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The Long-Run Performance of REIT Stock Repurchases

Carmelo Giaccotto*

Erasmo Giambona+

CF Sirmans#

First Draft: January 2003

This Draft: March 2004

Please, do not quote

* Professor, Department of Finance, School of Business, University of Connecticut, 2100 Hillside Road,

Unit 1041, Storrs, CT, 06269-1041, tel. 860 486-4360, e-mail: carmelo@business.uconn.edu.

+ Contact author: Assistant Professor, Gabelli School of Business, Roger Williams University, One Old

Ferry Road, Bristol, RI 02809-2921, tel. 401 254-3836, e-mail: egiambona@rwu.edu.

# Professor, Department of Finance, School of Business, University of Connecticut, 2100 Hillside Road,

Unit 1041, Storrs, CT, 06269-1041, tel. 860 486-3227, e-mail: cf@business.uconn.edu.

We are grateful to Ozcan Sezer for providing the data on stock repurchase announcements.

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The Long-Run Performance of REIT Stock Repurchases

Abstract

This study investigates the long-horizon performance of open-market stock repurchases for

REITs. We develop a new methodology to model the autocorrelation of monthly returns into

long-horizon buy-and-hold abnormal return estimators. Serial correlation can introduce bias

(autocorrelation bias) because the bid-ask bounce documented by Blume and Stambaugh (1983)

may affect monthly returns for sample firms and non-sample firms in a different fashion.

Previous long-horizon event studies have overlooked this source of bias. There is compelling

evidence that the market underreacts to the stock repurchase announcements. The evidence holds

for different measures of the variance and the effects of cross-correlation of abnormal returns

emphasized by Fama (1998) and Mitchell and Stafford (2000). Results are also robust to the

traditional buy-and-hold abnormal return and the wealth relative estimators. We investigate the

nature of the underreaction and find strong support for the undervaluation hypothesis.

JEL Classifications: G14, G35, C22, C51, C52

Keywords: Real Estate Investment Trusts (REITs), Stock Repurchases, Undervaluation Hypothesis,

Autocorrelation Bias

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The Long-Run Performance of REIT Stock Repurchases

Introduction

Measuring performance over long horizons can be ''treacherous'' (Ikenberry, Lakonishok

and Vermaelen (1995), Lyon, Barber and Tsai (1999)). The existing literature has identified

several potential sources of bias that could affect the reliability of test statistics against the null

hypothesis of no long-horizon abnormal returns in the presence of major firm’s events (i.e.,

IPOs, SEOs, stock repurchase announcements and so on). A number of solutions have been

suggested.

This study develops a new methodology to study the long-run performance of Real Estate

Investment Trusts (REITs) after the announcement of a stock repurchase program. We model the

effects of mean reversion in monthly returns, and also show how to correct for cross-sectional

correlation of returns1. Serial correlation of monthly returns may be present in the data for a

number of different reasons; one possible source may be the bid-ask bounce effects that arise

from the recording practice of daily return data in the Center for Research in Security Prices

(CRSP) database (Blume and Stambaugh, 1983). Other potential reasons for mean reversion may

be found in Summers (1986), Campbell, Lo and MacKinley (1997), and Lewellen (2002). An

important consequence of serial correlation is that the buy-and-hold abnormal return will be

upward biased; the autocorrelation bias leads to rejection of a true null hypothesis of no

abnormal performance more often than the pre-specified significance level.

1 To compute long-horizon returns one could use daily, weekly or monthly returns. However, to minimize potential

problems due to missing daily returns or non-synchronous trading it has become standard practice in long-horizon

event studies to compound monthly returns.

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Another problem with long horizon event studies is known as rebalancing bias (Lyon,

Barber and Tsai (1999)). Rebalancing reference portfolios lead to a negative bias in the buy-and-

hold abnormal returns. However, it may be possible to reduce this bias substantially by carefully

constructing reference portfolios (see section 3.1).

Hypothesis tests for the presence of abnormal performance following a corporate event

present a challenge because long run returns are not normally distributed; by construction they

are asymmetric -- most likely right skewed. Moreover, measurement errors in the computation of

single period expected returns will affect both mean and variance of long run abnormal returns.

Thus, the bad model problem (Fama, 1998) interacts with the skewness problem. Equally

disturbing is the fact that even if one had a perfect measure for expected returns, skewness would

still be present because of the compounding of single period returns. We attempt to deal with

some of these problems by developing a new methodology that allows closed form solutions for

the mean and variance of holding period abnormal returns.

One possible strategy to counteract this long litany of problems is to use more than one

test. We study the long-horizon performance of open-market stock repurchases for REITs using

both traditional methods and our new methodology. In particular, we test the statistical

significance of post event abnormal returns with three different statistics: (i) buy-and-hold

abnormal returns (BHARs), (ii) wealth relative ratios (WR) proposed by Ritter (1991), and (iii)

our own percentage buy-and-hold abnormal returns (PBHARs).

We find compelling evidence of positive and significant long-horizon abnormal returns in the

twenty-four months following the announcement2. This finding is consistent with the

2 Evidence of abnormal returns has been used to test the undervaluation hypothesis for stock repurchase

announcements in the short term. See, for instance, Dann (1981), Vermaelen (1981), Asquith and Mullins (1986),

Comment and Jarrell (1991) and, more recently, Stephens and Weisbach (1998).

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underreaction hypothesis proposed by Ikenberry, Lakonishok and Vermaelen (1995). According

to this hypothesis, the market reacts skeptically to the announcement of a stock repurchase

program and therefore prices remain undervalued for a relatively long period of time. The

evidence reported below suggests that undervaluation is a fundamental determinant of the long-

horizon abnormal returns for our sample of REITs3.

The paper is organized as follows. The next section briefly reviews the buy-and-hold

abnormal return methodology commonly used in long run event studies, and discusses some of

its limitations. Section 2 describes the data, explains the construction of sample and reference

portfolios and discusses their comparability. Section 3 presents the three event study

methodologies: BHARs, WR and PBHARs. Section 4 reports the results based on all three test

statistics. The section also reports robustness checks to autocorrelation bias and cross-

correlation of abnormal returns. Section 5 presents the evidence on the undervaluation

hypothesis. Section 6 concludes the study.

1. Long Horizon Event Studies: A Review

Since Brown and Warner (1985) the standard practice in short horizon event studies of

market efficiency has been to use cumulative abnormal returns. A new line of research,

beginning with Ritter (1991), Ikenberry, Lakonishok and Vermaelen (1995) and others, has been

evolving to study long run performance following corporate events such as stock splits, stock

buybacks, etc. One of the major hurdles in this area is the accurate measurement of abnormal

returns and the associated test statistics for periods longer than one year. Barber and Lyon (1997)

3 In a survey conducted in the year 2000 by Sezer (2002), chief financial officers of 172 REITs member of NAREIT

- an organization for REITs - were asked to motivate the decision to announce or not to announce a repurchasing

program. Of the 80 responding REITs, 52 were announcing REITs. Consistently with previous surveys, 88% of the

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present convincing evidence that cumulative abnormal returns are biased estimators of buy and

hold (i.e., compounded) returns. Hence, on statistical as well as conceptual grounds they reject

the use of cumulative abnormal returns in favor of buy-and-hold abnormal returns. Barber and

Lyon argue that using the (average) buy-and-hold abnormal return is advisable because it

“precisely measures investor experience” over a particular time horizon.

Typically, BHARs are computed as the difference between buy-and-hold returns for the

sample firm and its compounded expected return under the null hypothesis:

()

(1) ) 1 (

1

=

) 1 (

1

=

∏∏

+−+=

T

t

t i

r

T

t

t i

r

i

E BHAR

where T is the number of months after the announcement over which to measure the buy-and-

hold return; rit is the return of firm i in month t and E(.) is its expected return under the null of no

abnormal performance. Typically, this expected return is approximated by a reference portfolio,

or some other benchmark. The bad model problem arises because the expected value cannot be

estimated exactly.

