Event study models

BAB III

model Event Study

(draf buku : metodologi penelitian manajemen keuangan : metode event study)

Dr. Joubert B Maramis, SE, MSi

(Dosen fakultas Ekonomi Universitas Sam Ratulangi Manado)

email : barensmaramis@yahoo.com/ Hp. 08582322566

1.    Model dasar event study

Kothari and Warner (2004),  Let t = 0 represent the time of the event. For each sample security i, the return on the security for time period t relative to the event, _Rit, is:

Rit = Kit + eit(1)

where _Kit is the “normal” (i.e., expected or predicted return given a particular model of expected returns), and _eit is the component of returns which is abnormal or unexpected.² Given this return decomposition, the abnormal return, _eit, is the difference between the observed return and the predicted return:

eit = Rit - Kit                                                                             

Equivalently, _eit is the difference between the return conditional on the event and the expected return unconditional on the event. Thus, the abnormal return is a direct measure of the (unexpected) change in securityholder wealth associated with the event. The security is typically a common stock, although some event studies look at wealth changes for firms’ preferred or debt claims.

A model of normal returns (i.e., expected returns unconditional on the event but conditional on other information) must be specified before an abnormal return can be defined. A variety of expected return models (e.g., market model, constant expected returns model, capital asset pricing model) have been used in event studies.³ Across alternative methods, both the bias and precision of the expected return measure can differ, affecting the properties of the abnormal return measures. Properties of different methods have been studied extensively, and are discussed later.

2.    Pengujian model event study (statstic test)

·         Kothari and Warner (2004), For a given performance measure, such as the CAR, a test statistic is typically computed and compared to its assumed distribution under the null hypothesis that mean abnormal performance equals zero.⁴ The null hypothesis is rejected if the test statistic exceeds a critical value, typically corresponding to the 5% or 1% tail region (i.e., the test level or size of the test is 0.05 or 0.01).

·         Kothari and Warner (2004), The test statistic is a random variable because abnormal returns are measured with error. Two factors contribute to this error. First, predictions about securities’ unconditional expected returns are imprecise. Second, individual firms’ realized returns at the time of an event are affected for reasons unrelated to the event, and this component of the abnormal return does not average to literally zero in the cross-section

3.    Criteria for “reliable” event study tests

·         Kothari and Warner (2004), Using the test statistics, errors of inference are of two types. A Type I error occurs when the null hypothesis is falsely rejected. A Type II error occurs when the null is falsely accepted. Accordingly, two key properties of event study tests have been investigated. The first is whether the test statistic is correctly specified. A correctly- specified test statistic yields a Type I error probability equal to the assumed size of the test. The second concern is power, i.e., a test’s ability to detect abnormal performance when it is present. Power can be measured as one minus the probability of a Type II error. Alternatively, it can be measured as the probability that the null hypothesis will be rejected given a level of Type I error and level of abnormal performance. When comparing tests that are well-specified, those with higher power are preferred.

4.     Determining specification and power

·         Kothari and Warner (2004), The joint-test problem. While the specification and power of a test can be statistically determined, economic interpretation is not straightforward because all tests are joint tests. That is, event study tests are well-specified only to the extent that the assumptions underlying their estimation are correct. This poses a significant challenge because event study tests are joint tests of whether abnormal returns are zero and of , whether the assumed model of expected returns (i.e. the CAPM, market model, etc.) is correct. Moreover, an additional set of assumptions concerning the statistical properties of the abnormal return measures must also be correct. For example, a standard t-test for mean abnormal performance assumes, among other things, that the mean abnormal performance for the cross-section of securities is normally distributed. Depending on the specific t-test, there may be additional assumptions that the abnormal return data are independent in time-series or cross-section. The validity of these assumptions is often an empirical question. This is particularly true for small samples, where one cannot rely on asymptotic results or the central limit theorem.

·         Kothari and Warner (2004), Brown-Warner simulation. To directly address the issue of event study properties, the standard tool in event study methodology research is to employ simulation procedures that use actual security return data. The motivation and specific research design is initially laid out in Brown and Warner (1980, 1985), and has been followed in almost all subsequent methodology research.

