's intercept set to zero while the prior

standard deviation is set to five percent (see Section IV.B). We find that over the prior formation

period, the posterior means of the intercepts are positive for two-thirds of our sample firms

suggesting that b's prior beliefs are likely to be higher now. Indeed, when we compute, for each

size quintile, the average ofb's prior means, we find that there is near uniformity between the

latter prior and posterior averages. We conclude that employing the three-factor model while

allowing for mispricing provides a potential explanation for the above discrepancy.

The second explanation for the above pattern rests on an alternative interpretation of the

parameter b. We have assumed so far that b, the long-run ratio of target prices relative to market

prices, provides an estimate of the unconditional annual expected return. An alternative view,


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however, is that it is an estimate of the conditional expected return, where the conditioning is on

favorable news.22 This hypothesis suggests that rather than using the full prior distribution for

b, analysts, in effect, calculate conditional expected returns based on a truncated prior

distribution of annual return. Entertaining a more favorable realization of a future state of nature

leads to a higher truncation, and therefore to a higher implied conditional mean.

We examine this hypothesis by calculating, for each firm, the truncation percentile of the

prior distribution that leads to equality ofb's conditional prior and posterior means. For example,

Table V shows that, for IBM, when mispricing is ruled out, the prior ( )bp0 is a normal

distribution with mean b = 11.7%, standard deviation b = 4.9%. The first panel in the same

table shows that b's posterior distribution is centered at 20.4%. Given these parameters, it is

easily verified, using the moments of a truncated Normal distribution, that one would have to

truncate the mass below the 93rd percentile in order for the conditional mean of the truncated

prior to equal 20.4%. When we repeat this calculation for all the firms in our sample we find a

large variation in these imputed percentiles. Specifically, while the mean (median) truncation

percentiles are 48 (49), these imputed percentiles are evenly spaced over the 1- 99 percent range.

One possible interpretation of these results is that, on average, analysts issue target prices which

condition on a firm annual return exceeding its expected return as dictated by the three-factor

model. The large dispersion that we find in these truncation percentiles, however, leads us to

conclude that it is unlikely that the conditioning hypothesis provides a complete explanation.

Since a large number of the imputed percentiles, including IBM's, are larger then 90 percent, it

seems more plausible that for some firms analysts condition both on favorable news andrely on

an asset pricing approach that allows for mispricing in determining target prices.

22William Epifanio, a J.P. Morgan analyst commented on a price target he had set on Red Hat in February 2000

The price target on the stock was contingent on a variety of things happening that did not happen. (Cassell Bryan-

Low [2000]).


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B. Posterior Beliefs Regarding the Response Coefficients, tp andmarket.

We begin with the full sample results given in the first row of Panel A of Table VI. The

seventh and eighth columns provide the grand-average oftpsposterior means. It is equal to 8.9

percent with a 4.3 percent standard deviation. These statistics imply that, for the average firm,

the analyst's periodic (i.e., weekly) response to a one-dollar deviation from the long-term

equilibrium is to revise the target price by 8.9 cents. As discussed earlier, a positive response

coefficient is consistent with analysts revising their target prices towards the long-term

equilibrium once the system has been shocked away. In contrast, the market price response

coefficient, market, is small and close to zero, as can be seen from column nine.

Panel B provides information regarding the response coefficients posterior standard

deviations. Consider tp first. The grand-average of the 900 posterior standard deviations is 2.5

percent which indicates that, for the typical firm, the analysts response coefficient posterior

distribution is centered at 8.9 percent with a 2.5 percent standard deviation. This evidence fits

nicely with the observation that virtually all of the posterior mass for this parameter is over the

positive range and is consistent with our interpretation of the results that analysts revise their

targets towards the long-term equilibrium. In contrast, the same statistics for market indicate that

across the 900 posterior distributions, a typical firms posterior distribution is centered at 1.5

percent with a large posterior standard deviation of 3.7 percent. Unlike analysts response

coefficient, the latter posterior distribution is centered close to zero indicating that there is little

posterior evidence that market prices react to deviations from long-term equilibrium.