A standard assumption in event studies is that rit is a normally distributed random

variable. But since Equation (1) is a non-linear function of single period returns, the distribution

of the aggregate holding period return will not be normal; if the time series of monthly returns is

uncorrelated, then BHARs will be skewed right (Barber and Lyon, 1997). Alternatively, the

presence of serial correlation adds another layer of complexity to the theoretical distribution of

long run abnormal returns. However, there is a positive benefit to mean reversion; it can be

shown both theoretically and empirically that the degree of asymmetry in compounded returns

will grow at a much slower rate than the horizon time T when serial correlation is present. Test

statistics based on the normality assumption will be less biased in this case.

announcing REITs declared that undervaluation was a “very important” determinant (in a scale from not important

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The sampling properties of BHARs have been investigated extensively in the literature

and a number of problems have been identified. First, reference portfolios may include newly

listed firms while sample firms have been usually tracked for a longer time. Because newly listed

firms, in general, underperform their benchmarks, the corresponding long-horizon buy-and-hold

abnormal return may be upward biased. This problem is often referred to as the new listing bias.

Second, a rebalancing bias arises when reference portfolios are periodically (for instance,

monthly) rebalanced, whereas sample firms do not change over the same time horizon. Consider

an equally weighted reference portfolio. If all securities have to maintain the same weight over

time (e.g., on a monthly basis), then it is implicitly assumed that securities that have

outperformed the market average are sold, while securities that have underperformed the market

average are bought. This rebalancing process is problematic for the following reason: If monthly

returns for individual securities are negatively correlated, then the rebalancing process is

implicitly done by selling securities that will not perform well in the coming month and by

buying securities that should perform above the market average during the same time frame.

Mean reversion will create an upward bias in the reference portfolio. Hence, large portfolio

returns, in part due to negative serial correlation, do not necessarily reveal a profitable strategy.

Third, end of period stock prices quite often represent bid or ask quotes rather than actual

market prices. Indeed, Blume and Stambaugh (1983) found that securities with high returns at

time t-1 have a higher probability to be recorded as traded at the ask price at time t, whereas

securities with low returns at time t-1 have a higher probability to be recorded as traded at the bid

price at time t. This bid-ask bounce creates negative serial correlation in the monthly returns of

individual firms and biases the return of an equally weighted reference portfolio. However, this

problem is more pronounced in daily rather than monthly returns.

to very important) of the decision to announce a stock repurchase program.

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Fourth and last is the so called bad model problem. This problem arises because any test

against the null hypothesis of zero abnormal returns is a joint-test of the hypothesis and the

specification of the asset pricing model used to conduct the test (Fama, 1970; 1998). Rejection of

the null hypothesis of no abnormal returns may be in part due to a bad model.

To minimize this and other problems, we are very careful about the choice of benchmark.

In particular, our reference portfolios are constructed with non-event firms from the same

industry (i.e., REITs that did not announce an open-market stock repurchase) according to size

and book-to-market ratio. Also, to minimize the new listing as well as rebalancing bias, we use

reference portfolios constructed without monthly rebalancing and/or investment in newly listed

firms after the event month (Lyon, Barber and Tsai (1999)).

2. The Data

2.1. Sample of Announcing REITs

The evidence reported in this study is based on a sample of REITs that announced an

open-market stock repurchase of common stocks in 19994. The initial sample consists of all

public REITs reported in the Snl Property Register for Real Estate Securities database. The

sample of announcing REITs is gathered by using the Lexis-Nexis database.

The initial sample consists of 75 REITs. We exclude from the final sample those

announcements that can be classified as an expansion of a previous announcement5. The

definition of an expansion used in this study is fairly broad to minimize confounding effects.

4 Unlike firms from other industries, REITs began to repurchases actively their own stocks from the open market

only during the very late 90s (Sezer, 2002). To avoid issues of structural market changes, we confine the analysis to

the year 1999.

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First, we exclude all REITs that explicitly declared their 1999 announcement as an expansion of

a previous announcement. Second, if a REIT had more than one announcement we excluded it

from the final sample if the second announcement came within two calendar years of the first

announcement. For instance, if a REIT announced in 1997 and again in 1999, it will not be in the

final sample; the logic here is that multiple announcements by the same firm may not reveal that

management has acquired new private information.

We also exclude from the final sample those REITs that did not limit the buyback to

common stocks. Finally, we require that for each REIT in the final sample monthly return data

and other market data are available in the CRSP database and book equity yearly data are

available in the COMPUSTAT database. The final sample consists of 42 observations.

We next construct subsamples according to size and book-to-market ratio. Size (or

market value of equity (ME)) is obtained as the product between the price and the number of

shares outstanding both on June 30 of the year of the announcement (i.e., 1999). This

information is gathered from CRSP. The book-to-market ratio is the ratio between the book

value of common equity (BE - COMPUSTAT data item 60) and ME both at the end of the year

prior to the announcement. Consistently with most of the literature on long-horizon performance,

by using prior year data, we avoid the look-ahead bias emphasized by Banz and Breen (1986).

We then sort the sample in three subgroups according to size (from small to large) and in an

independent sort according to book-to-market ratio (from low to high) and match them in nine

different portfolios. The percentage distribution is reported in table II.

2.2. Sample of Non-Announcing REITs

5 This is consistent with the finding reported in Ikenberry, Lakonishok and Vermaelen (1995) that repeated

announcements cannot explain the observed overall abnormal returns.

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We construct reference portfolios using all the public REITs reported in the SNL

Property Register for Real Estate Securities database that did not announce an open-market stock

repurchase in 1999. Using a control sample from the same industry should drastically reduce the

bad model problem because, under the null hypothesis of no abnormal returns, average returns

for event firms should not be different from returns for the reference portfolios. The remaining

misspecification of the test statistics is then mostly due to the cross-correlation of abnormal

returns. The methodology developed in this paper explicitly controls for the effects of cross-

sectional correlation of abnormal returns on the specification of the test statistic.

The initial sample contains 128 non-announcing REITs for the 1999. To reduce the

benchmark contamination bias, emphasized by Loughran and Ritter (2000), we filter the initial

sample using the following criteria. First, we eliminate from the initial sample those REITs that

announced an open-market stock repurchase either in 1997 or 1998 because the effects of the

announcement may endure over the 1999 and bias our findings. Second, we exclude those REITs

for which the CRSP number of shares outstanding decreased over the period from December 31,

1999 to December 31, 2000. The rationale behind this criterion is as follows. If managers have

private information that their stock is going to outperform the benchmark, then they might buy

back the security in the open market. This will result in a decrease in the number of shares

outstanding. To avoid that the decrease in the number of shares outstanding may be due to

formal activities such as reverse splits and similar, we apply the CRSP function that allows

identifying such activities to each REIT in the sample.

We also require that data on market prices, number of shares outstanding and monthly

returns be available in the CRSP files. Finally, book-to-market ratio data have to be available in

COMPUSTAT and be non-negative. The final sample consists of 67 observations. Following the

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same approach as for the case of announcing REITs, we construct nine portfolios according to

size and book-to-market ratio.

2.3. Announcing REITs versus Non-Announcing REITs

Table I shows that the sample of announcing and non-announcing REITs are comparable

in terms of size, $1,019 million versus $1,147 million, as measured by the market value of equity

on June 30, 1999, although the sample of announcing REITs is more skewed toward larger firms.

The book-to-market ratio, measured on December 31, 1998, on the other hand, is slightly higher

for the sample of non-announcing firms, 1.21 versus 0.98, but again the distribution of the book-

to-market ratio for announcing REITs is more skewed toward bigger book-to-market ratio.

Table II, panel A and B, reports respectively the distribution by size and book-to-market

ratio of announcing and non-announcing REITs into nine portfolios. The two samples seem to be

comparable. However, panel C shows that when announcing REITs are matched with the nine

portfolios of non-announcing REITs by size and book-to-market ratio, the former tend to

concentrate in the portfolios of non-announcing REITs with higher book-to-market ratio (i.e.,

76.19% of the announcing REITs matches with the medium and high book-to-market portfolios

of non-announcing REITs)6.