Much of what is known about general properties of event study tests comes from such large-scale simulations. The basic idea behind the event study simulations is simple and intuitive.⁷ Different event study methods are simulated by repeated application of each method to samples that have been constructed through a random selection of securities and random selection of an event date to each. If performance is measured correctly, these samples should show no abnormal performance, on average. This makes it possible to study test statistic specification, that is, the probability of rejecting the null hypothesis when it is known to be true. Further, various levels of abnormal performance can be artificially introduced into the samples. This permits direct study of the power of event study tests, that is, the ability to detect a given level of abnormal performance.

·         Kothari and Warner (2004), Analytical methods. Simulation methods seem both natural and necessary to determine whether event study test statistics are well-specified. Once it has been established using simulation methods that a particular test statistic is well-specified, analytical procedures have also been used to complement simulation procedures. Although deriving a power function analytically for different levels of abnormal performance requires additional distributional assumptions, the evidence in Brown and Warner (1985, p. 13) is that analytical and simulation methods yield similar power functions for a well-specified test statistic. As illustrated below, these analytical procedures provide a quick and simple way to study power.

5. Risk adjustment and expected returns

Kothari and Warner (2004, In long-horizon tests, appropriate adjustment for risk is critical in calculating abnormal price performance. This is in sharp contrast to short-horizon tests in which risk adjustment is straightforward and typically unimportant. The error in calculating abnormal performance due to errors in adjusting for risk a short-horizon test is likely to be small. Daily expected returns are about 0.05% (i.e., annualized about 12-13%). Therefore, even if the event firm portfolio’s beta risk is misestimated by as much as 0.4 (e.g., estimated beta risk of 1.0 when true beta risk is 1.4), the abnormal return would be misestimated only by 0.02% per day. If the event-window is 3 days, then the event portfolio’s abnormal return would be misestimated by about 0.06%, which is economically small, especially compared to the abnormal return of 1% or more that is typically documented in short-window event studies. Not surprisingly, Brown and Warner (1985) conclude that simple risk-adjustment approaches to conducting short- window event studies are quite effective in detecting abnormal performance. In multi-year long-horizon tests, risk-adjusted return measurement is the Achilles heel for at least two reasons. First, even a small error in risk adjustment can make an economically large difference when calculating abnormal returns over horizons of one year or longer, whereas such errors make little difference for short horizons. Thus the precision of the risk adjustment becomes far more important in long-horizon event studies. Second, it is unclear which expected return model is correct, and estimates of abnormal returns over long horizons are highly sensitive to model choice. We now discuss each of these problems in turn.

Kothari and Warner (2004, Errors in risk adjustment. Such errors can make an economically non-trivial difference in measured abnormal performance over one-year or longer periods. The problem of risk adjustment error is exacerbated in long-horizon event studies because the potential for such error is greater for longer horizons. In many event studies, (i) the event follows unusual prior performance (e.g., stock splits follow good performance), or (ii) the event sample consists of firms with extreme (economic) characteristics (e.g., low market capitalization syocks, low-priced stocks, or extreme book-to-market stocks), or (iii) the event is defined on the basis of unusual prior performance (e.g., contrarian investment strategies in DeBondt and Thaler, 1985, and Lakonishok, Shleifer, and Vishny, 1994). Under these circumstances, accurate risk estimation is difficult, with historical estimates being notoriously biased because economic performance negatively impacts the risk of a security. Therefore, in long-horizon event studies, it is crucial that abnormal- performance measurement be on the basis of post-event, not historical risk estimates (see Ball and Kothari, 1989, Chan, 1988, and Ball, Kothari, and Shanken, 1995, and Chopra, Lakonishok, and Ritter, 1992). However, how the post-event risk should be estimated is itself a subject of considerable debate, which we summarize below in an attempt to offer guidance to researchers.

Kothari and Warner (2004), Model for expected returns. The question of which model of expected returns is appropriate remains an unresolved, contentious issue. As noted earlier, event studies are joint tests of market efficiency and a model of expected returns (e.g., Fama, 1970). On a somewhat depressing note, Fama (1998, p. 291) concludes that “all models for expected returns are incomplete descriptions of the systematic patterns in average returns,” which can lead to spurious indications of abnormal performance in an event study. With the CAPM as a model of expected returns being thoroughly discredited as a result of the voluminous anomalies evidence, a quest for a better-and-improved model began. The search culminated in the Fama and French (1993) three-factor model, further modified by Carhart (1997) to incorporate the momentum factor. However, absent a sound economic rationale motivating the inclusion of the size, book-to-market, and momentum factors, whether these factors represent equilibrium compensation for risk or they are an indication of market inefficiency has not been satisfactorily resolved in the literature (see, e.g., Brav and Gompers, 1997). Fortunately, from the standpoint of event study analysis, this flaw is not fatal. Regardless of whether the size, book-to-market, and momentum factors proxy for risk or indicate inefficiency, it is essential to use them when measuring abnormal performance. The purpose of an event study is to isolate the incremental impact of an event on security price performance. Since the price performance associated with the size, book-to-market, and momentum characteristics is applicable to all stocks sharing those characteristics, not just the sample of firms experiencing the event (e.g., a stock split), the performance associated with the event itself must be distinguished from that associated with other known determinants of performance, such as the aforementioned four factors.¹⁰