The posterior information about the response coefficients tp and market indicates that

there are no cross-sectional differences in analysts' and market reaction to deviations from the

long-term relationship across the size quintile sorts. As with the IBM results in Section IV, the

evidence supports the interpretation that market prices react to the information conveyed in an

analyst's report but that any correction to the equilibrium relationship between target and market

prices is, in effect, done by analysts alone. Given this result, we explore in Section VI the

possibility that analysts' target price revisions are predictable and revisit some of the event-study


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results presented earlier in Section III.23

VI. Are Target Price Revisions Predictable?

The evidence presented in the preceding sections indicates that target price revisions are

associated with a significant market reaction and that subsequent corrections to the long-term

equilibrium relation between target prices and market price is, in effect, done by analysts alone.

Taken together, these findings raise the possibility that revisions in analysts target price are, to a

certain extent, predictable. For example, suppose that in response to a target price revision (or

change in stock price) the ratio of target to market price now deviates from its long-term

equilibrium. Then, it is more likely that the direction of a subsequent target price revision will be

back toward the long-term relation, rather than away from it. Indeed, market participants should

be able to predict the analysts revision towards the long-term equilibrium the further are current

target prices from market prices. Put differently, if the likelihood that a target price revision

towards the long-term relationship is increasing in the magnitude of the deviation from the long-

term equilibrium relation, then market reactions to target price revisions should be inversely

related to the extent of the pre-revision deviation.

We test this prediction by examining stock price reactions to target price revisions

conditional on: (i) the distance between the current ratio of the target to stock price and the long-

23

We have also attempted to quantify the average length of time within which the system of market and target prices

reverts to its long-term equilibrium by computing the price system's impulse response function (Lutkepohl and

Reimers [1992], Hamilton [1994], Koop [1996], Lee, Myers, and Swaminathan [1999]). Computation of an impulse

response function requires that we inject into the system a shock with respect to one of the variables and then

examine the path of both prices over time. Such a shock, say to target prices, is usually a one standard deviation

shock which is also orthogonalized with respect to the remaining variable, namely market prices. We obtain draws

from a firm's half-life posterior distribution as follows. First, recall that the derivation of posterior beliefs, described

in Appendix B, results in our having 1,000 simulated draws from each of the model parameters' posterior

distributions. Second, conditioning on each such draw we calculate a corresponding half-life and therefore obtain the

whole posterior distribution for the firm's half-life. A complication, however, which is common to both the Bayesian

and frequentist approaches, is that stationarity of the process is not imposed during the estimation. In our setting this

sometimes results in non-convergence of one realization of a half-life (out of a 1,000) and therefore inability to

report finite moments for the posterior distribution. While it is beyond the scope of this paper to impose finite

moments on these posterior beliefs we calculate, for each firm, only one half-life realization by using the posterior

means of each of the regression parameters. In this manner, 99 percent of the resulting half-lives are finite. For these

firms we find that both mean and median half-lives are equal to 10 weeks. We do not find any cross-sectional

differences in half-lives when we sort the sample firms by size.


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term value of this ratio and (ii) the direction of the revision. Specifically, we first compute, for a

given firm at its target price announcement event, an estimate of the long-term equilibrium

relation between target price and stock price by averaging all the ratios of target price to stock

price up until the event day (denoted LT(TP/P)t).24 We require a minimum of 10 weekly

observations to compute this estimate of the long-term ratio. Then, at the event-day, we obtain

the already outstanding target price issued by the same brokerage house and measure how far

this target price is from LT(TP/P)t. This distance is then scaled by the standard deviation of the

firms long-term target price to price ratio. We denote this firm and event-specific measure by

distanceit.

We calculate event-day abnormal returns for each target price announcement as in

Section III and then sort them into 12 different portfolios. These portfolios are constructed by

first dividing the sample into two portfolios based on the sign of the deviation from the long-term

ratio (distanceit is above/below the long-term ratio). Then, within each of these two portfolios,

we form three additional portfolios based on the magnitude of the event-specific measure

distanceit. Finally, each of the resulting six portfolios is further partitioned into two on the basis

of the sign of the target price revision (upgrade/downgrade relative to the previous target price

issued by the same broker).