In synthesis, evidence in Tables I and II shows that, although the two samples are

comparable in several respects, they still have some differences that could be sources of bias if

ignored. Matching announcing firms with reference portfolios by size and book-to-market ratio

will reduce these potential sources of bias.

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3. Measurement of Long Horizon Abnormal Returns

3.1 Buy-and-Hold Abnormal Returns

Equation (1) in Section 1 defines the theoretical buy and hold abnormal return for a

sample firm as the holding period compounded return over T periods minus its expected return

under the null hypothesis. To make this definition operational, we need to specify a model of

expected returns for sample firms. A number of choices are available to researchers, including

the single factor market model, Fama-French three factor model, single control firm or reference

portfolio chosen on the basis of size and book-to-market ratio.

Barber and Lyon (1997) and Kothari and Warner (1997) advocate the use of a single

control firm as a benchmark because reference portfolios introduce new listing, rebalancing and

skewness bias in the calculation of buy-and-hold abnormal returns. However, Lyon, Barber and

Tsai (1999) point out that carefully constructed reference portfolios, as we do in this study,

overcome these sources of bias and smooth out the measurement noise related to the use of a

single control firm.

return (

Hence, we use the idea of a reference portfolio as a proxy for the expected holding period

)

∏=

t

E

1

) 1 (

+

T

t ir

in Equation (1). Specifically, for each event firm (i.e., a REIT that

announced an open-market stock repurchase in 1999), we compute its size and book-to-market

ratio. We construct a reference or benchmark using a number of non-event (i.e., non-announcing)

REITs chosen such that they are as close as possible to each event firm in terms of size and

book-to-market ratio.

6 As high book-to-market ratios are considered evidence of undervaluation, the result is consistent with the

hypothesis that undervaluation is a determinant of stock repurchases. This issue will be addressed more completely

in section 6.

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The long-horizon buy-and-hold return for the reference portfolio (BHRRP) for event firm i

is obtained by compounding the returns on securities constituting the reference portfolio and then

taking the simple arithmetic average of these returns:

(2)

)] 1 (

1

=

n

[

1

1

1

∑∏

=

j

+

=

i

i

i

n

T

t

jt

RP

r

BHR

where

is the number of firms in the reference portfolio for firm i in month 1 (i.e., the month of

the announcement) and r

i

n1

jt is the market return of firm j in month t as obtained from the CRSP

files. Notice that , the number of firms constituting the reference portfolio for firm i, does not

change after month 1. Using equation (2) to obtain buy-and-hold return for the reference

portfolio will avoid the afore discussed new listing and rebalancing bias. Assuming that size and

book-to-market ratio control accurately for risk,

is to be interpreted as the long-horizon

expected return for firm i without the effects of the announcement (i.e., the buy-and-hold return

under the null hypothesis of no abnormal return).

i

n1

RP

BHR

To test the null hypothesis we use the following test statistic:

n BHAR

BHAR

t

T

T

BHAR

/ )(

σ

=

(3)

where

T

BHAR is the sample average buy-and-hold abnormal return,

)(

T

BHAR

σ

is the cross-

sectional sample standard deviation, and n is the total number of event firms. The ratio

should behave like a student’s t-statistic (Lyon and Barber, 1997), hence large (absolute) values

constitute evidence against the null.

BHAR

t

3.2 Percentage Buy-and-Hold Abnormal Returns: A New Approach

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As argued above, the mean buy-and-hold abnormal return has replaced the cumulative

abnormal return statistic in long-horizon event studies because its buy-and-hold nature “precisely

measures investor experience” (Barber and Lyon, 1997). Nevertheless, statistical analyses based

on BHARs may be biased as a result of mean reversion and cross-correlation of returns.

We propose a new definition of abnormal returns as percentage buy-and-hold abnormal

returns:

(4)

) 1 (

1

=

) 1 (

1

=

∏

∏

+

+

=

T

t

Bt

T

t

it

i

r

r

PBHAR

where rit is firm i return in month t,

j

nj

jt

Bt

n

r

r

j

∑=

=

1

is the reference portfolio return in month t and T

is the number of months after the stock repurchase announcement. This ratio should be greater

than one for firms with positive abnormal performance relative to their appropriate benchmark.

The null hypothesis corresponds to a ratio of one.

The new estimator proposed in equation (4) is similar to the wealth relative (WR)

measure introduced by Ritter (1991):

(5)

) 1 (

1

i

RP

T

t

t i

r

i

BHR

WR

∏=

+

=

The main difference between our measure of abnormal performance and the wealth relative in

(5) is the reference portfolio; our benchmark return in equation (3) - rBt - implicitly assumes

monthly rebalancing. Consequently, PBHARi is affected by serial correlation induced in part by

the rebalancing bias. On the positive side, however, our metric leads to a tractable distribution

for hypothesis tests, and allows us to integrate mean reversion as well as cross-sectional

correlation of returns.

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3.3 Theoretical Distribution of PBHARs

In this section we derive closed-form solutions for mean, variance and covariance of

PBHARs when monthly excess are modeled by a first order autoregressive process AR(1). This

assumption is not critical to our analysis; the AR(1) model is a simple way to account for mean

reversion present in returns data; our methodology can be generalized to higher order

autoregressive or moving average processes.

We define the continuously compounded period t return for firm i as

, and

for its benchmark

, where r

)1 ln(

it it

rR

+=

)1 ln(

Bt Bt

rR

+=

it and rBt are the corresponding discrete time returns as

defined above. Then,

. We model the time series behavior of monthly

excess returns for firm i from the reference portfolio – (R

∑

=

=

−

T

t

Bt it RR

i

e PBHAR

1

)(

it – RBt) – as an AR(1) process:

(6) )() 1 ()(

11

itBtitiii Btit

RRRR

εφφµ+−+−=−

−−

For the time being assume also that

0),(

=

jt it

Cov

εε

for

ji ≠ . That is, the contemporaneous

covariances between the excess return for firm i and j are equal to zero.

If this model holds for each firm and assuming that

, then the mean

percentage buy and hold return is:

. We recognize this expectation as

the moment generating function for a normal random variable evaluated at 1.0, thus it has the

following closed form solution:

); 0 (

N

~

2

σε

ε

i

iid

it

][)(

1

)(

∑=

t

−

=

T

Btit RR

i

eE PBHARE

(7) . )(

11

)]}([

2

1

)]([{ ∑

e

∑

=

==

−+−

T

t

T

t

Btit Btit

RR VarRRE

i

PBHARE

The variance for firm i can then be obtained as follows:

(8) ]}[{][)(

2

)(2

1

i

RR

i

PBHAREeE PBHAR Var

T

t

Bt it

−

∑

=

=

−

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We note that the first term on the RHS of (8) is the moment generating function for a normal

random variable evaluated at 2.0; hence its value may be computed as follows:

∑∑

=

∑

===

−+−−

T

t

T

t

Btit Btit

T

t

Brit

RR Var

2

RRERR

eeE

111

)]}([ )]([2{)(2

][.

To integrate mean reversion into the analysis of abnormal returns, let

t Btt

yRR

=−

)( ,

where the subscript i is omitted for convenience, and consider the entire time series of excess

returns

. The autoregressive process in equation (6) can be written in vector

form as follows:

) ,....,,(

21

'

T yyyY =

(9) .

E

) 1 (

0

ByAY

++−=Φ

φφµ

where A is a column vector of ones, B is a column vector with T elements, the first being 1 and

all others are set at 0,

is the t = 0 period excess return and is therefore a known

constant.

is a vector of white noise random errors, and Φ is a

TxT matrix defined as follows: 1s along the main diagonal, -φ in each cell right below the main

diagonal and 0 everywhere else.