4.3 Approaches to abnormal performance measurement

While post-event risk-adjusted performance measurement is crucial in long- horizon tests, actual measurement is not straightforward. Two main methods for assessing and calibrating post-event risk-adjusted performance are used: characteristic- based matching approach and the Jensen’s alpha approach, which is also known as the calendar-time portfolio approach (see Fama, 1998 or Mitchell and Stafford, 2000). Analysis and comparison of the methods is detailed below. Despite an extensive literature, there is still no clear winner in a horse race. Both have low power against economically interesting null hypotheses, and neither is immune to misspecification.

4.3.1 BHAR approach

In recent years, following the works of Ikenberry, Lakonishok, and Vermaelen (1995), Barber and Lyon (1997), Lyon et al. (1999), the characteristic-based matching approach (or also known as the buy-and-hold abnormal returns, BHAR) has been widely used. Mitchell and Stafford (2000, p. 296) describe BHAR returns as “the average multiyear return from a strategy of investing in all firms that complete an event and selling at the end of a prespecified holding period versus a comparable strategy using otherwise similar nonevent firms.” An appealing feature of using BHAR is that buy-and­hold returns better resemble investors’ actual investment experience than periodic (monthly) rebalancing entailed in other approaches to measuring risk-adjusted performance.¹¹ The joint-test problem remains in that any inference on the basis of BHAR hinges on the validity of the assumption that event firms differ from the “otherwise similar nonevent firms” only in that they experience the event. The researcher implicitly assumes an expected return model in which the matched characteristics (e.g., size and book-to-market) perfectly proxy for the expected return on a security. Since corporate events themselves are unlikely to be random occurrences, i.e., they are unlikely to be exogenous with respect to past performance and expected returns, there is a danger that the event and nonevent samples differ systematically in their expected returns notwithstanding the matching on certain firm characteristics. This makes matching on (unobservable) expected returns more difficult, especially in the case of event firms experiencing extreme prior performance.

Once a matching firm or portfolio is identified, BHAR calculation is straightforward. A T- month BHAR for event firm i is defined as:

BHARi(t, T) = Ðt = 1 to T (1 + _Ri,t) - Ð t = 1 to T (1 + RB,t)                        (7)

where RB is the return on either a non-event firm that is matched to the event firm i, or it is the return on a matched (benchmark) portfolio. If the researcher believes that the Carhart (1997) four-factor model is an adequate description of expected returns, then firm-specific matching might entail identifying a non-event firm that is closest to an event firm on the basis of firm size (i.e., market capitalization of equity), book-to-market ratio, and past one-year return. Alternatively, characteristic portfolio matching would identify the portfolio of all non-event stocks that share the same quintile ranking on size, book-to-market, and momentum as the event firm (see Daniel, Grinblatt, Titman, and Wermers, 1997, or Lyon, Barber, and Tsai, 1997, for details of benchmark portfolio construction). The return on the matched portfolio is the benchmark portfolio return, RB. For the sample of event firms, the mean BHAR is calculated as the (equal- or value- weighted) average of the individual firm BHARs.

4.3.2 Jensen-alpha approach

The Jensen-alpha approach (or the calendar-time portfolio approach) to estimating risk-adjusted abnormal performance is an alternative to the BHAR calculation using a matched-firm approach to risk adjustment. Jaffe (1974) and Mandelker (1974)

introduced a calendar time methodology to the financial-economics literature, and it has since been advocated by many, including Fama (1998) and Mitchell and Stafford (2000). ¹³ The distinguishing feature of the most recent variants of the approach is to calculate calendar-time portfolio returns for firms experiencing an event, and calibrate whether they are abnormal in a multifactor (e.g., CAPM or Faama-French three factor)

regression. The estimated intercept from the regression of portfolio returns against factor returns is the post-event abnormal performance of the sample of event firms.