Table VII presents results of the analysis. Column (1) provides the three ranks of

distanceit labeled "Smallest", "Intermediate", "Furthest". Columns (2) and (3) present average

abnormal returns associated with target price revisions whose pre-event target price to market

price ratio is below its long-term estimated level, conditional on the type of revision (i.e.

upgrades or downgrades). Columns (4) and (5) present similar statistics for target price revisions

whose pre-event target price to market price ratio is above its long-term estimated level.

24Alternatively, we can calculate the time t long-term equilibrium relation between target price and stock price

using the cointegration framework presented in section IV. Such computations, however, would involve enormous

amount of time and computing power, as they require an estimation of the system of equations for each of the 900

stocks andeach revision in a target price.


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Consistent with our prediction, we find that, controlling for the type of news (i.e., target

price upgrades or downgrades), average abnormal returns associated with target price revisions

towardthe estimated long-term target price to stock price ratio are smaller than those associated

with revisions away from the long-term equilibrium relation. For example, the average abnormal

return associated with a downward target price revision away from the long-term ratio is 2.514

percent (last row, column (2)). However, the average abnormal return associated with a

downward target price revisions towards the long-term ratio is 1.745 percent (last row, column

(4)). Similarly, the average abnormal return when we consider upward revisions toward the

long-term ratio is 1.160 percent compared with average abnormal return of 1.448 percent for

upward revisions away from the long-term ratio. Standard t-tests for differences in means reject

the null of equality for both comparisons (p-values equal to 0.001 and 0.031, respectively).

These differences in abnormal returns are consistent with the market partially anticipating

some of analysts' target price revisions. We further refine these results by sorting events based on

the distanceit measure into three equal sized terciles. For example, in column (3), we take all

events for which distanceit


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equality of means for the two comparisons reject the null of equality (p-values equal to 0.003 and

0.014, respectively).

Results associated with the effect of distanceit for revisions away from the long-term

relation are less conclusive. In particular, results in columns (2) and (5) suggest that market

reaction to revisions away from the long-term ratio is only weakly related to the magnitude of the

deviation from the long-term equilibrium ratio. Overall, however, the results in this section

support the view that market participants are able to anticipate, at least partially, the direction of

target price revisions.

VII. Conclusion and Future Research

Using a large database of analysts' target prices, stock recommendations, and earnings

forecasts, we examine short-term market reactions to target price announcements and long-term

co-movement of target prices vis--vis stock prices. Consistent with our predictions, we find that

target prices are informative both unconditionally and conditional on a contemporaneously

issued recommendation and earnings forecasts revisions. Recommendations and earnings

forecast revisions are, however, also informative in the presence of target prices. Furthermore,

we document a role for the degree of the recommendations change for a given target price

change, suggesting that the degree of the stock recommendation revision conveys analysts'

posterior uncertainty in the overall assessment of the firms prospects.

In the second part of the analysis, we argue that while both sets of prices are

nonstationary, cointegration of the two price series implies that there is a linear combination that

is stationary and is termed as the long-term equilibrium of the price series. Intuitively, both

variables are linked to the underlying firm fundamental value and therefore share a long-run

common relationship. We capture this association by the ratio of target prices to market prices

and provide direct evidence regarding both the magnitude of the long-term relationship and the

dynamics that force the two sets of prices to converge to the long-run equilibrium. For a typical


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firm, we find that in this equilibrium the one-year ahead target prices are 22 percent higher than

current market prices. We also examine whether the long-term equilibrium is related to firm size

and find that a typical small firm's target price is 27 percent higher than the contemporaneous

market price while a large firm's target price is 19 percent higher than the market price. We find

that these cross-sectional differences can be explained if we allow for mispricing uncertainty

(Pastor and Stambaugh [1999]) about the Fama and French three-factor model. Furthermore, we

provide evidence consistent with the hypothesis that target prices can be viewed as forecasts that

are based on expectations that condition only on favorable outcomes over the forecast period.