000

B

RRy

−=

) ; 0 (

N

~) ,....,,(

2

21

'

TT

IE

ε

σεεε

=

It is evident from the discussion above that the distribution of PBHARs is determined by

the first two moments of the sum

. These are respectively:

, and . Although these moments

are based on the inverse matrix Φ

)(

11

tB

T

t

t i

T

t

t

RRyS

−==

∑

=

∑

=

) 1 (][

1'

0

1'

BAyAASE

−−

Φ+Φ−=

φφµ

)(][

'11'2

AAS Var

−−ΦΦ=

ε

σ

-1, which can be of quite large order and cumbersome to

compute, the following transformation (due to Ali, 1977) can be used to develop simple

expressions for the moments of S. Thus, define the vector

or,

equivalently,

1'

21

'

) ...., , ,(

−

Φ=≡

AzzzZ

T

''

AZ

=Φ

. Then, each element of Z may be computed recursively as , 1

1+

+

=

kk

zz

φ

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with starting value for k = T+1. Hence, we have:, and

. The expected value and variance of PBHARs follow immediately:

0

1=

+

Tz

10

1

) 1 (][

zyzSE

T

k

k

φφµ+−=

∑

=

∑

=

k

=

T

kzS Var

1

22

][

ε

σ

∑

=

k

∑

=

k

++−=

TT

kki

zzyz PBHARE

11

22

10

(10) ]

2

1

) 1 ( exp[)(

ε

σφφµ

and

(11) . ]2) 1 (2 exp[

]22) 1 (2 exp[)(

1

2

k

2

10

1

1

2

k

2

10

1

∑

=

k

∑

=

k

∑

=

k

∑

=

k

++−

−++−=

TT

k

TT

ki

zzyz

zzyz PBHAR Var

ε

ε

σφφµ

σφφµ

Notice that, under the null hypothesis of no abnormal returns, equation (10) measures the

percentage buy-and-hold abnormal return that is due to the serial correlation of monthly returns.

That is, it measures the net effect of rebalancing bias, and sample autocorrelation bias on the

percentage buy-and-hold abnormal returns for firm i. By filtering the PBHARs from its serial

correlation component, we obtain a more reliable test against the null hypothesis of no abnormal

returns.

The last part of this section deals with cross-sectional covariance between PBHARi and

PBHARj for i different from j. By definition, we have:

∑

=

t

∑

=

t

∑

=

t

∑

=

t

−−

−−−=

TT

BtjtBt it

TT

Bt jtBt itji

RRERRE

RRRRE PBHAR PBHAR Cov

11

11

(12) .))]([exp())]([exp(

))](exp( ))( [exp(),(

We note that the second term on the RHS of equation (12) is the product by E(PBHARi) and

E(PBHARj), hence they can obtained from equation (10) above. To obtain the first term, we use

Page 18

17

some results for log-normal random variable from Rubenstein’s (1974) appendix. The formula

for the covariance of any two PBHARs may be shown to be:

(13) . ] 1

−

) )[exp(()(),(

1

,,

=

∑

=

k

T

kjki j ijiji

zz PBHARE PBHARE PBHARPBHAR Cov

σ

where σi,j = Cov(εi,εj) can be estimated by the covariance between the residuals from the

autoregressive equation (6) for firms i and j, and zi, k and z j, k are the elements of the Z vector for

firms i and j.

4. Results

This section describes the long-horizon performance for our sample of open-market stock

repurchases for REITs. Results are based on the PBHARs metric presented above. We develop

three different hypothesis tests based on different assumptions about the variance and cross-

correlations of PBHARs. As a robustness check, we also report results from the traditional buy-

and-hold abnormal return (BHAR) and the wealth relative approach (WR).

4.1 Percentage Buy-and-Hold Abnormal Returns

The average raw 24-Month PBHAR is equal to 25.10% (table III – Panel A). The

interpretation of this result is that buy-and-hold returns for sample firms are on average 25.10%

over and above the buy-and-hold return on the control sample of non-announcing REITs.

In order to adjust the PBHAR for the autocorrelation of monthly returns, we estimate for

each sample REIT the expected percentage buy-and-hold abnormal return using equation (10)

under the null hypothesis of no abnormal returns and non-zero serial correlation (i.e., µ = 0 and φ

≠ 0). We then take the average of these estimates and subtract it from the average raw 24-Month

PBHAR (i.e.,

)(PBHARE PBHAR−

). The rationale for correcting the raw average PBHAR for its

Page 19

18

expected mean value )(PBHARE

is that the presence of mean reversion might be mistaken for a

profitable investment strategy.

The 24-Month

)(PBHARE

is equal to 4.62%. Therefore, ) )((

PBHARE PBHAR−

is equal

to 19.48% (table III – Panel A – column 3). If we estimate the expected percentage buy-and-hold

abnormal return (i.e.,

)(PBHARE

) for each sample REIT assuming both no abnormal returns

and no serial correlation of monthly returns (i.e., both µ = 0 and φ = 0), then equation (10) will

compound in a linear fashion.

)(PBHARE

will account in this case for the skewness bias only.

)(PBHARE

is equal to 6.03% in this case; therefore, ) )((

PBHARE PBHAR−

is equal to 19.07%

(table IV – Panel A - column 2).The difference between

)(PBHARE

under the null hypothesis of

no abnormal returns (i.e., µ = 0 and φ ≠ 0) and

)(PBHARE

estimated when both µ = 0 and φ = 0

(i.e., 6.03% - 4.62% = 1.41%) measures serial correlation or rebalancing bias.

Panel B and C in table III report the results respectively for the 12-Month and 3-Month

PBHARs. The raw average 12-Month PBHAR is equal to 4.82%. As for the 24-Month

performance, we subtract from the raw average PBHAR its expected value (i.e.,

)(PBHARE

)

under the null hypothesis of no abnormal returns (i.e., µ = 0 and φ ≠ 0) and when both µ = 0 and

φ = 0. The corrected average 12-Month PBHAR is equal to 1.89% under µ = 0 and φ ≠ 0 and

1.87% when both µ = 0 and φ = 0. Similarly, Panel C in table III reports the results for the 3-

Month PBHAR. The raw average is equal to 1.91%. The corrected average 3-Month PBHAR is

equal to 0.89% under µ = 0 and φ ≠ 0 and 1.18% when both µ = 0 and φ = 0. We address the

statistical significance of these results in the next section.

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19

4.2 Hypothesis Tests

In section 4.1, we presented the results for the average PBHARs with and without a

correction for mean reversion. The purpose of this section is to test whether the corrected

PBHAR (i.e.,

) )((

PBHARE PBHAR−

) is statistically different form zero. We test the null

hypothesis of no long run abnormal performance using three different measures for the variance

of PBHARs.

4.2.1 The Case of Equal Variance

We first assume that Var (PBHARi) = Var (PBHARj) for any i and j firm in the sample

and Cov (PBHARi, PBHARj) = 0 for i ≠ j. Therefore, under the null hypothesis of no abnormal

returns,

) )((

PBHARE PBHAR−

has mean zero and variance equal to Var(PBHAR)/n, where n is

the number of sample firms. The t-statistic reported in column 3 of Panel A - table III shows that

corrected average 24-Month PBHAR is different from zero (i.e., 19.48%) at the 5% significance

level when

)(PBHARE

is estimated assuming µ = 0 and φ ≠ 0. The evidence does not change

when we estimate

)(PBHARE

under the more conservative hypothesis that both µ = 0 and φ = 0.

Indeed, the average PBHAR is still different from zero (i.e., 19.07%) at the 5% significance level

(column 2 – Panel A - table III). The t-statistics reported in column 2 and 3 of Panel B and C –

table III – respectively for the corrected 12-Month and 3-Month PBHARs suggest that the null

hypothesis can never be rejected in these cases.

Table IV reports the results for the corrected PBHAR when each observation is weighted

according to the size of the share repurchases (weights scaled to sum to one). Evidence in

Page 21

20

column 2 and 3 of Panel A, B and C respectively for the corrected 24-Month, 12-Month and 3-

Month PBHAR is not different from the equally weighted case.

