...introduce (autocorrelation bias) because the bid-ask bounce 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. 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.

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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 article develops a new methodology to analyze the long-run performance of real estate investment trusts (REITs) after the announcement of a stock repurchase program. At the outset, an important question to ask is whether it is worthwhile to study REITs as a separate group independently of other financial or industrial firms. One might conjecture that the extensive finance literature should apply equally to this group, hence there is no need for a study specifically designed for this industry (see the literature review in the next section). However, there are several reasons to doubt this conclusion. First, REITs are required by law to pay out 90% of their taxable income; this requirement, unique across the spectrum of firms, reduces the level of financial slack. Jensen's (1986) agency theory is less likely to hold for our sample; therefore, if we find a positive relationship between abnormal returns and free cash flow, then we have a more powerful test of this hypothesis.

Similarly, the information asymmetry hypothesis is a less likely explanation of buyback programs for the following reason. There exists a relatively active market for assets similar to those owned by REITs; when properties are sold anyone can observe their market prices--hence, there should be fewer opportunities for stock market misvaluation. On the other hand, because REITs own portfolios of real estate assets, and because the value of these assets is dependent on local market conditions, REIT managers could likely be expected to have better information relative to other market participants. For these reasons and others we believe that REITs offer a more powerful way of testing hypotheses about the motivation of firms to engage in buyback programs.

In this article we model the effects of mean reversion in monthly returns, and we also show how to correct for cross-sectional correlation of returns. (1) 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 MacKinlay (1997) and Lewellen (2002). An important consequence of serial correlation is that the buy-and-hold abnormal return (BHAR) will be upward biased; the autocorrelation bias leads to rejection of a true null hypothesis of no abnormal performance more often than the prespecified significance level.

Another problem with long-horizon event studies is known as rebalancing bias (Lyon. Barber and Tsai 1999). Rebalancing of the reference portfolio leads to a negative bias in the buy-and-hold abnormal returns. However, as discussed later in the article, it may be possible to reduce this bias substantially by carefully constructing reference portfolios.

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 24 months following the announcement. (2) This finding is consistent with the 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 REITs. (3)

The article 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. We also review the existing literature on why firms buy back stock. The third section presents the three-event study methodologies: BHARs, WR and PBHARs. The fourth section describes the data, explains the construction of sample and reference portfolios and discusses their comparability. The fifth section reports the results based on all three test statistics. The section also reports robustness checks to autocorrelation bias and cross-correlation of abnormal returns. The sixth section presents the evidence on the undervaluation hypothesis. The final section concludes the study.

Literature Review

Long-Horizon Event Studies

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 1 year. Barber and Lyon (1997) 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 BHARs. Barber and Lyon argue that using the (average) BHAR is advisable because it "precisely measures investor experience" over a particular time horizon.

Typically, BHARs are computed as the difference between the sample firm's buy-and-hold returns and its compounded expected return under the null hypothesis:

BHA[R.sub.i] = [T.[product].[t=1]] (1 + [r.sub.it]) - E ([T.[product].[t=1]] (1 + [r.sub.it])), (1)

where T is the number of months after the announcement over which to measure the BHAR; [r.sub.it] 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 [r.sub.it] is a normally distributed random variable. But because Equation (1) is a nonlinear 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). The presence of a 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 negative serial correlation is present. (4) Test statistics based on the normality assumption will be less biased in this case.

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 BHAR 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 of being 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 it biases the return of an equally weighted reference portfolio. However, this problem is more pronounced in daily rather than monthly returns.

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...

NOTE: All illustrations and photos have been removed from this article.



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