Finally, while market prices react to the information conveyed in analysts' reports, we

show that once the system has been shocked away from this long-run equilibrium, the median

half-life of the shock to the system is ten weeks. More importantly, we show that any subsequent

correction towards the long-term equilibrium are done primarily by analysts, while market prices

do not contribute much to this correction phase. We provide evidence that the market

understands the latter relationship and therefore is able to anticipate, at least partially, analysts'

target price revisions.

Target prices have recently received considerable attention and have been subject to a

great deal of criticism in the business press. Our paper is the first to explore and document

evidence on their informativeness and time-series behavior. Our finding should serve as a

starting point for further research on various related questions. For example, are there any cross-

sectional differences in market reaction based on firm and brokerage house characteristics? How

do analysts determine their target prices? Are these prices based on a valuation model whose

input includes their own earnings forecasts? What governs their decision to issue or withhold

their target prices? What, if any, are the consequences on analysts' reputation for providing

incorrect target prices or chasing the stock price? Are there any differences in target prices

between "affiliated" and "unaffiliated" analysts (Michaely and Womack [1999])? Do analysts

learn over time as in Mikhail, Walther, and Willis [1997]? We leave these interesting questions

for future research.


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Appendix

A. Additional Descriptive Statistics on the Recommendation and Target Price Databases

In this Appendix we examine the frequency of inclusion of target prices in a brokerage

houses report. While analysts' reports always include a recommendation, they do not necessarily

include a target price. According to conversations with analysts, some brokerage houses have an

explicit policy prohibiting their analysts from issuing target prices. In our sample, 135 of 325

brokerage houses do not issue any target price. Recommendations issued by these 135 brokerage

houses account for about 5 percent of all recommendations.*

Table A.I provides a transition matrix of brokerage house stock recommendations (the

number on top in each cell) and the percentage of these recommendations issued with price

targets (bottom number) for the period of 1997 to 1999. In computing the statistics, we

employed the following procedures: (1) all recommendations outstanding in the database for

more than one year were assumed invalid; (2) the most recent brokerage house recommendation

was assumed to have been reiterated for target price reports that were not accompanied by a

corresponding recommendation observation in First Calls recommendation database. The

validity of this procedure was confirmed with an official at First Call who indicated that since

target price revisions are issued more frequently than recommendation revisions, many target

price revisions are only recorded in the target price database and, as long as the corresponding

recommendation remains unchanged, First Call does not reiterate the existing recommendation in

the recommendation database (see also Krische and Lee [2000]). This criterion accounts for

different number of observations between table I and table A.I. (3) Strong Sell and Sell

recommendations were combined due their relatively small frequency in the data; (4) because

*While we do not study the analyst's decision to omit a target price form the report, we conjecture several possible

reasons. First, in many cases analysts simply do not derive a target price and based their recommendations on

heuristics, relative valuation of a peer group, or some informal valuation model (see Stickel [2001] for determinants

of stock recommendations). Second, even if the analyst derives a target price he may still choose to withhold it in

circumstances where his cost of providing an ex-post incorrect price target exceeds the potential benefits from

issuing it. For example, assume that analysts' compensation is related to the trading commissions that they generate

and these, in turn, are generated mainly in recommending securities for purchase. Then, if incorrect target prices are,

ex-post, costly, then analysts would tend to issue target prices mainly with Buy recommendations rather than with

Sells.


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some brokerage houses do not issue any target price reports, we only included in table A.I

brokerage houses/firm combinations with at least one target price report. While results are

qualitatively similar, removing the latter restriction reduces the off-diagonal percentages.