4.2.2 The Case of Unequal Variances

We now assume that Var (PBHARi) ≠ Var (PBHARj) for any i and j firm in the sample

and Cov (PBHARi, PBHARj) = 0 for i ≠ j. Therefore, under the null hypothesis of no abnormal

returns, ) )((

PBHARE PBHAR−

has mean zero and variance equal to

∑

=

n

i

i

PBHARVar

1

n

2

)(

1

,

where n is the number of sample firms. Notice that in this case Var (PBHARi) is obtained by

estimating equation (11) for each REIT for the case when µ = 0 and φ ≠ 0 and for the case when

both µ = 0 and φ = 0. The t-statistic reported in column 5 of Panel A - table III shows that

corrected average 24-Month PBHAR is different from zero (i.e., 19.48%) at the 1% significance

level when

)(PBHARE

is estimated assuming µ = 0 and φ ≠ 0. The evidence does not change

when we estimate

)(PBHARE

under the more conservative hypothesis that both µ = 0 and φ = 0.

Indeed, the average PBHAR is still different from zero (i.e., 19.07%) at the 1% significance level

(column 4 – Panel A - table III). The t-statistics reported in column 4 and 5 of Panel B and C –

table IV – respectively for the corrected 12-Month and 3-Month PBHARs suggest that the null

hypothesis can never be rejected in these cases.

Table IV reports the results for the corrected PBHAR when each observation is weighted

according to the size of the share repurchases (weights scaled to sum to one). Evidence in

column 4 and 5 of Panel A, B and C respectively for the corrected 24-Month, 12-Month and 3-

Month PBHAR is not different from the equally weighted case.

Page 22

21

4.2.3 Unequal Variances and Cross-Correlations Different from Zero

Results discussed so far are based on the assumption that the cross-correlation of

PBHARs is equal to zero. Fama (1998) and Mitchell and Stafford (2000) argue that ignoring

contemporaneous cross-correlation may cause overly rejecting the null hypothesis of no

abnormal returns. Above we provide an estimator for the contemporaneous covariance for our

PBHAR estimator (see equation (13)).

Assume that Var (PBHARi) ≠ Var (PBHARj) for any i and j firm in the sample and Cov

(PBHARi, PBHARj) ≠ 0 for i ≠ j. Therefore, under the null hypothesis of no abnormal returns, the

difference

) )((

PBHAREPBHAR−

has zero mean, and variance equal to

∑

=

∑

=

∑

=

≠

+

n

i

n

j

ji

ji

n

i

i

PBHAR PBHARCov

1

PBHARVar

1

n

1

2

)],()([

1

. Notice that in this case Var(PBHARi)

and Cov(PBHARi,PBHARj) are obtained by estimating, respectively, equation (11) and equation

(13) for each REIT for the case when µ = 0 and φ ≠ 0, and for the case when both µ = 0 and φ =

0.

The t-statistic reported in column 7 of Panel A - table III shows that corrected average

24-Month PBHAR is different from zero (i.e., 19.48%) at the 1% significance level when

)(PBHARE

is estimated assuming µ = 0 and φ ≠ 0. The evidence does not change when we

estimate

)(PBHARE

under the more conservative hypothesis that both µ = 0 and φ = 0. Indeed,

the average PBHAR is still different from zero (i.e., 19.07%) at the 1% significance level

(column 6 – Panel A - table III)7. The t-statistics reported in column 6 and 7 of Panel B and C –

7 Mitchell and Stafford (2000) are the only ones who propose a direct approximation for the contemporaneous cross-

correlation of abnormal returns. We check if our evidence is also robust to their approximation of the

contemporaneous cross-correlation of abnormal returns and find that there is still strong evidence against the null

hypothesis of no abnormal returns.

Page 23

22

table IV – respectively for the corrected 12-Month and 3-Month PBHARs suggest that the null

hypothesis can never be rejected in these cases.

Table IV reports the results for the corrected PBHAR when each observation is weighted

according to the size of the share repurchases (weights scaled to sum to one). Evidence in

column 6 and 7 of Panel A, B and C respectively for the corrected 24-Month, 12-Month and 3-

Month PBHAR is not different from the equally weighted case.

4.3. Buy-and-Hold Abnormal Returns and WRs

We check further robustness of the results reported above by using the traditional BHAR

and WR estimators described in sections 1 and 3 and show that the evidence is consistent with

the results obtained with our PBHAR estimator. The average 24-Month BHAR8 for the sample

firms is 15.56%, which is different from zero at the 5% significance level (column 4 – Panel A -

table V). The interpretation of this result is that buying and holding securities from announcing

REITs gives an average return that is 15.56% higher than the buy-and-hold return on the

corresponding control sample of non-announcing REITs. The t-statistics reported in column 2

and 3 of Panel A – table V – respectively for the 3-Month and 12-Month BHARs suggest that the

null hypothesis can not be rejected in these cases.

Also consistently with the above result, the 24-Month wealth relative (WR) is equal to

19.41%, which is different from zero at the 1% significance level (column 4 – Panel B - table V).

The interpretation of this result is that buy-and-hold returns for sample firms are on average

8 Notice that the performance measure used in this study is not adjusted for the market beta. This is consistent with

the evidence reported by Ang and Zhang (2002) that the market loading factor is not relevant in explaining firms’

returns. The average market beta is 0.33 for sample REITs and 0.41 for non-sample REITs (table I). The

implication, if anything, is that using buy-and-hold returns without adjusting for beta differences leads to

conservative estimates of the outperformance for the sample of announcing REITs. That is, the evidence reported in

this study is robust to adjusting for the market risk.

Page 24

23

19.41% over and above the buy-and-hold return on the control sample of non-announcing

REITs. The t-statistics reported in column 2 and 3 of Panel B – table V – respectively for the 3-

Month and 12-Month WRs suggest that the null hypothesis can never be rejected in these cases.

Table VI – Panel A and B – report respectively the results for the BHAR and the WR

estimators when each observation is weighted according to the size of the share repurchases

(weights scaled to sum to one). Evidence is not different from the equally weighted case.

5. The Undervaluation Hypothesis

The evidence discussed above suggests that there is compelling evidence that the market

underreacts to open-market stock repurchase announcements by REITs. Both the traditional WR

and the PBHAR estimators indicate that the average abnormal return over a twenty four-month

period is about 19%. The evidence holds if we use different specifications for variance and cross-

correlation of abnormal returns and is robust to weighting each observation to the size of the

stock repurchase.

The next issue is whether long-lived undervaluation is one of the motives for stock

repurchase announcements. The purpose of this section is to clarify whether the market

underreaction is indeed the consequence of a slow movement of the security price toward its

fundamental value or other motives. If the security is undervalued at the time of the

announcement, then there is positive information that is not yet fully reflected in the market

price. Making assessments about the undervaluation hypothesis as a motive for stock

repurchases means to able to establish ex ante that a security is undervalued.

Page 25

24

Traditionally9, the book-to-market ratio has been used as a proxy for undervaluation. In

particular, if a stock is undervalued, its market value will be low and the book-to-market ratio

will be consequently high.

As argued above, panel C in Table II shows that most of the announcing REITs (i.e.,

76.19%) match with the medium and high book-to-market reference portfolios of non-

announcing REITs. This implies that announcing REITs might be better characterized as value

firms than non-announcing REITS. Because high book-to-market ratios are considered evidence

of undervaluation (e.g., Ikenberry, Lakonishok and Vermaelen (1995)), this result is consistent

with the hypothesis that undervaluation is an important motive of stock repurchase

announcements.

The validity of the above conclusion rests on the assumption that a high book-to-market

ratio is “often” a good proxy for undervaluation. However, the book-to-market ratio can be low

and yet the security be undervalued if positive information is not fully reflected in the price. To

shed more light on the issue we also use a multivariate approach.