For a variation of the Jensen-alpha approach, see Ibbotson (1975) returns across time and securities (RATS) methodology, which is used in Ball and Kothari (1989) and others.

To implement the Jensen-alpha approach, assume a sample of firms experiences a corporate event (e.g., an IPO or an SEO).¹⁴ The event might be spread over several years or even many decades (the sample period). Also assume that the researcher seeks to estimate price performance over two years (T = 24 months) following the event for each sample firm. In each calendar month over the entire sample period, a portfolio is constructed comprising all firms experiencing the event within the previous T months. Because the number of event firms is not uniformly distributed over the sample period, the number of firms included in a portfolio is not constant through time. As a result, some new firms are added each month and some firms exit each month. Accordingly, the portfolios are rebalanced each month and an equal or value-weighted portfolio excess return is calculated. The resulting time series of monthly excess returns is regressed on the CAPM market factor, or the three Fama-French (1993) factors, or the four Carhart (1997) factors as follows:

Rpt – Rft = ap + bp (Rmt – Rft) + sp SMBt + hp HMLt + mp UMDt + ept (8)

where

Rpt is the equal or value-weighted return for calendar month t for the portfolio of event firms that experienced the event within previous T years,

Rft is the risk-free rate,

Rmt is the return on the CRSP value-weight market portfolio,

SMBpt is the difference between the return on the portfolio of “small” stocks and “big” stocks;

HMLpt is the difference between the return on the portfolio of “high” and “low” book-to-market stocks; UMDpt is the difference between the return on the portfolio of past one-year “winners” and “losers,”

ap is the average monthly abnormal return (Jensen alpha) on the portfolio of event firms over the T-month post-event period,

bp, sp, hp, and mp are sensitivities (betas) of the event portfolio to the four factors.

Inferences about the abnormal performance are on the basis of the estimated ap and its statistical significance. Since ap is the average monthly abnormal performance over the T- month post-event period, it can be used to calculate annualized post-event abnormal performance.

Recent work on the implications of using the Jensen-alpha approach is mixed. For example, Mitchell and Stafford (2000) and Brav and Gompers (1997) favor the Jensen-alpha approach. However, Loughran and Ritter (2000) argue against using the Jensen-alpha approach because it might be biased toward finding results consistent with market efficiency. Their rationale is that corporate executives time the events to exploit mispricing, but the Jensen-alpha approach, by forming calendar-time portfolios, under-

weights managers’ timing decisions and over-weights other observations. In the words of Loughran and Ritter (2000, p. 362): “If there are time-varying misvaluations that firms capitalize on by taking some action (a supply response), there will be more events involving larger misvaluations in some periods than in others    In general, tests that
weight firms equally should have more power than tests that weight each time period equally.” Since the Jensen-alpha (i.e., calendar-time) approach weights each period equally, it has lower power to detect abnormal performance if managers time corporate events to coincide with misvaluations. As a means of addressing the problem, Fama (1998) recommends weighting calendar months by the number of event observations in the month, or some other suitable approach to weighting monthly observations

4.4 Significance tests for BHAR and Jensen-alpha measures

The choice between the matched-firm BHAR approach to abnormal return measurement and the calendar time Jensen-alpha approach (also known as the calendar- time portfolio approach) hinges on the researcher’s ability to accurately gauge the statistical significance of the estimated abnormal performance using the two approaches. That is, unbiased standard errors for the distribution of the event-portfolio abnormal returns are not easy to calculate, which leads to test misspecification. Assessing the statistical significance of the event portfolio’s BHAR has been particularly difficult because (i) long-horizon returns depart from the normality assumption that underlies many statistical tests; (ii) long-horizon returns exhibit considerable cross-correlation because the return horizons of many event firms overlap and also because many event firms are drawn from a few industries; and (iii) volatility of the event firm returns exceeds that of matched firms because of event-induced volatility. We summarize below the econometric inferential issues encountered in performing long-horizon tests and some of the remedies put forward in recent studies.

Analisis dalam event study: residua analysis (uji beda) dan regresi berganda

·         Thompson (1985),

the model (conditional return-generating process / residual analysis / event study) is a particularly simple one, designed only to capture the essence of the event study problem. The resulting return process include parameters that representative the mean shift in return due to the economic impact of events. The parameters can be estimated using residual analysis or multiple regression.