Table A.I: Transition Matrix of Analysts' Stock Recommendations and Target Prices

To Recommendation

From

RecommendationStrong Buy Buy Hold Sell/Strong Sell

45,671 5,692 3,297 77Strong Buy

99% 52% 36% 39%

6,108 36,823 5,186 114Buy

60% 99% 35% 40%

2,485 4,315 12,579 427Hold

71% 70% 98% 42%

63 86 424 527Sell/Strong Sell

56% 60% 41% 92%

16,374 15,194 8,622 510Initiated/Resumed as

82% 79% 49% 53%

70,701 62,110 30,108 1,655Overall

91% 88% 66% 61%

A number of interesting regularities are observed in this table. First, price targets are

overall more likely to be issued along with Strong Buy or Buy recommendations (91 percent and

88 percent, respectively) than with Hold (66 percent) or Sell/Strong Sell (61 percent)

recommendations. This is consistent with findings in Bradshaw [1999]. Second, within

recommendation categories, a recommendation upgrade (below diagonal cells) is more likely to

be accompanied by a price target than a recommendation downgrade (above diagonal cells). For

example, price targets are included in 70 percent of the upgrade reports from Hold to Buy

recommendations but only in 35 percent of the downgrade reports from Buy to Hold

recommendations. This evidence is consistent with the common claim that analysts' are biased

toward issuing favorable news and withholding (or minimizing) the amount bad news. The

statistics on the diagonal indicate that virtually all recommendation reiterations include a target

price. Since the typical duration of a stock recommendation is relatively long, analysts may


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choose to convey new and perhaps more subtle information to the market via target price

revisions and less frequently by recommendation revisions. Note that the high percentage of

target prices on the diagonal is however partially driven by our assumption (2) above. Absent

this assumption we find that about 50% of the recommendation reiterations are accompanied by

a target price.

Finally, analysts are more likely to initiate or resume coverage with a Strong Buy or a Buy

recommendation and are also more likely to include a target price in those reports than with other

recommendations. This is consistent with prior findings (e.g., McNichols and OBrien [1997],

and Barber, Lehavy, McNichols and Trueman [2001]), and with the common claim that analysts

are likely to avoid issuing recommendations and/or target prices when the cost of providing an

ex-post incorrect assessment is likely to exceed the potential benefits from issuing such

assessments.

B. Derivation of Posterior Moments for the Mean Monthly Expected Excess Return

This Appendix illustrates the formation of the prior beliefs for IBM's monthly expected

excess return, , and therefore prior beliefs on the annual expected return, b. The formationfollows closely the procedure in Pastor and Stambaugh [1999] (hereafter "PS"). We refer the

interested reader to their paper for a full-scale analysis and focus on four key steps that were

taken with emphasis on the subtleties of their approach. The four steps are summarized as

follows.

Step 1: Derivation of Posterior Beliefs of IBM's Three-factor Loadings

Recall that our price data begins in January 1997. Hence, we are interested in generating

investor's beliefs in the period immediately prior to this month. Specifically, we form the

Bayesian investors posterior beliefs using data from the five-year period from January 1992 to

1996. We obtain, from CRSP, all firms traded on the NYSE, AMEX, and NASDAQ with at least

24 continuous monthly returns over this period (6,626 firms). Then, we estimate firm specific


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three-factor ordinary least-squares regressions and record the firms' intercepts, factor loadings,

(the elements in the vector (see equation (7) above)), and residual standard deviations, denoted

.

The grand average of the vector of factor loadings, , and the grand average of the

estimated residual standard deviations serve as the central tendencies towards which IBM's

ordinary least-squares estimates of and residual standard deviation are shrunk (pulled) towards.

The strength of the shrinkage is governed by 's prior variance-covariance matrix. We construct

this matrix as in PS (see pages 76-78) and impose that this matrix be diagonal to ensure positive-

definiteness.

Table B.I provides the parameters governing prior beliefs, and is structured as in PS (see

their Table I, Panel A). Note that prior beliefs regarding the intercept, 0,are centered at zero

and the standard deviation about this central tendency,0

, is allowed to vary. Consequently,

with large uncertainty about a zero intercept, the investor is allowed to form posterior beliefs that

permit a certain amount of mispricing. For example, IBM's estimate of the intercept is 2.09

percent per month so unless the investor has a dogmatic belief in lack of mispricing ( 00= )

his posterior b

an empirical analysis of analysts target price

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