Managers can have positive information that is not fully reflected in the security price

(i.e., the book-to-market ratio is not low enough). Yet, the operating performance of the years

adjacent to the announcement must signal this information if it can be assumed, realistically, that

operating returns are the fundamentals of net income and market prices. In this framework, net

income, market prices and operating performance can all be a proxy for undervaluation. This

argument suggests that the following cross-sectional regression model can be used test the

undervaluation hypothesis over long horizons:

9 See, for instance, Ikenberry, Lakonishok and Vermaelen (1995).

Page 26

25

.

i

α

iiii

i

i

i

α+

iii

ROI ROIROE ROE

ShOut

ShSought

Size

ME

98

BE

MktBeta AlphaPBHAR

εαα

αααααα

+++

++++++=

9999 98

9876

543210 24,

PBHARi,24 is the percentage buy-and-hold abnormal return for REIT i as defined above.

Alphai and MktBetai are obtained from the estimation of the following market model using one

year of daily data from CRSP prior to the announcement:

sisMiMisi

tt

,,,,

Re Re

εβα++=

, where

Reti,s is REIT i's day s rate of return from CRSP and RetM,s is the market rate of return on day s,

as measured by the CRSP value-weighted portfolio return of all stocks. Sizei is the market value

for REIT i on June 30, 1999 as defined above.

i

SharesOut

ShSought

is the ratio between number of shares

sought and number of shares outstanding for REIT i both at the announcement of the repurchase

program.

i

ME

BE

is the book-to-market ratio for REIT i on December 31, 1998 as defined above.

ROE98i (ROE99i) and ROI98i (ROI99i) are respectively return on equity and return on

investment for REIT i on the year prior to (and the year of) the announcement. The last three

variables are used in particular to test the undervaluation hypothesis. Market beta is used to

control for systematic risk. Alpha tests whether mean reversion effects or momentum strategies

can explain long-horizon returns. Size and announcement effects are controlled by including

respectively Sizei and

i

SharesOut

ShSought

10.

Results11 reported in table VII show that the coefficient for ROI99i is significant and

positive. This is evidence in favor of the undervaluation hypothesis. The coefficient for the book-

10 Data on ROE and ROI are gathered from COMPUSTAT. The number of shares sought at the announcement for

each REIT is obtained from the Lexis-Nexis database. The number of shares outstanding is obtained from CRSP.

11 Results do not change when we use BHAR or WR as dependent variable of the regression model.

Page 27

26

to-market ratio is not significant. This is consistent with the argument used above that the book-

to-market ratio may not be a good proxy for undervaluation especially when, as in this study, the

PBHAR is obtained matching sample firms with non-sample firms by size and book-to-market

ratio. The coefficient for ROE99i, the other variable used to test for undervaluation, is significant

and negative. This result, in combination with the evidence of a positive coefficient for ROI99i,

implies that operating performance should be used to make assessments about the

undervaluation hypothesis. Return on equity, indeed, may depend on factors less related to the

core business of the company. Finally, the coefficients for Alphai and

i

SharesOut

ShSought

, although

significant only at the ten percent level, bring some evidence respectively that momentum

strategies and announcement effects can also explain long-horizon abnormal returns.

6. Concluding Remarks

This study investigates whether the market underreacts to open-market stock repurchase

announcements for REITs. We find compelling evidence of long-horizon performance using the

traditional buy-and-hold abnormal return estimator. We notice, however, that the buy-and-hold

abnormal return estimator may be affected by the serial correlation of monthly returns

(autocorrelation bias). This problem arises because the bid-ask bounce, discussed by Blume and

Stambaugh (1983), can have a different impact on monthly returns for sample REITs and non-

sample REITs. The methodology developed in this study models the serial correlation of

monthly excess returns and therefore our estimate of expected abnormal returns is free of serial

correlation bias, and rebalancing bias.

When we use the autocorrelation bias-free estimator, we still find very strong evidence of

long-horizon abnormal performance. Results are robust to different measures of variance of

Page 28

27

abnormal returns. Following the warning by Fama (1998) and Stafford and Mitchell (2000), we

correct the test statistic for the cross-correlation of abnormal returns and still find very strong

evidence against the null hypothesis of no abnormal returns.

Finally, we investigate whether undervaluation is a motive for the long-horizon abnormal

returns. Both univariate and multivariate analysis support the undervaluation hypothesis.

Page 29

28

References

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Banz, R., and Breen, W., 1986, Sample-dependent results using accounting and market data:

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Barber, B., and Lyon, J., 1997, Detecting long-run abnormal stock returns: The empirical power

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Blume, M., and Stambaugh, R., 1983, Biases in computed returns: An Application to the size

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Brown, S., and Warner, J., 1985, Using daily stock returns: The case of event studies, Journal of

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Campbell, J., Lo, A., and MacKinlay, A., 1997, The Econometrics of Financial Markets,

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Comment, R., and Jarrell, G., 1991, The relative signaling power of Dutch auction, fixed price

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Dann, L., 1981, Common stock repurchases: An analysis of returns to bondholders and

stockholders, Journal of Financial Economics, 9, 113-138.

Fama, E., 1970, Efficient capital markets: A review of theory and empirical work, Journal of

Finance, 25, 383-417.

Fama, E., 1998, Market efficiency, long-term returns, and behavioral finance, Journal of

Financial Economics, 49, 283-306.

Ikenberry, D., Lakonishok, J., and Vermaelen, T., 1995, The underreaction to open market share

repurchases, Journal of Financial Economics, 39, 181-208.

Kothari, S., and Warner, J., 1997, Measuring long-horizon security performance, Journal of

Financial Economics, 43, 301-339.

Lewellen, J., 2002, Momentum and Autocorrelation in Stock Returns, Review of Financial

Studies, 15, 533-563.

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Loughran, T., and Ritter, J., 2000, Uniformly least powerful tests of market efficiency, Journal

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Lyon, J., Barber, B. and Tsai, C., 1999, Improved methods for tests of long-run abnormal stock

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Sezer, O., 2002, Empirical investigations on share repurchase programs by Real Estate

Investment Trusts (REITs), Unpublished Ph.D. dissertation, University of Connecticut.

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Summers, L., 1986, “Does the Stock Market Rationally Reflect Fundamental Values?” Journal

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30

Table I

Descriptive Statistics

The table presents the descriptive statistics for Size, Book-to-Market Ratio and Market Beta for both the sam ple of REITs that

announced an open-m arket stock repurchase program in 1999 and for the control sam ple of REITs that did not announce a

repurchasing program of stocks from the open m arket. Size is the product between m arket price and num ber of shares

outstanding reported on CRSP on June 30, 1998. Book-to-Market is the ratio between the book value of equity (BE) and the

m arket value of equity (ME) on Decem ber 31, 1998. BE is the COMPUSTAT data item 60 on Decem ber 31, 1998. ME is the

product between the m arket price and the num ber of shares outstanding reported on CRSP on Decem ber 31, 1998. Market Beta

is obtained from the estim ation of the following m arket m odel:

Re

, where Ret

si

sM

t

iM

is it

,

,

Re

,

,

εβα++=

i,s is REIT i’s

day s rate of return from CRSP and RetM,s is the m arket rate of return on day s, as m easured by the CRSP value-weighted

portfolio return of all stocks. The estim ation period is one year prior to the announcem ent of the stock repurchase program .

Statistics on m arket betas for non-announcing REITs are based on 65 observations because daily returns to estim ate the m arket

m odel are not available on CRSP for two REITs.

Announcing

REITs

Size (Million of Dollars)

Mean 1,019

Median 620

Min 45

Max 6,608

Skewness 2.95

Kurtosis 11.70

N 42

Non-Announcing REITs

1,147

654

183

5,388

1.98

4.47

67

Book-to-Market

Mean

Median

Min

Max

Skewness

Kurtosis

N

0.98

0.82

0.32

5.77

4.66

25.71

42

1.21

0.94

0.66

3.12

1.84

2.20

67

Market Beta

Mean

Median

Min

Max

Skewness

Kurtosis

N

0.33

0.29

0.03

0.83

0.81

0.73

42

0.41

0.47

0.30

1.64

2.10

3.87

65

Page 32

31

Page 33

32

Table II

Distribution of Announcing REITs and Non-Announcing REITs by Size and Book-to-

Market Ratio

Panel A and B present respectively the distribution (in percent) of announcing and non-announcing REITs by Size and Book-to-

Market ratio. Size is the product between m arket price and num ber of shares outstanding reported on CRSP on June 30, 1998.

Book-to-Market is the ratio between the book value of equity (BE) and the m arket value of equity (ME) on Decem ber 31, 1998.

BE is the COMPUSTAT data item 60 on Decem ber 31, 1998. ME is the product between the m arket price and the num ber of

shares outstanding reported on CRSP on Decem ber 31, 1998. REITs are first ranked according to Size in three different groups

from sm all to large. In an independent sort, firm s are then ranked according to Book-to-Market in three different groups from low

to high. The six groups are finally com bined to obtain nine distinct portfolios. Sam ple REITs are finally m atched with the portfolios

of non-sam ple REITs by Size and Book-to-Market Ratio. The m atching distribution is reported in Panel C.

Book-to-Market

Low

2

High

Total

Panel A: Announcing REITs

Size

Sm all

2

Large

9.52

9.52

14.29

4.76

19.05

9.52

19.05

4.76

9.53

33.33

33.33

33.34

100

Total

Panel B: Non-Announcing REITs

Sm all

2

Large

33.33

33.33

33.34

5.97

10.45

16.42

11.94

10.45

10.45

14.93

11.94

7.45

32.84

32.84

34.32

100

Total

Panel C: Announcing REITs Matched with Non-

Announcing

Sm all

2

Large

32.84

32.84

34.32

0.00

7.14

16.67

0.00

14.29

23.81

4.76

23.81

9.52

4.76

45.24

50

100

Total

23.81

38.10

38.09

Page 34

33

Table III

Serial Correlation-Adjusted Long-Horizon Percentage Buy-and-Hold Abnormal

Returns (PBHARs)

This table presents results for the serial correlation adjusted percentage buy-and-hold abnorm al returns (i.e., average PBHAR -

average E(PBHAR)) for the sam ple of REITs that announced an open-m arket stock repurchase program in 1999. Results for the

24-Month, 12-Month and three-m onth PBHAR are reported respectively in Panel A, B and C. Percentage buy-and-hold abnorm al

return (PBHAR) is the ratio between the buy-and-hold return (BHR) on the sam ple REITs over 24, 12 and 3 m onths after the

announcem ent and the BHR of the average m onthly return for the Size/Book-to-Market reference portfolio of non-announcing

REITs over the sam e tim e period. E(PBHAR) is the expected PBHAR estim ated under the hypothesis that µ = 0 and φ ≠ 0 and

under the hypothesis that both µ = 0 and φ = 0. Statistical significance is assessed using two different assum ptions regarding

cross-correlation of abnorm al returns. Results in colum ns 2, 3, 4 and five assum e that the cross-correlation of abnorm al return is

equal to zero. The traditional Student’s t-statistics reported in the second and third colum n assum e equal variance for the

distribution of individual PBHARs. The t-statistics reported in the fourth and fifth colum n are calculated assum ing unequal

variance for the distribution of individual PBHARs. Individual REITs variances are estim ated using equation (11) under the

hypothesis that µ = 0 and φ ≠ 0 as well as under the hypothesis that both µ = 0 and φ = 0. Consistently with Fam a (1998) and

Mitchell and Stafford (2000), the t-statistics in the sixth and seventh colum n are corrected for the cross-correlation of abnorm al

returns. Cross-correlations of abnorm al returns are estim ated using equation (13) under the hypothesis that µ = 0 and φ = 0 as

well as under the hypothesis that both µ = 0 and φ = 0.

PANEL A: Raw 24-Month PBHAR Mean in Percent: 25.10

Cross-Correlation of Abnorm al Returns Equal to Zero

Cross-Correlation of Abnorm al

Returns Different from Zero

Unequal Variances

Equal Variances

µ = 0, φ = 0

Unequal Variances

µ = 0, φ = 0

µ = 0, φ ≠ 0

µ = 0, φ ≠ 0

µ = 0, φ = 0

µ = 0, φ ≠ 0

19.48

Corrected 24-

Month

PBHAR

Mean in

Percent

t-statistic

19.07

19.48

19.07

19.48

19.07

(2.25)* *

(2.30)* *

(3.21)*

(3.48)*

(3.08)*

(3.33)*

Skewness

0.93

0.82

42

0.92

0.82

42

0.93

0.82

42

0.92

0.82

42

0.93

0.82

42

0.92

0.82

42

Kurtosis

N

Page 35

34

(Table III continued)

PANEL B: Raw 12-Month PBHAR Mean in Percent: 4.82

Cross-Correlation of Abnorm al Returns Equal to Zero

Cross-Correlation of Abnorm al

Returns Different from Zero

Unequal Variances

Equal Variances

µ = 0, φ = 0

Unequal Variances

µ = 0, φ = 0

µ = 0, φ ≠ 0

µ = 0, φ ≠ 0

µ = 0, φ = 0

µ = 0, φ ≠ 0

1.89

Corrected 12-

Month

PBHAR

Mean in

Percent

t-statistic

1.87

1.89

1.87

1.89

1.87

(0.51)

(0.51)

(0.47)

(0.51)

-0.49

-0.13

42

(0.46)

(0.49)

Skewness -0.48

-0.10

-0.49

-0.13

42

-0.48

-0.10

42

-0.48

-0.10

42

-0.49

-0.13

42

Kurtosis

N

42

PANEL C: Raw 3-Month PBHAR Mean in Percent: 1.91

Corrected 3-

Month

PBHAR

Mean in

Percent

t-statistic (0.69)

1.18

0.89

1.18

0.89

1.18

0.89

(0.52)

-0.84

0.03

42

(0.63)

-0.76

-0.15

42

(0.49)

-0.84

0.03

42

(0.60)

-0.76

-0.15

42

(0.47)

-0.84

0.03

42

Skewness -0.76

-0.15

42

Kurtosis

N

* indicates that the m ean is different from zero at the one percent level.

* * indicates that the m ean is different from zero at the five percent level.

Cross-sectional t-statistics are reported in parentheses.

Page 36

35

Table IV

Weighted Serial Correlation-Adjusted Long-Horizon Percentage Buy-and-Hold

Abnormal Returns (PBHARs)

This table presents results for the serial correlation adjusted percentage buy-and-hold abnorm al returns (i.e., average PBHAR -

average E(PBHAR)) for the sam ple of REITs that announced an open-m arket stock repurchase program in 1999. Observations

are weighted according to the size of the stock repurchase (weights scaled to sum to one). Results for the 24-Month, 12-Month

and three-m onth PBHAR are reported respectively in Panel A, B and C. Percentage buy-and-hold abnorm al return (PBHAR) is

the ratio between the buy-and-hold return (BHR) on the sam ple REITs over 24, 12 and 3 m onths after the announcem ent and

the BHR of the average m onthly return for the Size/Book-to-Market reference portfolio of non-announcing REITs over the sam e

tim e period. E(PBHAR) is the expected PBHAR estim ated under the hypothesis that µ = 0 and φ ≠ 0 and under the hypothesis

that both µ = 0 and φ = 0. Statistical significance is assessed using two different assum ptions regarding cross-correlation of

abnorm al returns. Results in colum ns 2, 3, 4 and five assum e that the cross-correlation of abnorm al return is equal to zero. The

traditional Student’s t-statistics reported in the second and third colum n assum e equal variance for the distribution of individual

PBHARs. The t-statistics reported in the fourth and fifth colum n are calculated assum ing unequal variance for the distribution of

individual PBHARs. Individual REITs variances are estim ated using equation (11) under the hypothesis that µ = 0 and φ ≠ 0 as

well as under the hypothesis that both µ = 0 and φ = 0. Consistently with Fam a (1998) and Mitchell and Stafford (2000), the t-

statistics in the sixth and seventh colum n are corrected for the cross-correlation of abnorm al returns. Cross-correlations of

abnorm al returns are estim ated using equation (13) under the hypothesis that µ = 0 and φ = 0 as well as under the hypothesis

that both µ = 0 and φ = 0.

PANEL A: Raw 24-Month PBHAR Mean in Percent: 23.78

Cross-Correlation of Abnorm al Returns Equal to Zero

Cross-Correlation of Abnorm al

Returns Different from Zero

Unequal Variances

Equal Variances

µ = 0, φ = 0

Unequal Variances

µ = 0, φ = 0

µ = 0, φ ≠ 0

µ = 0, φ ≠ 0

µ = 0, φ = 0

µ = 0, φ ≠ 0

18.29

Corrected 24-

Month

PBHAR

Mean in

Percent

t-statistic

17.90

18.29

17.90

18.29

17.90

(2.10)* *

41

(2.14)* *

(3.02)*

41

(3.31)*

41

(2.86)*

41

(3.13)*

41

N

41

PANEL B: Raw 12-Month PBHAR Mean in Percent: 4.97

Corrected 12-

Month

PBHAR

Mean in

Percent

t-statistic (0.60)

2.09

2.06

2.09

2.06

2.09

2.06

(0.59)

(0.53)

(0.56)

(0.50)

(0.53)

Page 37

36

N

41

41

41

41

41

41

Page 38

37

(Table IV continued)

PANEL C: Raw 3-Month PBHAR Mean in Percent: 2.99

Corrected 3-

Month

PBHAR

Mean in

Percent

t-statistic (1.41)

2.28

1.89

2.28

1.89

2.28

1.89

(1.17)

41

(1.21)

41

(1.06)

41

(1.14)

41

(1.00)

41

N 41

* indicates that the m ean is different from zero at the one percent level.

* * indicates that the m ean is different from zero at the five percent level.

Cross-sectional t-statistics are reported in parentheses.

Page 39

38

Table V

Buy-and-Hold Abnormal Returns (BHARs) and Wealth Relative (WR)

Panel A and B present respectively results for the BHAR and the WR estim ators for the sam ple of REITs that announced an

open-m arket stock repurchase program in 1999. BHAR is the difference between the 3, 12 and twenty four-m onth buy-and-hold

return (BHR) on the sam ple REIT and the average BHR on the Size/Book-to-Market reference portfolio of non-announcing REITs

over the sam e tim e period. Wealth relative (WR) is the ratio between the 3, 12 and twenty four-m onth buy-and-hold return (BHR)

on the sam ple REIT and the average BHR on the Size/Book-to-Market reference portfolio of non-announcing REITs over the

sam e tim e period.

PANEL A: BHAR

3-Month Buy-and-Hold

Abnorm al Returns

(BHARs) in Percent

(BHARs) in Percent

12-Month Buy-and-Hold

Abnorm al Returns

24-Month Buy-and-Hold

Abnorm al Returns

(BHARs) in Percent

15.56

(2.43)* *

-0.52

1.03

42

Mean

t-statistic

2.22

4.87

(1.21)

-0.55

-0.12

42

(1.39)

-0.60

-0.71

Skewness

Kurtosis

N

42

PANEL B: WR

3-Month Wealth

Relative (WR) in

Percent

12-Month Wealth

Relative (WR) in

Percent

24-Month Wealth

Relative (WR) in

Percent

19.41

(2.96)*

Mean

t-statistic

2.46

(1.55)

-0.54

-0.81

42

5.90

(1.55)

-0.30

-0.19

42

Skewness

0.67

1.03

42

Kurtosis

N

* indicates that the m ean is different from zero at the one percent level.

* * indicates that the m ean is different from zero at the five percent level.

Cross-sectional t-statistics are reported in parentheses.

Page 40

39

Table VI

Weighted Buy-and-Hold Abnormal Returns (BHARs) and Wealth Relative (WR)

Panel A and B present respectively results for the BHAR and the WR estim ators for the sam ple of REITs that announced an

open-m arket stock repurchase program in 1999. Observations are weighted according to the size of the stock repurchase

(weights scaled to sum to one). BHAR is the difference between the 3, 12 and twenty four-m onth buy-and-hold return (BHR) on

the sam ple REIT and the average BHR on the Size/Book-to-Market reference portfolio of non-announcing REITs over the sam e

tim e period. Wealth relative (WR) is the ratio between the 3, 12 and twenty four-m onth buy-and-hold return (BHR) on the sam ple

REIT and the average BHR on the Size/Book-to-Market reference portfolio of non-announcing REITs over the sam e tim e period.

PANEL A: BHAR

3-Month Buy-and-Hold

Abnorm al Returns

(BHARs) in Percent

(BHARs) in Percent

12-Month Buy-and-Hold

Abnorm al Returns

24-Month Buy-and-Hold

Abnorm al Returns

(BHARs) in Percent

13.79

(2.22)* *

41

Mean

3.13

(2.05)* *

41

5.03

(1.34)

41

t-statistic

N

PANEL B: WR

3-Month Wealth

Relative (WR) in

Percent

12-Month Wealth

Relative (WR) in

Percent

24-Month Wealth

Relative (WR) in

Percent

18.30

(2.75)*

41

Mean

3.42

(2.23)* *

41

5.84

(1.64)

41

t-statistic

N

* indicates that the m ean is different from zero at the one percent level.

* * indicates that the m ean is different from zero at the five percent level.

Cross-sectional t-statistics are reported in parentheses.

Page 41

40

Table VII

Multivariate Results for the Undervaluation Hypothesis

This table presents the results of the estim ation of the following cross-sectional regression m odel:

ii

ROI

i

ROI

i

ROE

i

ROE

i

ShOut

ShSought

i

Size

i

ME

BE

i

MktBeta

i

Alpha

i

PBHAR

εαααααααααα++++++++++=

99

9

98

8

99

7

98

6543210 24,

.

MktBeta and Alpha are respectively the m arket beta and alpha obtained from the estim ation of the following m arket

m odel:

, where Ret

sisM

t

iMis it

,,

Re

,,

Re

return on day s, as m easured by the CRSP value-weighted portfolio return of all stocks. The estim ation period is one year prior to

the announcem ent of the stock repurchase program . BE/ME is the ratio between the book value of equity (BE) and the m arket

value of equity (ME) on Decem ber 31, 1998. BE is the COMPUSTAT data item 60 on Decem ber 31, 1998. ME is the product

between the m arket price and the num ber of shares outstanding reported on CRSP on Decem ber 31, 1998. Size is the product

between m arket price and num ber of shares outstanding reported on CRSP on June 30, 1998. ShSought/ShOut is the ratio

between num ber of shares sought to num ber of shares outstanding for REIT i both at the announcem ent of the repurchase

program . The num ber of shares sought is gathered from the Lexis-Nexis database and the num ber of shares outstanding from

CRSP. ROE98 (ROE99) and ROI98 (ROI99) are respectively return on equity and return on investm ent for REIT i on the year

prior to (and the year of) the announcem ent. Data are gathered from COMPUSTAT.

Constant Alpha MktBeta

ME ShOut

εβα++=

i,s is REIT i’s day s rate of return from CRSP and RetM,s is the m arket rate of

BE

Size

ShSought

ROE98

ROE99

ROI98

ROI99

2

R

3.04

(1.75)

2.05

(1.88)* *

0.41

(0.81)

0.03

(0.26)

-0.17

(-1.99)* *

4.17

(1.84)* *

0.05

(1.66)

-0.08

(-2.10)*

-0.19

(-1.49)

0.38

(2.61)*

0.24

* indicates significance at the five percent level. * * indicates significance at the ten percent level. Cross-sectional t-statistics are

reported in parentheses.